The statistical equilibria of the (conservative) dynamics of the Gross-Pitaevskii equation
(GPE) with a finite range of spatial Fourier modes are characterized using a new algorithm …

The analysis of bifurcations and chaotic dynamics for nonlinear systems of a large size is a
difficult problem. Analytical and numerical approaches must be used to deal with this …

Two fully pressure–velocity coupled approaches to time-integration of two-and three-
dimensional Navier–Stokes equations discretized by finite volume method are proposed …

We present a Newton method to compute the stochastic solution of the steady
incompressible Navier–Stokes equations with random data (boundary conditions, forcing …

Many physical processes are described by elliptic or parabolic partial differential equations.
For linear stability problems associated with such equations, the inverse Laplacian provides …

In this article, a study of long-term behavior of reaction–diffusion systems augmented with
self-and cross-diffusion is reported, using an augmented Gray–Scott system as a generic …

The problem of bifurcation analysis for large scale systems is very challenging and requires
complex approach that takes into account system spectral and algebraic properties, specific …

The integration of synaptic inputs in a neuron can be nonlinear not just at the axon, but also
locally in the dendrites if they are imbued with active voltage-gated ion channels. For …