Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...

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.

In this paper we statistically analyze the Fokker-Planck (FP) equation of Schramm-Loewner evolution (SLE) and its variant SLE(κ,ρc). After exploring the derivation and the properties of the Langevin equation of the tip of the SLE trace, we obtain the long- and short-time behaviors of the chordal SLE traces. We analyze the solutions of the FP and the corresponding Langevin equations and connect ...

We study balanced model reduction of partially-observed stochastic differential equations of Langevin type. Upon balancing, the Langevin equation turns into a singularly perturbed system of equations with slow and fast degrees of freedom. We prove that in the limit of vanishing small Hankel singular values (i.e., for infinite scale separation between fast and slow variables), its solution conve...

Theoretical tools for adequately treating stochastic effects are important for understanding their role in biological processes. Although master equations provide rigorous means for investigating effects associated with fluctuations of discrete molecular copy numbers, they can be very challenging to treat analytically and numerically. Approaches based on the Langevin approximation are often mor...

An exact lattice Langevin equation is derived for the ballistic deposition model of surface growth. The continuum limit of this equation is dominated by the Kardar-Parisi-Zhang (KPZ) equation at all length and time scales. For a one-dimensional substrate the solution of the exact lattice Langevin equation yields the KPZ scaling exponents without any extrapolation. For a two-dimensional substrat...

A generalized Langevin equation with fluctuating diffusivity (GLEFD) is proposed, and it shown that the GLEFD satisfies a fluctuation-dissipation relation. If memory kernel power law, exhibits subdiffusion, non-Gaussianity, stretched-exponential relaxation. The case in which given by single exponential function also investigated as an analytically tractable example. In particular, mean-square d...

We study the treatment of the constraints in stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking account of the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochast...