Mostrando recursos 1 - 20 de 29

  1. Sequential eigenfunction expansion for certain nonlinear Hammerstein equations

    Tam, K. K.; Andonowati; Kiang, M. T.

  2. Angular layer of a singularly perturbed parabolic problem with corner singularity

    Shih, Shagi-Di
    For a linear singularly perturbed time-dependent convection diffusion problem, the solution possesses angular layer behavior if the input data don't satisfy certain compatibility conditions at the inflow corner. Its angular layer structure is investigated by virtue of a method of matched asymptotic expansions. The magnitudes of the jump discontinuities of the outer solution and its first two derivatives are derived and are then used to construct an angular layer function, which is solved in terms of the first iterated integral of the complementary error function. The asymptotic approximation obtained is shown to be uniformly valid with the first order accuracy...

  3. Dynamics of bottom trapped currents with application to the Strait of Georgia

    Reszka, Mateusz K.; Swaters, Gordon E.
    We present a numerical study of bottom-trapped, density-driven flows using a frontal geostrophic model in which the ambient ocean is continuously stratified. The model focuses on the release of gravitational potential energy associated with the descent of a gravity current down an incline in a rotating reference frame. In the resulting system, the overlying fluid is stratified and quasigeostrophic, while the deep current is homogeneous and the interface is allowed to intersect the oceanic bottom. We show that such currents preferentially develop plumes on the downslope side, which rapidly roll up into more coherent features. In response to deformations of...

  4. Two-prey one-predator system with discrete delay

    Kumar, Ravinder
    A Lotka-Volterra model of two competing preys and a predator with discrete time delay due to gestation is considered when it possesses a positive interior equilibrium. Sufficient conditions for its global stability are derived. It is shown that whenever equilibrium in the competition plane is bistable, interior equilibrium for the system cannot be globally stable for at least small and large values of time delay. Further, in this case, persistence cannot occur at least for small values of time delay. A criterion for Hopf bifurcation to occur is given. Conditions for no change in the local stability of the interior...

  5. Mathematical models of predator mutualists

    Freedman, H. I.; Kumar, R.; Easton, A. K.; Singh, M.
    Systems of differential equations are proposed as models of predator mutualists which cooperate in hunting for prey. In the case that the mutualism is facultative on at least one of the predators, it is shown that both predators may persist on only one prey population. In the case of obligate mutualism, it is shown that if the mutualism is sufficiently strong, then a reversal of outcome is possible in the sense that there may exist a positive stable invariant set.

  6. Stability analysis of a Volterra predator-prey system with two delays

    Tang, Yanbin; Beretta, Edoardo; Solimano, Fortunata
    The objective of this paper is to systematically study the qualitative properties of a predator-prey system with two delays. First, we investigate the effect of two distinct delays on stability of the unique positive equilibrium by analyzing the corresponding characteristic equation. The stability criteria involving the delays and the parameters are given. Second, we prove a permanence result for the system. Third, we describe the global stability of the positive equilibrium while the sum of two delays is small, via constructing a proper Liapunov functional in a restricted region. Finally, we give an example to show the application of our...

  7. A discrete valuation of swing options

    Lari-Lavassani, Ali; Simchi, Mohamadreza; Ware, Antony
    A discrete forest methodology is developed for swing options as a dynamically coupled system of European options. Numerical implementations are fully developed for one- and two-factor, mean-reverting, underlying processes, with application to energy markets. Convergence is established via finite-difference methods. Qualitative properties and sensitivity analysis are considered.

  8. Spectral decomposition for partial neutral functional differential equations

    Adimy, Mostafa; Ezzinbi, Khalil; Laklach, Mostafa
    A class of partial neutral functional differential equations with a non dense domain is considered. In the first part the spectral decomposition of a state space into stable, unstable and center subspaces is obtained. In the second part a variation-of-constants formula for the perturbed linear equation is given. In the third part, the existence of bounded solutions is investigated. As a consequence in the hyperbolic case, the existence of periodic (or almost periodic) solutions is established. This work extends our previous results on partial functional differential equations with non dense domain [4] and results in [54].

  9. On the finite-amplitude development of near-singular modes of the Bickley jet

    Swaters, Gordon E.
    The linear stability spectrum of the Bickley jet has neutral modes which have a phase velocity equal to the maximum jet velocity. Previous numerical simulations initialized with a monochromatic near-singular mode with a nonzero phase shift across the critical levels have shown that there is a slow time oscillation in the transverse transport of perturbation energy in which the energy flux goes from one critical level to the other and then reverses and so on, all the while satisfying no net energy transfer from the mean flow to the perturbation field. Weakly nonlinear asymptotics suggests that higher harmonics are generated...

  10. Modeling equator-crossing currents on the ocean bottom

    Choboter, Paul F.; Swaters, Gordon E.
    Observations unambiguously show that deep ocean currents carry a significant amount of fluid across the equator. Away from the equator in either hemisphere, these currents are relatively quiescent so that planetary vorticity dominates relative vorticity within the fluid. Thus, the potential vorticity of cross-equatorial flow changes sign en route. The breakdown of geostrophic balance at the equator because of the vanishing horizontal component of the Coriolis force and the fact that potential vorticity is not conserved in these flows constitute formidable challenges to modeling these cross-equatorial currents. Recent research points to friction as being crucial to the crossing process since...

