Related papers: The Shortest Path Across the Mesoscopic System
The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-squared displacement (MSD) grows linearly with time.…
We computationally study the flow of Newtonian fluids through sinusoidal expansion-contraction microchannels at low Reynolds number. We first use a perturbation method to analytically derive series solutions for the stream function and…
Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time…
We report the investigation of the dynamic conductance fluctuation of disordered mesoscopic conductors including 1D, 2D and quantum dot systems. Our numerical results show that in the quasi-ballistic regime the average emittance is negative…
We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…
Variable-range hopping conductivity has long been understood in terms of a canonical prescription for relating the single-particle density of states to the temperature-dependent conductivity. Here we demonstrate that this prescription…
Probabilistic analysis for metric optimization problems has mostly been conducted on random Euclidean instances, but little is known about metric instances drawn from distributions other than the Euclidean. This motivates our study of…
We present a new method to compute the first crossing distribution in excursion set theory for the case of correlated random walks. We use a combination of the path integral formalism of Maggiore & Riotto, and the integral equation solution…
We propose a mesoscopic modeling framework for optimal transportation networks with biological applications. The network is described in terms of a joint probability measure on the phase space of tensor-valued conductivity and position in…
Macroscopic mechanical properties of polymers are determined by their microscopic molecular chain distribution. Due to randomness of these molecular chains, probability theory has been used to find their micro-states and energy…
By Girsanov's thoerem and using the existing log-Harnack inequality for distribution independent SDEs, the log-Harnack inequality is derived for path-distribution dependent stochastic Hamiltonian systems. As an application, the exponential…
Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. The correction to the conductivity due to inelastic scatterings by oscillating potentials is shown to be a universal…
The sampling of the configuration space in diffusion Monte Carlo (DMC) is done using walkers moving randomly. In a previous work on the Hubbard model [\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B \textbf{60},…
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…
We consider the mean distribution functions Phi(r|l), Phi(B)(r|l), and Phi(S)(r|l), giving the probability that two sites on the incipient percolation cluster, on its backbone and on its skeleton, respectively, connected by a shortest path…
Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for…
The Fourier-Bessel expansion of a function on a circular disc yields a simple series representation for the end-to-end probability distribution function w(R,phi) encountered in a planar persistent random walk, where the direction taken in a…