We consider the nonlinear Schrödinger–Langevin equation for both signs of logarithmic nonlinearity. explicitly compute dynamics Gaussian solutions large times, which is obtained through study a particular differential order 2. then give asymptotic behavior general energy weak under some regularity assumptions. Some numerical simulations are performed in to corroborate theoretical results.

Influence of mesoscopic channel noise on excitable dynamics of living cells became a hot subject within the last decade, and the traditional biophysical models of neuronal dynamics such as Hodgkin-Huxley model have been generalized to incorporate such effects. There still exists but a controversy on how to do it in a proper and computationally efficient way. Here we introduce an improved Langev...

A century after the celebrated Langevin paper [C.R. Seances Acad. Sci. 146, 530 (1908)] we study a Langevin-type approach to subdiffusion in the presence of time-dependent force fields. Using a subordination technique, we construct rigorously a stochastic Langevin process, whose probability density function is equal to the solution of the fractional Fokker-Planck equation with a time-dependent ...

A new characterization of sufficient conditions for the Lie-Trotter splitting to capture the numerical invariant measure of nonlinear ergodic Langevin dynamics up to an arbitrary order is discussed. Our characterization relies on backward error analysis and needs weaker assumptions than assumed so far in the literature. In particular, neither high weak order of the splitting scheme nor symplect...

The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-depen...

We compare the effectiveness of different simulation sampling techniques by illustrating their application to united atom butane, alanine dipeptide, and a small solvated protein, BPTI. We introduce an optimization of the Shadow Hybrid Monte Carlo (SHMC) algorithm, a rigorous method that removes the bias of molecular dynamics (MD). We also evaluate the ability of constant-temperature MD methods ...