恒化器中两种群适应性生长模型

研究两种微生物基于恒化器培养的数学模型.微生物1因适应生存环境营养供给的变化而具有休眠特性,表现为活跃生长与休眠两种生存状态.微生物2不能休眠.经过数学分析和数值模拟,结论是当系统生产常数μ_0<1时,两种微生物不能在恒化器中生存.而当μ_0>1,会出现多种稳定的极限状态E_i,i=1,2,3,4,5.数值模拟也显示出当营养吸收转化率和定量输入的营养浓度确定时,两种微生物的最大生长率决定了竞争结果.     

Global Steady State Analytical Solution of Cadmium Uptake Model for Plant Roots

The concentration distribution of cadmium ion in soil is studied by the phytoavailability model. According to the states of the cadmium complex: fully inert, fully labile and partially labile, we establish three corresponding cadmium uptake sub-models, and derive respective global analytical solutions at steady state. In particular, when the complex is partially labile, we give the steady analytical solution of cadmium ion concentration in cylindrical geometry composed of the analytical solutions of partially labile complex and fully inert complex in planar geometry and fully inert complex in cylindrical geometry, that is, the ration approximation method. In this paper, the global analytical solutions are compared with the results of literature and numerical simulations. Therefore, the double check is realized to ensure the rationality of the analytical method. The global concentration profile of cadmium ions in the whole rhizosphere can be described by the steady state analytical solutions: the concentration of cadmium ion increases with the distance from the root surface and finally reaches the initial value; the change rate of cadmium ion concentration is the largest when the complex is fully labile; whatever the state of the complex is, cadmium ions never accumulate on the root surface. Finally, we discuss and compare the effects of moving and fixed right boundaries of the model on the results. The results show that it is more reasonable to take the fixed right boundary, and plant roots can uptake cadmium ions in a wider range.     

Locomotion and Control of a Self-Propelled Shape-Changing Body in a Fluid

In this paper we study the locomotion of a shape-changing body swimming in a two-dimensional perfect fluid of infinite extent. The shape changes are prescribed as functions of time satisfying constraints ensuring that they result from the work of internal forces only: conditions necessary for the locomotion to be termed self-propelled. The net rigid motion of the body results from the exchange of momentum between these shape changes and the surrounding fluid.     

Steady Combustion Waves Driven by a Recombination Reaction in a Gas Mixture

Steady combustion waves in one space dimension are studied by means of fluid-dynamic reactive Navier?CStokes equations derived from kinetic theory. By using the conservation laws, the problem is reduced to a three-dimensional dynamical system, with different solutions of deflagration or detonation type according to several various sub-regions in the parameter space. The delicate question of the flame eigenvalue is addressed, and a suitable numerical algorithm is used in order to catch these special solutions and to deal with the relevant unstable equilibrium states. Numerical examples of smooth weak deflagrations or detonations are shown.     

Steady motion of a rotating stratified fluid bounded by porous disks

The motion of a stratified fluid between two parallel infinite porous disks rotating about a vertical axis with slightly different angular velocities has been investigated. The closed form solutions are presented either when the temperature of the disks are prescribed or when the heat flow from the upper to the lower disk is prescribed. The effects of porosity on the flow field have been discussed.     

Steady Magnetogasdynamic Flow Past a Source

This paper presents an asymptotic solution for the disturbanceat large distance from a source placed in a flow of conductingcompressible fluid in the presence of an applied magnetic field.The solution is obtained by a Fourier transform method usingtechniques developed for magnetohydrodynamic waves by Lighthill(1960). The results are discussed in detail for the cases ofthe undisturbed flow aligned with and perpendicular to the field,although they apply for any angle between the two, and showa Mach cone type of disturbance together with Alfvénwaves.     

Steady state stresses induced in a transversely isotropic elastic solid by a moving dislocation

An unbounded, transversely isotropic, elastic solid, is subjected to a dislocation moving at constant speed. By means of an appropriate coordinate transformation, the transient version of this problem is used to obtain the steady state solution. The solution for the plane stress field is explicit and valid for dislocation speeds which are sub-, tran-, or super-sonic with respect to the material wave speeds. The previously discovered transonic speed at which the Mach head wave was annihilated for the transient problem, is found to be present in the steady state problem also.     

