Related papers: Spatial-Stochastic Simulation of Reaction-Diffusio…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically-reacting species is built on the stochastic trajectories of reaction events obtained from the Chemical Master Equation. However, when the molecular populations…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
We describe a new algorithm for simulating complex Markoff-processes. We have used a reaction-cell method in order to simulate arbitrary reactions. It can be used for any kind of RDS on arbitrary topologies, including fractal dimensions or…
The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process,…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
We consider biochemical reaction chains and investigate how random external fluctuations, as characterized by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption that the number of…
By discretising space into compartments and letting system dynamics be governed by the reaction-diffusion master equation, it is possible to derive and simulate a stochastic model of reaction and diffusion on an arbitrary domain. However,…
Simulations of macromolecular diffusion and adsorption in confined environments can offer valuable mechanistic insights into numerous biophysical processes. In order to model solutes at atomic detail on relevant time scales, Brownian…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
The coarse-grained molecular dynamics (MD) or Brownian dynamics (BD) simulation is a particle-based approach that has been applied to a wide range of biological problems that involve interactions with surrounding fluid molecules or the…
In this study, we introduce a sensitivity analysis methodology for stochastic systems in chemistry, where dynamics are often governed by random processes. Our approach is based on gradient estimation via finite differences, averaging…
Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…
Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking…
We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are…
Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…