We study the deterministic and stochastic rotational dynamics of ferromagnetic nanoparticles in a precessing magnetic field. Our approach is based on the system of effective Langevin equations and on the corresponding Fokker-Planck equation. Two key characteristics of the rotational dynamics, namely the average angular frequency of precession of nanoparticles and their average magnetization, ar...

High-performance computing approaches that combine molecular-scale and macroscale continuum mechanics have long been anticipated in various fields. Such approaches may enrich our understanding of the links between microscale molecular mechanisms and macroscopic properties in the continuum. However, there have been few successful examples to date owing to various difficulties associated with ove...

In this paper we investigate the use of Langevin Monte Carlo methods on the probability simplex and propose a new method, Stochastic gradient Riemannian Langevin dynamics, which is simple to implement and can be applied to large scale data. We apply this method to latent Dirichlet allocation in an online minibatch setting, and demonstrate that it achieves substantial performance improvements ov...

We construct an infinite particle/infinite volume Langevin dynamics on the space of configurations in R having velocities as marks. The construction is done via a limiting procedure using N-particle dynamics in cubes (−λ, λ] with periodic boundary conditions. A main step to this result is to derive an (improved) Ruelle bound for the canonical correlation functions of N-particle systems in (−λ, ...

We construct a theory for the (1+1)-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the first part of this work the classical Langevin equations of motion, governing the nonrelativistic dynamics of a free Brownian particle in the presence of a he...

We present the Langevin rigid approach, a technique for animating the dynamics of immersed rigid bodies in viscous incompressible fluid in real-time. We use generalized Kirchhoff equations to ensure forces and torques from the surrounding fluid that create realistic motion of immersed rigid bodies. We call our method the Langevin rigid approach because the generalized Langevin equations are app...

Langevin approach is proposed as an intuitive phenomenological framework to describe nuclear dissipative phenomena such as heavy ion reactions and fission decay. We present a method to integrate Langevin equation directly with the computer-simulated langevin force. Examples are given for a free motion of Brownian particle and for nuclear fission as a diffusion over a barrier.

One way to avoid overfitting in machine learning is to use model parameters distributed according to a Bayesian posterior given the data, rather than the maximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is one algorithm to approximate such Bayesian posteriors for large models and datasets. SGLD is a standard stochastic gradient descent to which is added a controlled am...

A dynamics between Newton and Langevin formalisms is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding a vanishing zero-frequency friction the corresponding non-Markovian Brownian dynamics exhibits anomalous behavior which is characterized by ballistic diffusion and accelerated transport. We also investigate the role of a possible initial correlati...

We present here an application of the standard Langevin dynamics to the problem of perturbative expansions on the Lattice QCD. This method can be applied in the computation of the most general observables. In this work we will concentrate in particular on the computation of the perturbative terms of the 1 × 1 Wilson loop, up to fourth order. It is shown that a stochastic gauge fixing is a possi...