In presence of the spherically confined three-dimensional potentials with impenetrable boundaries, the generalized pseudospectral method is shown to provide accurate eigenvalues, eigenfunctions, and radial expectation...
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In presence of the spherically confined three-dimensional potentials with impenetrable boundaries, the generalized pseudospectral method is shown to provide accurate eigenvalues, eigenfunctions, and radial expectation values for (a) the isotropic harmonic oscillator, (b) the H atom and (c) the Davidson oscillator. Several novel degeneracy conditions are obtained for (a) when the radius of confinement is suitably chosen at the radial nodes corresponding to the free states. (c) 2006 Elsevier B.V. All rights reserved.
A method is presented for the prediction of transonic flutter by the Euler equations on a stationary Cartesian mesh. Local grid refinement is established through a series of embedded meshes, and a gridless method is i...
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A method is presented for the prediction of transonic flutter by the Euler equations on a stationary Cartesian mesh. Local grid refinement is established through a series of embedded meshes, and a gridless method is implemented for the treatment of surface boundary conditions. For steady flows, the gridless method applies surface boundary conditions using a weighted average of the flow properties within a cloud of nodes in the vicinity of the surface. The weighting is established with shape functions derived using a least-squares fitting of the surrounding nodal cloud. For unsteady calculations, a perturbation of the shape functions is incorporated to account for a fluctuating surface normal direction. The nature of the method provides for efficient and accurate solution of transient flow problems in which surface deflections are small (i.e. flutter calculations) without the need for a deforming mesh. Although small deviations in angle of attack are considered, the mean angle of attack can be large. Results indicate good agreement with available experimental data for unsteady flow, and with computational results addressing flutter of the Isogai wing model obtained using traditional moving mesh algorithms. (c) 2005 Elsevier Ltd. All rights reserved.
The present paper gives a comparative analysis of spectral properties of two hyperbolic systems in a bounded plane domain. The basis property of systems of eigenelements is widely used in the construction of explicit ...
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The present paper gives a comparative analysis of spectral properties of two hyperbolic systems in a bounded plane domain. The basis property of systems of eigenelements is widely used in the construction of explicit solutions of boundaryvalueproblems in the form of biorthogonal series in the corresponding systems; thus special attention is paid in our investigations to this problem of spectral theory. The main results of the present paper are the following: (1.) the study of the spectrum structure and (2.) the analysis of properties of vector eigenfunctions: completeness, minimality, basis property, and conditional basis property. It is noteworthy that the systems of equations that we study have different spectral characteristics. [ABSTRACT FROM AUTHOR]
Nonlinear systems of differential equations with a degenerate matrixmultiplying the derivativeswere considered by Boyarintsev, Chistyakov, Danilov, Loginov, Yakovets,and others. They usuallyassumed that the “rank-deg...
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Nonlinear systems of differential equations with a degenerate matrixmultiplying the derivativeswere considered by Boyarintsev, Chistyakov, Danilov, Loginov, Yakovets,and others. They usuallyassumed that the “rank-degree” criterion is satisfied. It is in this casethat existence and uniqueness theorems for the Cauchy problem were proved and efficient numericalintegration algorithms were developed for such systems [1, pp. 159–177]. Asymptotic formulas forthe solution of the Cauchy problem for a singularly perturbed system of differential equationssatisfying the “rank–degree” criterion are given in [2]. In the present paper, we prove a theoremon the existence of a periodic solution of a nonlinear singularly perturbed system of differentialequations with an identically degeneratematrix multiplying the derivatives and give an algorithm forconstructing the asymptotic expansion of this solution. Note that the results of the present papergeneralize the well-known studies [3–5] of periodic solutions of linear singularly perturbedsystems with an identically degenerate matrix multiplying the derivatives.
Conditions for the n-fold completeness of the system of root functions(eigenfunctions and associated functions) of the pencil (1), (2) in L_2(0, 1) (see [1, p. 10~2; 2])were obtained in [3]. In the lack of n-fold comp...
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Conditions for the n-fold completeness of the system of root functions(eigenfunctions and associated functions) of the pencil (1), (2) in L_2(0, 1) (see [1, p. 10~2; 2])were obtained in [3]. In the lack of n-fold completeness, the problem on conditions for the k-foldcompleteness (0 < k < n) of the system of root functions arises.
The completeness of the system of eigenfunctions corresponding to a problemwith a spectral parameter in the boundary condition was analyzed in the space Lp(0, 1), p > 1, in[1]. In the present paper, we prove the ba...
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The completeness of the system of eigenfunctions corresponding to a problemwith a spectral parameter in the boundary condition was analyzed in the space Lp(0, 1), p > 1, in[1]. In the present paper, we prove the basis property of this system in the space Lp(0, 1), p > 1.
Let y = -y" + a(x)y be a linear differential expression, where x ∈ [0, 1]and a(x) is a continuous function on [0, 1], and let L1y and L2y be boundary forms. The differentialexpression and the boundary forms gene...
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Let y = -y" + a(x)y be a linear differential expression, where x ∈ [0, 1]and a(x) is a continuous function on [0, 1], and let L1y and L2y be boundary forms. The differentialexpression and the boundary forms generate a differential operator L with domain D in some functionspace E. We are interested in the behavior of the eigenvalues and eigenfunctions of thisdifferential operator. This problem has been quite comprehensively studied in the case of regularboundary conditions Liy = 0 (i = 1, 2) (see [1, 2] and the bibliography therein). The case ofirregular boundaryconditions, in particular, nonlocal conditions (where the forms Li, i = 1, 2,contain some integrals of the function y), was considered by various authors (e.g., see [3–6]).They analyzed spectral properties of the corresponding operator (spectrality, eigenfunctions, andthe adjoint problem,mainly, in the space L2); however, as a rule, the boundary forms contained thevalues of y(x) and its derivative at the endpoints of the interval.
The long-time asymptotics are analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that...
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The long-time asymptotics are analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that each finite energy solution converges as t -> +/-infinity to the set of 'nonlinear eigenfunctions' psi(x)e(-iwt).
The study of spectral problems for some differential operators necessitatesthe analysis of basic properties (completeness, minimality, basis property, etc.) of exponentialsystems with degenerate coefficients of the fo...
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The study of spectral problems for some differential operators necessitatesthe analysis of basic properties (completeness, minimality, basis property, etc.) of exponentialsystems with degenerate coefficients of the form {A~+(t)ω~+(t)e~(int); A~-(t)ω~-(t)e~(-ikt)}_n≥0,k≥1.
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