PHYS 117

Computational Modeling in Modern Physics

Course Description

The aim of computational physics is to aid in the understanding of physical systems and processes using numerical techniques and computers. This course, PHYS 117, has the same theme as PHYS 115 and continues the discussions initiated there on solving realistic physics problems using numerical and computational tools. The student is further introduced to computational physics techniques through discussions on how to model and implement computational solutions to problems in electricity and magnetism, thermodynamics, disordered systems, and molecular dynamics. Specific computational problems studied in this course include the calculation of the electric potential, electric field, and magnetic field in a region of space, the modeling of random walks and disordered systems, the physical description of a second-order phase transition, and the classical dynamics of molecules in a dilute gas. Similar to PHYS 115, the emphasis of this course is the physics, not numerical analysis.

Course Learning Outcomes

After completing this course, you should be able to:

• design computational models of the essential physics in electromagnetism, thermodynamics, and molecular dynamics;

• implement numerical calculations and simulations of physical processes; and

• evaluate the accuracy of the results of computer simulations.

Course Outline

  1. Electromagnetic potential and fields

    • Laplace's and Poisson's Equations

    • Electric potentials and fields

    • Jacobi and Gauss-Seidel Relaxation Methods

    • Magnetic field produced by a current-carrying wire

  2. Random systems

    • Random walks in one and three dimensions

    • Random walks and diffusion

    • Site percolation on a square lattice

    • Hoshen-Kopelman algorithm

  3. Monte Carlo Methods in Statistical Physics

    • The Ising Model in two dimensions

    • Mean Field Theory

    • Metropolis Algorithm

    • Second-order phase transition

  4. Molecular Dynamics

    • Verlet Method in solving the equations of motion

    • Lennard-Jones potential

    • Periodic boundary condition

Mode of Delivery

The course will follow the schedule stated in this Syllabus. All course materials, i.e., this Syllabus, the Lecture Activities, Laboratory Activities, lecture slides, sample programs, and supplementary materials, are going to be available in the PHYS 171 Canvas Learning Management System (LMS). Online lectures are going to be held twice a week via Zoom meetings. Students can also post questions and start a discussion in the Discussions page of the Canvas LMS.

Necessary Equipment and Software

Since this course is both purely online and requires students to write computer programs, each student must have access to a computer with a modern Fortran compiler and graphing software such as Grace for two-dimensional plots and Gnuplot for three-dimensional plots. It is recommended that the computer runs on Linux as its operating system, although Microsoft Windows and the MacOS should also work. If the student is using Windows, it is highly recommended that the Windows Subsystem for Linux (WSL) app and the Ubuntu flavor of Linux should be installed.

References

The main reference for this course is:

• N.J. Giordano and H. Nakanishi, Computational Physics, 2nd Edition, Pearson-Prentice Hall, 2006.

Supplementary references are:

• J. Franklin, Computational Methods for Physics, Cambridge University Press, 2013.

• A.L. Garcia, Numerical Methods for Physics, 2nd Edition, Prentice-Hall, 2000.

References in Fortran:

• S. Chapman, Fortran for Scientists and Engineers, 4th Edition, McGraw-Hill, 2017.

• M. Metcalf, J. Reid, and M. Cohen, Modern Fortran Explained: Incorporating Fortran 2018, 5th Edition, Oxford University Press, 2018.

About the Instructor

Name: Eduardo C. Cuansing Jr., Ph.D.

Email Address: eccuansing at up.edu.ph

Homepage: https://sites.google.com/up.edu.ph/eduardo-c-cuansing/home

Eduardo C. Cuansing Jr., Ph.D., is a Professor at the Institute of Mathematical Sciences and Physics. He earned his B.S. Physics from the University of the Philippines Diliman and his Ph.D. Physics from Purdue University. He was a postdoctoral researcher at the University of Pittsburgh and the National University of Singapore. He was also previously a faculty member at the University of the Philippines Diliman, De La Salle University, and the Ateneo de Manila University. He currently heads the Quantum Transport and Quantum Thermodynamics (QT2) research group. His research is in theoretical and computational physics, in specific areas such as quantum transport, nonequilibrium physics, quantum thermodynamics, and phase transitions and critical phenomena.