Janis Bajars defends thesis on simulation of Hamiltonian systems

CWI researcher Janis Bajars has developed new methods for numerical simulations of forced Hamiltonian systems. These can be used to simulate complex problems such as the development of internal ocean waves or climate models more accurately. He defended his thesis on 7 December 2012 at the University of Amsterdam. By improving numerical simulations of Hamiltonian systems, a wide range of problems in climatology and oceanography can be more accurately modeled, such as the role of wave focusing in ocean mixing and distribution of kinetic energy in turbulent atmosphere and ocean flows.
 
An Hamiltonian system is a mathematical description of a physical system that changes in time, such as a game of billiards, a planetary system or ocean waves. It can be described with a set of differential equations that express the conservation of energy. For complex systems, these equations cannot be solved exactly but need to be solved computationally using numerical methods. Because the equations are continuous but the numerical simulations are discrete, system properties such as energy conservation can be lost, creating serious inaccuracies. Bajars has worked on methods that can fix several of these inaccuracies in situations where energy is disturbed by external forces. His thesis includes developing methods to study the interaction between energy conservation and external forcing, as well as thermostat methods that ensure a correct probability distribution of the energy levels while sampling.
 
Thesis: Geometric Integration and Thermostat Methods for Hamiltonian Systems
By: Janis Bajars (CWI Computational and Stochastic Dynamics-group)
Promotor: prof. dr. ir. Jason Frank (CWI and UvA)
Date: 7 December 2012, 14.00h
Place: Agnietenkapel, Oudezijds Voorburgwal 231, Amsterdam

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