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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

Inertial manifolds

Robinson, James Cooper January 1995 (has links)
No description available.

The application of transmission-line modelling implicit and hybrid algorithms to electromagnetic problems

Wright, S. J. January 1988 (has links)
No description available.

Homoclinic bifurcations

Drysdale, David January 1994 (has links)
Previously obtained results from the study of homoclinic bifurcations in ordinary differential equations are presented. The standard technique of analysis involves the construction of a Poincaré map on a surface near to the homoclinic point. This map is the composition of an inside map, with behaviour linearized about the homoclinic point, together with an outside map, with behaviour linearized about the homoclinic orbit. The Poincaré map is then reduced to a one-dimensional map, involving the return time between successive visits to the Poincaré surface. These standard techniques in the contemplation of homoclinic systems are then extended to a class of partial differential equations, on unbounded domains. This follows a method introduced by Fowler [Stud. Appl. Math. 83 (1990), pp. 329–353]. This extension involves more technicalities than in the case of ordinary differential equations. The method of Fowler is extended to cover the case of vector-valued partial differential equations, and to consider the consequences of symmetry invariances. A Poincaré map is derived, and then is reduced to a finite-dimensional map. This map has dimension equal to the number of symmetry invariances of the system. Some simple examples of this finite-dimensional map are studied, in isolation. A number of interesting bifurcation pictures are produced for these simple examples, involving considerable variation with the values of coefficients of the map. Partial differential equations on finite domains are then considered, yielding similar results to the ordinary differential equation case. The limit as domain size tends to infinity is examined, yielding a criterion for distinction between the applicability of finite and infinite domain results. Finally, these methods are applied to the Ginzburg-Landau system. This involves the numerical calculation of coefficients for the finite-dimensional map. The finite-dimensional map thus derived supports an interesting interlocked isola structure, and moreover correlates with numerical integration data.

Analysis of a reaction-diffusion system of λ-w type

Garvie, Marcus Roland January 2003 (has links)
The author studies two coupled reaction-diffusion equations of 'λ-w' type, on an open, bounded, convex domain Ω C R(^d) (d ≤ 3), with a boundary of class C², and homogeneous Neumann boundary conditions. The equations are close to a supercritical Hopf bifurcation in the reaction kinetics, and are model equations for oscillatory reaction-diffusion equations. Global existence, uniqueness and continuous dependence on initial data of strong and weak solutions are proved using the classical Faedo-Galerkin method of Lions and compactness arguments. The work provides a complete case study for the application of this method to systems of nonlinear reaction-diffusion equations. The author also undertook the numerical analysis of the reaction-diffusion system. Results are presented for a fully-practical piecewise linear finite element method by mimicking results in the continuous case. Semi-discrete and fully-discrete error estimates are proved after establishing a priori bounds for various norms of the approximate solutions. Finally, the theoretical results are illustrated and verified via the numerical simulation of periodic plane waves in one space dimension, and preliminary results representing target patterns and spiral solutions presented in two space dimensions.

Divergence form equations arising in models for inhomogeneous materials

Kinkade, Kyle Richard January 1900 (has links)
Master of Science / Department of Mathematics / Ivan Blank / Charles N. Moore / This paper will examine some mathematical properties and models of inhomogeneous materials. By deriving models for elastic energy and heat flow we are able to establish equations that arise in the study of divergence form uniformly elliptic partial differential equations. In the late 1950's DeGiorgi and Nash showed that weak solutions to our partial differential equation lie in the Holder class. After fixing the dimension of the space, the Holder exponent guaranteed by this work depends only on the ratio of the eigenvalues. In this paper we will look at a specific geometry and show that the Holder exponent of the actual solutions is bounded away from zero independent of the eigenvalues.

Chaos in models of double convection

Rucklidge, Alastair Michael January 1991 (has links)
No description available.

A class of Petrov-Galerkin finite element methods for the numerical solution of the stationary convection-diffusion equation

Perella, Andrew James January 1996 (has links)
A class of Petrov-Galerkin finite element methods is proposed for the numerical solution of the n dimensional stationary convection-diffusion equation. After an initial review of the literature we describe this class of methods and present both asymptotic and nonasymptotic error analyses. Links are made with the classical Galerkin finite element method and the cell vertex finite volume method. We then present numerical results obtained for a selection of these methods applied to some standard test problems. We also describe extensions of these methods which enable us to solve accurately for derivative values of the solution.

