Related papers: Kinetics of Aggregation-Annihilation Processes
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…
Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses…
In a wide range of physical phenomena, we find propagating surfaces {\Omega}t which need mathematical treatment. In this article, we review the theory of the system of kinematical conservation laws (KCL), which govern the evolution of these…
We consider a stochastic process that describes several particles interacting by either merging or annihilation. When two particles merge, they combine their masses; when annihilation occurs, only the particle of smallest mass survives.…
A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For…
We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting…
We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. The novelty is that we will consider observables achieving a global maximum value (possible infinite) at…
Non-aligning self-propelled particles with purely repulsive excluded volume interactions undergo athermal motility-induced phase separation into a dilute gas and a dense cluster phase. Here, we use enhanced sampling computational methods…
We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically…
How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though…
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with…
Species complexes are groups of closely related populations exchanging genes through dispersal. We study the dynamics of the structure of species complexes in a class of metapopulation models where demes can exchange genetic material…
To understand the processes that build up galaxies we investigate the stellar structure and gas kinematics of spiral and irregular galaxies out to redshift 1. We target 92 galaxies in four cluster (z = 0.3 & 0.5) fields to study the…
We study a system of self-propelled, proliferating finite-size disks with game-theoretical interactions, where growth rates depend on local population composition. We analyze how these interactions influence spatial distribution,…
Dissipation in granular media leads to interesting phenomena as there are cluster formation and crystallization in non-equilibrium dynamical states. The freely cooling system is examined concerning the energy decay and the cluster evolution…
A hierarchical system of equations is introduced to describe dynamics of `sizes' of infinite clusters which coagulate and fragmentate with homogeneous rates of certain form. We prove that this system of equations is solved weakly by…
At both conceptual and applied levels, quantum physics provides new opportunities as well as fundamental limitations. We hypothetically ask whether quantum games inspired by population dynamics can benefit from unique features of quantum…
Three-dimensional molecular dynamics simulations of dissipative particles (~ 10^6) are carried out for studying the clustering kinetics of granular media during cooling. The inter-connected high particle density regions are identified,…
Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…
We present a new model for extinction in which species evolve in bursts or `avalanches', during which they become on average more susceptible to environmental stresses such as harsh climates and so are more easily rendered extinct. Results…