computational physics phd programs

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Graduate studies, commencement 2019.

The Harvard Department of Physics offers students innovative educational and research opportunities with renowned faculty in state-of-the-art facilities, exploring fundamental problems involving physics at all scales. Our primary areas of experimental and theoretical research are atomic and molecular physics, astrophysics and cosmology, biophysics, chemical physics, computational physics, condensed-matter physics, materials science, mathematical physics, particle physics, quantum optics, quantum field theory, quantum information, string theory, and relativity.

Our talented and hardworking students participate in exciting discoveries and cutting-edge inventions such as the ATLAS experiment, which discovered the Higgs boson; building the first 51-cubit quantum computer; measuring entanglement entropy; discovering new phases of matter; and peering into the ‘soft hair’ of black holes.

Our students come from all over the world and from varied educational backgrounds. We are committed to fostering an inclusive environment and attracting the widest possible range of talents.

We have a flexible and highly responsive advising structure for our PhD students that shepherds them through every stage of their education, providing assistance and counseling along the way, helping resolve problems and academic impasses, and making sure that everyone has the most enriching experience possible.The graduate advising team also sponsors alumni talks, panels, and advice sessions to help students along their academic and career paths in physics and beyond, such as “Getting Started in Research,” “Applying to Fellowships,” “Preparing for Qualifying Exams,” “Securing a Post-Doc Position,” and other career events (both academic and industry-related).

We offer many resources, services, and on-site facilities to the physics community, including our electronic instrument design lab and our fabrication machine shop. Our historic Jefferson Laboratory, the first physics laboratory of its kind in the nation and the heart of the physics department, has been redesigned and renovated to facilitate study and collaboration among our students.

Members of the Harvard Physics community participate in initiatives that bring together scientists from institutions across the world and from different fields of inquiry. For example, the Harvard-MIT Center for Ultracold Atoms unites a community of scientists from both institutions to pursue research in the new fields opened up by the creation of ultracold atoms and quantum gases. The Center for Integrated Quantum Materials , a collaboration between Harvard University, Howard University, MIT, and the Museum of Science, Boston, is dedicated to the study of extraordinary new quantum materials that hold promise for transforming signal processing and computation. The Harvard Materials Science and Engineering Center is home to an interdisciplinary group of physicists, chemists, and researchers from the School of Engineering and Applied Sciences working on fundamental questions in materials science and applications such as soft robotics and 3D printing.  The Black Hole Initiative , the first center worldwide to focus on the study of black holes, is an interdisciplinary collaboration between principal investigators from the fields of astronomy, physics, mathematics, and philosophy. The quantitative biology initiative https://quantbio.harvard.edu/  aims to bring together physicists, biologists, engineers, and applied mathematicians to understand life itself. And, most recently, the new program in  Quantum Science and Engineering (QSE) , which lies at the interface of physics, chemistry, and engineering, will admit its first cohort of PhD students in Fall 2022.

We support and encourage interdisciplinary research and simultaneous applications to two departments is permissible. Prospective students may thus wish to apply to the following departments and programs in addition to Physics:

• Department of Astronomy
• Department of Chemistry
• Department of Mathematics
• John A. Paulson School of Engineering and Applied Sciences (SEAS)
• Biophysics Program
• Molecules, Cells and Organisms Program (MCO)

If you are a prospective graduate student and have questions for us, or if you’re interested in visiting our department, please contact  [email protected] .

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MIT Doctoral Programs in Computational Science and Engineering

The Center for Computational Science and Engineering (CCSE) offers two doctoral programs in computational science and engineering (CSE) – one leading to a standalone PhD degree in CSE offered entirely by CCSE (CSE PhD) and the other leading to an interdisciplinary PhD degree offered jointly with participating departments in the School of Engineering and the School of Science (Dept-CSE PhD).

While both programs enable students to specialize at the doctoral level in a computation-related field via focused coursework and a thesis, they differ in essential ways. The standalone CSE PhD program is intended for students who intend to pursue research in cross-cutting methodological aspects of computational science. The resulting doctoral degree in Computational Science and Engineering is awarded by CCSE via the the Schwarzman College of Computing. In contrast, the interdisciplinary CSE PhD program is intended for students who are interested in computation in the context of a specific engineering or science discipline. For this reason, this degree is offered jointly with participating departments across the Institute; the interdisciplinary degree is awarded in a specially crafted thesis field that recognizes the student’s specialization in computation within the chosen engineering or science discipline.

For more information about CCSE’s doctoral programs, please explore the links on the left. Information about our application and admission process is available via the ‘ Admissions ‘ tab in our menu. MIT Registrar’s Office provides graduate tuition and fee rates as set by the MIT Corporation and the Graduate Admissions section of MIT’s Office of Graduate Education (OGE) website contains additional information about costs of attendance and funding .

Department of Physics

Mellon college of science, computational physics.

Computational Physics is a rapidly growing and highly interdisciplinary research area. Carnegie Mellon features two main thrusts in Computational Physics: computer simulation and data mining/analysis. Researchers collaborate extensively with other departments at CMU such as Chemical Engineering, Computer Science, Materials Science, Mathematics and Statistics. Interactions with the Pittsburgh Supercomputing Center ( PSC ) provides access to a superb team of professional computational scientists as well as ready access to the latest supercomputing hardware.

Our Faculty

• Shila Banerjee
• Rupert Croft
• Markus Deserno
• Tiziana Di Matteo
• Frank Heinrich
• Michael Levine (Emeritus)
• Curtis Meyer
• Colin Morningstar
• Robert Sekerka (Emeritus)
• Robert Swendsen (Emeritus)
• Michael Widom

Shila Banerjee 's group integrates theory, simulations, and data-driven modelling to understand how physical forces and chemical signalling control the shapes and architecture of living cells. They use concepts from statistical physics and dynamical systems to understand the principles that guide the organization and mechanics of sub-cellular matter, and predict how changes in sub-cellular organization control the spatiotemporal patterns of growth and movement in cells and tissues.

Rupert Croft simulates the growth of structure in the Universe including gravitational, hydrodynamic and radiative effects. The physical processes are complex, non-linear and interlinked. Analyzing the data from these models can explain the growth of stars, galaxies and larger structures.

Markus Deserno uses both theoretical and computational techniques to study lipid membranes. On the theoretical side, a continuum elastic description is used, and on the computational side, coarse-grained simulations in which the physical system is not represented in atomic detail are utilized. This renouncement of chemical resolution allows one to study much larger systems on much longer time scales and to access a new arena for physical questions, many of which turn out to have biological significance.

Tiziana Di Matteo 's research focuses on the formation and growth of black holes, and their interaction with galaxies and the rest of the Universe. Massively parallel hydrodynamic simulations are necessary to follow the gas dynamics, radiative cooling and gravitational evolution of hundreds of millions of mass elements. One of her current projects involves simulating the growth of black holes in the full cosmological context, starting from small fluctuations after the Big Bang and following the evolution of the Universe to the present day.

Frank Heinrich uses supercomputing resources for Monte Carlo Markov chain-based data modeling and the quantitative assessment of the information content of experimental data in neutron scattering.

Michael Levine (Emeritus) is the former co-director of the PITTSBURGH SUPERCOMPUTING CENTER . He developed computational hardware and numerical and algebraic algorithms to perform high order perturbative calculations in quantum electrodynamics.

Curtis Meyer 's computational activities revolve around experimental studies of hadrons (particles built from quarks and antiquarks). The techniques employed are amplitude and partial wave analysis. Current activities are focused on the analysis of data from a Jefferson Lab (JLab) experiment which is used to search for baryons (excited partners to the familiar proton and neutron) in very large data sets.

Colin Morningstar uses lattice quantum chromodynamics (QCD) to investigate hadron formation and quark confinement. He has computed the mass spectrum of glueballs in the Yang-Mills theory of gluons, studied the excitation spectrum of the effective QCD string between a static quark-antiquark pair, and produced the first glimpse of the nucleon excitation mass spectrum from QCD. He is a member of a large nationwide collaboration of lattice QCD theorists dedicated to Monte Carlo calculations of QCD observables on large-scale computing clusters. He and Curtis Meyer built and maintain the CMU QCD cluster.

Robert Sekerka (Emeritus) solves partial differential equations representing crystal growth to understand morphological instabilities leading to cellular and dendritic structures. Other interests include development of lattice-Boltzmann techniques to simulate solutions of the Navier-Stokes equations of hydrodynamics.

Robert Swendsen (Emeritus) develops computational algorithms for the efficient simulation of phase transitions and novel data analysis techniques to extract information from these simulations. Additional work addresses methods for efficient simulation of biological molecules.

Michael Widom carries out Monte Carlo and molecular dynamics simulations of metal alloys and employs ab-initio methods for band structure and total energy calculation. Current areas of interest include high entropy alloys and other complex and intrinsically disordered structures such as borides, quasicrystals and metallic glasses.

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PhD in Physics, Statistics, and Data Science

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Many PhD students in the MIT Physics Department incorporate probability, statistics, computation, and data analysis into their research. These techniques are becoming increasingly important for both experimental and theoretical Physics research, with ever-growing datasets, more sophisticated physics simulations, and the development of cutting-edge machine learning tools. The Interdisciplinary Doctoral Program in Statistics (IDPS)  is designed to provide students with the highest level of competency in 21st century statistics, enabling doctoral students across MIT to better integrate computation and data analysis into their PhD thesis research.

Admission to this program is restricted to students currently enrolled in the Physics doctoral program or another participating MIT doctoral program. In addition to satisfying all of the requirements of the Physics PhD, students take one subject each in probability, statistics, computation and statistics, and data analysis, as well as the Doctoral Seminar in Statistics, and they write a dissertation in Physics utilizing statistical methods. Graduates of the program will receive their doctoral degree in the field of “Physics, Statistics, and Data Science.”

Doctoral students in Physics may submit an Interdisciplinary PhD in Statistics Form between the end of their second semester and penultimate semester in their Physics program. The application must include an endorsement from the student’s advisor, an up-to-date CV, current transcript, and a 1-2 page statement of interest in Statistics and Data Science.

The statement of interest can be based on the student’s thesis proposal for the Physics Department, but it must demonstrate that statistical methods will be used in a substantial way in the proposed research. In their statement, applicants are encouraged to explain how specific statistical techniques would be applied in their research. Applicants should further highlight ways that their proposed research might advance the use of statistics and data science, both in their physics subfield and potentially in other disciplines. If the work is part of a larger collaborative effort, the applicant should focus on their personal contributions.

For access to the selection form or for further information, please contact the IDSS Academic Office at  [email protected] .

Required Courses

Courses in this list that satisfy the Physics PhD degree requirements can count for both programs. Other similar or more advanced courses can count towards the “Computation & Statistics” and “Data Analysis” requirements, with permission from the program co-chairs. The IDS.190 requirement may be satisfied instead by IDS.955 Practical Experience in Data, Systems, and Society, if that experience exposes the student to a diverse set of topics in statistics and data science. Making this substitution requires permission from the program co-chairs prior to doing the practical experience.

• IDS.190 – Doctoral Seminar in Statistics and Data Science ( may be substituted by IDS.955 Practical Experience in Data, Systems and Society )
• 6.7700[J] Fundamentals of Probability or
• 18.675 – Theory of Probability
• 18.655 – Mathematical Statistics or
• 18.6501 – Fundamentals of Statistics or
• IDS.160[J] – Mathematical Statistics: A Non-Asymptotic Approach
• 6.C01/6.C51 – Modeling with Machine Learning: From Algorithms to Applications or
• 6.7810 Algorithms for Inference or
• 6.8610 (6.864) Advanced Natural Language Processing or
• 6.7900 (6.867) Machine Learning or
• 6.8710 (6.874) Computational Systems Biology: Deep Learning in the Life Sciences or
• 9.520[J] – Statistical Learning Theory and Applications or
• 16.940 – Numerical Methods for Stochastic Modeling and Inference or
• 18.337 – Numerical Computing and Interactive Software
• 8.316 – Data Science in Physics or
• 6.8300 (6.869) Advances in Computer Vision or
• 8.334 – Statistical Mechanics II or
• 8.371[J] – Quantum Information Science or
• 8.591[J] – Systems Biology or
• 8.592[J] – Statistical Physics in Biology or
• 8.942 – Cosmology or
• 9.583 – Functional MRI: Data Acquisition and Analysis or
• 16.456[J] – Biomedical Signal and Image Processing or
• 18.367 – Waves and Imaging or
• IDS.131[J] – Statistics, Computation, and Applications

Grade Policy

C, D, F, and O grades are unacceptable. Students should not earn more B grades than A grades, reflected by a PhysSDS GPA of ≥ 4.5. Students may be required to retake subjects graded B or lower, although generally one B grade will be tolerated.

Unless approved by the PhysSDS co-chairs, a minimum grade of B+ is required in all 12 unit courses, except IDS.190 (3 units) which requires a P grade.

