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Organizer : Dr. Drew Sills
Date: Friday, April 29
Time: 2:30 – 3:20 PM
Location: Math/Physics Bldg 2028
Speaker: Dr. Alex Stokolos (Georgia Southern University)
Title: Stability in Discrete Autonomous Dynamical Systems
Abstract: In this talk I will demonstrate how the standard college mathematics can do a great job in study of important problems in dynamical systems theory.
Date: Monday, April 18
Time: 4:00 – 4:50 PM
Location: Math/Physics Bldg 2028
Speaker: Matthew Just (Georgia Southern University)
Title: Numerical Estimates to Laplace's Equation Using Absorbing Markov Chains
Abstract: Markov chains are used in a multitude of fields to model processes that are either stochastic by nature (such as the interaction of human or animal populations), or deterministic systems with an incalculable number of constituents in which a probabilistic interpretation of the system is more practical (such as the behavior of fluids). By using an absorbing Markov chain model, solutions to Laplace's equation for a potential field subject to Dirichlet conditions may be numerically estimated at a set of transient nodes by simultaneously calculating the transition probabilities of transitions from these free nodes to a set of absorbing nodes for which the potential is known. A program is written in R to construct high-order numerical estimations of an analytically solvable system from Electrostatics and results are compared to test the accuracy of the absorbing Markov chain model. The technique is then applied to a system with no analytic solutions to demonstrate a practical application.
Date: Friday, April 8
Time: 2:30 – 3:20 PM
Location: Math/Physics Bldg 2028
Speaker: Dr. Mark Edwards (Fuller E. Callaway Professor of Physics, Georgia Southern University)
Title: Variational Approximations of Solutions of the Nonlinear Schrödinger Equation
Abstract: I will talk about some of the problems we are solving that required solutions of the nonlinear Schrödinger equation with the cubic nonlinearity which is called the Gross-Pitaevskii equation (GPE) in our literature. I will describe the so-called Lagrangian variational method and give some examples where we have used it to find solutions of the GPE non possible on the computer.
Date: Monday, March 28
Time: 4:00 – 4:50 PM
Location: Math/Physics Bldg 2028
Speaker: Dr. Andrew Sills (Georgia Southern University)
Title: Identities of Rogers-Ramanujan Type
Abstract: Rodney Baxter (Australian National University) won the Boltzmann Medal in 1980 and the Lars Onsager Prize in 2006 "for his original and groundbreaking contributions to the field of exactly solved models in statistical mechanics, which continue to inspire profound developments in statistical physics and related fields."
Central to the mathematics involved in Baxter's solution to the hard-hexagon model are the Rogers-Ramanujan identities and identities of similar type. I shall discuss the introductory aspects of these identities and their precursors in the work of Euler.
Date: Friday, March 11
Time: 2:30 – 3:20 PM
Location: Math/Physics Bldg 2028
Speaker: Dr. Maxim Durach (Georgia Southern University)
Date: Monday, February 29
Time: 4:00 – 4:50 PM
Location: Math/Physics Bldg 2028
Speaker: Dr. Shijun Zheng (Georgia Southern University)
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