Hybrid journal (It can contain Open Access articles) ISSN (Print) 0272-4960 - ISSN (Online) 1464-3634 Published by Oxford University Press[369 journals]

Authors:Liu M; Fan M. Abstract: Stability in distribution of solutions (SDS) is important but challenging in stochastic population models with delays since the traditional methods are difficult to apply. This article focuses on a three-species stochastic delay prey-mesopredator-superpredator system and explores its SDS by a new approach. The new approach avoids the difficulties of some existing methods and can also be applied to investigate the SDS of other stochastic delay population models. The study reveals that the complete dynamic scenarios of SDS are characterized by three parameters $\eta_1>\eta_2>\eta_3$: if $\eta_11>\eta_2>\eta_3$, then the prey converges weakly to a unique ergodic invariant distribution (UEID) while both the mesopredator and the superpredator are extinct; if $\eta_1>\eta_2>1>\eta_3$, then both the prey and the mesopredator converge weakly to a UEID while the superpredator are extinct; if $\eta_3>1$, then the distributions of prey-mesopredator-superpredator converge weakly to a UEID. PubDate: 2017-03-17

Authors:Wu B; Yu J. Abstract: This article concerns an inverse problem for a strongly coupled reaction-diffusion system, which has many applications including the cross diffusion resulted from the influence of one component on another. This inverse problem aims to determine a spatially varying coefficient in the reaction-diffusion system from internal observation data on an arbitrary subdomain. We use a new Carleman estimate to derive Hölder stability for this inverse problem. Different from the existing methods dealing with weakly or strongly coupled system, such as Fan & Chen (2012, Stability estimates for a strongly coupled parabolic system. Tamkang J. Math., 43, 137–144.) and Bellassoued & Yamamoto (2013, Carleman estimate and inverse source problem for Biot’s equations describing wave propagation in porous media. Inverse Probl., 29, 115002 (20pp).), we consider the two equations governing the strongly coupled system as a whole to establish the needed Carleman estimate, assuming only that the determinant of coefficient matrix of principle terms is not zero. PubDate: 2017-01-23

Authors:Chen Q; Li F, Wang F. Abstract: In this article, we study the dynamics of a two-species competition model with two different free boundaries in heterogeneous time-periodic environment, where the two species adopt a combination of random movement and advection upward along the resource gradient. We show that the dynamics of this model can be classified into four cases, which form a spreading–vanishing quartering. The notion of the minimal habitat size for spreading is introduced to determine if species can always spread. Rough estimates of the asymptotic spreading speed of free boundaries and the long-time behaviour of solutions are also established when spreading occurs. Furthermore, some sufficient conditions for spreading and vanishing are provided. PubDate: 2017-01-11

Authors:Matei A; Sofonea M. Abstract: We consider a mathematical model which describes the quasistatic contact of a piezoelectric body with an electrically conductive foundation. The material’s behaviour is described by means of an electro-viscoelastic constitutive law, the contact is bilateral and is associated to Tresca’s law of dry friction. We derive a mixed variational formulation of the problem, which is in form of an evolutionary system for the displacement field, the electric potential and two Lagrange multipliers. Then we provide the existence of a unique weak solution to the model. Also, under additional assumptions, we establish its continuous dependence with respect to the friction bound and the electric conductivity coefficient. PubDate: 2016-12-24

Authors:Cox SM; Yu J, Goh W, et al. Abstract: This paper gives the first systematic perturbation analysis of the audio distortion and mean switching period for a self-oscillating class-D amplifier. Explicit expressions are given for all the principal components of audio distortion, for a general audio input signal; the specific example of a sinusoidal input is also discussed in some detail, yielding an explicit closed-form expression for the total harmonic distortion. A class-D amplifier works by converting a low-frequency audio input signal to a high-frequency train of rectangular pulses, whose widths are slowly modulated according to the audio signal. The audio-frequency components of the pulse-train are designed to agree with those of the audio signal. In many varieties of class-D amplifier, the pulse-train is generated using a carrier wave of fixed frequency, well above the audio range. In other varieties, as here, there is no such fixed-frequency clock, and the local frequency of the pulse-train varies in response to the audio input. Such self-oscillating designs pose a particular challenge for comprehensive mathematical modelling; we show that in order to properly account for the local frequency variations, a warped-time transformation is necessary. The systematic nature of our calculation means it can potentially be applied to a range of other self-oscillating topologies. Our results for a general input allow ready calculation of distortion diagnostics such as the intermodulation distortion, which prior analyses, based on sinusoidal input, cannot provide. PubDate: 2016-12-24

