Related papers: Cluster geometry and survival probability in syste…
In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…
Globular clusters contain multiple stellar populations, with some previous generation of stars polluting the current stars with heavier elements. Understanding the history of globular clusters is helpful in understanding how galaxies merged…
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…
We explore the morphological and dynamical evolution of galaxy clusters in simulations using scalar and vector-valued Minkowski valuations and the concept of fundamental plane relations. In this context, three questions are of fundamental…
The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic…
We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a…
Accounting for the triaxial shapes of galaxy clusters will become important in the context of upcoming cosmological surveys. We show that, compared to the gas density distribution, the cluster gravitational potential can be better…
We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an…
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
We investigate a recently proposed cross-diffusion system modelling the growth of gliobastoma taking into account size exclusion both in the migration and proliferation process. In addition to degenerate nonlinear cross-diffusion the model…
The alpha cluster states of 16C are investigated by using the antisymmetrized molecular dynamics. It is shown that two different types of alpha cluster states exist: triangular and linear-chain states. The former has an approximate…
Monte Carlo simulations of the 1D Ising model with ferromagnetic interactions decaying with distance $r$ as $1/r^{1+\sigma}$ are performed by applying the Swendsen-Wang cluster algorithm with cumulative probabilities. The critical behavior…
For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix $R_{mn}$, whose elements converge to two constants. This allows for an effective extrapolation of the…
Starting from a Zimm model we study selfdiffusion in a solution of crosslinked monomers. We focus on the effects of the hydrodynamic interaction on the dynamics and the critical behaviour at the sol-gel-point. Hydrodynamic interactions…
We study the probability, $P_S(t)$, of a cluster to remain intact in one-dimensional cluster-cluster aggregation when the cluster diffusion coefficient scales with size as $D(s) \sim s^\gamma$. $P_S(t)$ exhibits a stretched exponential…
The critical and multicritical behavior of the simple cubic Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions is studied using the cube and star-cube approximations of the cluster variation method and the…
Reaction-diffusion equation model for a 2-dimensional gas discharge system is introduced in close relationship with the recent experiment by Nasuno. The model shows formation of spots, molecule-like organization of a cluster of spots,…
A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$.…
We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other…