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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 77 for “"Heat equation"”.
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An analog to the heat equation in complex space variables
… = $-$1, P bears a remarkable resemblance to the heat operator in one space variable. The "only" difference is that the space variable is now complex. In spite of this superficial similarity, P is quite different from the heat operator. It is neither hypoelliptic nor parabolic. The key result is a …
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Efficient high-order integral equation methods for the heat equation
Efficient high-order integral equation methods have been developed for solving the boundary value problems of the heat equation with complex geometries in two and three dimensions. First of all, the classical heat potential theory is applied to convert such problems to Volterra integral equations …
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A control system viewpoint for manipulating heat equation and maximum entropy principle for design of experiments
… method and basis function approach to discretize heat equation into a linear time invariant (LTI) system. This aids in borrowing control theoretic approaches to manipulate the thermal properties of materials. In this regard, we demonstrate a robust optimal control approach to modify the …
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A Solution of the Heat Equation with the Discontinuous Galerkin Method Using a Multilivel Calculation Method That Utilizes a Multiresolution Wavelet Basis
… standard Discontinuous Galerkin Method for the heat equation, but with cheaper computational cost. The results are demonstrated using a standard one-dimensional homogeneous heat problem.</p>
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Methods of Computing Functional Gains for LQR Control of Partial Differential Equations
… defined by parabolic partial differential equations. In particular, we study various methods for computing functional gains to boundary control problems for the heat equation. These methods require us to solve various equations including the algebraic Riccati equation, the Riccati partial …
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Comprehensive Theory of Heat Transfer in Heterogeneous Materials
… researchers have attempted to refine the Fourier heat equation to model heat transfer in engineering materials. The equation cannot accurately predict temperatures in some applications, such as during transients in microscale (< 10^-12 s) situations. However, even in situations where the time …
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Krylov Subspace Spectral Methods with Non-homogenous Boundary Conditions
… will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their accuracy and scalability can be improved. We will solve the heat equation in …
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On qualitative properties and convergence of time-discretization methods for semigroups
… by applying the results to the one-dimensional heat equation. The Dunford-Taylor functional calculus is employed to obtain an estimate on the stability constant of the restricted denominator approximation method applied to the one dimensional, space-discretized heat equation. Finally, we propose …
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Path integrals on manifolds with boundary and their asymptotic expansions
… from physical heuristics that solutions to the heat equation on a Riemannian manifold can be represented by a path integral. However, the problem with such path integrals is that they are notoriously ill-defined. One way to make them rigorous (which is often applied in physics) is …
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Approximations and Object-Oriented Implementation for a Parabolic Partial Differential Equation
This work is a numerical study of the 2-D heat equation with Dirichlet boundary conditions over a polygonal domain. The motivation for this study is a chemical vapor deposition (CVD) reactor in which a substrate is heated while being exposed to a gas containing precursor molecules. The interaction …
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A study of control system radii for approximations of infinite dimensional systems
… control systems governed by partial differential equations. Finite element approximations of the heat equation (parabolic), the wave equation (hyperbolic) and the equations of thermoelasticity (mixed) are used as test cases. Balanced realizations, reduced order models and other transformed models …
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A Multigrid Homotopy Method For Computing Eigenfunctions of Differential Operators With Two-Dimensional Heterogeneity
… differential operator for the two-dimensional heat equation with a piecewise constant coefficient and periodic boundary conditions. The piecewise constant coefficient is created by the discontinuity of the diffusivity coefficient across the interfaces between two or more heterogeneous …
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Optimal Linear Feedback Control for Incompressible Fluid Flow
… for large systems of differential algebraic equations arising from discretization of saddle point problems. Necessary conditions are derived by applying the Maximum Principle and have the form of constrained Riccati equations. We consider two approaches for solving the feedback control …
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Finite dimensional approximations of distributed parameter control systems
… are applied to a control problem governed by the heat equation. We present a comparison of the resulting finite dimensional models.
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Efficient multiscale methods for micro/nanoscale solid state heat transfer
… for solving the linearized Boltzmann transport equation (BTE) in the relaxation-time approximation for describing small-scale solidstate heat transfer. We first discuss a Monte Carlo (MC) solution method that builds upon the deviational energy-based Monte Carlo method presented in [J.-P. Péraud …
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Coefficient recovery in parabolic initial boundary value problems
… in linear, parabolic, partial differential equations with specified initial and boundary conditions. We primarily explore the recovery of the diffusivity coefficient in the heat equation using a very limited amount of data on a portion of the spatial boundary. In the process, we show that …
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Distributed Parameter Control of Thermal Fluids
… of the coupled set of Navier-Stokes and heat equations. The control is applied through Dirichlet boundary conditions. We concentrate on a two-dimensional mode and use a semidiscrete Galerkin scheme for numerical computations. We construct both a linear control and a non-linear quadratic …
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Investigations of the thermal properties of human and animal tissues
… tissue are required, in conjunction with a bio-heat equation, to allow the formation of computational models to simulate the temperature distribution inside the human body. These computational models are also useful in the analysis of tomographic temperature measurements, and are essential to …
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Some application of Malliavin calculus to SPDE and convergence of densities
… calculus to stochastic partial differential equations (SPDEs) and to normal approximation theory are studied in this dissertation. In Chapter 3, a Feynman-Kac formula is established for a stochastic heat equation driven by Gaussian noise which is, with respect to time, a fractional Brownian …
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Relations between two classes of singular integrals
… properties of solutions of Poisson's equation. Recently, Jones made some observations on the fundamental solution of the heat equation and gave another class of singular integrals. In this thesis it is shown that a special case of Jones's kernel is of Calderon-Zygmund type and a real, …
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