Related papers: Rapid calculation of maximum particle lifetime for…
The timescales of many physical, chemical, and biological processes are determined by first passage times (FPTs) of diffusion. The overwhelming majority of FPT research studies the time it takes a single diffusive searcher to find a target.…
The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single molecule and single cell level can add…
Diffusion probabilistic models have made their way into a number of high-profile applications since their inception. In particular, there has been a wave of research into using diffusion models in the prediction and design of biomolecular…
This paper presents a simple tool for characterising the timescale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the…
Counting how many particles pass through a specific space within a specific time is an interesting question in applied physics and social science. Here a logistic model is developed to estimate the total number of flowing particles. This…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…
Time course measurement of single molecules on a cell surface provides detailed information on the dynamics of the molecules, which is otherwise inaccessible. To extract the quantitative information, single particle tracking (SPT) is…
We present an improved statistical method for calculation of mean lifetime of nuclei in a decay chain with uncertain relation between mother and daughter nuclei. The method is based on formation of time distribution of intervals between…
Viewed as one of the grandest questions in modern science, understanding fundamental physical constants has been discussed in high-energy particle physics, astronomy and cosmology. Here, I review how condensed matter and liquid physics…
We consider a particle diffusing outside a compact planar set and investigate its boundary local time $\ell_t$, i.e., the rescaled number of encounters between the particle and the boundary up to time $t$. In the case of a disk, this is…
Subdiffusion equation and molecule survival equation, both with Caputo fractional time derivatives with respect to another functions $g_1$ and $g_2$, respectively, are used to describe diffusion of a molecule that can disappear at any time…
The study of interactions between biomimetic membranes and micron-sized particles is crucial for understanding various biological processes. Here, we control microparticle spontaneous engulfment by giant lipid vesicles by tuning particle…
We calculate the first passage time distribution for diffusion through a cylindrical pore with sticky walls. A particle diffusively explores the interior of the pore through a series of binding and unbinding events with the cylinder wall.…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
We calculate the survival probability of a diffusing test particle in an environment of diffusing particles that undergo coagulation at rate lambda_c and annihilation at rate lambda_a. The test particle dies at rate lambda' on coming into…
We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…
Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth…