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.
In the present paper, we investigate the instability, adiabaticity, and controlling effects of external fields for a dark state in a homonuclear atom-tetramer conversion that is implemented by a generalized stimulated...
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In the present paper, we investigate the instability, adiabaticity, and controlling effects of external fields for a dark state in a homonuclear atom-tetramer conversion that is implemented by a generalized stimulated Raman adiabatic passage. We analytically obtain the regions for the appearance of dynamical instability and study the adiabatic evolution by a newly defined adiabatic fidelity. Moreover, the effects of the external field parameters and the spontaneous emissions on the conversion efficiency are also investigated.
India's primary source of income is agriculture. Farmers in India have differing perspectives on how to integrate technology into their farming operations. However, farmers lack the knowledge necessary to put tech...
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In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and tran...
In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and transport solutions and formulate novel coupled constraint cell problems to capture the multiscale property, where oversampled regions are utilized to avoid boundary effects. Assuming the smoothness of macroscopic variables, we obtain a multicontinuum system composed of macroscopic elliptic equations and convection–diffusion–reaction equations with homogenized effective properties. Finally, we present numerical results for various coefficient fields and boundary conditions to validate our proposed algorithm.
An iterative scheme is proposed for numerically solving the integro-differential equations arising in geomagnetic induction problems. The method is tested successfully on two simple models, both involving an infinite ...
An iterative scheme is proposed for numerically solving the integro-differential equations arising in geomagnetic induction problems. The method is tested successfully on two simple models, both involving an infinite strip. The results indicate that for induction problems generally, the iterations should converge rapidly. It is believed that the method will have applications in other fields of interest.
It is pointed out that in the point-ion formulation of the modified Poisson–Boltzmann equation the pair distribution function has a power decay parallel to the surface. The relationship of the modified Poisson–Boltz...
It is pointed out that in the point-ion formulation of the modified Poisson–Boltzmann equation the pair distribution function has a power decay parallel to the surface. The relationship of the modified Poisson–Boltzmann results to recent cluster-analysis work on the structure of the surface of an electrolyte solution is also mentioned.
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