Related papers: Pemantle's min-plus binary tree
A binary mixture of two-different-sizes proliferating motile disks is studied. As growth is space-limited, we focus on the conditions such that there is coexistence of both large and small disks, or dominance of the larger disks. The study…
The majority of massive stars are found in close binaries which: (i) are prone to merge and (ii) are accompanied by another distant tertiary star (triples). Here, we study the evolution of the stellar post-merger binaries composed of the…
We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \mu. In addition, there is an aggregate, which…
We extend mass scale sequence to a mass tree. From mass tree, the evolution of the universe is described by three stages: chaos, inflation and expansion. The first two stages have c mutations and the inflation appears as a step by step…
For itinerant fermionic and bosonic systems, we study `particle entanglement', defined as the entanglement between two subsets of particles making up the system. We formulate the general structure of particle entanglement in many-fermion…
We consider branching Brownian motion in which initially there is one particle at $x$, particles produce a random number of offspring with mean $m+1$ at the time of branching events, and each particle branches at rate $\beta = 1/2m$.…
We study a percolation process on the planted binary tree, where clusters freeze as soon as they become larger than some fixed parameter N. We show that as N goes to infinity, the process converges in some sense to the frozen percolation…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
We present a model for the formation of high-mass close binary systems in the context of forming massive stars through gas accretion in the centres of stellar clusters. A low-mass wide binary evolves under mass accretion towards a high-mass…
We investigate the kinetics of many-species systems with aggregation of similar species clusters and annihilation of opposite species clusters. We find that the interplay between aggregation and annihilation leads to rich kinetic behaviors…
Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
We introduce a simple dynamical rule in which each particle locates a particle that is farthest from it and moves towards it. Repeated application of this algorithm results in the formation of unusual dynamical patterns: during the process…
We study a lattice-gas model of penetrable particles on a square-lattice substrate with same-site and nearest-neighbor interactions. Penetrability implies that the number of particles occupying a single lattice site is unlimited and the…
We review the main physical processes that lead to the formation of stellar binary black holes (BBHs) and to their merger. BBHs can form from the isolated evolution of massive binary stars. The physics of core-collapse supernovae and the…
We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of divergence-controlled positive symmetric tensors in…
The final state of a binary black hole merger is predicted with high precision by numerical relativity, but could there be a simple thermodynamic principle within general relativity that governs the selection of the remnant? Using…
The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ with equal probability, and a finite diffusivity. In one dimension, the interplay between…
Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with…
We study the mixing of elementary and composite particles. In quantum field theory the mixing of composite particles originates in the couplings of the constituent quarks and for neutrinos in self-energy diagrams. In the event that the…