Spread of a catalytic branching random walk on a multidimensional lattice

For a supercritical catalytic branching random walk on ${\mathbb{Z}}^d$, $d\in \mathbb{N}$, with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in ${\mathbb{R}}^d$ which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation.     

A numerical method for nonlinear age-structured population models with finite maximum age

We propose a new numerical method for the approximation of solutions to a non-autonomous form of the classical Gurtin-MacCamy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations.     

具扩散的年龄结构脉冲随机时滞种群方程的均方稳定性(英文)

本文考虑一类具扩散的年龄结构脉冲随机时滞种群方程.主要目的是研究具扩散的年龄结构脉冲随机时滞种群平凡解的均方稳定性,给定两个使平凡解均方稳定的充分条件.     

Dynamic Mechanical Properties of Aged Filled Rubbers

Abstract

It is well known that the macromolecular structure and the microstructure of the fillers play an important role in the mechanical properties of filled rubbers. This paper focuses on the dependence of the complex modulus of aged natural rubber vulcanizates on the filler network and polymer structure. Dynamic mechanical analysis (DMA) at 30°C, 50°C, and 70°C on the aged rubbers with/without prestrain showed the Payne effect, i.e., a storage modulus drop with increasing amplitude, and the appearance of a loss tangent maximum at strain of about a few percent. The storage modulus increased with the aging time at 70°C, 24 < 72 < 240 hr, in the case of nonprestrain. When the prestrain was applied, strain‐induced crystallization was generated that enhanced the storage modulus. As time passed, the prestrain relaxed and the crystalline structures began to disappear. After 72 hr, the crystalline structures had almost disappeared, and they had only a weak effect. Consequently, there existed a higher modulus for an aging time of 24 hr than 72 hr at testing temperatures of 30°C and 50°C. It was concluded that the storage modulus was determined by the postvulcanization, strain‐induced crystallization, aging, and relaxing time.     

THE ROLE OF DOUBLE-HELIX FORMATION IN WATER DIFFUSION AND AGING OF INJECTION-MOLDED STARCH*

Native potato starch has been processed without the use of any additive. Moldings of initial high strength and ductility have been achieved. However, mechanical properties change with time. Thermogravimetric experiments at different temperatures show that aging takes place in three different steps. The first is characterized by a strong formation of double helices (as revealed by wide-angle X-ray scattering [WAXS]) in parallel with strong water loss. Hardness, strength, and elongation at break increase in this time range: Double helices act as reinforcing elements. When the yield elongation is surpassed, double helices are unraveled, providing a higher elongation at break. With further aging (drying), due to a shrinking process, a temporary reduction of double helices, causing a resoftening, seems to take place. In a third step, the starch moldings become quite brittle due to the lack of molecular mobility. At room conditions, it takes approximately 1 year (beginning of range 3) to lose the good mechanical properties. It is proposed that the mechanical behavior of starch moldings is controlled by a molecular network that consists of singlehelix molecules bound by double helices within an amorphous structure.

     

Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population

We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat’s law, and the non-Gibrat’s property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat’s property, and quasi-time-reversal symmetry.     

Optimal control of age-structured population dynamics for spread of universally fatal diseases II

In our preceding paper [Sun B, Wu MX. Appl. Anal. 2013;92:901–921], we investigated an optimal control problem of age-structured population dynamics for spread of universally fatal diseases and derived the necessary optimality condition for the problem in fixed final horizon case. As a follow-up, in this paper, under weaker additional conditions, we address ourselves to the investigation of the foregoing system in free final horizon case and present further new results of current interests.     

Development of a macro-scale model from a meso-scale model for cell culture population dynamics

In this paper, we present a novel macro-scale analytical model that allows the prediction of how the population size will change in a cell culture starting from an arbitrary initial value. General biological knowledge and some empirical observations are used to design an agent-based discrete-time model at the meso-scale, which then serves as a simulation environment and provides the necessary insights for the development of the continuous-time, differential equation-based, compact macro-scale model. This model can be parameter-tuned and employed for predicting how the population size changes. The paper gives a procedure for the estimation of parameter values of the macro-scale model via some simple tests to be conducted on the cell culture at hand. The performance of the macro-scale model is validated via simulation results that show how well the macro-scale model captures the population dynamics as obtained from the meso-scale model, while the biological plausibility of the meso-scale model is taken for granted.     

A Note on Attenuant Cycles of Population Models with Periodic Carrying Capacity

In this short note, we consider attenuant cycles of population models. This study concerns the second conjecture of Cushing and Henson [A periodically forced Beverton-Holt equation, J. Diff. Eq. Appl., 8 (2002), pp. 1119–1120], which was recently resolved affirmatively by Elaydi and Sacker [Global stability of periodic orbits of nonautonomous difference equations in population biology and the Cushing-Henson conjectures, Proc. 8th Inter. Conf. Diff. Eq., Brno, (in press)]. They showed that the periodic fluctuations in the carrying capacity always reduce the average of population densities in the Beverton-Holt equation. We extend this result and give a class of population models in which the periodic fluctuations in the carrying capacity always reduce the average of population densities.     

Approximate reduction of non-linear discrete models with two time scales

The aim of this work is to present a general class of nonlinear discrete time models with two time scales whose dynamics is susceptible of being approached by means of a reduced system. The reduction process is included in the so-called approximate aggregation of variables methods which consist of describing the dynamics of a complex system involving many coupled variables through the dynamics of a reduced system formulated in terms of a few global variables. For the time unit of the discrete system we use that of the slow dynamics and assume that fast dynamics acts a large number of times during it. After introducing a general two-time scales nonlinear discrete model we present its reduced accompanying model and the relationships between them. The main result proves that certain asymptotic behaviours, hyperbolic asymptotically stable (A.S.) periodic solutions, to the aggregated system entail that to the original system.