Authors:Borcea CS; Streinu I. Abstract: For materials science, diamond crystals are almost unrivalled for hardness and a range of other properties. Yet, when simply abstracting the carbon-bonding structure, the corresponding periodic framework is far from rigid. We study the kinematics of this type of periodic bar-and-joint articulated system, with particular regard to the volume variation of a unit cell. For potential applications to nano-mechanism design, we determine conditions for planar auxetic behaviour. PubDate: 2016-12-24

Authors:Dai M; Gao C, Schiavone P. Abstract: We study the uncoupled steady-state thermo-elastic problem of a circular nano-inhomogeneity embedded in an elastic plane subjected to a uniform remote heat flux. Nanoscale influences are included in the continuum-based model of deformation by incorporating interface effects arising from both heat conduction and elasticity (in the absence of surface tension) on the material interface. Complex variable methods are used to derive closed-form solutions for the corresponding temperature and thermal stress fields. Numerical examples are presented to examine how each of the heat or elastic interface effects influence the thermal stress field. In fact, we show that the contribution of heat related interface effects to the thermal stress field decays in both the matrix and the inhomogeneity as the heat conductivity of the inhomogeneity increases. On the other hand, the contribution of elastic interface effects to the thermal stress field decays in the matrix but increases for the inhomogeneity as the inhomogeneity becomes harder. PubDate: 2016-12-24

Authors:Chillingworth DJ. Abstract: Two corrections have been made to this article: The image used in Fig. 2 has been replaced and a new caption has been added to comply with permissions requirements.The author's initials have been corrected to D. R. J. Chillingworth. PubDate: 2016-11-17

Authors:Craske J. Abstract: This article reviews and builds upon recent progress that has been made in understanding the mathematical properties of integral models for unsteady turbulent jets. The focus is on models that describe the evolution of the volume flux and the momentum flux in a jet, whose source conditions are time dependent. A generalized approach that postpones making assumptions about the ‘internal’ properties of the flow, such as the radial dependence of the longitudinal velocity profile, turbulent transport and pressure, allows one to understand how the resulting integral equations are affected by model-specific assumptions. Whereas the assumptions invoked in previous unsteady jet models have resulted in a parabolic system of equations, generalized equations that are derived from first principles have a hyperbolic character and statistical stability that depends sensitively on assumptions that are normally invoked a priori. Unsteady axisymmetric jets with Gaussian velocity profiles have special properties, including a tendency to remain straight-sided (conical) and marginal stability in response to source perturbations. A distinct difference between planar jets and axisymmetric jets is that the mean energy flux, which plays a leading-order role in determining the unsteady dynamics of jets, is significantly lower in planar jets. We hypothesize that in order to maintain marginal stability the turbulence and pressure fields in planar jets adjust themselves, relative to axisymmetric jets, to compensate for the lower mean energy flux. PubDate: 2016-10-17

Authors:Ayton LJ. Abstract: An analytic solution is obtained for the sound generated by gust-aerofoil interaction for aerofoils with thickness, camber and angle of attack. The model is based on the linearization of the Euler equations about a steady subsonic flow, and is an extension of previous work which considered restrictive aerofoil geometries. Only high-frequency incident gusts are considered. The aerofoil thickness, camber and angle of attack are such that the steady flow past the aerofoil is seen as a small perturbation to uniform flow. The method of matched asymptotic expansions is used to identify regions around the aerofoil where different processes govern the generation or propagation of sound. Key local regions at the leading and trailing edges of the aerofoil determine the generation of noise whilst transition regions along the rigid aerofoil surface, and outer regions away from the surface play key roles in the propagation of sound. The effects of varying thickness and camber angle are discussed, along with the effects of varying the radius of the leading edge. PubDate: 2016-09-01

Authors:Black JP; Breward CW, Howell PD. Abstract: This paper concerns mathematical modelling of charge transport across a thin poorly conducting layer between two electrodes. We describe and analyse two alternative approaches to model quantum effects within a continuum theory: the density gradient confinement (DGC) and density gradient tunnelling (DGT) theories. In either case, quantum effects are characterized by a small parameter, which we exploit to analyse the problems asymptotically. We thus find simplified approximate solutions which show excellent agreement with numerical solutions of the full models, and demonstrate previously undocumented oscillatory behaviour both in the charge density profile and in the variation of current with applied potential difference. PubDate: 2016-08-20