Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 108 for “"eigenfunctions"”.
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Eigenfunctions in chaotic quantum systems
… In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of …
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Topology of the nodal and critical point sets for eigenfunctions of elliptic operators,
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1971.
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A Multigrid Homotopy Method For Computing Eigenfunctions of Differential Operators With Two-Dimensional Heterogeneity
<p>In this thesis, we develop an accurate algorithm for computing the smallest eigenvalues of the self-adjoint spatial differential operator for the two-dimensional heat equation with a piecewise constant coefficient and periodic boundary conditions. The piecewise constant coefficient is created by …
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Nodal geometry of eigenfunctions on smooth manifolds and hardy-littlewood-sobolev inequalities on the heisenberg group
… Λ. We analyze the asymptotic behavior of eigenfunctions as Λ go to ∞ (i.e., limit of high energy states) in terms of the following aspects.</p> <p>(1) Local and global properties of eigenfunctions, including several crucial estimates for further investigation.</p> <p>(2) Write the nodal …
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A Technique for Solving the Singular Integral Equations of Potential Theory
… function theory are used to identify the eigenfunctions associated with the dominant parts of the onedimensional singular equations. Hilbert spaces spanned by these eigenfunctions are then constructed and an operator theory developed for the general class of integral equations. Numerical …
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The growth of density fluctuations in a finite sized inhomogeneous plasma
… by expanding the density fluctuations in eigenfunctions of the bounded inhomogeneous plasma. A variational technique has been developed to calculate these spatial eigenfunctions. Three separate approximations for the resulting temporal equations have been taken, which show that coupling …
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A dynamical systems approach to the study of local phenomena in fluid flows
… fluid dynamics, prominent examples are Koopman eigenfunctions (through dynamic mode decomposition) and spectral submanifolds. Due to their immense popularity, both of these techniques have been studied extensively, to the point that most aspects regarding their implementation are now fully …
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Intrinsic contractivity for some non-symmetric Lévy processes with non-local operators
… process. We derive sharp estimates for the eigenfunctions of the Feynman- Kac semigroups of these two types of processes and established their intrinsic contractivities. Our methods are mainly probabilistic and depend essentially on the sharp estimates of heat kernels.
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Numerical Treatment of Schrödinger’s Equation for One-Particle and Two-Particle Systems Using Matrix Method
… code is developed to extract the eigenvalues and eigenfunctions with the help of PETSc and SLEPc open-source packages. The eigenvalues represent the energies, and eigenfunctions represent the orbitals of atoms.</p> <p>The test cases include both one-particle and two-particle systems. The …
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Examination of a Semi-Analytic Finite Element for Plate Bending Problems
… A computer program is described in which the eigenfunctions of free vibration of uniform beams are used as the analytic functions. Rectangular plates with any combination of simply supported, clamped or free edges and with any variation of loading or flexural rigidity, including plates with …
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Optical Properties of Type III-V Semiconductor Spherical Quantum Dot Heterostructures
… to simplify the problem, then we obtain the eigenfunctions and eigenenergies of the QD, and use them to model optical transitions. We assume a quasi-equilibrium Fermi-Dirac distribution for electrons and holes and obtain the microscopic transition rates and absorption coefficients. …
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Quantum Resonant Beats and Revivals in the Morse Oscillators and Rotors
<p>Analytical eigenfunctions and eigenvalues for the Morse oscillator were applied to investigate the quantum resonant beats and revivals of wave packet propagation. A concise way for exact prediction of the complete revival period of the Morse oscillator was given for the first time. It was …
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EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS
… harmonic Steklov eigenvalues and associated eigenfunctions. The new space is strictly larger than the standard Sobolev-Hilbert H-space, as it only needs square integrability of the gradients of the functions involved. Our results generalize exactly certain well-known results on Laplace's …
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Nonlinear Solutions to a Two-Layer Quasi-Geostrophic Model of the Gulf Stream
… is expanded in terms of the complete set of the eigenfunctions in the north-south direction and a Fourier series in the east-west direction. Using a certain form of orthogonality of the eigenfunctions, a 6-dimensional dynamical system which solves for the amplitudes of the components is derived. …
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Analysis of passive and active discrete-distributed linear dynamical systems using Green's function methods
… discrete-continuous nature of the operators and eigenfunctions is explicitly addressed.
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On the Cauchy problem for the linearized GPKdV and gauge transformations for a quadratic pencil and AKNS system
… first one, Lax pairs associated with prolonged eigenfunctions and prolonged squared eigenfunctions (prolonged squares) are derived for a Schrödinger equation with a potential depending polynomially on the spectral parameter (of degree N) and its respective hierarchy of nonlinear evolution …
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Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues
… also prove the analogous results concerning the eigenfunctions.
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The F [subscript N] method for a bare critical cylinder
… and orthogonality properties of the singular eigenfunctions are used to derive an expression for the emerging angular flux, which is represented by a power series. The resulting equations are reduced to matrix form and computer solved. Examples of the results of this method for different …
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Parameter identification and control of distributed-parameter systems
… The lowest frequencies and associated eigenfunctions are identified using an extension of a time-domain approach developed for discrete systems. The extension to distributed systems is carried out in this dissertation. To this end, the sensors output is interpolated to identify the …
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