Related papers: Explicit formulas for reaction probability in reac…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
Modeling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The basic model includes a multidimensional set of coupled parabolic equations and…
We confront, quantitatively, the theoretical description of the reaction-diffusion of a second order reaction to experiment. The reaction at work is \ca/CaGreen, and the reactor is a T-shaped microchannel, 10 $\mu$m deep, 200 $\mu$m wide,…
The reaction-diffusion master equation (RDME) is commonly used to model processes where both the spatial and stochastic nature of chemical reactions need to be considered. We show that the RDME in many cases is inconsistent with a…
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
We derive analytical expressions for the reactivity of a Single-File System with fast diffusion and adsorption and desorption at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size,…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
Numerical values of charged-particle thermonuclear reaction rates for nuclei in the A=14 to 40 region are tabulated. The results are obtained using a method, based on Monte Carlo techniques, that has been described in the preceding paper of…
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical…
A method is proposed for the calculation of diffusion constants for one-dimensional maps exhibiting deterministic diffusion. The procedure is based on harmonic inversion and uses a known relation between the diffusion constant and the…
We derive the multi-fractal scaling of probability distributions of multi-particle configurations for the binary reaction-diffusion system $A+A \to \emptyset$ in $d \leq 2$ and for the ternary system $3A \to \emptyset$ in $d=1$. For the…
Molecular dynamics simulation has been used to model pattern formation in three-dimensional Rayleigh--Benard convection at the discrete-particle level. Two examples are considered, one in which an almost perfect array of hexagonally-shaped…
Parameterized tight-binding models fit to first principles calculations can provide an efficient and accurate quantum mechanical method for predicting properties of molecules and solids. However, well-tested parameter sets are generally…
Ultracold atomic Fermi gases in two-dimensions (2D) are an increasingly popular topic of research. The interaction strength between spin-up and spin-down particles in two-component Fermi gases can be tuned in experiments, allowing for a…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the…
Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…