Though not required, it is strongly encouraged for a member of the MIT  Statistics and Data Science Center (SDSC)  to serve on a student’s doctoral committee. This could be an SDSC member from the Physics department or from another field relevant to the proposed thesis research.

Thesis Proposal

All students must submit a thesis proposal using the standard Physics format. Dissertation research must involve the utilization of statistical methods in a substantial way.

PhysSDS Committee

• Jesse Thaler (co-chair)
• Mike Williams (co-chair)
• Isaac Chuang
• Janet Conrad
• William Detmold
• Philip Harris
• Jacqueline Hewitt
• Kiyoshi Masui
• Leonid Mirny
• Christoph Paus
• Phiala Shanahan
• Marin Soljačić
• Washington Taylor
• Max Tegmark

Can I satisfy the requirements with courses taken at Harvard?

Harvard CompSci 181 will count as the equivalent of MIT’s 6.867.  For the status of other courses, please contact the program co-chairs.

Can a course count both for the Physics degree requirements and the PhysSDS requirements?

Yes, this is possible, as long as the courses are already on the approved list of requirements. E.g. 8.592 can count as a breadth requirement for a NUPAX student as well as a Data Analysis requirement for the PhysSDS degree.

If I have previous experience in Probability and/or Statistics, can I test out of these requirements?

These courses are required by all of the IDPS degrees. They are meant to ensure that all students obtaining an IDPS degree share the same solid grounding in these fundamentals, and to help build a community of IDPS students across the various disciplines. Only in exceptional cases might it be possible to substitute more advanced courses in these areas.

Can I substitute a similar or more advanced course for the PhysSDS requirements?

Yes, this is possible for the “computation and statistics” and “data analysis” requirements, with permission of program co-chairs. Substitutions for the “probability” and “statistics” requirements will only be granted in exceptional cases.

For Spring 2021, the following course has been approved as a substitution for the “computation and statistics” requirement:   18.408 (Theoretical Foundations for Deep Learning) .

The following course has been approved as a substitution for the “data analysis” requirement:   6.481 (Introduction to Statistical Data Analysis) .

Can I apply for the PhysSDS degree in my last semester at MIT?

No, you must apply no later than your penultimate semester.

What does it mean to use statistical methods in a “substantial way” in one’s thesis?

The ideal case is that one’s thesis advances statistics research independent of the Physics applications. Advancing the use of statistical methods in one’s subfield of Physics would also qualify. Applying well-established statistical methods in one’s thesis could qualify, if the application is central to the Physics result. In all cases, we expect the student to demonstrate mastery of statistics and data science.

Graduate Coordinator: Vasyl Tyberkevych 274 Hannah Hall (248) 370-3421 [email protected]

Program description

The College of Arts and Sciences offers a physical sciences doctoral program in Applied and Computational Physics, at the Department of Physics. With a concentration in materials experimental research and computer modeling, this program will prepare graduates for industry and academic careers in areas related to various experimental and theoretical aspects of one of the largest fields in physics: Materials science. More generally, the curriculum prepares the students to engage in research in condensed matter physics, with materials research currently being the most technologically important area. This program emphasizes both practical, engineering applications (applied physics track) and theoretical and fundamental physical concepts (computational physics track). Ph.D. candidates may elect to do their dissertation with one of a number of Oakland University faculty currently involved in applied and computational physics research. In addition to available Oakland University graduate assistantships, many of the faculty in the Department may provide individual support for qualified students. Interested students should consult the program coordinator for details.

Admission terms and application deadlines

Before an applicant’s file can be reviewed for full program admission, all application documents must be received in Oakland University Graduate School by the semester deadlines listed below. Incomplete applications will not be sent to departments for admission review. Those students may want to request special graduate status.

• February 15 (early) April 15 (regular) and July 15 (late) for fall semester
• October 1 (early) and November 15 (regular) for winter semester
• March 1 (regular) for summer semester
• International Students    

Application requirements

To be considered for graduate admission, applicants must submit all Graduate Application Requirements and additional department requirements by the published application deadlines:

• Graduate Application Requirements       
• Additional department application requirements

Admission review and assessment

Admission to graduate school at Oakland University is selective. In making admission recommendations to Oakland University Graduate School, each department assesses the potential of applicants for success in the program by examining their undergraduate records, goal statement, letters of recommendation, prerequisite courses and any other admission requirements established by the academic department.

Related links

• Readmission (not enrolled for two years)      
• Transferring to Oakland University
• Transferring to a new program

Proficiency of entering students

Students with an earned MS degree can obtain up to 32 credits reduction for their graduate studies with approval from the program committee. On entering the program, each MS student will be given a preliminary examination consisting of three parts: thermodynamics, quantum mechanics, and electricity and magnetism (the course content of PHY 4210, 4720, and 4820, respectively). Failure in any of the three parts of the exam will obligate the student to take the corresponding course.

Degree requirements

The Doctor of Philosophy in Applied and Computational Physics is awarded upon satisfactory completion of a minimum of 80 credits in an approved program of study, successful completion of a qualifying examination, and successful completion of a dissertation.

A minimum of 80 credits beyond the bachelor’s degree is required for the Ph.D. in Applied and Computational Physics program, including at least 30 credits of dissertation research. The total course requirement is 12 courses (46 credits) and a research seminar (2 credits), with a minimum of 8 core courses and 2 courses not directly related to the dissertation topic. There are 2 free electives.

The basic requirements for the Ph.D. in Applied and Computational Physics are completion of a program of formal course work and independent research approved by the candidate’s dissertation committee and the Joint Committee on Applied and Computational Physics.

Course requirements

A. core courses (minimum of 8 core courses + research seminar - 32 credits).

• PHY 5220 - Statistical Thermodynamics (4 credits)
• PHY 5520 - Theoretical Physics (4 credits)
• PHY 5620 - Mechanics II (4 credits)
• PHY 5740 - Introduction to Solid-State Physics (4 credits)
• PHY 5830 - Classical Electrodynamics (4 credits)
• PHY 6730 - Quantum Mechanics (4 credits)
• SCI 5110 - Ethics and Practice of Science (2 credits)

and one of the following two courses:

• PHY 5420 - Advanced Electronics (4 credits)
• PHY 5530 - Numerical Methods in Theoretical Physics (4 credits) (for the Computational Physics track)

The students will be encouraged to attend the research seminar (the Department of Physics colloquium). Students will take two semesters of PHY 6940    (1 credit per semester). The students will also take 16 credits of elective courses: 8 credits from the listed recommended courses and 8 credits of free electives.

b. Electives (at least 8 credits from the appropriate track)

1. applied physics track.

• PHY 5450 - Nuclear Magnetic Resonance (4 credits)
• CHM 4700 - Industrial Chemistry
• CHM 5410 - Advanced Physical Chemistry (3 credits)
• CHM 5420 - Topics in Physical Chemistry (3 credits)
• ECE 5140 - Instrumentation and Measurements (4 credits)
• ECE 5300 - Electromagnetic Engineering (4 credits)

2. Computational physics track

• PHY 5350 - Modeling Complex Systems (4 credits)
• PHY 5300 - Bioelectric Phenomena (4 credits)
• PHY 5040 - Advanced Astrophysics I (4 credits)
• PHY 5650 - Physics of Continuous Media (4 credits)
• PHY 6740 - Advanced Quantum Mechanics (4 credits)
• APM 5333 - Numerical Methods (4 credits)
• APM 5334 - Applied Numerical Methods: Matrix Methods (4 credits)
• APM 6334 - Numerical Methods for Partial Differential Equations (4 credits)
• APM 6558 - Mathematical Modeling in Industry: Continuous Models (4 credits)
• STA 5225 - Stochastic Processes I (4 credits)
• ME 5510 - Intermediate Fluid Mechanics (4 credits)
• ME 7510 - Gas Dynamics (4 credits)

c. Dissertation (at least 30 credits)

• PHY 8999 - Doctoral Research (1 to 12 credits) (per semester)

Approval of research oriented dissertation submitted for internal and external review.

Satisfactory academic progress

Satisfactory Academic Progress (SAP) is the term used to denote a student’s successful completion of coursework toward a certificate or degree. Federal regulations require the Office of Financial Aid to monitor Satisfactory Academic Progress for all financial aid recipients each semester.

Students who fall behind in their coursework, or fail to achieve minimum standards for grade point average and completion of classes, may lose their eligibility for all types of federal, state and university aid. Contact the Office of Financial Aid for additional details.

Good academic standing

All graduate students are expected to remain in good academic standing throughout the entire course of their graduate program. To be in good academic standing, a graduate student must make satisfactory progress toward fulfilling degree requirements, including the completion of critical degree milestones as set forth by the academic program. The student must also maintain a minimum semester and overall GPA of 3.0.

Good academic standing is a requirement for:

• Holding a Graduate Assistantship
• Receiving a fellowship or scholarship
• Advancing to candidacy for a graduate degree
• Going on a leave of absence
• Obtaining a graduate certificate or degree from Oakland University.

Additionally, graduate students must meet all department academic standards which may be more stringent than the minimum set forth by the University.

Graduate students who are not in good academic standing for any reason are subject to probation and/or dismissal from further graduate study.

Related program information

Plan of study.

All accepted applicants, in consultation with their assigned faculty program adviser, must develop a plan of study that details specific courses the students will use to satisfy their degree requirements. The plan of study must be approved by the faculty program adviser and submitted by the student to Oakland University Graduate School.

Master’s and graduate certificate students must submit a department-approved plan of study by the end of their first semester of graduate coursework. Doctoral students must submit an approved plan of study prior to completion of the first year of coursework.

Note:  Credit granted for successful completion of a course toward an undergraduate degree program may not be repeated for a graduate degree. If a substitution is approved, the minimum number of program-approved graduate credits will be required. A Petition of Exception - OU Course Waiver/ Substitution requesting the substitution must be approved.

Qualifying examination

Typically, within two years after admission into the program, the student must pass a comprehensive qualifying examination. The comprehensive examination will consist of a written examination followed by an oral examination. The written examination will consist of two parts: Mathematics and Theoretical Physics. The oral exam will include the student’s presentation of his/her research. The examination is intended to determine the extent of the student’s knowledge and readiness for the doctoral degree and will be designed and evaluated by the dissertation committee. If the student does not pass the examination, the committee may allow the student to retake the examination within one year. Failure to pass the examination within two attempts shall constitute failure in the Ph.D. program.

Dissertation Committee

A dissertation committee consisting of at least three members (one of whom will serve as dissertation adviser) will be formed. The majority of the committee will consist of faculty members of the Department of Physics. The student’s dissertation adviser will be chairperson of the committee. The committee is charged with the guidance of the student in course selection, review of dissertation proposals before initiation of a project, and approval of the completed dissertation.

Research and dissertation

An integral and major component of the program is the successful completion of original research either utilizing state-of-the-art experimental methods or taking theoretical and/or computational approach to study a problem of current interest. Each student shall, in consultation with his or her adviser, prepare:

·     A dissertation proposal outlining the problem to be studied and the relation of this problem to practical applications

·     A survey of the appropriate literature

·     A description of the appropriate techniques

·     And an outline of the experiments to be performed.

The student shall, at the request of the dissertation committee, orally defend the proposal and elaborate on the methods for data collection and analysis.

The project shall be deemed ready for preparation of the the dissertation at such time as the student’s dissertation committee agrees that the student has completed the project and that the student is an expert in the use of the specific theoretical and/or experimental methods required by the project. The student shall then prepare a doctoral dissertation for submission to the committee and shall defend the dissertation in a public oral examination conducted by the dissertation committee.

All students are required to fulfill a residency requirement for this program. Although students may complete some of the program on a part-time basis, continuous full-time enrollment is highly preferred. The minimal residency requirement shall be full-time residency (8 credits per semester) for at least three consecutive full semesters with at least two of these devoted primarily to the student’s research project.

Continuous enrollment

The continuous enrollment policy for doctoral students requires continuous registration of graduate students for at least 1 credit each semester in the academic year to maintain an active graduate student status. This includes semesters in which the comprehensive, preliminary or qualifying examination is taken, defense, and each subsequent term (fall and winter) until the degree requirements are met and the dissertation is submitted to Graduate Study and Lifelong Learning.

Some agency and graduate assistantship eligibility may have course-load requirements that exceed the minimum registration requirements of the Continuous Enrollment Policy (e.g., Veterans Affairs, Immigration and Naturalization for international students, and federal financial aid programs). Therefore, it is the student’s responsibility to register for the appropriate number of credits that are required for funding eligibility and/or compliance as outlined by specific agency regulations under which they are governed.

Time to degree

The maximum time limit for completing a Ph.D. degree is no more than ten years from the term of the first course enrollment in the doctoral program.

The Time Limit for Completing a Ph.D. Degree policy requires a student to achieve candidacy within six years from the first course enrollment in the doctoral program. After being advanced to candidacy, a student is expected to complete the remaining degree requirements within four years (including the dissertation defense).

