On nonlinear dynamics of interacting populations: Coupled kink waves in a system of two populations

We discuss a nonlinear model of the spatial–time interaction among populations which reproduction and intensity of interaction depend on their spatial density. For the particular case of two populations with constant growth rates and competition coefficients we obtain analytical nonlinear waves of kink kind. The kinks are connected to propagation of the deviations from the stationary densities corresponding to fixed points in the phase space of the population densities. The kinks are coupled, i.e. the changes of the densities of the two populations are synchronous. Coupled kink solutions are obtained also for the general case of variable growth rates and variable coefficients of interactions.     

Boundary layer due to the axisymmetric spreading of material on the surface of a fluid

The effect of the axisymmetric spreading of a layer of material (oil or solid particles) on the surface of a viscous fluid is studied. Assuming high Reynolds numbers, the boundary layer equation is derived and solved for general power law surface velocities. The composite streamlines show sharp turns near the surface.     

Modeling the depletion of dissolved oxygen due to algal bloom in a lake by taking Holling type-III interaction

In this paper a non-linear mathematical model for depletion of dissolved oxygen due to algal bloom in a lake is proposed and analyzed. The model is formulated by considering four variables namely, cumulative concentration of nutrients, density of algal population, density of detritus and concentration of dissolved oxygen. In the modeling process it is assumed that nutrients are continuously coming with a constant rate to the lake through water runoff from agricultural fields and domestic drainage. The Holling type-III interaction between nutrients and algal population is considered. Equilibrium values have been obtained and their stability analysis has also been performed. Numerical simulations are carried out to explain the mathematical results.     

A nonlinear fractional model to describe the population dynamics of two interacting species

In this paper, the approximate analytical solutions of Lotka–Volterra model with fractional derivative have been obtained by using hybrid analytic approach. This approach is amalgamation of homotopy analysis method, Laplace transform, and homotopy polynomials. First, we present an alternative framework of the method that can be used simply and effectively to handle nonlinear problems arising in several physical phenomena. Then, existence and uniqueness of solutions for the fractional Lotka–Volterra equations are discussed. We also carry out a detailed analysis on the stability of equilibrium. Further, we have derived the approximate solutions of predator and prey populations for different particular cases by using initial values. The numerical simulations of the result are depicted through different graphical representations showing that this hybrid analytic method is reliable and powerful method to solve linear and nonlinear fractional models arising in science and engineering. Copyright © 2017 John Wiley & Sons, Ltd.     

Effect of stochastic perturbation on a two species competitive model

In this paper first we study the stability and bifurcation of a two species competitive model with a delay effect. Next we extend the deterministic model system to a stochastic delay differential system by incorporating multiplicative white noise terms in growth equations of both species. We consider the stochastic stability of a co-existing equilibrium point in terms of mean square stability by constructing a suitable Lyapunov functional. We perform a numerical simulation to validate our analytical findings.     

Upper branch nonstationary modes of the boundary layer due to a rotating disk

A treatment of asymptotic calculation of upper branch nonstationary instability modes is undertaken in the boundary layer flow due to a rotating disk. A numerical spectral solution of the eigenvalue problem shows good agreement with the results of a rational asymptotic approach, based on the extension of the multideck theory of [1].     

On the dynamics of stock price bubbles: comments on a model by Miao and Wang

Central European Journal of Operations Research - We consider the model by Miao and Wang (Am Econ Rev 108:2590–2628, 2018), in which endogenous collateral constraints may generate stock price...     

Conditional length distributions induced by the coverage of two points by a Poisson Voronoï tessellation: application to a telecommunication model

The end points of a fixed segment in the Euclidian plane covered by a Poisson Voronoï tessellation belong to the same cell or to two distinct cells. This marks off one or two points of the underlying Poisson process that are the nucleus(i) of the cell(s). Our interest lies in the geometrical relationship between these nuclei and the segment end points as well as between the nuclei. We investigate their probability distribution functions conditioning on the number of nuclei, taking into account the length of the segment. The aim of the study is to establish some tools to be used for the analysis of a telecommunication problem related to the pricing of leased lines. We motivate and give accurate approximations of the probability of common coverage and of the length distributions that can be included in spreadsheet codes as an element of simple cost functions. Copyright © 2006 John Wiley & Sons, Ltd.     

Fast Legendre spectral method for computing the perturbation of a gradient temperature field in an unbounded region due to the presence of two spheres

The temperature distribution around two spheres is considered when the main field has a constant gradient at infinity. Bispherical coordinates are used, together with a transformation of the dependent variable that leads to separation of variables. Then the solution can be sought in Legendre series with respect to one of the bispherical coordinates. An important element of the proposed work is the effective way to reduce an essentially 3D problem to a set of three 2D problems. The Legendre spectral method is shown to have an exponential convergence which is confirmed by the computations. The efficiency is so high that even for the hard cases of two closely situated spheres, an accuracy of 10^?10 is achieved with as few as 20 terms in the expansion. Solutions with both longitudinal and transverse gradients at infinity are obtained, and the contour lines of the temperature field are presented graphically. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Effect of a radial temperature gradient on the stability of the flow of a second-order fluid between two co-axial cylinders

Summary It has been found that the effect of a radial temperature gradient on the Taylor stability problem for a viscoelastic fluid and for a Newtonian fluid is the same.

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Résumé On montre que l'effet d'un gradient de la température radial sur le problème de stabilité de Taylor pour un fluide viscoélastique est semblable à celui d'un fluide Newtonien.

