The Computational Physics program is being developed by Dr. Vladimir Florinski, a winner of the prestigeous National Science Foundation CAREER award. Modern research in physics is inconceivable without a solid knowledge of computational methods. The CP progam prepares future scientists for the realities and demands of modern computational environment. Students from a diverse range of backgrounds from science and engineering to business and finance, are encouraged to enroll. The curriculum is developed with input from the Huntsville area science and technology business community. The Space Science Department with its close partnership with CSPAR has emerged as a regional leader in computational science research and education. Major contributers to the program are Nick Pogorelov (UAH/SPA), Ken Nishikawa (UAH/Physics), Babak Shotorban (UAH/MAE), and Vladimir Kolobov (CFDRC).
We currently offer 4 courses within the program:
SPA 662 Computational Physics
This course provides a broad introduction to computational methods with applications to classical dynamics, electromagnetism, quantum mechanics, and statistical physics. It is taugh using an actual programming language (C and C++) and teaches how to develop, compile, and run scientific codes. We learn numerical integration and differentiation, root finding, data fitting, numerical linear algebra, introductory Monte-Carlo method, linear and nonlinear ODEs, Fourier analysis, finite difference methods for elliptic, parabolic, and hyperbolic partial differential equations, and nonlinear wave propagation. Students also learn how to graph and visualize their results using open source visualization software. Every class we have an interactive session where students compete to finish a small computational project in real time. In place of a final exam students complete a class projects on applying computational methods to their own research field. Textbooks are Landau, Paez, and Bordeinau "Computational Physics" and Pang "An Introduction to Computational Physics". This course is offered every year.
Links to selected 2012 student research presentations:
Links to selected 2013 student research presentations:
PH 698 (Special Topics) Computational Plasma Physics
This course provides students with basic concepts of computer simulation using particle-in-cell (PIC) codes to understand kinetic processes in plasmas. In order to understand the lectures, students need to take “Introduction to Plasmas Dynamics” and “Electromagnetic Theory”. It is preferable to take “High Energy Astrophysics” in advance. We cover the fundamental concepts of plasma simulation such one-dimensional electrostatic codes and electromagnetic codes, and the numerical methods and analysis. Starting with plasma physics theory background, we then discuss the mathematics and physics behind the algorithms. We explore how the PIC simulations reveal highly nonlinear phenomena in plasmas. The final part of this course is an introduction to modern three-dimensional simulations using super computers. We teach students how to parallellize their codes using the message passing interface (MPI), enabling them to run on modern multi-core or multi-processor machines or even large scale distributed memory clusters. Textbook is Birdsall and Langdon "Plasma Physics via Computer Simulation".
SPA 663 Computational Fluid Dynamics and MHD
The aim of the course is to give graduate students knowledge of the numerical approaches to solve gas dynamics and magnetohydrodynamics (MHD) equations sufficient for performing independent computations of plasma flows in laboratory and astrophysical environments. This is a computational fluid dynamics (CFD) and MHD course which describes not only numerical schemes, but also mathematically justified ways to formulate physical problems and appropriate boundary conditions. The course starts with a brief description of finite-difference and finite-volume approximations for the advection equations, accompanied by their stability and accuracy analysis. We consider traditional (central and upwind) Lax-Friedrichs, Lax-Wendroff, Beam-Warming, MacCormack, and Courant-Isaacson-Rees schemes, and their total variation diminishing analogues. The flux corrected transport (FCT) approach is used to introduce the notion of contemporary nonlinear schemes. All of these schemes are used throughout the course to solve CFD and MHD problems of different complexity as homeworks and projects. Different approaches to solve gas dynamics and MHD Riemann problems are discussed together with their application to systems of PDEs. Particular attention is paid to discontinuous solutions obtained with shock-capturing and shock-fitting methods. The evolutionary diagram for the MHD system is considered, and examples of spurious, nonevolutionary solutions are given as well as approaches to avoid them in numerical simulations. Numerical approaches to magnetic field divergence cleaning are analyzed and compared. Textbooks are Kulikovski, Pogorelov, and Semenov "Mathematical Aspects of Numerical Solutions of Hyperbolic Systems" and LeVeque "Finite Difference Methods for Ordinary and Partial Differential Equations".
PH 698 (Special Topics) Stochastic Methods in Computational Physics
This course will provide an introduction to stochastic processes, Ito calculus and stochastic differential equations (SDEs). Emphasis will be on the differential Chapman-Kolmogorov equation and its special cases such as diffusion, Levi flights, and jump processes. We will discuss numerical solution methods for SDEs including Euler-Maruyama, Milstein, and Runge-Kutta explicit and implicit schemes. Applications will include turbulent diffusion, dynamical system stability, and some examples from chemistry, biology, and finance. A background in undergraduate probability theory and programming (C/C++) is highly recommended. Students are required to bring their laptop computer for in class exercises. Recommended textbooks are Gardiner, "Stochastic Methods" and Kloeden and Platen, "Numerical Solutions of Stochastic Differential Equations".
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