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Showing 1 to 18 of 18 for “"Laplace's equation"”.
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Separation of Laplace's equation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1948.
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Laplace's equation on perturbed domains
Laplace's equation is a prototypical elliptic PDE that appears in many electromagnetic and fluid dynamics problems. We develop two methods for solving Laplace's equation on domains that are perturbations of a circle. These methods are derived from governing equations and applied to several test …
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Solution of Laplace's equation in inverted coordinate systems
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering, 1948.
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Solution of LaPlace's equation by Monte Carlo method
Thesis: B.S., Massachusetts Institute of Technology, Department of Electrical Engineering, 1959
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The programming of Laplace's equation for solution by iteration on Whirlwind I
Thesis (B.S.) Massachusetts Institute of Technology. Dept. of Physics, 1950.
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On the Hausdorff dimension of a certain measure arising from a positive weak solution to a divergence type PDE
… quasilinear elliptic partial differential equation in a simply connected domain in the plane. We also assume that the solution vanishes on the boundary of the domain. Then it is shown that the Hausdorff dimension of this measure is less than one, equal to one, greater than one depending on …
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Dynamic Modeling With Implicit Surfaces and Polygonal Meshes
… the shape. This thesis solves a relaxed form of Laplace's equation to find a ""fair"" Morse function with a user-controlled number and configuration of critical points."
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Issues related to finite element techniques for two dimensional transmission structures
… gradient method to solve linear systems of equations. Application to electromagnetic problems will be demonstrated in the static, quasi-static, and full-field regimes. Laplace's equation is solved for various transmission line geometries to obtain capacitance and characteristic impedance. A …
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Mathematical Models of Quiescent Solar Prominences
… a current free atmosphere. Secondly a diffusion equation with convection terms is assigned to a two-dimensional region below the photosphere to represent the convection zone, and this is matched to Laplace's equation above the photosphere to represent the corona. The PDE's are solved numerically …
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An investigation into the use of conformal transformations in two-dimensional field theory.
… the use of Conformal Transformations in solving Laplace's equation for two-dimensional field problems. Conformal Transformations is one of several analytical methods available for this purpose and its usefulness is generally limited to those problems in which the transformation integral is …
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Feature-based design of solids with local composition control
… geometric features; and functions that use Laplace's equation to blend smoothly various boundary conditions including values and gradients of the material composition on the boundaries. The Euclidean digital distance transform and the boundary element method are adapted to the efficient …
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Interconnect capacitance extraction under geometric uncertainties
… is proposed for the finite element solution of Laplace's equation for the calculation of the per-unit-length capacitance matrix of a multi-conductor interconnect structure embedded in a multi-layered insulating substrate and in the presence of statistical variation in conductor and substrate …
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Coherent excitation of ultracold atoms between ground and Rydberg states
… to that calculated by numerical solution of Laplace's equation; the bulk dielectric is found to have a strong effect on the local electric field experienced by the atoms. The exaggerated properties of Rydberg states make these systems ideal for quantum information processing and precision …
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New symmetries from old: exploiting lie algebra structure to determine infinitesimal symmetries of differential equations
… known Lie symmetries of a system of differential equations to help find more symmetries of the system. A Lie (or infinitesimal) symmetry of a system of differential equations is a transformation of its dependent and independent variables, depending on continuous parameters, which maps any solution …
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Refraction of isotherms: applications to define rift basin geometry
… plates in perfect thermal contact and solving Laplace's equation in two dimensions. The normalized heat flow is calculated for the models and is also approximated by an empirically derived equation. The equation for normalized heat flow can be derived from the analytical solution to Laplace’s …
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Plasma processes in pulsar environments
… in the pulsar magnetosphere. The full nonlinear equations in cylindrical geometry for a streaming cold pair plasma are solved numerically, together with Maxwell's equations, using a Finite-Difference Time Domain method. Electrostatic oscillations are induced in a streaming plasma in the presence …
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Free Surface Penetration of Inverted Right Circular Cones at Low Froude Number
In this thesis the impact of inverted cones on a liquid surface is studied. It is known that with the right combination of velocity, geometry, and surface treatment, a cavity of air can be formed behind an impacting body and extended for a considerable distance. Other investigators have shown that …
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Feature profile evolution during the high density plasma etching of polysilicon
… on the feature surface and solving Poisson's equation over the entire simulation domain. Calculation of the potential profiles with the resistive feature representation involved treating the feature as a large resistive network, determining the steady-state currents to the feature surface and …