     

Effects of suction/blowing on the lower branch modes of the incompressible boundary layer flow due to a rotating-disk

In this study a theoretical approach is pursued to investigate the effects of suction and blowing on the structure of the lower branch neutral stability modes of three-dimensional small disturbances imposed on the incompressible von Karman’s boundary layer flow induced by a rotating-disk. Particular interest is placed upon the short-wavelength, non-linear and nonstationary crossflow vortex modes developing within the presence of suction/blowing at sufficiently high Reynolds numbers with reasonably small scaled frequencies. Following closely the asymptotic framework introduced in [1], the role of suction on the non-linear disturbances of the lower branch described first in [2] for the stationary modes only, is extended in order to obtain an understanding of the behavior of non-stationary perturbations. The analysis using the rational asymptotic technique based on the triple-deck theory enables us to derive initially an eigenrelation which describes the evolution of linear modes. The asymptotic linear modes calculated at high Reynolds number limit are found to be destabilizing as far as the non-parallelism accounted by the approach is concerned, and they compare fairly well with the numerical results generated directly by solving the linearized system with the usual parallel flow approximation. An amplitude equation is derived next to account for the effects of non-linearity. Even though the form of this equation is the same as that of found in [2] for no suction, it is under the strong influence of suction and blowing. This amplitude equation is shown to be adjusted by a balance between viscous and Coriolis forces, and it describes the evolution of not only the stationary but also the non-stationary modes for both suction and injection applied at the disk surface. A close investigation of the amplitude equation shows that the non-linearity is highly destabilizing for both positive and negative frequency waves, though finite amplitude growth of a disturbance having positive frequency close to the neutral location is more effective at destabilization of the flow under consideration. Finally, a smaller initial amplitude of a disturbance is found to be sufficient for the non-linear amplification of the modes in the case of suction, whereas a larger amplitude is required if injection is active on the surface of the disk.     

Forward dynamics applied to a three-dimensional continuum-mechanical model of the upper limb

This paper introduces, for the first time, a methodology to achieve a forward dynamics simulation of the musculoskeletal system using three-dimensional continuum-mechanical skeletal muscle models. This is achieved by coupling one- and three-dimensional skeletal muscle models. The feasibility of this methodology is demonstrated through a forward dynamics simulation of the upper limb involving the biceps and triceps muscle. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mathematical model of the dynamics of a population affected by harmful substances

A mathematical model is presented of the dynamics of a population with individuals subjected to the effects of pollutants entering with food. We assume that the product of interaction of ingested pollutants is harmful for the individuals and increases the rate of their death. We describe the equations of the model and study the properties of solutions, including the existence and stability of equilibria. The conditions are obtained for the population becoming extinct as well as the conditions which guarantee that the total population is maintained at a nonzero stationary level. Some results of simulation are presented.     

Resistance on a circular cylinder due to any number of vortices lying in two rows

Zusammenfassung In dieser Arbeit wird der unterschiedliche Widerstand an einem Kreiszylinder berechnet, der in einem steten Strom angebracht ist und von einer Anzahl von Wirbelbewegungen in zwei Reihen begleitet ist.     

New classes of ground states for the Potts model with random competing interactions on a Cayley tree

We consider the Potts model with random competing interactions on a Cayley tree. We study the domain of ground states of this model.     

On the dynamics of a fluid-particle interaction model: The bubbling regime

This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space Ω⊂R³ which may be unbounded. The system under investigation describes the evolution of particles dispersed in a viscous compressible fluid and is expressed through the conservation of fluid mass, the balance of momentum and the balance of particle density often referred as the Smoluchowski equation. The coupling between the dispersed and dense phases is obtained through the drag forces that the fluid and the particles exert mutually by the action-reaction principle. We show that solutions exist globally in time under reasonable physical assumptions on the initial data, the physical domain, and the external potential. Furthermore, we prove the large-time stabilization of the system towards a unique stationary state fully determined by the masses of the initial density of particles and fluid and the external potential.     

The application of a vehicle routing model to a waste-collection problem: two case studies

In this paper we suggest a unique model for estimating the operating cost of each of three waste-collection systems. Under the traditional system, which is widely used, waste is typically collected in plastic bags and a three-man crew is needed on each vehicle. The other two systems require a one-man crew for vehicle collecting street containers. The side-loader system with fixed body automatically empties street containers into the vehicle body and empties the load at the disposal site. The side-loader system with demountable body allows the separation of the waste collection phase from transport to the disposal site, since the vehicle body can be demounted. We also present two case studies and show how the estimation of operating costs is a critical issue in decisions regarding the type of system to be used for waste collection.     

A numerical approach for a model of the precancer lesions caused by the human papillomavirus

We develop two numerical methods to approximate the solutions of a pioneer model of the lesions at the cervical cells caused by the human papillomavirus. Such model is given by a nonlinear advection–diffusion-reaction partial differential equation and the goal of the schemes is to analyze the behaviour of the evolution of infected cells. The developed schemes consist of two explicit non standard finite differences numerical schemes which satisfy positivity conditions. They are based on the subequation method in the context of the non standard scheme methodology. Our approach provides an alternative method to the early diagnosis of the disease and may open up new lines of research.     

Statics and dynamics of the Coleman model: Comment on Braun

A new version of the Coleman model is given in this comment It is modeled as a simple barter economy with Cobb‐Douglas utility function. So, standard microeconomic results can be applied for the dynamic analysis of the Coleman model.