The doctoral degree in Computational Science with an emphasis in physics prepares students for either academic or professional careers within fields in which computational physics plays an essential role. The program combines the power of mathematics, physics, and computer science to train students to be successful in such careers, by providing them with the opportunity to engage in research activity that transcends disciplinary boundaries.

Admission Requirements

In addition to meeting the Admission Requirements and Procedures   , applicants must submit GRE scores. Applicants whose native language is not English must earn a TOEFL score of at least 550 (TOEFL PBT), 217 (TOEFL CBT), or 80 (TOEFL iBT), or a IELTS score of at least 6.5.

• Official GRE Test Scores
• Statement of Purpose
• Three Letters of Recommendation

Program Requirements and Academic Policies

Students must comply with the General Degree Requirements    prescribed by the Graduate School, and follow the policies listed under General Academic Information   .  In addition, the following requirements must be satisfied:

• If entering the program with a bachelor’s degree, completion of the Master of Science in Physics.
• A comprehensive examination covering the core courses.  A maximum of two attempts is allowed.
• Completion of research tool requirements, as specified by the doctoral committee.
• Successful defense of the dissertation by the end of the eighth year.

Course Requirements (54 hours)

• PHY 710 - Computational Methods for Physical Systems I 3 hrs
• PHY 711 - Computational Methods for Physical Systems II 3 hrs.
• COS 701 - Visual Techniques 3 hrs.
• COS 702 - Data Analysis Techniques 3 hrs.
• COS 703 - Data Handling Techniques 3hrs.
• COS 898 - Dissertation 12 hrs. (A total of 12 hrs.)
• PHY, COS, and approved electives as needed to complete 54 hours total

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• Computational Sciences PhD

Reach the highest level of academic achievement in mathematical modeling, machine learning, and theoretical computer science.

Computational Science is concerned with the construction of mathematical models to solve problems in science, technology, engineering and mathematics. This is accomplished through the design and implementation of numerical, probabilistic and statistical models, machine learning and theoretical computer science. The methods and applications are necessarily cross disciplinary.

A typical example is the use of topological data analysis—which has roots in algebraic topology in pure mathematics—to analyze protein data or large data clouds. Other examples include environmental modeling via image processing, risk management and forecasting in finance via stochastic simulations, which in turn can be used in computational biology to understand the roles of non-coding RNA in cancer.

The Computational Sciences PhD Program at UMass Boston coordinates and promotes multidisciplinary exchange of ideas among researchers and graduate students. The program involves faculty and graduate students in various departments at the College of Sciences and Mathematics. Departments currently participating in the program include: Biology, Chemistry, Computer Science, Engineering, Physics and Mathematics. The program is built on the existing strong scientific collaborations among faculty and industry partners. Graduates from the program are expected to be competitive for securing positions in academia or at companies seeking expertise in data analytics and high-end implementation of computational modeling.

You can select from the following tracks:

• Data Analytics
• Bioinformatics
• Computational Physics

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Plan Your Education

How to apply.

Applicants must also meet general graduate admission requirements in addition to the following program-specific requirements:

• Applicants will be required to determine the track they are interested in pursuing (Data Analytics, Bioinformatics, or Computational Physics) and demonstrate adequate preparation at the undergraduate level in the form of relevant coursework and research experience.
• Given the multi-disciplinary nature of the Computational Science program, we expect that our applicants will be undergraduates with bachelor of science degrees in computer science, mathematics, biology, chemistry, physics, or graduates with master’s degrees in these areas.
• Applicants are required to take the general GRE test.
• The program requires three letters of recommendation submitted with the application.

Transfer Requirements

Students who transfer to the Computational Science program will receive transfer credit or advanced standing for their previous work if they can demonstrate course equivalency. Credits for previous work will be given at the discretion of the Program Committee. Transfer students will still be required to pass written and oral qualifying exams and fulfill all other candidacy requirements.

Deadlines & Cost

Deadlines: February 15 for fall; October 1 (priority deadline) or December 1 (final deadline) for spring

Application Fee: The nonrefundable application fee is $75. UMass Boston alumni and current students that plan to complete degree requirements prior to graduate enrollment can submit the application without paying the application fee.

Program Cost Information: Bursar's website

Core Courses (16 Credits)

• MATH 625 - Numerical Analysis 4 Credit(s)
• MATH 626 - Numerical Linear Algebra& 4 Credit(s)
• MATH 647 - Probability Models 4 Credit(s)
• MATH 648 - Computational Statistics 4 Credit(s)

Track Courses (15 to 18 Credits)

Complete five courses. Three courses from your declared track and one course from each of the other two tracks.

Data Analytics Courses:

• CS 624 - Analysis of Algorithms 3 Credit(s)
• CS 670 - Artificial Intelligence 3 Credit(s)
• CS 671 - Machine Learning 3 Credit(s)
• CS 724 - Topics in Algorithm Theory and Design 3 Credit(s)

Computational Physics Courses:

• PHYSIC 610 - Topics in Medical Imaging 4 Credit(s)
• PHYSIC 611 - Theory of Classical Mechanics and Fluid Mechanics 4 Credit(s)
• PHYSIC 616 - Mathematical Methods for Physicists 4 Credit(s)
• PHYSIC 638 - Quantum Measurement Theory 4 Credit(s)
• BIOL 370 Molecular Biology (see Undergraduate Catalog)
• BIOL 625 - Genomics and Biotechnology 3 Credit(s)
• BIOL 664 - Bioinformatics for Molecular Biologists 3 Credit(s)
• BIOL 674 - Cell Signaling 3 Credit(s)
• CS 612 - Algorithms in Bioinformatics 3 Credit(s)

Bioinformatics Courses:

Electives (9 to 12 Credits)

Complete three courses from below. Additional track courses from above may be applied toward this requirement with permission of the graduate program director.

• BIOL 615 - Immunology 3 Credit(s)
• BIOL 677 - Advanced Eukaryotic Genetics 3 Credit(s)
• BIOL 681 - Network Biology 3 Credit(s)
• CHEM 601 - Thermodynamics & Kinetics 4 Credit(s)
• CHEM 602 - Quantum Mechanics & Spectroscopy 4 Credit(s)
• CS 630 - Database Management Systems 3 Credit(s)
• CS 636 - Database Application Development 3 Credit(s)
• CS 680 - Object-Oriented Design and Programming 3 Credit(s)
• CS 681 - Object-Oriented Software Development 3 Credit(s)
• CS 682 - Software Development Laboratory I 3 Credit(s)

Research Seminars (4 Credits)

Consult with you advisor for course options.

Dissertation (20 Credits)

Complete 20 credits of dissertation research by registering for a science dissertation course to be approved by your faculty advisor.

Graduation Criteria

Complete 64 to 70 credits from at least 15 courses including 40 credits of course work from four core courses, five track courses, three electives, and four credits of research seminar; and 20 credits of dissertation research.

Track: Students must choose a track in data analytics, bioinformatics, or computational physics. Doctoral candidacy: Pass a comprehensive examination after completion of 30 credits of course work. This examination consists of two parts: written and oral. Passing the written examination is a prerequisite to enter the oral examination. Dissertation: Compose and defend a dissertation based on original research.

Minimum grade: No course with a grade below B may be applied toward program requirements. Statute of limitations: Seven years.

Graduate Program Director Kourosh Zarringhalam kourosh.zarringhalam [at] umb.edu (617) 287-7486

Student Success Program Coordinator Velina Batchvarov velina.batchvarov [at] umb.edu (617) 287-3283

Computer Science

Learn more about UMass Boston's Computer Science department, our research, and our faculty.

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Learn more about the faculty, research, and programs that make up our College of Science and Mathematics.

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Ph.D. in Scientific Computing

This program is intended for University of Michigan Ph.D. students who will make extensive use of large-scale computation, computational methods, or algorithms for advanced computer architectures in their doctoral studies. A firm knowledge of the scientific discipline is essential.

This is not a stand-alone degree; it is a joint degree program . Students must be accepted into the Ph.D. program of a home department at the University of Michigan. The actual degree name will have “…and Scientific Computing” appended to the the normal title, e.g., “Ph.D. Degree in Aerospace Engineering and Scientific Computing.”

Students in the Scientific Computing degree program come from many different disciplines. Our current enrollment exemplifies the breadth of departments, schools, and colleges represented by our Ph.D. students.

Students may enroll in the program after having completed one term in their home Ph.D. department. We recommend applying prior to being promoted to candidacy status, but can often accommodate students later in their degree progress.

Please contact MICDE at [email protected] if you have any questions about the Ph.D. in Scientific Computing.

Academic Requirements

Application procedures.

Current Students

Tracking Progress

Funding Resources

Current Enrollment

Students must complete the normal doctoral requirements of their home departments, as well as additional requirements in scientific computing. The specific requirements are:

Non-exhaustive examples of course selections for various departments can be seen on our  Example Course Choices page.

Group I Courses

Twenty-four (24) credit hours of coursework toward your home degree. You must complete your home degree requirements in order to receive the Ph.D. in Scientific Computing. It cannot be earned on its own. Group I may overlap with groups II or III. 

Group II Courses

Nine (9) credit hours of approved courses in scientific computing methodologies.

Group III Courses

Nine (9) credit hours of approved courses in computational science and applications in scientific computing outside the home department  (this typically includes courses in computer science, parallel algorithms, advanced computer architectures, computational fluid dynamics, or other courses in scientific computation not offered by a student’s home department).

Committee Composition

An emphasis on scientific computing reflected in doctoral thesis and doctoral committee composition. At least one faculty member on your committee should be an expert in scientific computing, affiliated with MICDE  or  MIDAS .

Demonstration of Understanding

Preliminary/Qualifying Exam Question: You must answer at least one question related to scientific computing during your department’s preliminary or qualifying examination.  If you join the program after having completed your qual/prelim, you can still use this option if you were asked a question related to computational methods or applications during your qual/prelim.  The student’s advisor or a MICDE  or  MIDAS -affiliated member of the committee must then email MICDE to confirm that this requirement is complete.

If the format of your PhD program’s preliminary/qualifying examination cannot accommodate this requirement, or if you are beyond this stage at the point of joining the program and were not asked a question on your prelim/qual, you have the following option to complete the Demonstration of Understanding requirement:

Literature Review: A 3-5 page critical assessment of previous research that has been done in your research area, specifically the scientific computing/computational aspect of your research problem.  This must be submitted to [email protected]  for review 2-4 semesters before your dissertation defense.

If you have any questions about fulfilling the Demonstration of Understanding requirement, please email [email protected] .

For Faculty:

Please send an email to [email protected] describing the scientific computing-related question that was asked during the examination and acknowledging that the student answered the question satisfactorily.

Ph.D. Seminar

If you enrolled in the Ph.D. in Scientific Computing in or after January 2022 , you are required to present at least once before graduation in the Ph.D. Student Seminar Series . Before presenting, you are strongly encouraged to attend as many sessions of the the Ph.D. Seminar Series as you can, from students in your department and outside it. The Ph.D. Student Seminar Series is an opportunity to learn how to simplify your explanation of your research problems and methods in order to talk about them to colleagues outside of your lab or your home department, which will help you prepare for future job searches.

Sign up to present in 2023-2024 on the MICDE Ph.D. Student Seminar Sign-Up form .

Students are expected to work closely with their academic advisors and with MICDE to develop a plan to meet these requirements.

• Talk to your academic advisor about your interest in the Ph.D. in Scientific Computing. Your department must approve your enrollment in the program.
• Submit the Course Audit form . You don’t have to have a full plan in place before filling out the Course Audit form, but please spend some time considering each of the questions and put your answers in the formats requested.
• After the MICDE program administrator checks your Audit Form and transcript, they will contact you to schedule an advising session with an MICDE Management & Education Committee faculty member. During the session, you, the faculty member, and the MICDE program administrator will finalize your plan to meet the requirements of the Ph.D. in Scientific Computing.
• After your advising session, you can apply to the Ph.D. in Scientific Computing . In order to apply, you must complete the Rackham Application Form , have it signed by your department, and submit it to [email protected] . You are not enrolled in the program unless you have completed this step.

Questions? Contact the Program Administrator at [email protected] .

Eligibility

This is not a stand-alone degree; it is a   joint degree program . Students must be accepted into the Ph.D. program of a home department at the University of Michigan-Ann Arbor.

Enrollment Deadlines

Students are enrolled on a rolling basis as they apply.

Information for Current Students

Please contact the program administrator ( [email protected] ) for all questions related to the Ph.D. in Scientific Computing.

We track students’ progress through the Ph.D. in Scientific Computing Web Progress Form . Your Web Progress Form is created after the advising session, and is accessible by prospective students as well as those who are enrolled. Every summer we will reach out to students to update their Web Progress Form with anything that has changed since the previous summer.

