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Showing 1 to 18 of 18 for “"eigenfunction expansion"”.
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Eigenfunction expansion of the time and space-dependent neutron survival probability equation
… probability is well-approximated by the first eigenfunction of the linear portion of the equation. Not only is strong agreement observed with the semi-analytical solution, extension to other geometries is made accessible and the impact that varying geometry has on the survival probability is …
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Convergence Properties of the Eigenfunction Expansion of the Biharmonic Equation on Rectangular and Semi-Infinite Strips
We consider the problem (DELTA)('2)(w(x,y)) = 0, w((+OR-)1,y) = w(,x)((+OR-)1,y) = 0 with boundary conditions w(,xx)(x,0) = f(x) w(,yy)(x,0) = g(x) on the semi-infinite strip -1 (LESSTHEQ) x (LESSTHEQ) 1, 0 < y.
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A Near-Zone to Far-Zone Transformation Process Utilizing a Formulated Eigenfunction Expansion of Spheroidal Wave-Harmonics
… in doing so. Our approach uses a formulated eigenfunction expansion of spheroidal wave-harmonics to develop two distinct, yet closely related, NZ-FZT algorithms for each type of spheroidal transformation surface. The process only requires knowledge of the E-field along the transformation …
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Diagonalization of 1-D Schrodinger Operators with Piecewise Constant Potentials
… practical. The method used here will apply an eigenfunction expansion technique used in previous research that eliminates the current time-stepping problems.</p>
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Finite Element Analysis of Multilayer Transmission Lines and Circuit Components
… used to truncate the simulation domain, and the eigenfunction expansion method is used to connect the circuit component to signal inputs and outputs. A new E-H type eigenfunction expansion formulation is used for inhomogeneous port boundary conditions. Various types of planar structures are …
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A Simplified Model of Planetary Chemical Vapor Deposition Reactors
… to derive the reactor modeling equation, and the eigenfunction expansion solution is subsequently computed using a previously developed MATLAB object-oriented computational framework. The simulation result for the deposition profile is improved by modifying the inlet boundary condition, and is …
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Oscillations and waves in anisotropic plasmas
… solutions are put into the form of a generalized eigenfunction expansion with eigenmodes corresponding to zeros of the appropriate plasma dispersion function. The expansion coefficients for eigenmodes corresponding to simple and second order real zeros of the plasma dispersion function are also …
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A functional analytic approach to multigroup transport theory
… and invertible transfer matrix. The Case-type eigenfunction expansion formulas for the solutions of these problems are explicitly obtained. For the half-space case, the formulas are expressed in terms of two matrices X and Y which provide the Wiener-Hopf factorization of the dispersion matrix. …
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Finite Element Analysis Of Left-handed Waveguides
… also analyzed using finite element method with eigenfunction expansion technique.
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Neoclassical polarization
… the H-R collisional calculation using an exact eigenfunction expansion of the collision operator to calculate neoclassical polarization for the entire range of frequencies. A semi-analytical fit of the exact results is obtained that gives the polarization to within 15% and allows the collisional …
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Numerical Modeling and Analysis of Composite Beam Structures Subjected to Torsional Loading
… based on Saint Venant's torsion theory. The eigenfunction expansion method was employed to solve the formulated problem. The analytical method is proposed in this study enabling one to solve the torsion problem of laminated composite beams. Instead of following the classical Saint Venant …
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Linear mixed effects models in functional data analysis
… the functional predictor using basis function or eigenfunction expansions. In the expansion, the coefficient vector can either be fixed or random. The random coefficient vector is also known as random effects and thus the regression models are in a mixed effects framework. The random effects …
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The harmonic excitation of a cylindrical bubble pinned to a plane surface: flow field and oscillation dynamics
… the steady streaming flow by means of an eigenfunction expansion, and compare the results to experimental observations. Finally, we examine the dynamics of a pinned bubble in response to an imposed oscillatory pressure by a balance of dynamic stresses across the interface. We propose a …
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Subordinacy and spectral analysis of Schrödinger operators
… In Chapter IV, it is shown that the general eigenfunction expansion theory of Weyl-Kodaira can be simplified for a Schrödinger operation in L2 (O,∞) whenever the corresponding operator on any finite interval containing the origin has singular spectrum and the potential is integrable at …
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Numerical Simulations of Stokes Flow by the Iterations of Boundary Conditions and Finite Difference Methods
… into two sub problems that are solvable by the eigenfunction expansion method. Once all necessary coefficients of the generalised Fourier series are known and the functions describing the boundary conditions are prescribed and represented in terms of the Fourier series, we then proceed to …
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Particle transport on the Alcator C-Mod tokamak
… space resolution and coverage of the plasma. An eigenfunction expansion method was used to obtain highly accurate solutions to the transport equation, using posited values of diffusion and convection coefficients and matching the data at the initial time and at the edge of the analysis region. …
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Solving variable coefficient partial differential equations using the boundary element method.
… is proposed which constructs the solution as an eigenfunction expansion. The eigenvalues and eigenvectors are determined using the DR-BEM. This method allows parabolic problems to be solved without requiring time-stepping or domain integration. This method is found to produce accurate results for …
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Eignefunctions for Partial Differential Equations on Two-Dimensional Domains With Piecewise Constant Coefficients
… that by computing the eigenvalues and eigenfunctions to construct a basis of such functions- both independently and simultaneously, in conjunction with the secant method- a mathematical model for heat diffusion through different materials in two space dimensions can be solved much more …