Nonlinear analysis of lipid tubules by nonlocal beam model

Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for lipid tubules. The lipid tubule is modeled as a nonlocal micro/nano-beam which contains small scale effect. The material properties are assumed to be size-dependent. The governing equation is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of lipid tubules. In contrast, it increases the nonlinear to linear frequency ratios slightly for the lipid tubule with immovable end conditions.     

Spatial segregation in competitive interaction-diffusion equations

Summary The effect of cross-population pressure on the Volterra type dynamics for two competing species is investigated. On the basis of cross-diffusion induced instability, spatial segregation is studied. Spatially discrete models are also discussed. It is shown that this effect has a tendency to enhance the stability assuring coexistence of species. In continuous and discrete cases, time-dependent segregation processes are studied numerically.     

Cell imaging and manipulation by nonlinear optical microscopy

Advances in the technologies for labeling and imaging biological samples drive a constant progress in our capability of studying structures and their dynamics within cells and tissues. In the last decade, the development of numerous nonlinear optical microscopies has led to a new prospective both in basic research and in the potential development of very powerful noninvasive diagnostic tools. These techniques offer large advantages over conventional linear microscopy with regard to penetration depth, spatial resolution, three-dimensional optical sectioning, and lower photobleaching. Additionally, some of these techniques offer the opportunity for optically probing biological functions directly in living cells, as highlighted, for example, by the application of second-harmonic generation to the optical measurement of electrical potential and activity in excitable cells. In parallel with imaging techniques, nonlinear microscopy has been developed into a new area for the selective disruption and manipulation of intracellular structures, providing an extremely useful tool of investigation in cell biology. In this review we present some basic features of nonlinear microscopy with regard both to imaging and manipulation, and show some examples to illustrate the advantages offered by these novel methodologies.     

Synthesis and high ranked NLT properties of new sulfonamide-substituted indium phthalocyanines

The synthesis and characterization of three new indium phthalocyanines bearing eight N-alkyl- or N-arylsulfonamide groups is described. The new compounds are {2,3,9,10,16,17,23,24-octakis[4-(4-methoxyphenylaminosulfonyl]phenoxy]phthalocyaninato}indium(III) chloride (7), {2,3,9,10,16,17,23,24-octakis[4-diethylaminosulfonyl)phenoxy]phthalocyaninato}indium(III) chloride (8) and {2,3,9,10,16,17,23,24-octakis[4-didodecylaminosulfonyl)phenoxy]phthalocyaninato}indium(III) chloride (9), and were obtained in 23-49% yields. The precursors of phthalocyanines 7-9 are sulfonamide-substituted phthalonitriles that can be prepared by reacting 4,5-bis(4-chlorosulfonylphenoxy)phthalonitrile (3) with amines. The nonlinear transmission (NLT) of complexes 7-9 was determined at 532 nm using ns pulses. All three phthalocyanines behave as reverse saturable absorbers with increasing efficiency of optical limiting in the order 7 < 8 < 9. A comparative analysis of the NLT results is attempted in terms of the structural differences in 7-9.     

Utilization of nonlinear optical absorption in eosin-Y for all-optical switching

Nonlinear triplet-triplet absorption in organic molecules can be used to construct all-optical switches and spatial light modulators (SLMs). SLM experiments were performed on eosin/PVA films using Ar laser light for writing and He-Ne laser for reading. The results indicate that triplet quenching is a limiting factor in the SLM performance. Better results in terms of writing intensity and contrast ratio are obtained in transient waveguide switch configuration.     

An adaptive model for synchrony in the firefly Pteroptyx malaccae

We describe a new model for synchronization of neuronal oscillators that is based on the observation that certain species of fireflies are able to alter their free-running period. We show that by adding adaptation to standard oscillator models it is possible to observe the frequency alteration. One consequence of this is the perfect synchrony between coupled oscillators. Stability and some analytic results are included along with numerical simulations.This work was partially supported by NSF Grant DMS9002028 and the Mathematical Research Branch of The National Institutes of Health     

Diffusion coefficient of modern humans outcompeting Neanderthals

A nonlinear mathematical model is used to describe Neanderthals extinction about 35,000 years before present. Using archaeological data, radiocarbon re-calibrate speed among others, we show that the diffusion coefficient describing Modern Humans spread corresponds to 1596 km²/yr. The model is well established since all archaeological parameters, including Neanderthal-Modern interaction coefficient, become estimated.     

Experimental and numerical exploration of intrinsic localized modes in an atomic lattice

This review focuses attention on the experimental studies of intrinsic localized modes (ILMs) produced in driven atomic lattices. Production methods involve the application of modulational instability under carefully controlled conditions. One experimental approach is to drive the atomic lattice far from equilibrium to produce ILMs, the second is to apply a driver of only modest strength but nearby in frequency to a plane wave mode so that a slow transformation from large amplitude standing waves to ILMs takes place. Since, in either case, the number of ILMs produced is small, the experimental observation tool appropriate for this task is four-wave mixing. This nonlinear detection technique makes use of the nonlinearity associated with an ILM to enhance its signal over that produced by the more numerous, but linear, spin waves. The final topic deals with numerical simulations of a nonlinear nanoscale atomic lattice where the new feature is running ILMs.     