Updating the Web Progress Form

Please plan to update your Web Progress Form each summer with new information, including:

• If you answered questions about scientific computing in your quals/prelims and your Web Progress Form does not reflect this, please describe the questions in the Candidacy Status section.
• If you have formed your doctoral committee, please list the members in the Committee Information section.
• If you have made any changes to the courses you took or plan to take to fulfill requirements for the Ph.D. in Scientific Computing (including changing courses from “planned” to “completed” once you’ve taken them) please update the Course requirements section.
• If you have made progress in your research that is not yet reflected on your WPF (awards, fellowships, conference presentations, publications, etc.) please update the Research Progress section.
• Please make sure that your current estimated graduation term is listed in the  Future Plans section. This is not set in stone, but helps us to understand where you are in your degree process.

Enrollment Status

Note that each student has one of the following 5 statuses on the Web Progress Form . If you believe the enrollment status listed on your Web Progress Form is incorrect, please email [email protected] .

• Enrolled  ( had an advising session, turned in their application form to MICDE and Rackham has processed the application )
• Prospective  ( had an advising session, but has not yet enrolled ) Please let us know if you are still interested in enrolling in the program so we can finish your enrollment. You can log in to the Web Progress Form to see what courses were discussed in your original advising appointment.
• Leave of Absence  ( you are enrolled in the program, and currently in a leave of absence from your home program ) Please let us know when you return from a leave of absence.
• Graduated  ( you graduated from the program in 2015 or later)
• Discontinued  (you discontinued the Ph.D. in Scientific Computing and/or your home program)

You can view your Web Progress Form at any time. If you want to make any changes to your Web Progress Form outside of the summer window, or if you have any problems with accessing the form, please email [email protected] .

• Confirm that your transcript shows you are enrolled in the PhD in Scientific Computing.  If your transcript doesn’t show your enrollment in the program, please contact the program administrator ( [email protected] ) to find out your status within the program.
• If your transcript shows your enrollment in the Scientific Computing program, please review all the information we have on file for you on the Web Progress Form . In particular, check the Graduation requirements summary section at the top. If any of the boxes are blank or incomplete, please ask the program administrator ( [email protected] ) to review your requirements and confirm that they are complete.
• During the term you want to graduate, please contact the program administrator ( [email protected] ) to let them know so they can process your information.

Don’t forget to add the PhD in Scientific Computing program to the title page of your dissertation! For example:  (Physics and Scientific Computing)

A1: Please see  this list for examples. Note that they are only samples of what other students have done, but they are not the only choices. This degree is extremely individualized, so please email the program administrator ( [email protected] ) for more course information.

Q2: I met with the program director, but I get an error when I try to access the Web Progress Form. What can I do?

A2: Please contact the program administrator ( [email protected] ) to inquire about your status.

Q3: Can I change the courses listed on my form?

A3: Yes, but note that any course changes must be approved by MICDE. Email the program administrator ( [email protected] ) if you have any questions.

Q4: How often are students required to complete the Web Progress Form

A4: We ask students to fill out the form annually, by the end of summer each year.

Q5: What if I want to know if a course is approved before the Annual Form is due?

A5: Please contact the program administrator ( [email protected] ) to initiate the approval process. Once approved, they will record it in your form.

Q6: The form lists my status as “PROSPECTIVE” but I think I should be enrolled. What should I do?

This bar graph represents the numbers of students from different departments at U-M enrolled in the program. Students come from the College of Engineering, School of Kinesiology, College of LSA, Michigan Medicine, College of Pharmacy, Ross Business School, School for Environment and Sustainability, School of Information and the School of Public Health.

Departments include: Aerospace Engineering, Civil and Environmental Engineering, Biomedical Engineering, Chemical Engineering, Climate and Space Sciences and Engineering, Electrical Engineering and Computer Science, Industrial & Operations Engineering, Macromolecular Science & Engineering, Mechanical Engineering, Materials Science & Engineering, Naval Architecture & Marine Engineering, Nuclear Engineering & Radiological Sciences, Applied Physics, Chemistry, Chemical Biology, Earth and Environmental Sciences, Linguistics, Mathematics, Physics, Political Science, Psychology, Biostatistics, Environmental Health Sciences, Epidemiology, Health Behavior & Health Education, Kinesiology, Health Infrastructures & Learning Systems, Neuroscience, Pharmaceutical Sciences, Business and School for Environment and Sustainability.

This list is not exhaustive, and continues to grow.

Ph.D. in Scientific Computing years in existence

Current Ph.D. in Scientific Computing students

Alumni since 1992

History of the Ph.D. in Scientific Computing

Text Version

Faculty Leadership

For all questions about the Ph.D. in Scientific Computing, please email [email protected] .

Karthik Duraisamy

2022 – present

2004 – 2022

Bill Martin

1988 – 2004

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CSEM PhD Program

The University of Texas at Austin offers the Doctor of Philosophy (PhD) degree with a major in Computational Science, Engineering, and Mathematics (CSEM). We seek students who are committed to excellence, desire expertise in multiple disciplines, and are willing to take on new challenges while working alongside faculty involved in research at the forefront of computational science. CSEM doctoral students complete advanced coursework in applied mathematics, computer science, and in fields representing the application area. Graduates of the CSEM PhD Program have made significant contributions to research, academia, and technology.

Table of Contents

Csem concentration areas, degree options, preliminary exams, dissertation, phd dissertation committee, dissertation proposal.

• Proposal Presentation

Admission to PhD Candidacy

Phd dissertation and oral defense, other requirements, seminar attendance, annual progress reports, appeals and petitions.

Within this graduate studies program, each student must develop a program of study and research in Computational Science, Engineering, and Mathematics that includes a substantial component from each of the three CSEM concentration areas:

Applied mathematics

Area A encompasses the mathematical theory and foundations underlying the scientific models and computational science addressed in the overall research effort. It may involve, for example, functional analysis, partial differential equations, differential geometry, probability, data science, optimization, and approximation theory.

Numerical Analysis and Scientific Computation

Area B encompasses all areas of algorithms and computational simulation, as well as their development, verification, and analysis. It often covers, for example, issues of numerical stability and approximation, scientific programming, visualization, parallel computation, software design, and high performance computing.

Mathematical Modeling & Applications

Area C encompasses the scientific principles of the natural, engineered, social, or other system that motivates the research and aims to foster some scientific or societal goal through computational modeling and simulation. With the assistance of a CSEM faculty member, all students are expected to develop a concentration of coursework in a well-defined discipline of science, engineering, medicine, economics or the social sciences. Examples include physics, chemistry, biology, geology, biomedicine, all disciplines of engineering, and other areas of science and medicine that form the basis for developing mathematical and computational models.

CSEM has two degree options. Upon entering the program, each student must select an option.

The Computational and Applied Mathematics (CAM) option stresses the mathematical (Area A) side of the program, and is suited more to students with a solid undergraduate background in mathematics. This option also allows the student more time to explore and develop interests regarding an application topic for Area C.

The Computational Science and Engineering (CSE) option stresses the application area (Area C) and allows more time to develop graduate level proficiency in applicable mathematics (Area A). This option is suited to undergraduate engineering, science, and business students who generally know the application area of their interest, but who desire a slower-paced introduction to the intellectual demands of graduate level mathematics.

Every student is required to have a faculty dissertation advisor (or co-advisors). The primary advisor must be chosen from the CSEM Graduate Studies Committee (GSC) . The student must select an advisor willing to serve as a mentor, supervise the dissertation, and give advice on coursework. A dissertation advisor need not be selected until the end of the second long semester of the student's studies. Prior to the selection of a dissertation advisor, the CSEM Graduate Advisor will appoint a faculty mentor who, along with the Graduate Advisor, will advise the student on coursework and progress in the program.

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The student's overall cumulative grade point average must be 3.25 or better. The student must satisfactorily complete requirements in the three CSEM concentration areas A, B, and C. These requirements include 12 hours of approved graduate level coursework in each area, taken for a grade. The student must achieve a grade point average of 3.25 or better in those courses. Moreover, in one of Areas A, B, or C, the student must achieve a grade point average of 3.5 or better. The student must complete all required coursework by the end of the seventh long semester.

Note: specific course numbers are subject to change

Summary of requirements

• Taken for a grade
• Completed by end of 7 th long semester
• Minimum overall GPA of 3.25 in all coursework
• Minimum GPA of 3.25 in each Area
• Minimum GPA of 3.50 in at least one Area
• At least 6 hours (2 courses) must be listed or cross-listed with Math department
• Area B — 12 hours (4 courses)
• Area C — 12 hours (4 courses)

First year sequence

During the first full academic year of the program, the student must complete the following first year sequence, depending on the degree option.

Course requirements: First year sequence

CSE 386C Methods of Applied Mathematics I (Fall) and CSE 386D Methods of Applied Mathematics II (Spring)

CSE 386M Functional Analysis in Theoretical Mechanics (Fall) and CSE 386L Mathematical Methods in Science and Engineering (Spring)

CSE 383C Numerical Analysis: Linear Algebra (Fall) and one of the following – CSE 383L Numerical Analysis: Differential Equations (Spring) – CSE 382M Foundational Techniques of Machine Learning and Data Sciences (Spring)

Same requirements as CAM option

CSE 389C Introduction to Mathematical Modeling in Science and Engineering I (Fall) and CSE 389D Introduction to Mathematical Modeling in Science and Engineering II (Spring)

After completing the first-year sequence, students must complete the following additional coursework by the end of the seventh long semester:

• Area A : two graduate level courses (6 credit hours) approved by the Graduate Advisor. At least two courses (6 credit hours) of all Area A coursework must be listed or cross-listed with the Mathematics Department.
• Area B : two graduate level courses (6 credit hours) approved by the Graduate Advisor. If deemed appropriate by the student's advisor and the Graduate Advisor, up to 3 credit hours may be taken at the undergraduate (upper-division) level.
• Area C : two graduate level courses (6 credit hours) in some application area consistent with the student's proposed research area, approved by both the student's dissertation advisor and the Graduate Advisor. If deemed appropriate by the student's advisor and the Graduate Advisor, up to 3 credit hours may be taken at the undergraduate (upper-division) level.

At the end of the first full academic year, the student is required to demonstrate a graduate level proficiency in CSEM Areas A, B, and C by taking and passing a written preliminary examination in each area. These exams cover the subject material of the first year courses taken by the student.

A student failing any of the preliminary exams will be required by the examining committee to do one of the following:

• take a make-up exam before the start of the Fall semester
• repeat that particular exam the following year
• leave the program

See the preliminary exams page for more info.

The student and dissertation advisor must recommend to the Graduate Advisor a dissertation committee to pose the qualifying exam and evaluate the dissertation. The dissertation committee must consist of the advisor and at least four additional faculty members. The committee must include at least one CSEM Graduate Studies Committee faculty member representing Area A, a second representing Area B, and a third representing Area C, not including the student's advisor. Moreover, at least three of the committee members must represent distinct UT departments through positive time appointment. The Graduate Advisor must approve the composition of the committee. Minimum committee requirements summarized below:

• CSEM GSC faculty member from Area A
• CSEM GSC faculty member from Area B
• CSEM GSC faculty member from Area C
• Additional faculty member (must NOT be on the CSEM GSC)

Before the end of the sixth long semester, the student must propose research for their PhD dissertation.

The student must write a concise abstract of the dissertation proposal. The abstract must address how each of the three CSEM Concentration Areas A, B, and C will be addressed in, and form an integral part of, the proposed research ( Abstract Guidelines ). The student must meet with each member of his or her dissertation committee to discuss the abstract, the expertise the committee member will contribute to the dissertation, and the background knowledge expected of the student, as well as the types of questions that might be asked at the proposal presentation (see Dissertation Proposal Presentation section below.) The abstract must be signed by each member of the committee. Before the dissertation proposal presentation may be scheduled, this abstract must be submitted to and approved by the Graduate Studies Subcommittee (GSSC.) Submit the abstract in pdf format to the Graduate Coordinator who will make it available to the GSSC for review.

The student must write his or her dissertation proposal and submit it to each member of the dissertation committee, and to the Graduate Coordinator. The format of the proposal must conform to the CSEM PhD Proposal Requirements .

Dissertation Proposal Presentation

Approximately two weeks after submission of the written dissertation proposal, the student is required to give a private, oral presentation of the proposal to his or her dissertation committee. The presentation itself should be about 45 minutes in length. The committee will then examine the student to explore details of the proposal and to test his or her general background knowledge relevant to the proposed research, including the ability to integrate ideas from Areas A, B, and C. The committee will expect somewhat greater depth and breadth in Area A as opposed to Area C for students in the CAM option, and the opposite for students in the CSE option.

Once you have scheduled the proposal presentation, you must notify the Graduate Coordinator of the date, time, and room number.

The student's performance is satisfactory if the committee agrees, with at most one dissenting vote, that the student developed a sufficiently rich, original and interdisciplinary research program and demonstrated competence to complete the proposed research. In the event of an unsatisfactory performance, the committee is charged with explaining to the student the reasons that his or her performance was not satisfactory. The committee may impose requirements on the student, such as requiring changes to the proposal, additional coursework, and/or another presentation to be given within one year.

