A second moment turbulence closure model of the type used before for flows with density stratification, frame rotation and streamline curvature is augmented to describe MHD flows with small magnetic Reynolds number. I...
The question of whether all species in a multispecies community governed by differential equations can persist for all time is one of the most important in theoretical ecology. Criteria for this property vary widely, ...
The question of whether all species in a multispecies community governed by differential equations can persist for all time is one of the most important in theoretical ecology. Criteria for this property vary widely, asymptotic stability and global asymptotic stability being 2 of the conditions most widely used. Neither of these criteria appears to reflect intuitive concepts of persistence in a satisfactory manner: the 1st because it is only a local condition, the 2nd because it rules out cyclic behavior. A more realistic criterion is that of permanent coexistence, which essentially requires that there should be a region separated from the boundary (corresponding to a zero value of the population of at least 1 sp.) which all orbits enter and remain within. A mathematical technique for establishing permanent coexistence is illustrated by an application to the long-standing problem of predator-mediated coexistence in a 2-prey 1-predator community.
Predator mediated coexistence of 2 competing species with general frequency dependent switching in the predator is examined. The stability criterion used is permanent coexistence. This is a global criterion which ensu...
Predator mediated coexistence of 2 competing species with general frequency dependent switching in the predator is examined. The stability criterion used is permanent coexistence. This is a global criterion which ensures that eventually the species end up in a region M of phase space separated from the boundary (corresponding to extinction of at least one of the species), but which places no restriction on the behavior in M, and so allows, for example, the existence of a stable limit cycle. The principal determinant of survival turns out to be the strength of the switching when 1 prey is rare, the form of the switching elsewhere being irrelevant. Strong switching is a powerful influence for coexistence. In contrast with the conclusion of previous investigations, the influence of switching is complex, and under some circumstances weak switching can actually destroy coexistence in a system which without switching leads to survival of all species.
An FFT method for solving the discrete Poisson equation on a rectangle using a regular hexagonal grid is described and the results obtained for a model Dirichlet problem are compared with those obtained on a rectangul...
An FFT method for solving the discrete Poisson equation on a rectangle using a regular hexagonal grid is described and the results obtained for a model Dirichlet problem are compared with those obtained on a rectangular grid. For a given grid size the results demonstrate that the hexagonal method is more accurate, but rather less efficient, than the usual 5-point method, whereas for comparable accuracy to be achieved by both methods, the hexagonal method was found to be approximately 20 to 30 times faster than the 5-point method for the model problem.
An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is prove...
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An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.
This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. N...
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This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency.
A viscous incompressible fluid occupying the space theta < pi/2 and bounded by the wall theta=pi/2 of a spherical polar coordinate system (r,theta,phi), is stirred by a line vortex along the line theta=0 which is s...
A viscous incompressible fluid occupying the space theta < pi/2 and bounded by the wall theta=pi/2 of a spherical polar coordinate system (r,theta,phi), is stirred by a line vortex along the line theta=0 which is switched on at time t=0. The line vortex is perpendicular to the wall. The development of the flow configuration is considered for the case where the poloidal flow is weak and does not affect the structure of the inducing azimuthal flow. The problem is formulated in terms of the similarity variable r/2(nut)1/2 and the polar angle theta, where nu is the kinematic viscosity of the fluid. An analytical solution is constructed for the azimuthal flow. At any given station r the steady azimuthal velocity field is, practically, reached within time r2/nu. The equations governing the poloidal flow are coupled partial differential equations of mixed elliptic-parabolic type which are transformed to equations that are elliptic throughout the solution domain. These equations are solved numerically using the methods of successive overrelaxation and fast Fourier transform. The results show that the poloidal flow in a meridional plane at time t forms closed loops about the point r almost-equal-to 1.58(nut)1/2, theta=pi/4, where the velocity has only an azimuthal component. The case of a diffusing configuration from the steady state, due to switching off at t=0 of the agent generating the flow, is also considered. For this case the poloidal field consists of open streamlines and at t=2r2/nu its intensity is a very small fraction of that associated with the steady state.
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