相关论文: Monte Carlo Random Walk Simulations Based on Distr…

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…

Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…

Min et al. (2009) presented two complementary techniques that use the diffusion approximation to allow efficient Monte-Carlo radiation transfer in very optically thick regions: a modified random walk and a partial diffusion approximation.…

Under certain circumstances, the time behavior of a random walk is modulated by logarithmic periodic oscillations. The goal of this paper is to present a simple and pedagogical explanation of the origin of this modulation for diffusion on a…

We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…

We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…

A 3D copepod trajectory is recorded in the laboratory, using 2 digital cameras. The copepod undergoes a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We perform a statistical analysis of this…

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…

Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…

We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…

Current digital computers are about to hit basic physical boundaries with respect to integration density, clock frequencies, and particularly energy consumption. This requires the application of new computing paradigms, such as quantum and…

A Monte Carlo method for simulating a multi-dimensional diffusion process conditioned on hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges are obtained by superimposing an additional guiding…

We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in…

In this paper we study controlled continuous time random walks (CTRWs) and heuristically derive pay-off function dynamic programming (DP) equations which turn in the limit of standard scaling to fractional Hamilton Jacobi Bellman type…

Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…