The Candidacy Checklist outlines the steps for entering candidacy, from the formation of the dissertation committee to the submission of the candidacy application to the Graduate School.

After completing all coursework, preliminary examination, and proposal requirements, the student must submit a Graduate School application for candidacy. The CSEM Graduate Coordinator will send instructions for submitting the application once the student's advisor has confirmed that student has passed the proposal.

Information for scheduling your defense may be found at CSEM Defense Guidelines .

Generally, by the end of the tenth long semester, and definitely before the end of the fourteenth long semester, students must prepare a written dissertation of the results of their research and provide a copy to each member of their PhD dissertation committee and to the Graduate Coordinator. This dissertation must be presented in a seminar of about 45 minutes that is open to the public, and it must be announced publicly to CSEM faculty and students within the Oden Institute. Immediately after the presentation, the student will meet privately with the dissertation committee to face questions and orally defend the work. The dissertation committee will judge whether the dissertation and the oral defense are acceptable.

Both the dissertation and the oral defense must follow appropriate Graduate School requirements and procedures found on the Deadlines and Submission Instructions page.

Each student is expected to regularly attend regularly Oden Institute sponsored seminars. The GSSC will set the number required each semester.

Each student is required to submit an annual progress report of coursework, research activities, and financial support. Students not making satisfactory progress to the degree will be given specific requirements that must be met to return to good standing in the program.

Students failing to satisfy the requirements of the program in a timely manner will be put on probation by the GSSC, and their progress will be monitored closely. The student will remain on probation until satisfactory progress is achieved. A student may remain on probation for a maximum of two long semesters. A student who has been on probation for a total of two long semesters and is found to be out of compliance with the timely requirements of the program will not be allowed to continue in the program.

Students may appeal to or petition the CSEM GSSC for waiver or alteration of any CSEM requirement, except for waiver of an exam or waiver of a Graduate School degree requirement. Written appeals or petitions should be submitted to the GSSC through either the Graduate Advisor or the CSEM Graduate Studies Committee Chair.

Download full, official document in PDF format

Computational and Applied Physics

Coordinator.

• Mazzanti Castrillejo, Ferran

[email protected]

https://doctorat-fcia.postgrau.upc.edu/ca

Around 80 doctors focusing on 11 accredited lines of research participate in the doctoral study programme in Computational and Applied Physics; they include professors and researchers from the Department of Physics at the Universitat Politècnica de Catalunya. These studies maintain the distinguished Excellence Award, given by the Spanish Ministry of Education in a resolution from 6 October 2011, although the programme had already been awarded the Ministry’s Quality Award since it was first offered in 2002. These awards recognise the high scientific, technical and educational standards upheld in the programme and give access to related assistance programmes, such as those providing financing for mobility for high-level scientific researchers offering courses in various fields of research. The objective of the programme is to provide solid education and training in the fields of computational physics and applied physics, and to provide an optimal foundation in scientific research methodologies and techniques, in general. We aim to ensure that future doctors will be able to lead research and technological innovation in the aforementioned fields.

General information

Access profile.

Given the multidisciplinary nature of the scientific field of the programme, there are a wide range of degrees that qualify applicants for admission. The most suitable applicants to the doctoral programme in Computational and Applied Physics will, in the near future, be those with scientific and technological profiles who have completed the master’s programme in Computational and Applied Physics or a master’s-level programme in a similar scientific field. In addition to this academic background, certain personal characteristics are also considered important, such as interest in the research projects being carried out in the programme, critical and analytical capacities, having initiative, being consistent and persistent with work, being able to work in a team and being able to communicate properly both in writing and orally.

Output profile

Doctoral candidates who complete a doctoral degree will have acquired the following competencies, which are needed to carry out quality research ( Royal Decree 99/2011, of 28 January, which regulates official doctoral studies ):

a) A systematic understanding of the field of study and a mastery of the research skills and methods related to the field. b) An ability to conceive, design or create, put into practice and adopt a substantial process of research or creation. c) An ability to contribute to pushing back the frontiers of knowledge through original research. d) A capacity for critical analysis and an ability to assess and summarise new and complex ideas. e) An ability to communicate with the academic and scientific community and with society in general as regards their fields of knowledge in the manner and languages that are typical of the international scientific community to which they belong. f) An ability to foster scientific, technological, social, artistic and cultural progress in academic and professional contexts within a knowledge-based society.

The award of a doctoral degree must equip the graduate for work in a variety of settings, especially those requiring creativity and innovation. Doctoral graduates must have at least acquired the personal skills needed to:

a) Develop in contexts in which there is little specific information. b) Find the key questions that must be answered to solve a complex problem. c) Design, create, develop and undertake original, innovative projects in their field. d) Work as part of a team and independently in an international or multidisciplinary context. e) Integrate knowledge, deal with complexity and make judgements with limited information. f) Offer criticism on and intellectually defend solutions.

Finally, with respect to competencies, doctoral students must: a) have acquired advanced knowledge at the frontier of their discipline and demonstrated, in the context of internationally recognised scientific research, a deep, detailed and well-grounded understanding of theoretical and practical issues and scientific methodology in one or more research fields; b) have made an original and significant contribution to scientific research in their field of expertise that has been recognised as such by the international scientific community; c) have demonstrated that they are capable of designing a research project that serves as a framework for carrying out a critical analysis and assessment of imprecise situations, in which they are able to apply their contributions, expertise and working method to synthesise new and complex ideas that yield a deeper knowledge of the research context in which they work; d) have developed sufficient autonomy to set up, manage and lead innovative research teams and projects and scientific collaborations (both national and international) within their subject area, in multidisciplinary contexts and, where appropriate, with a substantial element of knowledge transfer; e) have demonstrated that they are able to carry out their research activity in a socially responsible manner and with scientific integrity; f) have demonstrated, within their specific scientific context, that they are able to make cultural, social or technological advances and promote innovation in all areas within a knowledge-based society; g) have demonstrated that they are able to participate in scientific discussions at the international level in their field of expertise and disseminate the results of their research activity to audiences of all kinds.

Number of places

Duration of studies and dedication regime.

Duration The maximum period of study for full-time doctoral studies is four years, counted from the date of first enrolment in the relevant programme until the date on which the doctoral thesis is deposited. The academic committee of the doctoral programme may authorise a doctoral candidate to pursue doctoral studies on a part-time basis. In this case, the maximum period of study is seven years from the date of first enrolment in the programme until the date on which the doctoral thesis is deposited. To calculate these periods, the date of deposit is considered to be the date on which the thesis is made publicly available for review.

If a doctoral candidate has a degree of disability equal to or greater than 33%, the maximum period of study is six years for full-time students and nine years for part-time students.

For full-time doctoral candidates, the minimum period of study is two years, counted from the date of an applicant's admission to the programme until the date on which the doctoral thesis is deposited; for part-time doctoral candidates it is four years.

When there are justified grounds for doing so, and the thesis supervisor and academic tutor have given their authorisation, doctoral candidates may request that the academic committee of their doctoral programme exempt them from the requirement to complete this minimum period of study.

Temporary disability leave and leave for the birth of a child, adoption or fostering for the purposes of adoption, temporary foster care, risk during pregnancy or infant feeding, gender violence and any other situation provided for in current regulations do not count towards these periods. Students who find themselves in any of these circumstances must notify the academic committee of the doctoral programme, which must inform the Doctoral School.

Doctoral candidates may request periods of temporary withdrawal from the programme for up to a total of two years. Requests must be justified and addressed to the academic committee responsible for the programme, which will decide whether or not to grant the candidate's request.

Extension of studies If a doctoral candidate has not applied to deposit their thesis before the expiry of the deadlines specified in the previous section, the academic committee of the doctoral programme may, at the request of the doctoral candidate, authorise an extension of this deadline of one year under the conditions specified for the doctoral programme in question.

Dismissal from the doctoral programme A doctoral candidate may be dismissed from a doctoral programme for the following reasons:

• The doctoral candidate submitting a justified application to withdraw from the programme.
• The doctoral candidate not having completed their annual enrolment or applied for a temporary interruption.
• The doctoral candidate not having formalised annual enrolment on the day after the end of the authorisation to temporarily interrupt or withdraw from the programme.
• The doctoral candidate receiving a negative reassessment after the deadline set by the academic committee of the doctoral programme to remedy the deficiencies that led to a previous negative assessment.
• The doctoral candidate having been the subject of disciplinary proceedings leading to their suspension or permanent exclusion from the UPC.
• A refusal to authorise the extensions applied for, in accordance with the provisions of Section 3.3 of these regulations.
• The doctoral candidate not having submitted the research plan in the period established in Section 8.2 of these regulations.
• The maximum period of study for the doctoral degree having ended, in accordance with the provisions of Section 3.4 of these regulations.

Dismissal from the programme means that the doctoral candidate cannot continue studying at the UPC and that their academic record will be closed. This notwithstanding, they may apply to the academic committee of the programme for readmission, and the committee must reevaluate the candidate in accordance with the criteria established in the regulations.

A doctoral candidate who has been dismissed due to having exceeded the time limit for completing doctoral studies or due to an unsatisfactory assessment may not be Academic Regulations for Doctoral Studies Universitat Politècnica de Catalunya Page 17 of 33 admitted to the same doctoral programme until at least two years have elapsed from the date of dismissal, as provided for in sections 3.4 and 9.2 of these regulations.

Legal framework

• Royal Decree 99/2011, of 28 January, which regulates official doctoral studies (consolidated version)
• Academic regulations for doctoral studies (CG/2023/09/08)

Organization

• Batiste Boleda, Oriol
• Guardia Manuel, Elvira
• Lopez Codina, Daniel
• Masoller, Cristina
• Ortega Fernandez, Ana Maria
• Pineda Soler, Eloi
• Sánchez Baena, Juan
• Torres Gil, Santiago
• Vazquez Arenas, Beni
• Department of Physics (PROMOTORA)

Access, admission and registration

Access requirements.

As a rule, applicants must hold a Spanish bachelor's degree or equivalent and a Spanish master's degree or equivalent, provided they have completed a minimum of 300 ECTS credits on the two degrees ( Royal Decree 43/2015, of 2 February ).

Applicants who meet one or more of the following conditions are also eligible for admission:

a) Holders of official Spanish degrees or equivalent Spanish qualifications, provided they have passed 300 ECTS credits in total and they can prove they have reached Level 3 in the Spanish Qualifications Framework for Higher Education. b) Holders of degrees awarded in foreign education systems in the European Higher Education Area (EHEA), which do not require homologation, who can prove that they have reached Level 7 in the European Qualifications Framework, provided the degree makes the holder eligible for admission to doctoral studies in the country in which it was awarded. c) Holders of degrees awarded in a country that does not belong to the EHEA, which do not require homologation, on the condition that the University is able to verify that the degree is of a level equivalent to that of official university master's degrees in Spain and that it makes the holder eligible for admission to doctoral studies in the country in which it was awarded. d) Holders of another doctoral degree. e) Holders of an official university qualification who, having been awarded a post as a trainee in the entrance examination for specialised medical training, have successfully completed at least two years of training leading to an official degree in a health sciences specialisation.

Note 1: Regulations for access to doctoral studies for individuals with degrees in bachelor's, engineering, or architecture under the system prior to the implementation of the EHEA (CG 47/02 2014).

Note 2: Agreement number 64/2014 of the Governing Council approving the procedure and criteria for assessing the academic requirements for admission to doctoral studies with non-homologated foreign degrees (CG 25/03 2014).

Admission criteria and merits assessment

Training complements.

The academic committee for the programme may require that doctoral students pass specific bridging courses. In this case, the committee will monitor the bridging courses and set up appropriate criteria to limit their length.

The courses could involve training in research or transversal education, but in no case will candidates be required to enrol in 60 or more ECTS credits (according to the academic regulations for doctoral studies, bridging courses could include transversal education, but there are plans to change to this so that these bridging courses exclusively provide research credits, especially in cases involving 300-ECTS-credit doctoral programmes).

Depending on the activities completed by the candidates, the programme’s Academic Committee may propose measures, in addition to those established by current regulations, that would disassociate candidates who do not meet the established requisites.

The doctoral programme may require potential candidates to complete certain bridging courses in order to better adapt their profiles to the programme’s requirements regarding the knowledge necessary to properly complete the doctoral studies.

The quantity of bridging courses required will depend on the education and training that students accredit having achieved, but candidates could be required to complete 10 to 30 additional ECTS credits at the master’s level. The decision regarding which master’s courses students will have to take to complete the bridging courses will be made jointly by the programme’s Academic Committee and the student’s tutor. In any case, the aim of the courses will always be to fill in the gaps that students are seen to have in their academic transcripts.

Enrolment period for new doctoral students

Students enrolling in the doctoral programme for the first time must do so by the deadline specified in the admission decision. Unless otherwise expressly indicated, enrolments corresponding to admission decisions issued from the second half of April on must be completed within the ordinary enrolment period for the current academic year.

More information at the registration section for new doctoral students

Enrolment period

Ordinary period for second and successive enrolments: first half of October.

