Spelling suggestions: "subject:"aymmetry."" "subject:"asymmetry.""
21 |
Symbolic software for symmetry reduction and computation of invariant solutions of differential equationsOlinov, Andrey I. 24 June 2011
Problems involving partial or ordinary differential equations arise in various fields of science. Therefore, the task of obtaining exact solutions of differential equations is of primary importance, and attracts high attention. The main purpose of the current thesis is the development of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, developed by Prof. Alexei Cheviakov. The reduction procedure is based on the Lie's classical symmetry reduction method involving canonical coordinates. The developed package is applicable for obtaining solutions arising from extension of Lie's method, in particular, nonlocal and approximate symmetries.
The developed software is applied to a number of PDE problems to obtain exact invariant solutions. The considered equations include the one-dimensional nonlinear heat equation, the potential Burgers' equation, as well as equations arising in nonlinear elastostatics and elastodynamics.
|
22 |
Symbolic software for symmetry reduction and computation of invariant solutions of differential equationsOlinov, Andrey I. 24 June 2011 (has links)
Problems involving partial or ordinary differential equations arise in various fields of science. Therefore, the task of obtaining exact solutions of differential equations is of primary importance, and attracts high attention. The main purpose of the current thesis is the development of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, developed by Prof. Alexei Cheviakov. The reduction procedure is based on the Lie's classical symmetry reduction method involving canonical coordinates. The developed package is applicable for obtaining solutions arising from extension of Lie's method, in particular, nonlocal and approximate symmetries.
The developed software is applied to a number of PDE problems to obtain exact invariant solutions. The considered equations include the one-dimensional nonlinear heat equation, the potential Burgers' equation, as well as equations arising in nonlinear elastostatics and elastodynamics.
|
23 |
Steady wave drift force on basic objects of symmetryGupta, Anupam 15 May 2009 (has links)
An exponential growth in the offshore industry has resulted in a corresponding increase in
demand for quick, accurate, and implementable designs. With the increase in size of the
structure relative to the wave amplitude, analysis should be performed using the diffraction
theory. The steady wave drift force on a submerged body is a second-order quantity. With a
potential flow assumption, the force arises from the diffraction and radiation of the waves
from the interaction with the body. For a fixed body in waves the steady force is
contributed from the wave diffraction effect alone. Numerical solutions for are generally
needed for the computation of the steady drift force on submerged structures. In this study
the steady wave drift forces on several fixed bodies of basic shapes are derived in closed
form. The thesis addresses the steady drift forces on the following basic structures: a box, a
vertical circular cylinder, a submerged horizontal cylinder, a bottom-seated horizontal half
cylinder, a bottom-seated hemisphere, a submerged sphere, and an ellipsoid. The results
developed demonstrate the importance of various independent non-dimensional parameters.
To achieve speed and accuracy of the analytical/numerical solutions for the second order forces on the basic bodies with symmetry has been presented. Mathematical
formulation of the boundary value problem and its second order solution have been
described using the different coordinates depending on the symmetry and nature of the
object. Charts and formulas have been developed to provide solution for the second order
wave forces on different basic structures like cylinder, sphere and ellipsoids. This study is
helpful for a first pass estimate of the steady drift force where the translational and
rotational contributions are neglected. The illustrative examples provide a sense of the
accuracy and an approach to bound the results of complex geometries by approximating
them as simpler geometries.
|
24 |
Symmetry energy and the isoscaling properties of the fragments in multifragmentation of 40Ca+58Ni, 40Ar+58Ni, and 40Ar+58Fe reactionsIglio, Jennifer Ann 17 September 2007 (has links)
The symmetry energy and the isoscaling properties of the fragments produced in
multifragmentation of 40Ar, 40Ca + 58Fe, 58Ni reactions at 25, 33, 45 and 53
MeV/nucleon were investigated within the framework of a statistical multifragmentation
model. The isoscaling parameter, ñ from the hot primary and cold secondary fragment
yield distributions, was studied as a function of the excitation energy, isospin (neutronto-
proton asymmetry), and fragment symmetry energy.
Through changing the symmetry energy in the statistical multifragmentation
model to describe the experimental data, it is observed that the isoscaling parameter ñ
decreases with increasing excitation energy and decreases with decreasing symmetry
energy. The parameter ñ is also observed to increase with increasing difference in the
isospin of the fragmenting system. The sequential decay of the primary fragments into
secondary fragments show very little influence on the isoscaling parameter when studied
as a function of excitation energy. However, the symmetry energy has a strong
influence on the isospin properties of the hot fragments. The results indicate that the
isospin properties of the fragments produced at high excitation energy and reduced
density in multifragmentation reactions are sensitive to the symmetry energy, indicating that the properties of hot nuclei at excitation energies, densities, and isospin away from
normal ground state nuclei are significantly different than those of normal (cold) nuclei
at saturation density.
|
25 |
Extensions of hook and completely splittable modules for the symmetric group /Hemmer, David J. January 2001 (has links)
Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2001. / Includes bibliographical references. Also available on the Internet.
|
26 |
Bound and free excitons in ZnO-optical selection rules in the absence and presence of time reversal symmetryNiyongabo, Prime. January 2009 (has links)
Thesis (M.Sc.(Natural and Agricultural Sciences)) -- University of Pretoria, 2009. / Summary in English. Includes bibliographical references (leaves 55-56).
|
27 |
Restricting modular spin representations of symmetric and alternating groups /Phillips, Aaron M., January 2003 (has links)
Thesis (Ph. D.)--University of Oregon, 2003. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 69-71). Also available for download via the World Wide Web; free to University of Oregon users.
|
28 |
Cityscapes for orchestraHendrix, Brandon 09 December 2010 (has links)
Cityscapes is a 13-minute work for full orchestra. It serves not only as a summary of my experiences while in Austin, Texas, but also as a representation of my musical style and creative influences. The composition consists of three movements, the first and second of which are elided into one another. The formal structure of Cityscapes is governed by the meshing and combining of recurring motivic figures, the framing of themes and sections based on two distinct scalar patterns, and the symmetry and intervallic design extrapolated from these two patterns. / text
|
29 |
FINITE TRANSFORMATIONS OF SU(3)Holland, Douglas Francis, 1938- January 1968 (has links)
No description available.
|
30 |
Conservative autonomous nonlinear differential systems with symmetriesHaley, David Reeves 12 1900 (has links)
No description available.
|
Page generated in 0.0462 seconds