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Showing 1 to 20 of 156 for “"Exact solutions"”.
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Exact Solutions to Lattice Models of Polymer Adsorption
… solved to study a variety of physical properties exactly. One solution method is to solve the recurrences with generating functions. Additionally, we may attempt to derive the partition function of the model, which explicitly provides the walk entropy per length. In this thesis, the solution to a …
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Exact Solutions of Planar Photonic Crystal Waveguides with Infinite Claddings
… dielectric structures. Using a novel approach, exact analytical solutions for guided modes in such waveguides are presented. The se rigorous solutions allow one to distinguish clearly between the index-guiding regime and guidance due to the photonic crystal effect. In the first part of this …
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Exact Solutions for Orthogonal and Non-Orthogonal Magnetohydrodynamic Stagnation-Point Flow
<p>The viscous plane flow of an electrically conducting fluid towards an infinite wall is solved in the presence of a magnetic field which is aligned with the flow far from the wall. The problem has two dimensionless parameters-- ε, the magnetic Prandtl number, and β, the square of the ratio of …
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Exact Solutions to Electromagnetic Scattering Problems with Multi-Layered Oblate Spheroidal Geometry
… validation methods involves comparisons with exact solutions derived from canonical EM scattering problems. These analytical solutions serve as benchmarks, providing reference results that numerical solutions must match under the same conditions. The novelty of this work lies in developing a …
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The use of mathematically exact solutions of structural dynamics models for structural control design
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1992.
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Exact Solutions of Some Dynamic Problems of Indentation and Transient Loadings of an Elastic Half Space
Made available in DSpace on 2014-12-08T23:57:24Z (GMT). No. of bitstreams: 1 7013514.pdf: 7386552 bytes, checksum: 6ab88bb8ba2077bc25f4b3cedf1461ce (MD5) Previous issue date: 1969
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Exact solutions and conservation laws of two-wave mode Kadomtsev-Petviashvili equation and a nonintegrable nonlinear equation
… and simplest equation methods to obtain exact solutions of a generalized two nonlinear partial differential equations.
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Modified nodal integral method for non-linear coupled neutronics-heat conduction problems and exact solutions based on method of manufactured solutions
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01
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Exact Solutions to the Six-Vertex Model with Domain Wall Boundary Conditions and Uniform Asymptotics of Discrete Orthogonal Polynomials on an Infinite Lattice
In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the ferroelectric phase region, we show that $Z_n=CG^nF^{n^2}(1+O(e^{-n^{1-\ep}}))$ for any $\ep>0$, and …
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Analysis of Infinite Domain Criticality Zones in Finite Reactors (Uniform Power, Minimum Fuel Density, Exact Solutions, Poles of Bromwich Integral, Reduction of Pde's)
A reactor that is infinitely large has two ideal properties: (1) The fission rate density and, hence, the power are uniform throughout, and (2) the fuel density needed for criticality is minimum. A finite reactor loaded in this way would be subcritical and would have to contain additional fuel to …
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Propagation Failure in Discrete Inhomogeneous Medium Using a Caricature of the Cubic
… rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under …
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A study of certain multi-dimensional partial differential equations using Lie symmetry analysis
… phenomena of the real world. Closed-form solutions and conservation laws are obtained for such equations using various methods. The multi-dimensional partial differential equations that are investigated in this thesis are (2+ 1) and (3+ 1 )-dimensional Boussinesq equations, a generalized …
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Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems
… Nearby Problems as a way to generate analytical exact solutions to problems governed by partial differential equations (PDEs). The method involves generating a numerical solution to the original problem of interest, curve fitting the solution, and generating source terms by operating the …
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Linear analysis of laminated composite plates using a higher-order shear deformation theory
… shear deformation theory of Whitney and Pagano. Exact solutions for cross-ply and anti-symmetric angle-ply laminated plates with all edges simply-supported are presented. A finite element model is also developed to solve the partial differential equations of the theory. The finite element model …
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Extrapolation-based Discretization Error and Uncertainty Estimation in Computational Fluid Dynamics
… estimates relies on the solution (or multiple solutions used in the estimate) being in the asymptotic range. The asymptotic range is used to describe the convergence of a solution, where an asymptotic solution approaches the exact solution at a rate proportional to the change in mesh spacing to …
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Numerical Treatment of Schrödinger’s Equation for One-Particle and Two-Particle Systems Using Matrix Method
… theory techniques. They are either approximate solutions to actual equations or exact solutions to approximate equations. Exact solutions have not found favor due to the computational expense of the problem. Hence, a novel numerical approach is developed and tested here using linear algebraic …
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Integration of Higher-Order Physics in the Community Ice Sheet Model: Scientific and Software Concerns
… as the software engineering process and design solutions used to integrate this model with the rest of CISM. I then build a case for the correctness of the integrated model by presenting the results of numerous experiments that compare this model to data, exact solutions, and a collection of …
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Integration of Higher-Order Physics in the Community Ice Sheet Model: Scientific and Software Concerns
… as the software engineering process and design solutions used to integrate this model with the rest of CISM. I then build a case for the correctness of the integrated model by presenting the results of numerous experiments that compare this model to data, exact solutions, and a collection of …
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Laplace's equation on perturbed domains
… We verify our methods by constructing exact solutions for the perturbed geometries.
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