We show the existence and uniqueness of solutions (either local or global for small data) for an equation arising in different aspects of surface growth. Following the work of Koch and Tataru we consider spaces critical with respect to scaling and we prove our results in the largest possible critical space such that weak solutions are defined. The uniqueness of global weak solutions remains unf...

In this paper we consider the classical Sinko-Streifer size-structured population model and derive sensitivity partial differential equations for the sensitivities of solutions with respect to initial conditions, growth rate, mortality rate and fecundity rate. Sample numerical results to illustrate use of these equations are also presented.

Abstract. Coloring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colors available at the nodes and their neighborhoods, given a predetermined number of colors. In the analytical framework of a tree approximation, solutions obtained by population dynamics show that existing ...

In the model, each person in a large population has a probability of adhering to some behavior, such as a social norm. At random, people observe each other and adjust their adherence probabilities in an imitative direction. In a main case of the model, there are high and low stable equilibria; the distribution of adherence probabilities evolves upward or downward, depending on initial condition...

We consider several one-species population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one is able to demonstrate that their ratio with respect to its initial value is universal. This ratio is independent from the initial condition and from the mo...

The most important event in human economic history before the Industrial Revolution was the Neolithic transition from a nomadic hunter-gatherer lifestyle to sedentary agriculture, beginning about 10,000 years ago. The transition made possible the human population explosion, the rise of non-foodproducing specialists, and the acceleration of technological progress that led eventually to the Indus...

A system of reaction-diffusion differential equations is utilized to model the diffusion of a population through annular patches with different carrying capacities. In the case of continuous solutions with continuous flux, it is shown that a unique, positive steady-state solution exists. In the case of radially symmetric initial conditions, it is shown that all solutions of the Cauchy problem a...

It is a well known fact that the local stability of an equilibrium point in a system of ordinary differential equations doesnot necessarily imply its global stability. However, the usual methods used in the analysis of stability of equilibrium points in population models establishes only local stability. The restriction to sufficiently small perturbations of the initial conditions frequently ru...

Kachanov’s simplifiedmodel ofmicrocrack interaction is applied to an investigationof the behaviour of a cracked body under predominantly compressive periodic loading, so that the cracks experience periods of closure and slip, with frictional dissipation. The model is shown to be equivalent to a discrete elastic frictional systemwith each crack representing one node. Theorems and algorithms from...

This study reports on three populations’ ratings of vocal attractiveness for 30 male and 30 female voices producing isolated words. Equal numbers of male and female listeners were recruited from three dialect areas: northern California, western Canada, and Minnesota. Attractiveness ratings across dialects were highly correlated, particularly for female voices. To determine the acoustic features...