Related papers: Generalized Smoluchowski equation with correlation…
The star formation rate (SFR) of the Milky Way remains poorly known, with often-quoted values ranging from 1 to 10 solar masses per year. This situation persists despite the potential for the Milky Way to serve as the ultimate SFR…
We present a method for solving the reaction-diffusion equation with general potential in free space. It is based on the approximation of the Feynman-Kac formula by a sequence of convolutions on sequentially diminishing grids. For…
The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution…
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels $K(x,y)=2$, $x+y$ and $xy$. In addition to the known self-similar solutions with exponential tails, there…
We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard…
An explicit perturbative computation of the Mori's memory function was performed by G\"otze and W\"olfle (GW) to calculate Generalized Drude scattering (GDS) rate for the case of electron-impurity and electron-phonon scattering in metals by…
We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation…
We are commenting on the article Phys. Rev. {\bf B 65}, 155112 (2002) by G. Biroli and G. Kotliar in which they make a comparison between two cluster techniques, the {\it Cellular Dynamical Mean Field Theory} (CDMFT) and the {\it Dynamical…
The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system.…
Because all stars contribute to its gravitational potential, stellar clusters amplify perturbations collectively. In the limit of small fluctuations, this is described through linear response theory, via the so-called response matrix. While…
We study the pairwise annihilation process $A+A\to$ inert of a number of random walkers, which originally are localized in a small region in space. The size of the colony and the typical distance between particles increases with time and,…
Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Green's functions in real time. Of particular interest is the effect of correlations. The system is therefore…
The secular evolution of a collisional star cluster of $N$-'point' stars have been conventionally discussed based on cumulative two-body relaxation process. The relaxation process requires a cut-off on the range of two-body encounter…
The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set…
We consider a class of stochastic damped semilinear wave equations, in the small-mass limit. It has previously been established that the solution converges to the solution of a stochastic semilinear heat equation. In this work we exhibit…
In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the…
Reactive and elastic cross-sections, and rate coefficients, have been calculated for the S(1D)+ D2 (v=0, j=0) reaction using a modified hyperspherical quantum reactive scattering method. The considered collision energy ranges from the…
Size-structured population models provide a popular means to mathematically describe phenomena such as bacterial aggregation, schooling fish, and planetesimal evolution. For parameter estimation, generalized sensitivity functions (GSFs)…
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…