Related papers: On the Statistics of Reaction-Diffusion Simulation…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
Information delivery using chemical molecules is an integral part of biology at multiple distance scales and has attracted recent interest in bioengineering and communication theory. Potential applications include cooperative networks with…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
In diffusion-based molecular communication, information particles locomote via a diffusion process, characterized by random movement and heavy tail distribution for the random arrival time. As a result, the molecular communication shows…
Recently, molecular communication (MC) has been studied as a micro-scale communication between cells or molecular robots. In previous works, the MC channels in unbounded environment was analyzed. However, many of the experimentally…
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,…
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
This letter develops a one-dimensional (1D) diffusion-based molecular communication system to analyze channel responses between a single transmitter (TX) and two fully-absorbing receivers (RXs). Incorporating molecular degradation in the…
We simulate reaction-diffusion processes with discrete fields. We use a novel algorithm to simulate different autocatalytic processes with trace densities. Anderson localization with a diffusive potential is studied. A reaction-diffusion…
We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as,…
The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is…
In this paper, we present an analytical model for a diffusive molecular communication (MC) system with a reversible adsorption receiver in a fluid environment. The time-varying spatial distribution of the information molecules under the…
Self-diffusion coefficients, $D^*$, are routinely estimated from molecular dynamics simulations by fitting a linear model to the observed mean-squared displacements (MSDs) of mobile species. MSDs derived from simulation exhibit statistical…
By considering potential health problems that a fully covering receiver may cause in vessel-like environments, the implementation of a partially covering receiver is needed. To this end, distribution of hitting location of messenger…
Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…
Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…
We provide an overview of Monte Carlo algorithms based on Markovian stochastic dynamics of interacting and reacting many-particle systems not in thermal equilibrium. These agent-based simulations are an effective way of introducing students…
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.…
This letter introduces a formalism for modeling time-variant channels for diffusive molecular communication systems. In particular, we consider a fluid environment where one transmitter nano-machine and one receiver nano-machine are…