Effects of acorn abundance on density dependence in a Japanese wood mouse (Apodemus speciosus) population

We analysed the effects of Quercus crispula acorn abundance on the density dependence of the large Japanese wood mouse Apodemus speciosus using time series data (1992–2007). The data were obtained in a forest in northern Hokkaido, Japan, by live-trapping rodents and directly counting acorns on the ground. Acorn abundance in one year clearly influenced the abundance of wood mice in the following year in all models examined based on the Gompertz and Ricker model; in addition, the abundance of wood mice had effects on the population. Acorn abundance influenced the strength of density dependence (intraspecific competition) of the wood mouse population. When the abundance of acorns was high, density dependence was relaxed, and as a result the equilibrium density at which the population growth rate decreased to zero became higher. Those effects of acorn abundance were regarded as a nonlinear perturbation effect (sensu Royama 1992). The nonlinearity of density dependence was also detected; higher densities had stronger effects on population growth rates. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On synchronization in semelparous populations

Synchronization, i.e., convergence towards a dynamical state where the whole population is in one age class, is a characteristic feature of some population models with semelparity. We prove some rigorous results on this, for a simple class of nonlinear one- population models with age structure and semelparity: (i) the survival probabilities are assumed constant, and (ii) only the last age class is reproducing (semelparity), with fecundity decreasing with total population. For this model we prove: (a) The synchronized, or Single Year Class (SYC), dynamical state is always attracting. (b) The coexistence equilibrium is often unstable; we state and prove simple results on this. (c) We describe dynamical states with some, but not all, age classes populated, which we call Multiple Year Class (MYC) patterns, and we prove results extending (a) and (b) into these patterns.Acknowledgement Boris Kruglikov contributed the nonlinear part of the formulation as well as the proof of Theorem 1. The authors are grateful for critical and constructive comments by N. Davydova and O. Diekmann. E.M. is also grateful for discussions with Marius Overholt concerning problems of proving Theorem 2.     

Stochastic modeling of nonlinear epidemiology

The objectives of this paper to analyse, model and simulate the spread of an infectious disease by resorting to modern stochastic algorithms. The approach renders it possible to circumvent the simplifying assumption of linearity imposed in the majority of the past works on stochastic analysis of epidemic processes. Infectious diseases are often transmitted through contacts of those infected with those susceptible; hence the processes are inherently nonlinear. According to the classical model of Kermack and McKendrick, or the SIR model, three classes of populations are involved in two types of processes: conversion of susceptibles (S) to infectives (I) and conversion of infectives to removed (R). The master equations of the SIR process have been formulated through the probabilistic population balance around a particular state by considering the mutually exclusive events. The efficacy of the present methodology is mainly attributable to its ability to derive the governing equations for the means, variances and covariance of the random variables by the method of system-size expansion of the nonlinear master equations. Solving these equations simultaneously along with rates associated influenza epidemic data yields information concerning not only the means of the three populations but also the minimal uncertainties of these populations inherent in the epidemic. The stochastic pathways of the three different classes of populations during an epidemic, i.e. their means and the fluctuations around these means, have also been numerically simulated independently by the algorithm derived from the master equations, as well as by an event-driven Monte Carlo algorithm. The master equation and Monte Carlo algorithms have given rise to the identical results.     

Distance of the reduced Brusselator from equilibrium

The new concept of a nonequilibrium parameter P is applied to a reduced Brusselator, considered as a kinetic model for cellular processes. The reduction corresponds to omitting a monomolecular reaction. The deviation from equilibrium is due to a fixed nonequilibrium value of an extracellular concentration B, responsible for energizing and determining the steady-state value of the overall chemical affinity ?. The value of ? is insensitive to different steady states possible for a given set of rate constants. In contrast, the parameter P is state dependent. In particular, it may jump together with state variables. Two limiting cases of high ? are investigated, B→ 0 and B→ 1. In the first case P grows monotonically with ?. In the second case there is always a steady state solution with P→ 0. The physical interpretation of this effect of “equilibrium far from equilibrium” reveals the real predictive power of the parameter P. Relaxation regimes are investigated for a doubly reduced Brusselator. Both P and ? are in general time dependent and have jumps in their time derivatives. The canonical form of P is compared with the noncanonical one in the context of robustness of the new concept with respect to incomplete information about the system studied. These forms of P are different in relaxation to a nonequilibrium state and coincide in relaxation to an equilibrium state.     

捕食-被捕食反应扩散方程非线性奇摄动问题

研究了非线性反应扩散方程奇摄问题,在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量和幂级数展开理论构造出解的形式渐近展开式．最后利用微分不等式理论,讨论了问题解的一致有效性和渐近性态。     

一类非线性非局部反应扩散方程奇摄动问题

本文研究了一类具有非线性非局部反应扩散方程奇摄动问题。在适当的条件下,利用微分不等式理论,讨论了问题解的渐近性态。     

Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread

Summary In this paper we use Aronson's and Weinberger's [1–4] concept of asymptotic speed to estimate the asymptotic behaviour of the solution of a nonlinear integral equation (with the nonlinearity not being monotone), which describes the development of a spatially distributed population.     

激光与DNA作用方程的稳定态分析

本文在庞小峰改进后的Ｙｏｍｏｓａ模型基础上,引进了激光与ＤＮＡ分子系统作用的非线性方程。     

Pattern formation in morphogenesis

We first treat the Gierer-Meinhardt equations by linear stability analysis to determine the critical parameter, at which the homogeneous distributions of activator and inhibitor concentrations become unstable. We find two types of instabilities: one leading to spatial pattern formation and another one leading to temporal oscillations. We consider the case where two instabilities are present. Using the method of generalized Ginzburg-Landau equations introduced earlier we then analyze the nonlinear equations. As we are mainly interested in spatial pattern formation on a sphere we consider the problem under an appropriate constraint. Combining the two occurring solutions we find patterns well-known in biology, such as a gradient system and temporal oscillations.