More information at the general registration section

Monitoring and evaluation of the doctoral student

Procedure for the preparation and defense of the research plan.

Doctoral candidates must submit a research plan, which will be included in their doctoral student activity report, before the end of the first year. The plan may be improved over the course of the doctoral degree. It must be endorsed by the tutor and the supervisor, and it must include the method that is to be followed and the aims of the research.

At least one of these annual assessments will include a public presentation and defence of the research plan and work done before a committee composed of three doctoral degree holders, which will be conducted in the manner determined by each academic committee. The examination committee awards a Pass or Fail mark. A Pass mark is a prerequisite for continuing on the doctoral programme. Doctoral candidates awarded a Fail mark must submit a new research plan for assessment by the academic committee of the doctoral programme within six months.

The committee assesses the research plan every year, in addition to all of the other activities in the doctoral student activity report. Doctoral candidates who are awarded two consecutive Fail marks for the research plan will be obliged to definitely withdraw from the programme.

If they change the subject of their thesis, they must submit a new research plan.

Formation activities

1. Activity: Tutorial.

Description: Counselling, assistance, supervision and follow-up regarding the candidate’s activities.

Type of activity: compulsory.

Number of hours: 288.

2. Activity: Mobility.

Description: Stays in foreign centres to carry out research activities and/or participate in conferences directly related with the candidate’s thesis or with another topic of interest to the candidate’s education.

Type of activity: optional.

Number of hours: 480.

3. Activity: Assessment based on follow-up with the Doctoral Student Activity Report and the research plan.

Description: Annual assessment report on the candidates by the Academic Committee.

Type of activity: compulsory. Number of hours: 4.

4. Activity: Training in information skills.

Description: Learn to identify when and why information is needed, where to find it and how to ethically evaluate, use and communicate that information.

Number of hours: 1,5.

5. Activity: Research methodologies.

Description: Provide conceptual and methodological research tools for qualitative and quantitative research.

Number of hours: 12.

6. Activity: Innovation and creativity.

Description: Introduction to models of creativity that have been developed in a wide range of disciplines, including marketing, advertising and neurolinguistic programming, all applied to the development of personal and professional projects.

Number of hours: 8.

7. Activity: Language and communication skills.

Description: Acquire a set of knowledge, capacities and attitudes needed to interpret and produce messages and communicate effectively in a wide range of contexts.

Number of hours: 18.

8. Activity: Courses and seminars.

Description: Attend courses, conferences and seminars.

Number of hours: 30.

9. Activity: Publications.

Description: Prepare publications and go through the revision process.

Number of hours: 250.

Procedure for assignment of tutor and thesis director

The academic committee of the doctoral programme assigns a thesis supervisor to each doctoral candidate when they are admitted or enrol for the first time, taking account of the thesis supervision commitment referred to in the admission decision.

The thesis supervisor will ensure that training activities carried out by the doctoral candidate are coherent and suitable, and that the topic of the candidate’s doctoral thesis will have an impact and make a novel contribution to knowledge in the relevant field. The thesis supervisor will also guide the doctoral candidate in planning the thesis and, if necessary, tailoring it to any other projects or activities undertaken. The thesis supervisor will generally be a UPC professor or researcher who holds a doctoral degree and has documented research experience. This includes PhD-holding staff at associated schools (as determined by the Governing Council) and UPC-affiliated research institutes (in accordance with corresponding collaboration and affiliation agreements). When thesis supervisors are UPC staff members, they also act as the doctoral candidate’s tutor.

PhD holders who do not meet these criteria (as a result of their contractual relationship or the nature of the institution to which they are attached) must be approved by the UPC Doctoral School's Standing Committee in order to participate in a doctoral programme as researchers with documented research experience.

The academic committee of the doctoral programme may approve the appointment of a PhD-holding expert who is not a UPC staff member as a candidate’s thesis supervisor. In such cases, the prior authorisation of the UPC Doctoral School's Standing Committee is required. A UPC staff member who holds a doctoral degree and has documented research experience must also be proposed to act as a co-supervisor, or as the doctoral candidate’s tutor if one has not been assigned.

A thesis supervisor may step down from this role if there are justified reasons (recognised as valid by the committee) for doing so. If this occurs, the academic committee of the doctoral programme will assign the doctoral candidate a new thesis supervisor.

Provided there are justified reasons for doing so, and after hearing any relevant input from the doctoral candidate, the academic committee of the doctoral programme may assign a new thesis supervisor at any time during the period of doctoral study.

If there are academic reasons for doing so (an interdisciplinary topic, joint or international programmes, etc.) and the academic committee of the programme gives its approval, an additional thesis supervisor may be assigned. Supervisors and co-supervisors have the same responsibilities and academic recognition.

The maximum number of supervisors of a doctoral thesis is two: a supervisor and a co-supervisor.

For theses carried out under a cotutelle agreement or as part of an Industrial Doctorate, if necessary and if the agreement foresees it this maximum number of supervisors may not apply. This notwithstanding, the maximum number of supervisors belonging to the UPC is two.

More information at the PhD theses section

The maximum period of study for full-time doctoral studies is four years, counted from the date of first enrolment in the relevant programme until the date on which the doctoral thesis is deposited. The academic committee of the doctoral programme may authorise a doctoral candidate to pursue doctoral studies on a part-time basis. In this case, the maximum period of study is seven years from the date of first enrolment in the programme until the date on which the doctoral thesis is deposited. To calculate these periods, the date of deposit is considered to be the date on which the thesis is made publicly available for review.

If a doctoral candidate has not applied to deposit their thesis before the expiry of the deadlines specified in the previous section, the academic committee of the doctoral programme may, at the request of the doctoral candidate, authorise an extension of this deadline of one year under the conditions specified for the doctoral programme in question.

Learning resources

• ANT, https://ant.upc.edu/en • BIOCOM-SC, https://biocomsc.upc.edu/en • CEMAD, https://cemad.upc.edu/en • DF, https://df.upc.edu/en • DILAB, https://dilab.upc.edu/en • DONLL, https://donll.upc.edu/en • GAA, https://gaa.upc.edu/en • GCM, https://gcm.upc.edu/en • GRPFM, https://grpfm.upc.edu/ca • SIMCON, https://simcon.upc.edu/en • AiEM, https://www.aie.upc.edu/ • ANCORA, https://futur.upc.edu/ANCORA • CPSV, https://futur.upc.edu/CPSV • DRM, https://creb.upc.edu/ca/dosimetria-i-radiofisica-medica • GAGE, https://gage.upc.edu/ • GICITED, https://gicited.upc.edu/ca • GIES, https://futur.upc.edu/GIES • GMNE, https://futur.upc.edu/GMNE • GRECDH, https://www.upc.edu/sct/ca/grupsrecerca/123/grup-recerca-cooperacio-desenvolupament-huma.html • ICARUS, https://icarus.upc.edu/en • IMEM, https://futur.upc.edu/IMEM • INSIDE, https://futur.upc.edu/IMEM • InSup, https://futur.upc.edu/InSup • LAB, http://www.lab.upc.edu/ • L’AIRE, https://www.recercaterrassa.upc.edu/ca/node/270 • LaCàN, https://www.lacan.upc.edu/ • LiTA, https://lita.upc.edu/ca • NEMEN, https://deq.upc.edu/ca/recerca/recerca-apartat-anterior/copy_of_nemen • RMEE, http://www.https.com//futur.upc.edu/RMEE • RSLAB, http://www.https.com//www.tsc.upc.edu/en/research/research-groups/rslab/ • SARTI, http://www.cdsarti.org/ • STH, https://sth.upc.edu/ca • TUAREG, https://futur.upc.edu/TUAREG Specific research centres at which teaching and research staff from the Department of Physics participate: • CEBIM, http://alggen.lsi.upc.edu/cebim/ • CREB, https://creb.upc.edu/ca • CRnE, https://crm.upc.edu/ • CTE‐CRAE, https://recerca.upc.edu/crae/en • CTTC, http://www.cttc.upc.edu/ • (MC)2, https://upcommons.upc.edu/handle/2117/427

Doctoral Theses

List of authorized thesis for defense.

Last update: 15/05/2024 04:45:17.

List of lodged theses

• LOPEZ BLANCO, SAMUEL: Current-controlled flash sintering for ultra-fine control of the microstructure of lead-free ferroelectric perovskites. Author: LOPEZ BLANCO, SAMUEL Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis) Programme: DOCTORAL DEGREE IN COMPUTATIONAL AND APPLIED PHYSICS Department: Department of Physics (FIS) Mode: Article-based thesis Deposit date: 09/05/2024 Deposit END date: 23/05/2024 Thesis director: GARCIA GARCIA, JOSE EDUARDO | OCHOA GUERRERO, DIEGO ALEJANDRO Committee:      PRESIDENT: PEREZ MAQUEDA, LUIS ALLAN      SECRETARI: JIMENEZ PIQUÉ, EMILIO      VOCAL: BELTRAN MIR, HECTOR Thesis abstract: The global environmental crisis imposes the need to perform changes in modern industrial manufacturing systems. In the context of ferroelectric ceramics, it is required to move towards energy efficient sintering methods and eco-friendly materials. Flash sintering emerges as a potential alternative owing to its rapid densification and reduced energy consumption. This technique has been investigated in depth since its discovery in 2010 but it is yet to be fully understood. In this thesis, flash sintering is employed in order to obtain dense environmentally-friendly ferroelectric ceramics. A proper control of the sintering parameters is used to achieve highly controlled microstructures and enhanced functional properties for specific applications. The flash technique is then taken a step further by exploring the current control mode, which proves to grant further dominion over the microstructure. In this work a comprehensive study of sintering parameters in multiple ferroelectric materials, from well-known compositions to complex perovskite-structured systems, is performed in order to accomplish fine microstructure tailoring. The ultimate goal was to demonstrate that flash sintering is an efficient method of obtaining ferroelectric polycrystals with high quality properties that can rival their conventional counterparts while overcoming the aforementioned environmental concerns.

Last update: 15/05/2024 04:30:27.

List of defended theses by year

Select a year: 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024

Committee:      PRESIDENT: CHAZEAU, LAURENT      SECRETARI: LI, CHUN      VOCAL: BRUNA ESCUER, PERE Thesis abstract: Metallic glasses, especially high-entropy metallic glasses, characterized by their unique microstructure and mechanical properties, provide an effective way for investigating relaxation dynamics and related aspects in the field of glass science. This doctoral thesis focuses on the dynamic and structural heterogeneity of metallic glasses, with an emphasis on high-entropy metallic glasses, unraveling the complex correlation between their microstructural characteristics, thermal behavior, and mechanical properties. The research aims not only to enhance the theoretical understanding of these materials but also to explore novel methods for their modulation and optimization. Firstly, an extensive characterization of dynamic and structural heterogeneity in metallic glasses is studied, with a focused analysis on the connection between ß relaxation and liquid-like zones. This is achieved through a methodical application of stress relaxation and recovery processes, supported by mechanical spectroscopy. This approach reveals a critical temperature-dependent decrease in dynamic heterogeneity and elucidates the complex interplay between ß relaxation, stress relaxation behavior, and the microstructural evolution of liquid-like zones. Through the application of the Kohlrausch-Williams-Watts equation and various other analytical techniques, the study enhances our comprehension of the fundamental properties of metallic glasses, especially in relation to their mechanical response.Furthermore, the modulation of dynamic heterogeneity in metallic glasses is unveiled. This exploration involves a variety of mechanical measurement techniques, each providing unique insights into the physical and mechanical behavior of metallic glasses, especially for high-entropy metallic glasses. Investigations of the internal friction behavior shed light on the influence of microstructural alterations, especially those induced by varying aging temperatures, on energy dissipation mechanisms in metallic glasses. Additionally, the studies through dynamic cyclic loading, creep testing, and stress relaxation measurements provide a more profound understanding of mechanical hysteresis loops and the mechanisms of inelastic deformation. These insights not only broaden the scope of our comprehension of the mechanical behaviors exhibited by metallic glasses but also demonstrate the potential of various mechanical interventions in tailoring their dynamic properties, thereby enhancing their functional efficacy and structural integrity. Finally, the intrinsic correlation between dynamics and thermodynamics in high-entropy metallic glasses is investigated across both super-high and extremely low frequency domains. High-frequency behavior is explored via electromagnetic acoustic transformation (EMAT), elucidating temperature-dependent mechanical responses and atomic-scale structural stability. In contrast, differential scanning calorimetry (DSC) facilitates the analysis of thermal properties at extremely low frequencies, uncovering gradual structural transformations and long-term material stability. This bifurcated frequency approach yields a holistic understanding of the mechanical and thermal dynamics of high-entropy metallic glasses, emphasizing the significance of the probed frequency window in determining their macroscopic properties.Overall, this dissertation contributes substantially to the domain of non-equilibrium physics in glassy materials. The comprehensive analysis and findings of this research provide novel insights into the aging and relaxation dynamics of metallic glasses, enhancing our understanding of these complex materials. The comprehensive analysis and novel findings presented herein have far-reaching implications for the development, optimization, and application of metallic glasses, paving the way for future advancements in their application and functionality

