Browsing by Author "Veit, Max"

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    Computation of Defects in Materials
    (2011-08-11) Veit, Max
    Abstract The purpose of this project is to investigate and assess, using the MATLAB computer language, some numerical methods used in several elds of computational molecular dynamics. First a theoretical model of a one-dimensional chain of atoms was studied. The atoms in this chain would interact based on the Lennard-Jones potential energy function. Several algorithms were investigated that found con gurations of the chain where the total potential energy was lowest. Aspects of the one-dimensional chain were then carried over into a model of a two-dimensional system of atoms. For this model a full simulation of the movement of the atoms in the system was used to study the system. It was found that one of the simplest atom con gurations, a square lattice pattern, was unstable. In the simulation, this structure evolved over time into several disconnected regions, called grains," of a more stable triangular-hexagonal lat- tice pattern. These structures are similar to crystal grains in real-world polycrystalline materials. Some basic computational thermodynamics (more specically, Langevin dynamics) was also used in the simulation. It was found that by regulating the temperature, or average kinetic energy, of the system, the formation of grains could be controlled to some degree.
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    Stochastic Simulation of Genetic Regulatory Networks with Delayed Reactions
    (2014-10-01) Veit, Max
    Many important processes in cells are controlled by genetic regulatory networks. To accurately model such networks, it is often necessary to include reactions with delays. In this work I apply the weighted ensemble (WE) method to simulate models of genetic regulatory networks that incorporate delays. In order to accurately capture the discreteness and stochasticity present in small systems, the Gillespie stochastic simulation algorithm (SSA), extended to include delayed reactions, is used to evolve trajectories in time. Tests of this method on two simple model systems show that theWEmethod yields an unbiased estimate of the system’s probability distribution in the presence of delays, despite the SSA’s non-uniform timesteps. I additionally use the extended SSA to investigate the assumptions used in analytical models of the simple delayed-degradation system. The numerical results indicate that a mean-field approximation is not justified near the system’s bifurcation point, but is conditionally justified both in the limit of small and (surprisingly) of large propensity of the delayed reaction.