A note on the onset of synchrony in avian ovulation cycles

Spontaneous oscillator synchrony occurs when populations of interacting oscillators begin cycling together in the absence of environmental forcing. Synchrony has been documented in many physical and biological systems, including oestrus/menstrual cycles in rats and humans. In previous work we showed that Glaucous-winged Gulls (Larus glaucescens) can lay eggs synchronously on an every-other-day schedule, and that synchrony increases with colony density. Here we pose a discrete-time model of avian ovulation to study the dynamics of synchronization. We prove the existence and uniqueness of an equilibrium solution which bifurcates to increasingly synchronous cycles as colony density increases.     

A design procedure to model a transiently excited wall

A procedure is described to model the thermal behaviour of a homogeneous slab together with its associated film resistance by one or two lumped capacities and associated resistances, when the expected excitation is of step form. The components are sized so as to fit approximately the well-known analytical solution for a transiently excited slab. The fit is made by minimizing the squared deviation between the responses.     

GOODWIN宏观经济学模型的一个注记

本文讨论了 Goodwin宏观经济学模型 ,给出了该模型的一种解法 ,得到了一些有意义的结论 ,并为进一步探讨该模型的性质打下了基础 .     

A model for the problem of ground vibration induced by the wheels of a moving train

This paper presents a three-dimensional model for the analysis of ground vibrations excited by forces transmitted to the ground from the wheels of a moving train through the track. The field equations are solved by using scalar wave functions. From the computed results presented here, certain qualitative conclusions can be made to enhance our understanding of the physical problem.     

Cannibalism may control disease in predator population: result drawn from a model based study

In the present study, we propose and analyze a predator–prey system with disease in the predator population. To understand the role of cannibalism, we modify the model considering predator population is of cannibalistic type. Local and global stability around the biologically feasible equilibria are studied. The conditions for the persistence of the system are worked out. We also analyze and compare the community structure of the model systems with the help of ecological and disease basic reproduction numbers. Finally, through numerical simulation, we observe that inclusion of cannibalism in predator population may control the disease transmission in the susceptible predator population. Copyright © 2014 John Wiley & Sons, Ltd.     

A stratified model of flow in a coastal trench

A stratified model of the circulation in a deep, narrow trench adjacent to a coast is described. The flow in the trench is driven by surface wind stress, coastal runoff and inflow at one end. The model is being developed to investigate the Norwegian coastal current flowing through the Norwegian Trench.     

A note on positive non-constant steady-state solutions to a reaction-diffusion model

In the present paper, we investigate a reaction-diffusion system with feedback effect subject to the homogeneous Neumann boundary condition and study the positive steady-state solutions. We establish a priori estimates for positive steady-state solutions and derive some results for non-existence of positive non-constant steady-state solutions. Our analysis complements the existing results on this model.     

A note on the global behaviour of the network-based SIS epidemic model

In this note we introduce the study of the global behaviour of the network-based SIS epidemic model recently proposed by Pastor-Satorras and Vespignani [Epidemic spreading in scale-free networks, Phys. Rev. Lett. 86 (2001) 3200], characterized in case of homogeneous scale-free networks by a very small epidemic threshold, and extended by Olinky and Stone [Unexpected epidemic threshold in heterogeneous networks: the role of disease transmission, Phys. Rev. E 70 (2004) 03902(r)]. We show that the above model may be read as a particular case of the classical multi-group SIS model proposed by Lajmainovitch and Yorke [A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci. 28 (1976) 221] and extended by Aronsson and Mellander [A deterministic model in biomathematics. Asymptotic behaviour and threshold conditions, Math. Biosci. 49 (1980) 207]. Thus, by applying the methods used for SIS multi-group models, we straightforwardly show, for the first time, that the local conditions identified in the physics literature also determine the global behaviour of a disease spreading on a network. Finally, we briefly study the case in which the force of infection is non-linear, by showing that multiple coexisting equilibria are possible, and by giving a global threshold condition for the extinction.     

A note on a diffusive predator-prey model and its steady-state system

In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.     

Remarks on the paper ‘Exact bounds on average granular pressures in a general bin model’

In the paper referred to in the title to this communication, Shahinpoor argued that increased density due to material consolidation of a bulk material in a vertical bin reduces the stresses the bulk material exerts on the bin wall below those that would be present if the material were unconsolidated. In this paper it is shown that increased density due to material consolidation actually increases rather than reduces these stresses. Shahinpoor's conclusions are incorrect because he misinterprets his analytical results.     

A note on the stochastic properties of a scale change random effects model

The scale change model in survival analysis incorporates unobserved heterogeneity through a frailty that enters the baseline hazard function to change the time scale. In this paper we examine the stochastic properties of the mixtures of scale change model and build dependence between the overall population variable and the frailty variable. We also carry out stochastic comparisons between overall population variables when their respective frailty or baseline variables are ordered in the sense of various stochastic orders. Finally, we demonstrate how the variation of the baseline variable has an effect on the model.     