Steady flow in a deformable porous medium

A nonlinear model for a steady flow in a deformable porous medium is considered. The flow is governed by the poroelasticity system consisting of an elasticity equation for the displacement of the porous medium and Darcy's equation for the pressure in the fluid. This poroelasticity system is nonlinear when the permeability in Darcy's equation is assumed to depend on the dilatation of the porous medium. Existence and uniqueness of a weak solution of this poroelasticity system is established under rather weak assumptions on the regularity of the data. Convergence of a finite element approximation is proved and verified through numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.     

Steady compressible Navier-Stokes flow in a square

We investigate a steady flow of compressible fluid with inflow boundary condition on the density and slip boundary conditions on the velocity in a square domain Q∈R². We show existence if a solution that is a small perturbation of a constant flow (, ). We also show that this solution is unique in a class of small perturbations of the constant flow . In order to show the existence of the solution we adapt the techniques known from the theory of weak solutions. We apply the method of elliptic regularization and a fixed point argument.     

Steady state oscillations in a buoyant fluid

In this article we consider small steady forced oscillations induced by immersed bodies moving at frequencies above the buoyancy frequency in stratified fluids. The model we treat takes the buoyancy frequency and the density to be constant, and consequently the governing differential equation is the same as for small steady oscillations in a uniformly rotating fluid.Our treatment of this problem has several aspects. The first is the formulation and transformation of the problem for quite arbitrary bodies and general boundary motions. The second is the solution of a number of simple problems in two and three dimensions. The solutions are given explicitly and in some detail and their limiting behavior for high frequency and at the buoyancy frequency is derived. This leads to some new observations and to a conjecture about the velocity field at the buoyancy frequency. We also give sequences of graphs of streamlines of some of the examples. These show in a striking way the changes in the flow field as the frequency varies.

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Zusammenfassung In der vorliegenden Arbeit behandeln wir kleine Schwingungen, die durch bewegte Körper in geschichteten Flüssigkeiten erzwungen werden. Die Schwingungsfrequenzen liegen oberhalb der Auftriebsfrequenz. In unserem Modell werden Auftriebsfrequenz und Dichte als konstant vorausgesetzt. Somit wird die massgebliche Differentialgleichung hier identisch mit derjenigen für kleine Schwingungen in einer gleichförmig rotierenden Flüssigkeit.Wir betrachten das Problem unter verschiedenen Gesichtspunkten: Zunächst wird das Problem für willkürlich gestaltete Körper und allgemeine Randbedingungen bezüglich der Bewegungen formuliert, Sodann werden explizite Lösungen für eine Reihe von einfachen zwei- und dreidimensionalen Problemen in Einzelheiten angegeben. Ihr Grenzverhalten bei hohen Frequenzen und für die Auftriebsfrequenz wird abgeleitet. Dies führt zu einigen neuen Beobachtungen und Vermutungen über das Geschwindigkeitsfeld für die Auftriebsfrequenz. In einigen Fällen fügen wir eine Folge graphischer Darstellungen der Stromlinien bei. Diese zeigen sehr eindrucksvoll, wie sich das Strömungsfeld mit der Frequenz ändert.

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This work supported by the Department of the Navy, Naval Sea Systems Command under Contract No. N00017-72-4401.     

Positive Steady States of a Competitor- Competitor-Mutualist Model

In this paper we deal with the positive steady states of a Competitor-Competitor-Mutualist modelwith diffusion and homogeneous Dirichlet boundary conditions.We first give the necessary conditions,and thenestablish the sufficient conditions for the existence of positive steady states.     

Steady vortical flow around a finite plate

An explicit solution for a layer of fluid with constant vorticitysurrounding a thin plate of finite length is obtained usingelementary conformal mapping methods. In the limit of largeplate length the behaviour of the solution near the ends ofthe plate tends to that of the previously known solution fora semi-infinite plate. Contour dynamics is used to investigatethe stability of the steady solutions.     