Committee:      PRESIDENT: IBORT LATRE, LUIS ALBERTO      SECRETARI: ROMAN ROY, NARCISO      VOCAL: OMS, CEDRIC Thesis abstract: In this thesis we study several mathematical objects that are essential to formulate and model physical systems. Applying the tools provided by differential geometry, we develop and analyze different mathematical structures that are used in three physical contexts: dissipative dynamics, integrable systems and geometric quantization. To do it, we mainly employ the setting of b-symplectic geometry, a natural extension of symplectic geometry which is specifically designed to address manifolds with boundary. It is based on the concept of b-forms introduced by Melrose and was initiated by Guillemin, Miranda and Pires.Firstly, in the context of dissipative dynamics, we introduce and discuss a variety of twisted b-cotangent models. In these models, defined on the cotangent bundle of a smooth manifold, the fundamental structure is a b-symplectic form that is singular within the fibers of the bundle. Our models give rise to dynamical systems governed by the standard Hamiltonian of a free particle, accompanied by a positiondependent potential. After examining different types of potentials and finding that all of them induce dissipation of energy in the system, we prove that these twisted bcotangent models offer a suitable Hamiltonian formulation for dissipative systems. Consequently, they expand the scope of Hamiltonian dynamics and bring a new approach to the study of non-conservative systems.Secondly, in the context of integrable systems, we introduce and investigate bsemitoric systems, a family of systems that generalizes simultaneously semitoric systems and b-toric systems, and which is tailored for b-symplectic manifolds. We provide a comprehensive definition of b-semitoric systems, that adapts the characteristics of semitoric systems to the framework of b-symplectic manifolds, and we construct three examples of this type of system. The three examples are based on modifications of the coupled angular momenta system, a classical semitoric system that represents the coupling of two rigid rotors. Our examination of the examples, which includes the classification of the singular points and the study of the global dynamics, allows us to highlight the unique characteristics of b-semitoric systems.Thirdly, in the context of geometric quantization, we introduce a Bohr-Sommerfeld quantization method for b-symplectic toric manifolds. We establish that the dimension of this quantization method depends on a signed count of the integer points in the image of the moment map of the toric action. Additionally, we demonstrate its equivalence with the formal geometric quantization of such manifolds. Furthermore, we present a geometric quantization model based on sheaf cohomology, suitable for integrable systems with non-degenerate singularities, that also relies on the count of the integer points in the image of the moment map.

Last update: 15/05/2024 05:00:40.

Theses related publications

Research projects, teaching staff and research groups, research groups.

UPC groups:

• (MC)2-UPC-Computational continuum mechanics
• AIEM-Architecture, energy and environment
• ANCORA-Analisi i control del ritme cardiac
• ANT-Advanced Nuclear Technologies Research Group
• BIOCOM-SC-Computational Biology and Complex Systems Group
• CEBIM-Molecular Biotechnology Centre
• CEMAD-Electrical Characterisation of Materials and Devices
• CPSV-Centre of Land Policy and Valuations
• CREB-Biomedical Engineering Research Centre
• CRnE-Barcelona Research Center in Multiscale Science and Engineering
• CTE-CRAE-Space Science and Technology Research Group
• CTTC - UPC-Heat and Mass Transfer Technological Center
• DF-Dinamica de Fluids: formacio d'estructures i aplicacions geofisiques
• DILAB-Dielectrics materials physic laboratory
• DONLL-Nonlinear dynamics, nonlinear optics and lasers
• DRM-Dosimetry and Medical Radiation Physics
• GAA-Astronomy and Astrophysics Group
• gAGE-Research Group of Astronomy and Geomatics
• GCM-Group of Characterization of Materials
• GICITED-Interdisciplinary Group on Building Science and Technology
• GIES-Geophysics and Earthquake Engineering
• GMNE-Numerical Methods in Engineering Group
• ICARUS-Intelligent Communications and Avionics for Robust Unmanned Aerial Systems
• INSIDE-Innovation in Systems for Engineering Design and Training
• InSup-Surface Interaction in Bioengineering and Materials Science Research Group
• L'AIRE-Laboratory of Aeronautical and Industrial Research and Studies
• LAB-Laboratory of Applied Bioacoustics
• LACAN - UPC-Numerical Methods for Applied Sciences and Engineering
• LiTA-Architectural Innovation and Technology Laboratory
• NEMEN-Nanoengineering of Materials Applied to Energy
• RMEE-Strength of Materials and Structural Engineering Research Group
• RSLAB-Remote Sensing Lab
• SARTI-Technological Development Center for Remote Acquisition and Data Processing System
• SIMCON-First-principles approaches to condensed matter physics: quantum effects and complexity
• STH-Sustainability, Technology and Humanism
• TUAREG-Turbulence and Aerodynamics in Mechanical and Aerospace Engineering Research Group

Doctoral Programme teachers

• Alarcon Jordan, Marta
• Alonso Maleta, Arantxa
• Alonso Muñoz, Sergio
• Alvarez Lacalle, Enric
• Anento Moreno, Napoleon
• Auguet Sangra, Carlota E.
• Belana Punseti, Juan
• Benadero Garcia-Morato, Luis
• Berart Diez, Sergio
• Bertran Canovas, Oscar
• Boronat Medico, Jordi
• Botey Cumella, Muriel
• Bravo Guil, Eduardo
• Calvete Manrique, Daniel
• Canales Gabriel, Manel
• Cañadas Lorenzo, Juan Carlos
• Casas Castillo, M. del Carmen
• Casulleras Ambros, Joaquim
• CAZORLA SILVA, CLAUDIO
• Cojocaru, Crina
• Crespo Artiaga, Daniel
• Diego Vives, Jose Antonio
• Echebarria Dominguez, Blas
• Falques Serra, Albert
• Fayos Valles, Francisco
• Fernandez Soler, Juanjo
• Ferrer Anglada, Nuria
• Font Garcia, Josep Lluis
• Garcia Garcia, Jose Eduardo
• Garcia Ojalvo, Jordi
• Garcia Senz, Domingo
• Gil Pons, Pilar
• Giro Roca, Antoni
• Gonzalez Cinca, Ricard
• Herrero Simon, Ramon
• Isalgue Buxeda, Antonio
• Jose Pont, Jordi
• Juan Zornoza, Jose Miguel
• Lacasta Palacio, Ana Maria
• Lana Pons, Francisco Javier
• Lloveras Muntane, Pol
• Lopez Lopez, Jose
• Lopez Perez, David O.
• Macovez, Roberto
• Marti Rabassa, Jordi
• Martinez Santafe, Maria Dolors
• Martorell Pena, Jordi
• Massignan, Pietro Alberto
• Meseguer Serrano, Alvaro
• Mudarra Lopez, Miguel
• Navarro Bosque, Javier
• Ochoa Guerrero, Diego
• Oriola Santandreu, David
• Pardo Soto, Luis Carlos
• Pastor Satorras, Romualdo
• Peñaranda Ayllon, Angelina
• Pino Gonzalez, David
• Pons Rivero, Antonio Javier
• Pradell Cara, Trinitat
• Prats Soler, Clara
• Ramirez de la Piscina Millan, Laureano
• Redondo Apraiz, Jose Manuel
• Rey Oriol, Rosendo
• Ribas Prats, Cesca
• Rodriguez Cantalapiedra, Inmaculada
• Rodriguez Perez, Ivette Maria
• Rodriguez Sola, Raul
• Sala Cladellas, Gloria
• Salud Puig, Josep
• Sanchez Umbria, Juan Jose
• Sellares Gonzalez, Jordi
• Serra de Larrocha, Carina
• Serra Tort, Anna
• Serrat Jurado, Carles
• Sese Castel, Gemma
• Soria Guerrero, Manel
• Talavera Sanchez, Pere
• Tamarit Mur, Josep Lluis
• Tauste Campo, Adrian Francisco
• Torres Herrera, Ramon
• Trull Silvestre, Jose Francisco
• Trullas Simo, Joaquim
• Valls Ribas, Quim

The Validation, Monitoring, Modification and Accreditation Framework (VSMA Framework) for official degrees ties the quality assurance processes (validation, monitoring, modification and accreditation) carried out over the lifetime of a course to two objectives—the goal of establishing coherent links between these processes, and that of achieving greater efficiency in their management—all with the overarching aim of improving programmes.

• Verification Memory (Doctoral Programme) - 2013
• Verification Resolution (MECD)
• Agreement of the Council of Ministers (BOE)
• Monitoring report (Doctoral Programme) - 2018
• University monitoring report (Doctoral School) - 2018

Accreditation

• Official Degree Accreditation Evaluation Report (AQU) - 2022

Registry of Universities, Centers and Degrees (RUCT)

• Registration of the Doctoral Programme in the RUCT

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Computational Physics

The Department of Physics offers a BS degree in physics with a concentration in computational physics: the study and implementation of numerical analysis to solve problems in physics. Computation is an integral part of modern science and engineering that is regarded as the third pillar of science along with experimentation and theory. Students will take a three-course sequence at introductory, intermediate, and advanced levels on scientific computing and computational modeling as applied to physical systems. Students successfully completing the concentration may purse graduate study or career paths in diverse areas including in scientific computing, information technology and applied engineering, and of course, physics.

Interested physics majors in good academic standing shall declare their intention in the concentration by completing the concentration declaration form prior to spring of their junior year.

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The field of computational and systems biology represents a synthesis of ideas and approaches from the life sciences, physical sciences, computer science, and engineering. Recent advances in biology, including the human genome project and massively parallel approaches to probing biological samples, have created new opportunities to understand biological problems from a systems perspective. Systems modeling and design are well established in engineering disciplines but are newer in biology. Advances in computational and systems biology require multidisciplinary teams with skill in applying principles and tools from engineering and computer science to solve problems in biology and medicine. To provide education in this emerging field, the Computational and Systems Biology (CSB) program integrates MIT's world-renowned disciplines in biology, engineering, mathematics, and computer science. Graduates of the program are uniquely prepared to make novel discoveries, develop new methods, and establish new paradigms. They are also well-positioned to assume critical leadership roles in both academia and industry, where this field is becoming increasingly important.

Computational and systems biology, as practiced at MIT, is organized around "the 3 Ds" of description, distillation, and design. In many research programs, systematic data collection is used to create detailed molecular- or cellular-level descriptions of a system in one or more defined states. Given the complexity of biological systems and the number of interacting components and parameters, system modeling is often conducted with the aim of distilling the essential or most important subsystems, components, and parameters, and of obtaining simplified models that retain the ability to accurately predict system behavior under a wide range of conditions. Distillation of the system can increase the interpretability of the models in relation to evolutionary and engineering principles such as robustness, modularity, and evolvability. The resulting models may also serve to facilitate rational design of perturbations to test understanding of the system or to change system behavior (e.g., for therapeutic intervention), as well as efforts to design related systems or systems composed of similar biological components.

More than 70 faculty members at the Institute participate in MIT's Computational and Systems Biology Initiative (CSBi). These investigators span nearly all departments in the School of Science and the School of Engineering, providing CSB students the opportunity to pursue thesis research in a wide variety of different MIT laboratories. It is also possible for students to arrange collaborative thesis projects with joint supervision by faculty members with different areas of expertise. Areas of active research include behavioral genetics and genomics; bioengineering and neuroengineering; biological networks and machine learning; cancer systems biology; cellular biophysics; chemical biology and metabolomics; evolutionary and computational biology; microbiology and systems ecology; molecular biophysics and structural biology; precision medicine and medical genomics; quantitative imaging; regulatory genomics, epigenomics, and proteomics; single cell manipulations and measurement; stem cell and developmental systems biology; synthetic biology and biological design; and systems immunology.

The CSB PhD program is an Institute-wide program that has been jointly developed by the Departments of Biology, Biological Engineering, and Electrical Engineering and Computer Science. The program integrates biology, engineering, and computation to address complex problems in biological systems, and CSB PhD students have the opportunity to work with CSBi faculty from across the Institute. The curriculum has a strong emphasis on foundational material to encourage students to become creators of future tools and technologies, rather than merely practitioners of current approaches. Applicants must have an undergraduate degree in biology (or a related field), bioinformatics, chemistry, computer science, mathematics, statistics, physics, or an engineering discipline, with dual-emphasis degrees encouraged.

All students pursue a core curriculum that includes classes in biology and computational biology, along with a class in computational and systems biology based on the scientific literature. Advanced electives in science and engineering enhance both the breadth and depth of each student's education. During their first year, in addition to coursework, students carry out rotations in multiple research groups to gain a broader exposure to work at the frontier of this field, and to identify a suitable laboratory in which to conduct thesis research. CSB students also serve as teaching assistants during one semester in the second year to further develop their teaching and communication skills and facilitate their interactions across disciplines. Students also participate in training in the responsible conduct of research to prepare them for the complexities and demands of modern scientific research. The total length of the program, including classwork, qualifying examinations, thesis research, and preparation of the thesis is roughly five years.

