We study the so called Cantor-like potential, probably one of the closest potential we can imagine as selfsimilar. The numerical calculation was carried out for the effective mass equation miming a GaAs-AlGaAs heteros...
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(纸本)9781934142080
We study the so called Cantor-like potential, probably one of the closest potential we can imagine as selfsimilar. The numerical calculation was carried out for the effective mass equation miming a GaAs-AlGaAs heterostructure made by following a Cantor algorithm. We show that the first eigenfunctions exhibit in a great extend a selfsimilar aspect. Another main result is that a fractal dimension is found for the spectrum. This can be seen as a demonstration that this kind of potentials have this peculiarity. It is reasonable to think that other similar potential show this property.
The analytical solution of excitation of the plane waveguide with perfectly conductive walls which coincide with the coordinate plane is well-known. In the case of lossy walls the problem can be reduced to transcenden...
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A numerical method using finite elements for the solution of the eigenvalues and eigenfunctions in non-uniform, non-axial ducted flows is described. The method is validated against results from the literature for swir...
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The eigenvalues and eigenfunctions for clusters with planar, cylindrical, and spherical geometry with arbitrary potential energy profiles were calculated by means of an implemented algorithm. The results of numerical ...
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The eigenvalues and eigenfunctions for clusters with planar, cylindrical, and spherical geometry with arbitrary potential energy profiles were calculated by means of an implemented algorithm. The results of numerical and analytical solutions for clusters of various geometry were compared. The proposed algorithm for determination of cluster eigenvalues and eigenfunctions shows a power law rate of convergence of the solution towards the target eigenfunction coinciding with the rate of convergence in the modified Wielandt method. This algorithm was used to calculate the geometrical potential of giant fullerene as a function of radius for the state with The numerical results are in good agreement with the theoretical results.
It is well known that the nonlinear PDE describing the dynamics of a hydrodynamically unstable planar flame front admits exact pole solutions as equilibrium states. Such a solution corresponds to a steadily propagatin...
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It is well known that the nonlinear PDE describing the dynamics of a hydrodynamically unstable planar flame front admits exact pole solutions as equilibrium states. Such a solution corresponds to a steadily propagating cusp-like structure commonly observed in experiments. In this work we investigate the linear stability of these equilibrium states-the steady coalescent pole solutions. In previous similar studies, either a truncated linear system was numerically solved for the eigenvalues or the initial value problem for the linearized PDE was numerically integrated in order to examine the evolution of initially small disturbances in time. In contrast, our results are based on the exact analytical expressions for the eigenvalues and corresponding eigenfunctions. In this paper we derive the expressions for the eigenvalues and eigenfunctions. Their properties and the implication on the stability of pole solutions is discussed in a paper which will appear later.
Vibrational eigenvalues with estimated errors <5x10(-2) cm(-1) and their corresponding cm eigenfunctions for J=0 5D (planar) acetylene modeled by the Halonen-Child-Carter potential-energy surface are obtained using...
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Vibrational eigenvalues with estimated errors <5x10(-2) cm(-1) and their corresponding cm eigenfunctions for J=0 5D (planar) acetylene modeled by the Halonen-Child-Carter potential-energy surface are obtained using an energy-shifted, imaginary-time Lanczos propagation of symmetry-adapted wave packets. A lower resolution (similar to 4 cm(-1)) vibrational eigenspectrum of the system is also calculated by the Fourier transform of the autocorrelation of an appropriate wave packet. The eigenvalues from both approaches are in excellent agreement. The wave function of the molecule is represented in a direct-product discrete variable representation (DVR) with nearly 300 000 grid points. Our results are compared with the previously reported theoretical and experimental values. We use our 69 computed eigenstates as a basis to perform an optimal control simulation of selective two-photon excitation of the symmetric CH-stretch made with an infrared, linearly polarized, transform-limited, and subpicosecond-picosecond laser guise. The resulting optimal laser pulses, which are then tested on the full DVR grid, fall within the capabilities of current powerful, subpicosecond, and tunable light sources. (C) 1997 American Institute of Physics.
We develop the compound matrix method and the Chebyshev tau method to be applicable to linear and nonlinear stability problems for convection in porous media, in a natural way. It is shown how to obtain highly accurat...
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We develop the compound matrix method and the Chebyshev tau method to be applicable to linear and nonlinear stability problems for convection in porous media, in a natural way. It is shown how to obtain highly accurate answers to problems which may be stiff, and spurious eigenvalues are avoided. A detailed analysis is provided for a porous convection problem of much current interest, namely convection with a horizontally varying temperature gradient. (C) 1996 Academic Press, Inc.
We consider the eigenvalue problem with Robin boundary condition Delta u + lambda u = 0 in Omega, partial derivative u/partial derivative u + alpha u = 0 on partial derivative Omega, where Omega subset of R-n, n >=...
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We consider the eigenvalue problem with Robin boundary condition Delta u + lambda u = 0 in Omega, partial derivative u/partial derivative u + alpha u = 0 on partial derivative Omega, where Omega subset of R-n, n >= 2 is a bounded domain with a smooth boundary, nu is the outward unit normal, alpha is a real parameter. We obtain two terms of the asymptotic expansion of simple eigenvalues of this problem for alpha -> +infinity. We also prove an estimate to the difference between Robin and Dirichlet eigenfunctions.
Recently a new transform method, called the Unified Transform or the Fokas method, for solving boundary value problems (BVPs) for linear and integrable nonlinear partial differential equations (PDEs) has received a lo...
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Recently a new transform method, called the Unified Transform or the Fokas method, for solving boundary value problems (BVPs) for linear and integrable nonlinear partial differential equations (PDEs) has received a lot of attention. For linear elliptic PDEs, this method yields two equations, known as the global relations, coupling the Dirichlet and Neumann boundary values. These equations can be used in a collocation method to determine the Dirichlet to Neumann map. This involves expanding the unknown functions in terms of a suitable basis, and choosing a set of collocation points at which to evaluate the global relations. Here, using these methods for the Helmholtz and modified Helmholtz equations and following the earlier results of [15], we determine eigenvalues of the Laplacian in a convex polygon. eigenvalues are characterised by the points where the generalised Dirichlet to Neumann map becomes singular. We find that the method yields spectral convergence for eigenfunctions smooth on the boundary and for non-smooth boundary values, the rate of convergence is determined by the rate of convergence of expansions in the chosen Legendre basis. Extensions to the case of oblique derivative boundary conditions and constant coefficient elliptic PDEs are also discussed and demonstrated. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.
In this paper, we consider a model eigenvalue problem with discontinuous coefficients in order to study the convergence of the Fourier methods applied to this problem. We prove that the rate of convergence of the Four...
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In this paper, we consider a model eigenvalue problem with discontinuous coefficients in order to study the convergence of the Fourier methods applied to this problem. We prove that the rate of convergence of the Fourier-Galerkin method is third order for the eigenvalues and order 2.5 for the eigenfunctions. For the Fourier collocation method we obtained only second order accuracy. We also show that the Fourier collocation method can be improved by a preprocessing of the coefficients. The theory is confirmed by numerical results.
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