Related papers: Exact closure and solution for spatial correlation…
Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit…
We propose an approach to analysing single trajectories of a particle, which moves randomly on a landscape distinct parts of which result in sufficiently various diffusion coefficients. The method based on the mapping the cumulative sum of…
Some models of diffusion-limited reaction processes in one dimension lend themselves to exact analysis. The known approaches yield exact expressions for a limited number of quantities of interest, such as the particle concentration, or the…
This paper is devoted to the analysis of some fundamental problems of linear elasticity in 1D continua with self-similar interparticle interactions. We introduce a self-similar continuous field approach where the self-similarity is…
We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of…
Understanding transport subject to molecular-scale confinement is key to advancing nanofluidics, yet classical hydrodynamic laws often fail at these scales. Here, we study a model system: transport of toluene as a solvent and small…
Correlated, or extended, impurities play an important role in the transport properties of dirty metals. Here, we examine, in the framework of a tight-binding lattice, the transmission of a single electron through an array of correlated…
The problem of the emergence of wave dispersion due to the heterogeneity of a transmission line (TL) is considered. An exactly solvable model helps to better understand the physical process of a signal passing through a non-uniform section…
We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show for an equilibrium liquid that this function is related to fluctuations in a bulk…
We consider a gas of point particles moving in a one-dimensional channel with a hard-core inter-particle interaction that prevents particle crossings --- this is called single-file motion. Starting from equilibrium initial conditions we…
In this article, we study a type of a one dimensional percolation model whose basic features include a sequential dropping of particles on a substrate followed by their transport via a pushing mechanism (see [S. N. Majumdar and D. S. Dean,…
We study particle transport in a class of open channels of finite length, made of identical cells of connected open polygonal billiards with parallel boundaries. In these systems the Mean Square Displacement (MSD) grows in time faster than…
We develop a general dynamical theory for studying a single photon transport in a one-dimensional (1D) waveguide coupled to multiple emitters which can be either identical or non-identical. In this theory, both the effects of the waveguide…
We focus on open questions regarding the uniqueness of distributional solutions of the fast diffusion equation (FDE) with a given source term. When the source is sufficiently smooth, the uniqueness follows from standard results. Assuming…
We introduce a non-exponential radiative framework that takes into account the local spatial correlation of scattering particles in a medium. Most previous works in graphics have ignored this, assuming uncorrelated media with a uniform,…
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
We show that for the mean zero simple exclusion process in $\mathbb {Z}^d$ and for the asymmetric simple exclusion process in $\mathbb{Z}^d$ for $d\geq3$, the self-diffusion coefficient of a tagged particle is stable when approximated by…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
As manifested in the similarity relation of diffuse light transport, it is difficult to assess single scattering characteristics from multiply scattered light. We take advantage of the limited validity of the diffusion approximation of…