The goal of the present study is to characterize solutions under a travelling wave formulation degenerate Fisher-KPP problem. With problem, we refer following: heterogeneous diffusion that formulated with high order operator; non-linear advection and non-Lipstchitz spatially reaction. paper examines existence solutions, uniqueness oscillatory properties (also called instabilities). Such behavio...

For reaction-diffusion-advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction-diffusion systems with both stiff reaction and diffusi...

Efficient sampling in both configuration and trajectory spaces, combined with mechanism analyses via data mining, allows a systematic investigation of the thermodynamics, kinetics, and molecular-detailed dynamics of chemical reactions in solution. Through a Bayesian learning algorithm, the reaction coordinate(s) of a (retro-)Claisen rearrangement in bulk water was variationally optimized. The b...

Error-related activity in the medial prefrontal cortex (mPFC) is thought to work in conjunction with lateral prefrontal cortex (lPFC) as a part of an action-monitoring network, where errors signal the need for increased cognitive control. The neural mechanism by which this mPFC-lPFC interaction occurs remains unknown. We hypothesized that transient synchronous oscillations in the theta range re...

We study effects of oscillatory convective flow in extracellular space on the velocity of chemical signal propagation having a form of a front wave above a cellular layer. We found that the time-averaged propagation velocity under oscillatory flow for a particular Péclet number amplitude is slower than the velocity under steady laminar flow regime for the same value of the Péclet number, but si...