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Isospectral transformations between soliton-solutions of the Korteweg-de Vries equation李達明, Lee, Tad-ming. January 1994 (has links)
published_or_final_version / abstract / toc / Physics / Master / Master of Philosophy
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Geometric discretization schemes and differential complexes for elasticityAngoshtari, Arzhang 20 September 2013 (has links)
In this research, we study two different geometric approaches, namely, the discrete exterior calculus and differential complexes, for developing numerical schemes for linear and nonlinear elasticity. Using some ideas from discrete exterior calculus (DEC), we present a geometric discretization scheme for incompressible linearized
elasticity. After characterizing the configuration manifold of volume- preserving discrete deformations, we use Hamilton’s principle on this configuration manifold. The discrete Euler-Lagrange equations are obtained without using Lagrange multipliers.
The main difference between our approach and the mixed finite element formulations is that we simultaneously use three different discrete spaces for the displacement field. We test the efficiency and robustness of this geometric scheme using some numerical examples. In particular, we do not see any volume locking and/or checkerboarding of pressure in our numerical examples. This suggests that our choice of discrete solution
spaces is compatible. On the other hand, it has been observed that the linear elastostatics complex can be used to find very efficient numerical schemes. We use some geometric techniques to obtain differential complexes for nonlinear elastostatics.
In particular, by introducing stress functions for the Cauchy and the second Piola-Kirchhoff stress tensors, we show that 2D and 3D nonlinear elastostatics admit separate kinematic and kinetic complexes. We show that stress functions corresponding to the first Piola-Kirchhoff stress tensor allow us to write a complex for 3D nonlinear
elastostatics that similar to the complex of 3D linear elastostatics contains both the kinematics an kinetics of motion. We study linear and nonlinear compatibility equations
for curved ambient spaces and motions of surfaces in R3. We also study the relationship between the linear elastostatics complex and the de Rham complex. The geometric approach presented in this research is crucial for understanding connections
between linear and nonlinear elastostatics and the Hodge Laplacian, which can enable one to convert numerical schemes of the Hodge Laplacian to those for linear and possibly nonlinear elastostatics.
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Applications of the Monge - Kantorovich theoryMaroofi, Hamed 05 1900 (has links)
No description available.
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Coherent structures and symmetry properties in nonlinear models used in theoretical physics.Harin, Alexander O. January 1994 (has links)
This thesis is devoted to two aspects of nonlinear PDEs which are fundamental
for the understanding of the order and coherence observed in the underlying physical
systems. These are symmetry properties and soliton solutions. We analyse these
fundamental aspects for a number of models arising in various branches of theoretical
physics and appli ed mathematics.
We start with a fluid model of a plasma in the case of a general polytropic
process. We propose a method of the analysis of unmagnetized travelling structures,
alternative to the conventional formalism of Sagdeev 's pseudopotential. This method
is then utilized to obtain the existence domain for compressive solitons and to establish
the absence of rarefactive solitons and monotonic double layers in a two-component
plasma.
The second class of models under consideration arises in (2+1)-dimensional condensed
matter physics. These are the Abelian gauge theories with Chern-Simons
term, which are currently considered as candidates for the description of high-Te
superconductivity and fra ctional quantum Hall effect. The emphasis here is on nonrelativistic
theories. The standard model of a self-gravitating gas of nonrelativistic
bosons coupled to the Chern-Simons gauge field is capable of describing asymptotically
vanishing field configurations , such as lump-like solitons. We formulate an
alternative model, which describes systems of repulsive particles with a background
electric charge and allows to incorporate asymptotically nonvanishing configurations,
such as condensate and its topological excitations. We demonstrate the absence of the condensate state in the standard nonrelativistic gauge theory and relate this fact
to the inadequate Lagrangian formulation of its nongauged precursor. Using an appropriate
modification of this Lagrangian as a basis for the gauge theory naturally
leads to the new model. Reformulating it as a constrained Hamiltonian system allows
us to find two self-duality limit s and construct a large variety of self-dual solutions.
We demonstrate the equivalence of the model with the background charge and the
standard model in the external magnetic field. Finally we discuss nontopological
bubble solutions in Chem-Simons-Maxwell theories and demonstrate their absence
in nonrelativistic theories.
Finally, we consider a model of a nonhomogeneous nonlinear string. We continue
the group theoretical classification of the string equations initiated by Ibragimov et
al. and present their preliminary group classification with respect to a countable dimensional subalgebra of their equivalence algebra. This subalgebra is an extension
of the 10-dimensional subalgebra considered by Ibragimov et al. Our main result here
is a table of non-equivalent equations possessing an additional symmetry. / Thesis (Ph.D.)-University of Natal, 1994.
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Feedback augmentation of pde-based image segmentation algorithms using application-specific exogenous dataKarasev, Peter A. 13 January 2014 (has links)
This thesis is divided into five chapters. The scope of problems considered is defined in chapter I.
Next, chapter II provides background material on image processing with
partial differential equations
and a review of prior work in the
field. Chapter III covers the medical imaging portion of the research;
the key contribution is a control-based algorithm for interactive image
segmentation. Applications of the feedback-augmented level set method to fracture reconstruction and surgical planning are shown. Problems in vision-based control are considered in Chapters IV and V. A method of improving performance in closed-loop target tracking using level set
segmentation is developed, with unmanned aerial vehicle or
next-generation missile guidance being the primary applications of interest.
Throughout this thesis, the two application types are connected into a
unified viewpoint of open-loop systems that are augmented by exogenous data.
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Variational discretization of partial differential operators by piecewise continuous polynomials.Benedek, Peter. January 1970 (has links)
No description available.
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Maximum principles and Liouville theorems for elliptic partial differential equationsZhou, Chiping January 1990 (has links)
Typescript. / Thesis (Ph. D.)--University of Hawaii at Manoa, 1990. / Includes bibliographical references. / Microfiche. / vi, 96 leaves, bound ill. 29 cm
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Model reduction and parameter estimation for diffusion systems /Bhikkaji, Bharath, January 2004 (has links)
Diss. (sammanfattning) Uppsala : Univ., 2004. / Härtill 8 uppsatser.
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Stable high-order finite difference methods for aerodynamics /Svärd, Magnus, January 2004 (has links)
Diss. (sammanfattning) Uppsala : Univ., 2004. / Härtill 8 uppsatser.
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Numerical computations with fundamental solutions /Sundqvist, Per, January 2005 (has links)
Diss. (sammanfattning) Uppsala : Uppsala universitet, 2005. / Härtill 5 uppsatser.
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