An attempt to generalize the Langevin dynamics simulation method is presented based on the generalized Langevin theory of liquids, in which the dynamics of both solute and solvent is treated by the generalized Langevin equations, but the integration of the equation of motion of solute is made in the manner similar to the ordinary molecular dynamics simulation with discretized time steps along a...

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 ...

This paper presents a Lie-Trotter splitting for inertial Langevin equations (Geometric Langevin Algorithm) and analyzes its long-time statistical properties.The splitting is defined as a composition of a variational integrator with an Ornstein-Uhlenbeck flow. Assuming the exact solution and the splitting are geometrically ergodic, the paper proves the discrete invariant measure of the splitting...

The inverse Langevin function cannot be represented in an explicit form and requires an approximation by a series, a non-rational or a rational function as for example by a Padé approximation. In the current paper an analytical method based on the Padé technique and the multiple point interpolation is presented for the inverse Langevin function. Thus, a new simple and accurate approximation of ...

In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. We improve, in terms of constants, the existing results when the accuracy of sampling is measured in the Wasserstein distance and provide further insights on relations between, on the one hand, the Lange...

Reduced Langevin recombination has been observed in organic solar cells (OSCs) for many years, but its origin is still unclear. A recent work by Burke et al. (Adv. Energy Mater.2015, 5, 1500123-1) was inspired by this reduced Langevin recombination, and they proposed an equilibrium model of charge-transfer (CT) states that correlates the open-circuit voltage of OSCs with experimentally availabl...

We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves ε error (in 2-Wasserstein distance) in O( √ d/ε) steps. This is a significant improvement over the best known rate for overdamped Langevin MCMC, which is O(d/ε) steps under the same smoothness/concav...

Recently, the subject of fractional differential equations has emerged as an important area of investigation. Indeed, we can find numerous applications in viscoelasticity, electrochemistry, control, electromagnetic, porous media, and so forth. In consequence, the subject of fractional differential equations is gaining much importance and attention. For some recent developments on the subject, s...

The Langevin description of Brownian motion in inhomogeneous suspensions is here revisited. Inhomogeneous suspensions are characterized by a position-dependent friction coefficient, which can significantly influence the dynamics of the suspended particles. Outstanding examples are suspensions in confinement or in the presence of a temperature gradient. The Langevin approach in inhomogeneous sys...

medicinal chemistry depends on many other disciplines ranging from organic chemistry andpharmacology to computational chemistry. typically medicinal chemists use the moststraightforward ways to prepare compounds. the validation of any design project comes from thebiological testing.studies of the binding site of vinblastine by a single cross—linking experiment identified it asbeing between resi...