................................................................................V DECLARATION OF ORIGINALITY ........................................... VII ACKNOWLEDGEMENTS........................................................... IX TABLE OF CONTENTS.............................................................. XI TABLE OF FIGURES.................................................................

We have elucidated the effect of statistical asymmetry on the directed current in Smoluchowski-Feynman ratchets driven by chaotic noise. Based on the inhomogeneous Smoluchowski equation and its generalized version, we arrive at analytical expressions of the directed current that includes a source term. The source term indicates that statistical asymmetry can drive the system further away from t...

Background: Effects of electromagnetic fields on healing have been investigated for centuries. Substantial data indicates that exposure to electromagnetic field can lead to enhanced healing in both soft and hard tissues. Helmholtz coil is a device that generates pulsed electromagnetic fields. Objective: In this study, a pair of Helmholtz coils for enhancing thehealing process in periodontitis w...

We prove global existence for a nonlinear Smoluchowski equation (a nonlinear FokkerPlanck equation) coupled with Navier-Stokes equations in 2d. The proof uses a deteriorating regularity estimate in the spirit of [5] (see also [1]) Key wordsNonlinear Fokker-Planck equations, Navier-Stokes equations, Smoluchowski equation, micro-macro interactions. AMS subject classification 35Q30, 82C31, 76A05.

A thermodynamic property model explicit in the Helmholtz energy is presented for the R-134a/245fa mixtures. A multi-fluid approximation based on pure-fluid Helmholtz energy equations of state forms the basis of the property model. The Helmholtz energy of the mixture is expressed as the sum of the ideal gas contribution, the compressibility contribution (real fluid contribution), and the contrib...

We develop the analogy between self-gravitating Brownian particles and bacterial populations. In the high friction limit, the self-gravitating Brownian gas is described by the Smoluchowski-Poisson system. These equations can develop a self-similar collapse leading to a finite time singularity. Coincidentally, the Smoluchowski-Poisson system corresponds to a simplified version of the Keller-Sege...

We present a simulation algorithm that accurately propagates a molecule pair using large time steps without the need to invoke the full exact analytical solutions of the Smoluchowski diffusion equation. Because the proposed method only uses uniform and Gaussian random numbers, it allows for position updates that are two to three orders of magnitude faster than those of a corresponding scheme ba...