A note on the simple structural regression model

In this paper we investigate some aspects like estimation and hypothesis testing in the simple structural regression model with measurement errors. Use is made of orthogonal parametrizations obtained in the literature. Emphasis is placed on some properties of the maximum likelihood estimators and also on the distribution of the likelihood ratio statistics.     

A dynamical model for the overland flow on an infiltrating catchment

An approximate lumped parameter model for the surface runoff phenomenon on a catchment is presented. It consists of two submodels which are spatial discretizations of the basic partial differential equations of overland flow and infiltration. The aim of the model is to describe the dynamical input-output relationship between the rainfall rate and the surface runoff from the catchment. The boundary conditions of the infiltration process are modelled in an approximate way so that the number of state variables in the model can be reduced. With the aid of a single model parameter it is possible to describe simple catchment shapes like linearly converging and diverging surfaces. The model structure is flexible so that it can also be applied to more complex catchment configurations. The simulation results show that the phenomenon under consideration can be properly described by the model structure presented.     

Finite element modelling of surface waves in a channel

A variational formulation of the vertically-integrated differential equations for free surface wave motion is presented. A finite element model is derived for solving this nonlinear system of hydrodynamic equations. The time integration scheme employed is discussed and the results obtained demonstrate its good stability and accuracy.Several applications of the model are considered: the first problem is an open channel of uniform depth and the second an open channel of linearly varying depth. The ‘inflow’ boundary condition is prescribed in terms of the velocity which represents a wavemaker and/or a flow source, while the ‘outflow’ boundary condition is specified in terms of the water elevation. The outflow condition is adjusted for two cases, a reflecting boundary (finite channel) and a non-reflecting boundary (open-ended channel). The latter boundary condition is examined in some detail and the results obtained show that the numerical model can produce the non-reflecting boundary that is similar to the analytical radiation condition for waves. Computational results for a third problem, involving wave reflection from a submerged cylinder, are also presented and compared with both experimental data and analytical predictions.The simplicity and the performance of the computational model suggest that free surface waves can be simulated without excessively complicated numerical schemes. The ability of the model to simulate outflow boundary conditions properly is of special importance since these conditions present serious problems for many numerical algorithms.     

A note on fractional moments for the one-dimensional continuum Anderson model

We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay of fractional moments of the Green function, which is shown to hold at arbitrary energy and for any single-site distribution with bounded, compactly supported density.     

A note on the comparison of two different formulations of a risky R&D model

The purpose of this note is to provide a link between the Kamien and Schwartz [2], and the Aldrich and Morton [1] formulations of the so-called Lucas [3], risky R&D model. It is shown that the solutions of these formulations are identical for the stationary, exponential case. Furthermore, the properties of these solutions are discussed in order to focus on some of the characteristics of the model.     

A note on a singular integral equation arising in water wave scattering

A quick method of solution of a singular integral equationof the first kind involving both logarithmic singularity aswell as Cauchy-type singularity is explained.     

A note on the Bayes factor in a semiparametric regression model

In this paper, we consider a semiparametric regression model where the unknown regression function is the sum of parametric and nonparametric parts. The parametric part is a finite-dimensional multiple regression function whereas the nonparametric part is represented by an infinite series of orthogonal basis. In this model, we investigate the large sample property of the Bayes factor for testing the parametric null model against the semiparametric alternative model. Under some conditions on the prior and design matrix, we identify the analytic form of the Bayes factor and show that the Bayes factor is consistent, i.e. converges to infinity in probability under the parametric null model, while converges to zero under the semiparametric alternative, as the sample size increases.     

A micropolar fluid model of blood flow through a tapered artery with a stenosis

A nonlinear two‐dimensional micropolar fluid model for blood flow in a tapered artery with a single stenosis is considered. This model takes into account blood rheology in which blood consists of microelements suspended in plasma. The classical Navier–Stokes theory is inadequate to describe the microrotations or particles' spin of such suspension in a viscous medium. The governing equations involving unsteady nonlinear partial differential equations are solved using a finite difference scheme. A quantitative analysis performed through numerical computation shows that the axial velocity profile and the flow rate decrease and the wall shear stress increases once the artery is narrower in the presence of the polar effect. Furthermore, the taper angle certainly bears the potential to influence the velocity and the flow characteristics to considerable extent. Copyright © 2010 John Wiley & Sons, Ltd.     

A note on self-normalization for a simple spatial autoregressive model

In this paper, we consider the problem of self-normalization for one rather simple autoregressive model X _t,s = aX _t−1,s + bX _t,s−1 + ɛ _t,s on a two-dimensional lattice. We show that there is some similarity between this problem and the corresponding problem for AR(1) time series model. The research was supported by the bilateral France-Lithuania scientific project Gilibert. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 220–233, April–June, 2007.