Steady supersonic flow past a curved cone

This paper studies the steady supersonic flow past a Lipschitz curved cone. Under the assumptions that the cone has an opening angle less than a critical value and has sufficiently small total variation of the tangent of the perturbation and that the Mach number of incoming flow is sufficiently large, the global weak solution is constructed via Glimm scheme for 1<γ<3.     

Steady supersonic flow over a bending wall

This paper studies the steady supersonic flow moving over a bending wall that is the small perturbation of a convex one. Under the assumption that the total variation of the tangent of the perturbation is sufficiently small, the global weak solution is constructed via wave-front tracking scheme.     

Steady flow generated by the differential rotation of a porous disk of finite thickness

When a body of fluid bounded by a porous disk of finite thickness is disturbed from a state of rigid rotation by an enhanced (or reduced) angular velocity of the disk, a few authors followed Darcys model and observed that the centrifugal pumping occurs through the entire porous layer regarded as a convection zone. The shear stress can develop only at the edge of the porous layer. We use a porous disk of high permeability that allows the fluid in the porous disk to deform in response to the changing angular velocity. Based on the Birkmans model, we solve for the steady non-linear flow and observe that there arises (i) a convection zone of nearly uniform angular velocity at the boundary (within the porous layer) and (ii) a transition zone adjacent to the convection zone which provides a smooth transition to the interior. This makes the model relevant to some astrophysical situations as described by some authors [1, 3]. The two point boundary value problem is solved subject to the boundary conditions, the far field conditions, and the matching conditions at the fluid-porous medium interface. The solution is obtained using a numerical procedure known as the method of Adjoints.Received: June 13, 2002; revised: July 7, 2003     

Steady flow generated by the differential rotation of a porous disk of finite thickness

When a body of fluid bounded by a porous disk of finite thickness is disturbed from a state of rigid rotation by an enhanced (or reduced) angular velocity of the disk, a few authors followed Darcys model and observed that the centrifugal pumping occurs through the entire porous layer regarded as a convection zone. The shear stress can develop only at the edge of the porous layer. We use a porous disk of high permeability that allows the fluid in the porous disk to deform in response to the changing angular velocity. Based on the Birkmans model, we solve for the steady non-linear flow and observe that there arises (i) a convection zone of nearly uniform angular velocity at the boundary (within the porous layer) and (ii) a transition zone adjacent to the convection zone which provides a smooth transition to the interior. This makes the model relevant to some astrophysical situations as described by some authors [1, 3]. The two point boundary value problem is solved subject to the boundary conditions, the far field conditions, and the matching conditions at the fluid-porous medium interface. The solution is obtained using a numerical procedure known as the method of Adjoints.     

Steady vortex patches near a nontrivial irrotational flow

In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function q corresponding to a nontrivial irrotational flow, there exists a family of steady vortex patches approaching the set of extreme points of q on the boundary of the domain. Furthermore, we show that each finite collection of strict extreme points of q corresponds to a family of steady multiple vortex patches approaching it.     

Steady two-dimensional flow past a normal flat plate

A vorticity/stream function formulation is used to obtain a numerical simulation of steady two-dimensional flow of a viscous incompressible fluid past a normal flat plate for a range of Reynolds numbers. A method of Fornberg [J. Fluid Mech. 98, 819 (1980)] is used to determine upstream and downstream boundary conditions on the stream function. Special care is taken in the neighbourhood of the singularities in vorticity at the plate edges and this is very important because any errors introduced are swept downstream and severely affect such quantities as the length and width of the attached eddies. The computed results are compared with those of a laboratory experiment in which a plane strip is drawn through water and ethylene glycol for the range of Reynolds numbers for which the experimental flow is stable.     

Steady Deep-Water Waves on a Linear Shear Current

The properties of steady, periodic, deep-water gravity waves on a linear shear current are investigated. Numerical solutions for all waveheights, up to and including the limiting ones, are computed from a formulation which involves only the wave profile (parametrized in a natural way) and some constants of the motion. It is found that for some shear currents the highest waves are not necessarily those waves with sharp crests known as extreme waves. Furthermore a certain nonuniqueness in the sense of a fold is shown to exist, and a new type of limiting wave is discovered. For both small-amplitude waves and extreme waves the numerical results are compared with theoretical predictions.