  11. On the effects of environmental fluctuations in a simple model of bacteria-bacteriophage infection

    Beretta, E.; Carletti, M.; Solimano, F.
    In this paper we discuss the outcomes of a Campbell-like model for phage-bacteria interaction ion in an open-marine environment. We consider both the deterministic and stochastic settings. In the former, the mathematical properties of the model are studied in detail, providing a new stability switch criterion for the endemic equilibrium $E_+$ . In the latter, we allow environmental fluctuations to affect the main parameters involved in the model and measure the intensities of such fluctuations by means of Fourier transform methods. Extensive computer simulations finally support our analytical results.

  12. The canonical product of the solution of the Sturm-Liouville equation in one turning point case

    Akbarfam, A. Jodayree; Mingarelli, A.
    The present paper is concerned with the function theoretic property of solutions of the equation \begin{displaymath}y^{\prime\prime}+(\lambda t-q(t))y=0,\quad -1\le t\le 1.\end{displaymath} Using the asymptotic solution as well as the distribution of positive and negative eigenvalues, we derive the canonical product of a particular solution of the Sturm-Liouville in one turning-point case.

  13. Interpretation of the stability and instability of the solitary waves governed by a forced Korteweg-de Vries equation

    Shen, Samuel S.; Moodie, T. Bryant; Shen, Bin
    In view of the maximum height of a solitary shallow-water wave in a channel, this paper provides an interpretation of the stability and instability of the solitary waves governed by a forced Korteweg-de Vries equation. The interpretation implies Malomed's conjecture: of the two cusped solitary waves of a locally forced Korteweg-de Vries equation, the lower one is stable. Numerical simulations show that the higher solitary wave degenerates into the lower, stable solitary wave and radiates a soliton upstream and wake down stream. This is a KdV soliton and is not a stable water-surface profile because its amplitude is higher than...

  14. Analysis of a two-stage population model with space limitations and state-dependent delay

    Rai, Sanjay; Robertson, Robert L.
    Bence and Nisbet introduced a system of nonlinear functional differential equations with constant delay to describe the growth of a population with space limitations. In their work, the population was divided into two groups: the juveniles and the adults. They included a local stability analysis of the system. Kuang and So gave a thorough mathematical analysis of the system, including results on positivity, boundedness, and stability of solutions. In this paper, a more general situation is considered: a system where the delay is a nonconstant function of total population, and the death rate of adults is nonlinear. Results on positivity,...

  15. A study of two-dimensional aspects of vortex shedding from a bluff body under transverse oscillations

    Kocabiyik, Serpil
    In this paper we describe a detailed study of the near wake structures associated with simulated two-dimensional flow past a circular cylinder that is in simple harmonic cross-flow oscillation. Results are examined for $R=10^3$ and a fixed motion amplitude of nondimensional oscillatory velocity $\alpha=1.5$ . The study concentrates on the forced oscillation frequency to Kármán vortex shedding frequency ratios between 1.25 and 5.0. The object of the study is to examine the effect of increase of forced oscillation frequency on the near-wake structure. Time-periodic states with asymmetric wake structures and the change in phase of vortex shedding is observed with...

  16. The initial flow past a uniformly accelerating inclined elliptic cylinder

    D'Alessio, S. J. D.; Chapman, F. W.
    This paper solves the problem of determining the initial two-dimensional motion of a viscous incompressible fluid past an inclined elliptic cylinder which is uniformly accelerated from rest. This motion is calculated using two types of methods. The first takes the form of a double series solution where an expansion is carried out in powers of the time, $t$ , and in powers of $\lambda=\sqrt{8t/R}$ where $R$ is the Reynolds number. This approximate analytical solution is valid for small times following the start of the motion and for large Reynolds numbers. The second method involves a spectral-finite difference procedure for numerically...

  17. Two-dimensional flow through an annular junction

    Chen, O. X.
    Bifurcating Stokes flow between two coaxial cylinders is studied. The flow is two-dimensional and is due to one line source and two line sinks on the outer boundary. It is found that separation of the streamlines can occur on the outer boundary only if there is sufficient asymmetry, either in the placement of the line sinks or their relative strengths.

  18. Global stability of cellular populations with unequal division

    Pujo-Menjouet, Laurent; Rudnicki, Ryszard
    A two-phase model for the growth of a single cellular population is presented. In this model the reproduction occurs by fission into two unequal parts. The evolution of the population is described by a nonlinear partial differential equation with time delay and integral term containing maturity variable. We give conditions for global stability of the solutions of this equation.

  19. An analysis of a Stokes flow in an annular region

    Hackborn, W. W.
    A study is made of the steady two-dimensional Stokes flow stirred by an infinitesimal rotating cylinder (a line rotlet) in the annular region between two fixed concentric cylindrical walls. It is shown that this simple flow exhibits a rich diversity of possible flow structures. Generally, one component of the flow is associated with a net flux through the annular region in either a clockwise or anticlockwise direction depending on whether the radial distance between the rotlet and the center axis of the bounding cylinders is greater or less than a unique value at which this flow component vanishes. The remaining...

  20. Modified linearized Burger's flow for two-dimensional viscous motion

    Fahimi, Rahmatullah
    In this expository paper we use a complex version of the two-dimensional steady flow Navier-Stokes equations, originally due to Legendre and develop a new linearization which is similar, but different from Burger's flow. A similarity solution is found where the stream function for the potential flow is a linear combination of the linear shear flow and stagnation-point flow in two dimensions. Such a similarity solution describes a flow impinging on a plane wall at an arbitrary angle of incidence and reduces the problem to a system of two ordinary differential equations which can be integrated numerically. The technique is similar...

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