Analysis and Implementation of Numerical Methods for Simulating Dilute Polymeric Fluids David Knezevic Doctor of Philosophy Balliol College Michaelmas Term 2008 In this thesis we develop, analyse and implement a number of numerical methods for simulating dilute polymeric fluids. We use a well-known model in which the polymeric fluid is represented by a suspension of dumbbells in a Newtonian sol...

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokk...

One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker–Planck equation in Rd with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear stochastic differential equation. The case of a nonlinear Fokker–Planck equation with linear space dependent drift is also studied.

We present a uniform L-stability estimate for mild solutions to the Fokker-Planck-Boltzmann equation. For stability estimate, we derive a Gronwall type estimate using dispersion estimates for mild solutions due to the hypoelliptic structure of the Vlasov-Fokker-Planck operator.

Physical and chemical stochastic processes described by the master equation are investigated. The system-size expansion, called the Ω-expansion, transforms the master equation to the corresponding Fokker-Planck equation. In this paper, we examine the entropy production for both the master equation and the corresponding Fokker-Planck equation. For the master equation, the exact expression of the...

Stochastic differential equations (SDE) are used to model many situations including population dynamics, protein kinetics, turbulence, finance, and engineering [5, 6, 1]. Knowing the solution of the SDE in question leads to interesting analysis of the trajectories. Most SDE are unsolvable analytically and other methods must be used to analyze properties of the stochastic process. From the SDE, ...

The Langevin equation approach to the evolution of the velocity distribution for the Brownian particle might leave you uncomfortable. A more formal treatment of this type of problem is given by the Fokker-Planck equation. We can either formulate the question in terms of the evolution of a nonstationary probability distribution from a defined initial condition, or in terms of the evolution of th...

We have carried out comparative study between direct N-body technique and Fokker-Planck approach for the dynamical evolution of rotating stellar systems. Because of limitations of computing resources, we have restricted to relatively small N (∼ 10,000) systems compared to realistic star clusters. We found that these two different approached generally give very similar results. Some minor differ...