Numerically Modeling Stochastic Lie Transport in Fluid Dynamics

Quantifying Transport in Numerically-Generated Velocity Fields

Geometric methods from dynamical systems are used to study Lagrangian transport in numerically-generated, time-dependent, two-dimensional vector elds. The ows analyzed here are numerical solutions to the barotropic, -plane, potential vorticity equation with viscosity, where the pde parameters have been chosen so that the solution evolves to a meandering jet. Numerical methods for approximating ...

stochastic Modeling of Neuronal Dynamics

Special iSSue i Modeling of brain processes has emerged as a promising research topic, which can help in the understanding of the human cognition. Investigations in this field have delivered successful implementations of learning and memory along with lines inspired by neural architectures. These findings have promoted optimism that a sufficiently complex artificial neural network would reprodu...

Variational principles for stochastic fluid dynamics

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the correspondi...

Computational Modeling in Biological Fluid Dynamics

A major problem in characterising the locomotion of freely-moving, isolated cells in culture is the large variability between individual cells and the large variation in motile characteristics with time. DRIMAPS (Digitally Recorded Interference Microscopy with Automatic Phase Shifting) is a technique developed at the Randall Institute that overcomes this problem by enabling data from large numb...

Computational Fluid Dynamics Modeling of Nitric Oxide Transport in a Rat Mesenteric Lymphatic Vessel