Bargmann transform and its applications to partial differential equations

Al Asmer, Nabil Abed Allah Ali Jr January 2021 (has links)
This thesis is devoted to the fundamental properties and applications of the Bargmann transform and the Fock-Segal-Bargmann space. The fundamental properties include unitarity and invertibility of the transformation in L2 spaces and embeddings of the Fock-Segal-Bargmann spaces in Lp for any p>0. Applications include the linear partial differential equations such as the time-dependent Schrödinger equation in harmonic potential, the diffusion equation in self-similar variables, and the linearized Korteweg-de Vries equation, and one nonlinear partial differential equation given by the Gross-Pitaevskii model for the rotating Bose-Einstein condensate. The main question considered in this work in the context of linear partial differential equation is whether the envelope of the Gaussian function remains bounded in the time evolution. We show that the answer to this question is positive for the diffusion equation, negative for the Schrödinger equation, and unknown for the Korteweg-de Vries equation. We also address the local and global well-posedness of the nonlocal evolution equation derived for the Bose-Einstein condensates at the lowest Landau level. / Thesis / Master of Science (MSc)

Strominger's system on non-Kähler hermitian manifolds

Lee, Hwasung January 2011 (has links)
In this thesis, we investigate the Strominger system on non-Kähler manifolds. We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holomorphically trivial canonical bundles. We will then consider explicit examples when M can be realized as a principal torus fibration over a Kähler surface S. We will solve the Strominger system on such construction which also includes manifolds of topology (k−1)(S²×S⁴)#k(S³×S³). We will investigate the anomaly cancellation condition on the principal torus fibration M. The anomaly cancellation condition reduces to a complex Monge-Ampère-type PDE, and we will prove existence of solution following Yau’s proof of the Calabi-conjecture [Yau78], and Fu and Yau’s analysis [FY08]. Finally, we will discuss the physical aspects of our work. We will discuss the Strominger system using α'-expansion and present a solution up to (α')¹-order. In the α'-expansion approach on a principal torus fibration, we will show that solving the anomaly cancellation condition in topology is necessary and sufficient to solving it analytically. We will discuss the potential problems with α'-expansion approach and consider the full Strominger system with the Hull connection. We will show that the α'-expansion does not correctly capture the behaviour of the solution even up to (α')¹-order and should be used with caution.

Existence of Critical Points for the Ginzburg-Landau Functional on Riemannian Manifolds

Mesaric, Jeffrey Alan 19 February 2010 (has links)
In this dissertation, we employ variational methods to obtain a new existence result for solutions of a Ginzburg-Landau type equation on a Riemannian manifold. We prove that if $N$ is a compact, orientable 3-dimensional Riemannian manifold without boundary and $\gamma$ is a simple, smooth, connected, closed geodesic in $N$ satisfying a natural nondegeneracy condition, then for every $\ep>0$ sufficiently small, $\exists$ a critical point $u^\ep\in H^1(N;\mathbb{C})$ of the Ginzburg-Landau functional \bd\ds E^\ep(u):=\frac{1}{2\pi |\ln\ep|}\int_N |\nabla u|^2+\frac{(|u|^2-1)^2}{2\ep^2}\ed and these critical points have the property that $E^\ep(u^\ep)\rightarrow\tx{length}(\gamma)$ as $\ep\rightarrow 0$. To accomplish this, we appeal to a recent general asymptotic minmax theorem which basically says that if $E^\ep$ $\Gamma$-converges to $E$ (not necessarily defined on the same Banach space as $E^\ep$), $v$ is a saddle point of $E$ and some additional mild hypotheses are met, then there exists $\ep_0>0$ such that for every $\ep\in(0,\ep_0),E^\ep$ possesses a critical point $u^\ep$ and $\lim_{\ep\rightarrow 0}E^\ep(u^\ep)=E(v)$. Typically, $E$ is only lower semicontinuous, therefore a suitable notion of saddle point is needed. Using known results on $\mathbb{R}^3$, we show the Ginzburg-Landau functional $E^\ep$ defined above $\Gamma$-converges to a functional $E$ which can be thought of as measuring the arclength of a limiting singular set. Also, we verify using regularity theory for almost-minimal currents that $\gamma$ is a saddle point of $E$ in an appropriate sense.

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