Related papers: Annihilation Catastrophe: From Formation to Univer…
Species populations often modify their environment as they grow. When environmental feedback operates more slowly than population growth, the system can undergo boom-bust dynamics, where the population overshoots its carrying capacity and…
When $2N/(N+1)<p<2$ and $0<q<p/2$, non-negative solutions to the singular diffusion equation with gradient absorption $$\partial\_tu-\Delta\_p u + |\nabla u|^q=0 \ \text{ in }\ (0,\infty)\times\mathbb{R}^N$$ vanish after a finite time. This…
We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The probability for a pair-annihilation event decays as a…
Perturbing the external control parameters of nonlinear systems leads to dramatic changes of its bifurcations. A branch of singular theory, the catastrophe theory, analyses the generating function that depends on state and control…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
We investigate the following repulsion-consumption system with flux limitation \begin{align}\tag{$\star$} \left\{ \begin{array}{ll} u_t=\Delta u+\nabla \cdot(uf(|\nabla v|^2) \nabla v), & x \in \Omega, t>0, \tau v_t=\Delta v-u v, & x \in…
Collapse and reverse to collapse explosion transition in self-gravitating systems are studied by molecular dynamics simulations. A microcanonical ensemble of point particles confined to a spherical box is considered; the particles interact…
We study the two particle annihilation reaction $A+B\rightarrow \emptyset$ on interconnected scale free networks, using different interconnecting strategies. We explore how the mixing of particles and the process evolution are influenced by…
This paper summarises an investigation of the statistical properties of orbits escaping from three different two-degree-of-freedom Hamiltonian systems which exhibit global stochasticity. Each H=H_{0}+eH', with H_{0} integrable and eH' a…
We study the extinction behavior of solutions to the fast diffusion equation $u_t = \Delta u^m$ on $\R^N\times (0,T)$, in the range of exponents $m \in (0, \frac{N-2}{N})$, $N > 2$. We show that if the initial data $u_0$ is trapped in…
We continue to explore, in the context of a toy model, the hypothesis that the interacting universe we see around us could result from single particle (undergraduate) quantum mechanics via a novel spontaneous symmetry breaking (SSB) acting…
This work considers a chemotaxis system for multi-species that includes birth or death rate terms, which implies no mass preservation of the populations. We aim to show the convergence to a $L^{\infty}\ -\ $weak solutions, that is local in…
We consider a system of particles undergoing the branching and annihilating reactions A -> (m+1)A and A + A -> 0, with m even. The particles move via long-range Levy flights, where the probability of moving a distance r decays as…
The mechanisms for phase separation in highly concentrated emulsions when subjected to a thermal phase transition remain to be elucidated. Here, we create a hexagonally close-packed monodisperse emulsion in 2D and show that during a…
We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely…
We finely describe the speed of "coming down from infinity" for birth and death processes which eventually become extinct. Under general assumptions on the birth and death rates, we firstly determine the behavior of the successive hitting…
Entanglement evolution in high dimensional bipartite systems under dissipation is studied. Discontinuities for the time derivative of the lower bound of entanglement of formation is found depending on the initial conditions for entangled…
We analyse the unreduced, nonperturbative dynamics of an arbitrary many-body interaction process with the help of the generalised effective potential method and reveal the well-specified universal origin of change (emergence), time and…
Dissipation, the irreversible loss of energy and coherence, from a microsystem, is the result of coupling to a much larger macrosystem (or reservoir) which is so large that one has no chance of keeping track of all of its degrees of…
We study the creep rupture of fiber composites in the framework of fiber bundle models. Two novel fiber bundle models are introduced based on different microscopic mechanisms responsible for the macroscopic creep behavior. Analytical and…