We derive a closed master equation for an individual-based population model in continuous space and time. The model and master equation include Brownian motion, reproduction via binary fission, and an interaction-dependent death rate moderated by a competition kernel. Using simulations we compare this individual-based model with the simplest approximation, the spatial logistic equation. In the ...

The classic Beverton-Holt (discrete logistic) difference equation, which arises in population dynamics, has a globally asymptotically stable equilibrium (for positive initial conditions) if its coefficients are constants. If the coefficients change in time, then the equation becomes nonautonomous and the asymptotic dynamicsmight not be as simple. One reason the coefficients can change in time i...

AlmtraEt--Dispersed phase systems may lx analyzed via population balances or by Monte Carlo simulation methods. This paper establishes the precise mathematical connection between the two procedures. The population balance equation is obtained by averaging the master density equation, while simulation procedures efficiently evaluate the solution to the master density equation by elimination of l...

Aggregation kinetics are often described by the population balance (or Smoluchowski coagulation) equation. The population balance equation is a mean-field equation for an aggregation process. An upper critical dimension d, calculated for a given aggregation frequency has been used by other investigators to characterize the validity of this mean-field equation. It is shown that the upper critica...

The relationship between aggression, pleasure and decision-making is analyzed applying a mediation model of structural equation modeling (SEM). The study explored it in two samples of similar age: young offenders and university students. A close relationship between aggression and pleasure was found in both populations. But, whereas in the case of university students, this congruence leads to a...

In this paper, we study a class of nonlinear Schrödinger equations (NLS) which admit families of small solitary wave solutions. We consider solutions which are small in the energy space H, and decompose them into solitary wave and dispersive wave components. The goal is to establish the asymptotic stability of the solitary wave and the asymptotic completeness of the dispersive wave. That is, we...