The CSB curriculum has two components. The first is a core that provides foundational knowledge of both biology and computational biology. The second is a customized program of electives that is selected by each student in consultation with members of the CSB graduate committee. The goal is to allow students broad latitude in defining their individual area of interest, while at the same time providing oversight and guidance to ensure that training is rigorous and thorough.

Core Curriculum

The core curriculum consists of three classroom subjects plus a set of three research rotations in different research groups. The classroom subjects are comprised of modern biology, computational biology, and a literature-based exploration of current research frontiers and paradigms, which is required of all first-year students in the program . Students also participate in three research rotations of one to two months' duration during their first year to expose them to a range of research activities in computation and systems biology, and to assist them in choosing a lab. Students are encouraged to gain experience in experimental and computational approaches taken across different disciplines at MIT.

Advanced Electives

To develop breadth and depth, add to the base of the diversified core, and contribute strength in areas related to their interest and research direction, students must take four advanced electives. Each student designs a program of advanced electives that satisfies the distribution and area requirements in close consultation with members of the graduate committee.

Additional Subjects

CSB PhD students may take classes beyond the required diversified core and advanced electives described above. These additional subjects can be used to add breadth or depth to the proposed curriculum, and might be useful to explore advanced topics relevant to the student's thesis research in later years. The CSB Graduate Committee works with each graduate student to develop a path through the curriculum appropriate for his or her background and research interests.

Training in the Responsible Conduct of Research

Throughout the program, students will be expected to attend workshops and other activities that provide training in the ethical conduct of research. This is particularly important in interdisciplinary fields such as computational and systems biology, where different disciplines often have very different philosophies and conventions. By the end of the fifth year, students will have had about 16 hours of training in the responsible conduct of research.

Qualifying Exams

In addition to coursework and a research thesis, each student must pass a written and an oral qualifying examination at the end of the second year or the beginning of the third year. The written examination involves preparing a research proposal based on the student's thesis research, and presenting the proposal to the examination committee. This process provides a strong foundation for the thesis research, incorporating new research ideas and refinement of the scope of the research project. The oral examination is based on the coursework taken and on related published literature. The qualifying exams are designed to develop and demonstrate depth in a selected area (the area of the thesis research) as well as breadth of knowledge across the field of computational and systems biology.

Thesis Research

Research will be performed under the supervision of a CSBi faculty member, culminating in the submission of a written thesis and its oral defense before the community and thesis defense committee. By the second year, a student will have formed a thesis advisory committee that they will meet with on an annual basis.

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Computational Physics Certificate

The Computational Physics Certificate is a certificate program through the Department of Physics and the College of Arts and Sciences. Students in the program engage in a coherent set of undergraduate coursework to prepare for and pursue computational physics as a career or to apply these skills in a research or graduate program.

Students in the Computational Physics Certificate are required to complete at least 12 credit hours overall from two required courses and two elective courses. 50% of the hours taken toward the certificate are permitted to double-count toward a different degree program (major, minor, other certificate, etc.).

Certificate program requirements and advising contact information are on the computational physics advising sheet: https://artsandsciences.osu.edu/sites/default/files/2024-02/certificate-computational-physics.pdf

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New work extends the thermodynamic theory of computation

by Santa Fe Institute

Every computing system, biological or synthetic, from cells to brains to laptops, has a cost. This isn't the price, which is easy to discern, but an energy cost connected to the work required to run a program and the heat dissipated in the process.

Researchers at the Santa Fe Institute and elsewhere have spent decades developing a thermodynamic theory of computation, but previous work on the energy cost has focused on basic symbolic computations—like the erasure of a single bit—that aren't readily transferable to less predictable, real-world computing scenarios.

In a paper published in Physical Review X , a quartet of physicists and computer scientists expands the modern theory of the thermodynamics of computation. By combining approaches from statistical physics and computer science, the researchers introduce mathematical equations that reveal the minimum and maximum predicted energy cost of computational processes that depend on randomness, which is a powerful tool in modern computers.

In particular, the framework offers insights into how to compute energy-cost bounds on computational processes with an unpredictable finish. For example: A coin-flipping simulator may be instructed to stop flipping once it achieves 10 heads. In biology, a cell may stop producing a protein once it elicits a certain reaction from another cell. The "stopping times" of these processes, or the time required to achieve the goal for the first time, can vary from trial to trial. The new framework offers a straightforward way to calculate the lower bounds on the energy cost of those situations.

The research was conducted by SFI Professor David Wolpert, Gonzalo Manzano (Institute for Cross-Disciplinary Physics and Complex Systems, Spain), Édgar Roldán (Institute for Theoretical Physics, Italy), and SFI graduate fellow Gülce Kardes (CU Boulder). The study uncovers a way to lower-bound the energetic costs of arbitrary computational processes. For example: an algorithm that searches for a person's first or last name in a database might stop running if it finds either, but we don't know which one it found.

"Many computational machines, when viewed as dynamical systems , have this property where if you jump from one state to another you really can't go back to the original state in just one step," says Kardes.

Wolpert began investigating ways to apply ideas from nonequilibrium statistical physics to the theory of computation about a decade ago. Computers, he says, are a system out of equilibrium, and stochastic thermodynamics gives physicists a way to study nonequilibrium systems. "If you put those two together, it seemed like all kinds of fireworks would come out, in an SFI kind of spirit," he says.

In recent studies that laid the groundwork for this new paper, Wolpert and colleagues introduced the idea of a "mismatch cost," or a measure of how much the cost of a computation exceeds Landauer's bound. Proposed in 1961 by physicist Rolf Landauer, this limit defines the minimum amount of heat required to change information in a computer. Knowing the mismatch cost, Wolpert says, could inform strategies for reducing the overall energy cost of a system.

Across the Atlantic, co-authors Manzano and Roldán have been developing a tool from the mathematics of finance—the martingale theory—to address the thermodynamic behavior of small fluctuating systems at stopping times. Roldán et. al.'s "Martingales for Physicists" has helped pave the way to successful applications of such a martingale approach in thermodynamics.

Wolpert, Kardes, Roldán, and Manzano extend these tools from stochastic thermodynamics to the calculation of a mismatch cost to common computational problems in their PRX paper.

Taken together, their research point to a new avenue for finding the lowest energy needed for computation in any system, no matter how it's implemented. "It's exposing a vast new set of issues," Wolpert says.

It may also have a very practical application, in pointing to new ways to make computing more energy efficient. The National Science Foundation estimates that computers use between 5% and 9% of global generated power, but at current growth rates, that could reach 20% by 2030.

But previous work by SFI researchers suggests modern computers are grossly inefficient: Biological systems, by contrast, are about 100,000 times more energy-efficient than human-built computers. Wolpert says that one of the primary motivations for a general thermodynamic theory of computation is to find new ways to reduce the energy consumption of real-world machines.

For instance, a better understanding of how algorithms and devices use energy to do certain tasks could point to more efficient computer chip architectures. Right now, says Wolpert, there's no clear way to make physical chips that can carry out computational tasks using less energy.

"These kinds of techniques might provide a flashlight through the darkness," he says.

Journal information: Physical Review X

Provided by Santa Fe Institute

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New work extends the thermodynamic theory of computation

May 13, 2024.

Every computing system, biological or synthetic, from cells to brains to laptops, has a cost. This isn’t the price, which is easy to discern, but an energy cost connected to the work required to run a program and the heat dissipated in the process. 

Researchers at SFI and elsewhere have spent decades developing a thermodynamic theory of computation, but previous work on the energy cost has focused on basic symbolic computations — like the erasure of a single bit — that aren’t readily transferable to less predictable, real-world computing scenarios. 

In a paper published in Physical Review X on May 13, a quartet of physicists and computer scientists expand the modern theory of the thermodynamics of computation. By combining approaches from statistical physics and computer science, the researchers introduce mathematical equations that reveal the minimum and maximum predicted energy cost of computational processes that depend on randomness, which is a powerful tool in modern computers. 

In particular, the framework offers insights into how to compute energy-cost bounds on computational processes with an unpredictable finish. For example: A coin-flipping simulator may be instructed to stop flipping once it achieves 10 heads. In biology, a cell may stop producing a protein once it elicits a certain reaction from another cell. The “stopping times” of these processes, or the time required to achieve the goal for the first time, can vary from trial to trial. The new framework offers a straightforward way to calculate the lower bounds on the energy cost of those situations. 

The research was conducted by SFI Professor David Wolpert , Gonzalo Manzano (Institute for Cross-Disciplinary Physics and Complex Systems, Spain), Édgar Roldán (Institute for Theoretical Physics, Italy), and SFI graduate fellow Gülce Kardes (CU Boulder). The study uncovers a way to lower-bound the energetic costs of arbitrary computational processes. For example: an algorithm that searches for a person’s first or last name in a database might stop running if it finds either, but we don’t know which one it found. “Many computational machines, when viewed as dynamical systems, have this property where if you jump from one state to another you really can’t go back to the original state in just one step,” says Kardes. 

Wolpert began investigating ways to apply ideas from nonequilibrium statistical physics to the theory of computation about a decade ago. Computers, he says, are a system out of equilibrium, and stochastic thermodynamics gives physicists a way to study nonequilibrium systems. “If you put those two together, it seemed like all kinds of fireworks would come out, in an SFI kind of spirit,” he says. 

In recent studies that laid the groundwork for this new paper, Wolpert and colleagues introduced the idea of a “mismatch cost,” or a measure of how much the cost of a computation exceeds Landauer’s bound. Proposed in 1961 by physicist Rolf Landauer, this limit defines the minimum amount of heat required to change information in a computer. Knowing the mismatch cost, Wolpert says, could inform strategies for reducing the overall energy cost of a system.

Across the Atlantic, co-authors Manzano and Roldán have been developing a tool from the mathematics of finance — the martingale theory — to address the thermodynamic behavior of small fluctuating systems at stopping times. Roldán et. al.’s “Martingales for Physicists” helped pave the way to successful applications of such a martingale approach in thermodynamics.

Wolpert, Kardes, Roldán, and Manzano extend these tools from stochastic thermodynamics to the calculation of a mismatch cost to common computational problems in their PRX paper. 

Taken together, their research point to a new avenue for finding the lowest energy needed for computation in any system, no matter how it’s implemented. “It’s exposing a vast new set of issues,” Wolpert says. 

It may also have a very practical application, in pointing to new ways to make computing more energy efficient. The National Science Foundation estimates that computers use between 5% and 9% of global generated power, but at current growth rates, that could reach 20% by 2030. But previous work by SFI researchers suggests modern computers are grossly inefficient: Biological systems, by contrast, are about 100,000 times more energy-efficient than human-built computers. Wolpert says that one of the primary motivations for a general thermodynamic theory of computation is to find new ways to reduce the energy consumption of real-world machines. 

For instance, a better understanding of how algorithms and devices use energy to do certain tasks could point to more efficient computer chip architectures. Right now, says Wolpert, there’s no clear way to make physical chips that can carry out computational tasks using less energy. 

“These kinds of techniques might provide a flashlight through the darkness,” he says.

Read the paper "Thermodynamics of Computations with Absolute Irreversibility, Unidirectional Transitions, and Stochastic Computation Times" in PRX  (May 13, 2024). DOI: 10.1103/PhysRevX.14.021026

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Coordinates of Elektrostal in decimal degrees

Coordinates of elektrostal in degrees and decimal minutes, utm coordinates of elektrostal, geographic coordinate systems.

WGS 84 coordinate reference system is the latest revision of the World Geodetic System, which is used in mapping and navigation, including GPS satellite navigation system (the Global Positioning System).

Geographic coordinates (latitude and longitude) define a position on the Earth’s surface. Coordinates are angular units. The canonical form of latitude and longitude representation uses degrees (°), minutes (′), and seconds (″). GPS systems widely use coordinates in degrees and decimal minutes, or in decimal degrees.

Latitude varies from −90° to 90°. The latitude of the Equator is 0°; the latitude of the South Pole is −90°; the latitude of the North Pole is 90°. Positive latitude values correspond to the geographic locations north of the Equator (abbrev. N). Negative latitude values correspond to the geographic locations south of the Equator (abbrev. S).

Longitude is counted from the prime meridian ( IERS Reference Meridian for WGS 84) and varies from −180° to 180°. Positive longitude values correspond to the geographic locations east of the prime meridian (abbrev. E). Negative longitude values correspond to the geographic locations west of the prime meridian (abbrev. W).

UTM or Universal Transverse Mercator coordinate system divides the Earth’s surface into 60 longitudinal zones. The coordinates of a location within each zone are defined as a planar coordinate pair related to the intersection of the equator and the zone’s central meridian, and measured in meters.

Elevation above sea level is a measure of a geographic location’s height. We are using the global digital elevation model GTOPO30 .

Elektrostal , Moscow Oblast, Russia