Related papers: Aggregation with Multiple Conservation Laws
I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys.…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average…
The inclusion of a fragmentation mechanism in population balance equations introduces complex interactions that make the analytical or even computational treatment much more difficult than for the pure aggregation case. This is specially…
Cluster growth in a coagulating system of active particles (such as microswimmers in a solvent) is studied by theory and simulation. In contrast to passive systems, the net velocity of a cluster can have various scalings dependent on the…
An approach for understanding the behavior of multiplicity distributions in restricted phase-space intervals derived on the basis of global observables is proposed. We obtain a unifying connection between local multiparticle clusters and…
The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities. Specializing to systems with a single conservation law, we find that the…
We study real space condensation in aggregation-fragmentation models where the total mass is not conserved, as in phenomena like cloud formation and intracellular trafficking. We study the scaling properties of the system with influx and…
The coupling of branching-annihilating random walks to a static field with a local conservation law is shown to change the scaling properties of their phase transitions to absorbing states. In particular, we find that DP-class transitions…
We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be utilized to solve the model. We show that for models where the conservation laws can be written in one-sided forms, like…
It is shown that in the presence of anisotropic kinetic dissipation existence of scale invariant power law spectrum of plasma turbulence is possible. Obtained scale invariant spectrum is not associated with the constant flux of any physical…
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…
We address the study of a class of 1D nonlocal conservation laws from a numerical point of view. First, we present an algorithm to numerically integrate them and prove its convergence. Then, we use this algorithm to investigate various…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
Hydrated granular packings often crack into discrete clusters of grains when dried. Despite its ubiquity, accurate prediction of cracking remains elusive. Here, we elucidate the previously overlooked role of individual grain shrinkage---a…
A microscopic model of interacting oscillators, which admits two conserved quantities, volume, and energy, is investigated. We begin with a system driven by a general nonlinear potential under high-temperature regime by taking the inverse…
In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…
Similarly to the derivation of the Gibbs-Boltzmann distribution for structureless indistinguishable particles, we consider multi-particle systems some of which are contained (or delimited) inside others (Problem 1), as well as systems of…