Although there have many studies of the population genetical consequences of environmental variation, little is known about the combined effects of genetic drift and fluctuating selection in structured populations. Here we use diffusion theory to investigate the effects of temporally and spatially varying selection on a population of haploid individuals subdivided into a large number of demes. ...

Approximate analytical methods have been used extensively for finding approximate solutions to nonlinear ordinary differential equations. In this paper we compare the recently developed direct normal form transformation with two other very well known and long standing methods, harmonic balance and the method of multiple scales. We will show that the direct normal form method combines some of th...

A model of homogeneous explosions with competing branching and recombination processes due to Kapila is analyzed by singular perturbation methods. In this model, the concentration of radicals is very low during a long induction period that ends with a rapid radical-growth stage in which all the reactants are consumed as the radicals reach their peak concentrations. The sudden jump in radical co...

The dynamics and response of particles in an asymmetric potential of the ratchet type is considered. An approximate asymmetric ratchet potential, which allows us to apply an analytical approach to investigate the systems’ response, is proposed based on the power series interpolation scheme. The method of multiple scales (MMS) is then employed to obtain an approximate solution at the principal r...

Thermal dependency of material characteristics in micro electromechanical systems strongly affects their performance, design, and control. Hence, it is essential to understand and model that in MEMS devices to optimize their designs. A thermal phenomenon introduces two main effects: damping due to internal friction, and softening due to Young modulustemperature relation. Based on some reported ...

The objective of this work is to analytically study the nonlinear dynamics of beam flexures with a tip mass undergoing large deflections. Hamilton’s principal is utilized to derive the equations governing the non-linear vibrations of the cantilever beam and the associated boundary conditions. Then, using a single mode approximation, these non-linear partial differential equations are reduced to...

The present paper deals with the classical problem of linear sound propagation in tubes with isothermal walls. The perturbation technique of the method of multiple scales in combination with matched asymptotic expansions is applied to derive the first-order solutions and, in addition, the second-order solutions representing the correction due to boundary layer attenuation. The propagation lengt...

This paper investigates the commonly overlooked “sensitivity” of sensitivity analysis (SA) to what we refer to as parameter “perturbation scale”, which can be defined as a prescribed size of the sensitivityrelated neighbourhood around any point in the parameter space (analogous to step size Dx for numerical estimation of derivatives). We discuss that perturbation scale is inherent to any (local...

In this paper, we consider the existence of multiple positive solutions for Kirchhoff-Schrödinger-Poisson system with the nonlinear term containing both general singularity and quasicritical nonlinearity. By combining the variational method with the perturbation method, we obtain the existence of two positive solutions with the parameter λ small enough. One of the solutions is the local minimum...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...