2.
Diffraction of SH-waves by collinear Griffith cracks in an infinite transversely isotropic medium - Das, S.; Debnath, L.
This paper deals with the diffraction of SH-waves by three collinear Griffith cracks located symmetrically in an infinite transversely isotropic medium. The Fourier transform technique [4] has been used to reduce the elastodynamic problem to the solution of a set of integral equations which are solved by using Hilbert transform technique and Cooke's result. The stress intensity factors at the crack tips has been derived for a low frequency vibration.
3.
Solvability of a nonlinear conjugate eigenvalue problem - Davis, John M.; Henderson, Johnny; Prasad, K. Rajendra; Yin, William K. C.
We consider the nonlinear conjugate eigenvalue problem \begin{eqnarray*}(-1)^{n-k} y^{(n)}(t)&=&\lambda a(t)f(y), \quad 0\leq t\leq ...... 0\leq i\leq k-1,\\y^{(j)}(1)&=&0, \quad 0\leq j\leq n-k-1.\end{eqnarray*} Values of the parameter $\lambda$ are determined for which the problem above has a positive solution. The methods used here extend recent works by allowing for a broader class of functions for $a(t)$ . Optimal eigenvalue intervals are given for some relevant examples.
4.
Lie algebras and the doubling in thermo field dynamics - de Montigny, M.; Khanna, F. C.; Santana, A. E.
The structure of thermo field dynamics (TFD) is based on an algebraic doubling. This gives rise to the standard representation of C*-algebras, and here we use its Hilbert space as the representation space of Lie algebras. From the group-theoretical point of view, our construction amounts to a simple application of the semi-direct product. In particular, we study these representations for su(2) symmetry. Our main results include the construction of new representations of the Duffin-Kemmer-Petiau (DKP) algebra, in particular, a four-dimensional representation for spin 0 particles in 2 + 1 space-time. We establish a connection among the doublings that appear in...
5.
Is two-dimensional oblique stagnation-point flow unique? - Dorrepaal, J. M.
The problem of two-dimensional oblique stagnation-point flow is reviewed and the two solutions which exist in the literature are reconciled. It is found that a family of solutions exists for the problem, but that a unique solution can be obtained by examining the second order terms in the asymptotic expansions at infinity. The slope-ratio constant is verified to be independent of the incidence angle of the impinging stream. A second ratio involving the locations of maximum pressure along the wall and vanishing tangential stress is shown to share the same incident angle independence.
6.
On a mixed finite element method for the p-Laplacian - Farhloul, Mohamed; Manouzi, Hassan
In this article we propose a mixed method for the p-Laplacian problem. We improve the result obtained in [6] by showing that the error estimates obtained, for a mixed finite element method, are valid in three dimensions without restrictions. The key of this improvement is the use of a more appropriate functional setting. This allows also to improve the previously known error estimates.
7.
Stability analysis for a class of diffusive coupled systems with applications to population biology - Gong, Ruey-Tarng; Hsu, Sze-Bi
In this paper we derive criteria for the local stability of synchronized equilibria or limit cycles for a class of lattice dynamical systems. We first prove a theorem of linear algebra then the criteria are obtained by the application of the theorem. The criteria reduce the stability of a large size problem or equivalently large matrix size eigenvalue problem to a small one. Several examples in population biology are presented to illustrate the usefulness of the criteria.
8.
Asymptotic behavior of the perturbation of the primitive equations of the ocean with vertical viscosity - Belmiloudi, Aziz
In this paper we consider an oceanic domain included in ${\bf R}^3$ in which there exist, at initial time, a current $U_0$ , a pressure $p_0$ and a density $\rho_0$ . The perturbation $U$ , $p$ and $\rho$ of the velocity, the pressure and the density are induced by a perturbation of the mean wind-stress. The equations are of Navier-Stokes type for the velocity and pressure, of transport-diffusion type for the density. They are modified by the physical assumptions including the Boussinesq approximation and the hydrostatic approximation with vertical viscosity. The existence of the solution for the variational problem is...
9.
Asymptotic behavior of a predator-prey system with delays - El-Owaidy, H. M.; Ismail, M.
In this paper the asymptotic behavior of solutions of a predator-prey system is determined. The model assumes that the prey disperses between three patches of a heterogeneous environment with barriers between patches and that the predator disperses between the patches with no barrier. Conditions are established for the permanence of the populations and the global attractivity of a positive equilibrium.
10.
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...
11.
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...
12.
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.
13.
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.
14.
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...
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.
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,...
17.
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...
18.
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.
19.
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.
20.
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...
1.
