Related papers: Cell Escape Probabilities for Markov Processes on …
Cellular scale decision making is modulated by the dynamics of signalling molecules and their diffusive trajectories from a source to small absorbing sites on the cellular surface. Diffusive capture problems are computationally challenging…
In this work, cascading transmission line failures are studied through a dynamical model of the power system operating under fixed conditions. The power grid is modeled as a stochastic dynamical system where first-principles…
We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…
The kinetic Monte Carlo method is a standard approach for simulating physical systems whose dynamics are stochastic or that evolve in a probabilistic manner. Here we show how to calculate the system time for such simulations.
When placed in parallel magnetic and electric fields, the electron trajectories of a classical hydrogen atom are chaotic. The classical escape rate of such a system can be computed with classical trajectory Monte Carlo techniques, but these…
We consider chaotic (hyperbolic) dynamical systems which have a generating Markov partition. Then, open dynamical systems are built by making one element of a Markov partition a hole through which orbits escape. We compare various estimates…
A computationally simple way to accommodate 'basins' of trapping sites in standard kinetic Monte Carlo simulations is presented. By assuming the system is effectively equilibrated in the basin, the residence time (time spent in the basin…
In this paper we study generalised Ising Glauber models with inflow of informa- tion in one dimension and derive expressions for the exit probability using well established analytical methods. The analytical expressions agree very well with…
Atomistic rigid lattice Kinetic Monte Carlo is an efficient method for simulating nano-objects and surfaces at timescales much longer than those accessible by molecular dynamics. A laborious part of constructing any Kinetic Monte Carlo…
Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…
Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of…
The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the…
A goal of systems biology is to understand the dynamics of intracellular systems. Stochastic chemical kinetic models are often utilized to accurately capture the stochastic nature of these systems due to low numbers of molecules. Collecting…
In line with the methodology introduced in our recent article for formulating probabilistic representations of integration by parts involving killed diffusion, we establish an integration by parts formula for the first exit time of…
The escape dynamics of sticky particles from textured surfaces is poorly understood despite importance to various scientific and technological domains. In this work, we address this challenge by investigating the escape time of adsorbates…
A new Markov Chain Monte Carlo method for simulating the dynamics of molecular systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is…
We present a numerical method to compute the survival function and the moments of the exit time for a piecewise-deterministic Markov process (PDMP). Our approach is based on the quantization of an underlying discrete-time Markov chain…
A dynamical theory which incorporates the electron-electron correlations and the effects of external magnetic fields for an electron escaping from a helium surface is presented. The degrees of freedom in the calculation of the escape rate…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
We present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models for chemosensitive movements set in an arbitrary geometry. We investigate the influence of the geometry on the collective behavior of…