Related papers: Two-time scale subordination in physical processes…
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…
The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single…
We investigate Lagrangian relative dispersion in direct numerical simulation of two-dimensional inverse cascade turbulence. The analysis is performed by using both standard fixed time statistics and an exit time approach. Our results are in…
Temporal causal analysis means understanding the underlying causes behind observed variables over time. Deep learning based methods such as transformers are increasingly used to capture temporal dynamics and causal relationships beyond mere…
This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy…
This work investigates the out-of-equilibrium dynamics of dipole and higher-moment conserving systems with long-range interactions, drawing inspiration from trapped ion experiments in strongly tilted potentials. We introduce a hierarchical…
We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by `controlled' Markov noise. In particular, both the faster and slower recursions have non-additive controlled Markov noise…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of…
A new single-time two-point closure is proposed, in which the equation for the two-point correlation between the displacement of a fluid particle and the velocity allows one to estimate a Lagrangian timescale. This timescale is used to…
Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this…
We discuss two important techniques, series expansion and Monte Carlo simulation, for random sequential adsorption study. Random sequential adsorption is an idealization for surface deposition where the time scale of particle relaxation is…
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time…
Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible…
A continuous-time Markov process $X$ can be conditioned to be in a given state at a fixed time $T > 0$ using Doob's $h$-transform. This transform requires the typically intractable transition density of $X$. The effect of the $h$-transform…
Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…
To sensitively test scaling in the 2D XY model quenched from high-temperatures into the ordered phase, we study the difference between measured correlations and the (scaling) results of a Gaussian-closure approximation. We also directly…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
Subdiffusion with reaction $A+B\rightarrow B$ is considered in a system which consists of two homogeneous media joined together; the $A$ particles are mobile whereas $B$ are static. Subdiffusion and reaction parameters, which are assumed to…
Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…