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Linear and nonlinear electron-acoustic waves in plasmas with two electron components.Mace, Richard Lester. January 1991 (has links)
Measurements of broadband electrostatic wave emIssons in conjunction
with particle distributions in the earth's magnetosphere, have provided motivation
for a number of studies of waves in plasmas with two electron
components. One such wave-the electron-acoustic wave-arises when the
two electron components have widely disparate temperatures (Watanabe &
Taniuti 1977), and has a characteristic frequency that lies between the ion
and electron plasma frequencies. Because of this broadband nature and because
it is predominantly electrostatic, it provides a likely candidate for the
explanation of the electrostatic component of "cusp auroral hiss" observed
in the dayside polar cusp at between 2 and 4 earth radii as well as the broadband
electrostatic noise (BEN) observed in the dayside polar regions and in
the geomagnetic tail. The electron-acoustic wave and its properties provide
the subjects for much of the investigation undertaken in this thesis.
The thesis is divided into two parts. Part I is concerned with certain
aspects of the linear theory of the electron-acoustic wave and is based on
a kinetic description of the plasma. The dispersion relation for plane electrostatic
waves obtained via linearisation of the Vlasov-Poisson system is
studied in detail using analytical and numerical/geometrical techniques, and
conditions under which the electron-acoustic wave arises are expounded.
This work represents an extension of earlier works on Langmuir waves (Dell,
Gledhill & Hellberg 1987) and the electron-acoustic wave (Gary & Tokar
1985). The effects of electron drifts and magnetization are investigated. These
result, respectively, in a destabilization of the electron-acoustic wave and a
modification of the dispersive properties. In this plasma configuration the
model more closely replicates the conditions to be found in the terrestrial
polar regions. We extend the parameter regimes considered in earlier works
(Tokar &Gary 1984) and in addition, identify another electron sound branch
related to the electron-cyclotron wave/instability.
Effects of ion-beam destabilization of the electron-acoustic wave are also
investigated briefly with a view to explaining BEN in the geomagnetic tail
and also to provide a comparison with the electron-driven instability.
In part II the nonlinear electron-acoustic wave is studied by employing
a warm hydrodynamic model of the plasma components. We first consider
weak nonlinearity and employ the asymptotic reductive perturbation technique
of Washimi &Taniuti (1966) to render the hydrodynamical equations
in the form of simpler evolutionary equations describing weakly-nonlinear
electron-acoustic waves. These equations admit solitary-wave or soliton solutions
which are studied in detail.
Wherever possible we have justified our small amplitude results with full
numerical integration of the original hydrodynamical equations. In so doing
we extended the range of validity of our results to arbitrary wave amplitudes
and also find some interesting features not directly predicted by the small
amplitude wave equations. In this respect we were able to determine the important
role played by the cool- to-hot electron temperature ratio for soliton
existence. This important effect is in accordance with linear theory where
the electron temperature ratio is found to be critical for electron-acoustic
wave existence.
The effects of magnetization on electron-acoustic soliton propagation is
examined. We found that the magnetized electron-acoustic solitons are governed
by a Korteweg-de Vries-Zakharov-Kusnetsov equation. In addition,
it is shown that in very strong magnetic fields ion magnetization can become
important yielding significant changes in the soliton characteristics.
Multi-dimensional electron-acoustic solitons, which have greater stability
than their plane counterparts, are also briefly discussed.
Employing a weakly-relativistic hydrodynamic model of the plasma, the
effect of a cool, relativistic electron beam on such soliton parameters as
width, amplitude and speed is studied in detail. Both small- and large amplitude
solitons are considered. The arbitrary-amplitude theory of Baboolal
et al. (1988) is generalised to include relativistic streaming as well
as relativistic thermal effects. The importance of the cool electron (beam)to-
hot electron temperature in conjunction with the beam speed is pointed
out.
Finally, we derive a modified Korteweg-de Vries (mKdV) equation in an
attempt to establish whether electron-acoustic double layers are admitted
by our fluid model. Although double layers formally appear as stationary
solutions to the mKdV equation, the parameter values required are prohibitive.
This is borne out by the full fluid theory where no double layer
solutions are found. / Thesis (Ph.D.)-University of Natal, Durban, 1991.
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Solitary wave interaction and evolutionHoseini, Sayed Mohammad. January 2007 (has links)
Thesis (Ph.D.)--University of Wollongong, 2007. / Typescript. Includes bibliographical references: leaf 87-91.
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Nonlinear and localized modes in hydrodynamics and vortex dynamicsYip, Lai-pan. January 2007 (has links)
Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.
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On the Cauchy problem for the linearized GPKdV and gauge transformations for a quadratic pencil and AKNS system /Yordanov, Russi Georgiev, January 1992 (has links)
Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 52-54). Also available via the Internet.
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Stability and dynamics of solitary waves in nonlinear optical materials /Farnum, Edward D. January 2005 (has links)
Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (leaves 94-98).
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Extensions of the nonlinear Schrödinger equation using MathematicaBeech, Robert. January 2009 (has links)
Thesis (Ph.D.)--University of Western Sydney, 2009. / A thesis presented to the University of Western Sydney, College of Health and Science, School of Computing and Mathematics, in fulfilment of the requirements for the degree of Doctor of Philosophy (PhD). Includes bibliographies.
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Topics in the physics of underdamped Josephson systemsTornes, Ivan Edward, January 2006 (has links)
Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 153-159).
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Estrutura algébrica dos modelos integráveisFrança, G. S [UNESP] 16 April 2007 (has links) (PDF)
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000855807.pdf: 420265 bytes, checksum: 0d551ee445aae9709b18c8ce3eed7d19 (MD5) / A estrutura das álgebras de Kac-Moody e suas representações constituem o ingrediente básico para a construção de hierarquias integráveis e de suas respectivas soluções solitônicas (obtidas através do método de dressing). Diversos modelos contidos nas hierarquias mKdVeAKNS são discutidos em detalhe e uma nova classe de equações integráveis, correspondente a graus negativos pares da hierarquia mKdV, é proposta. Diferentes soluções e operadores de recursão são construídos para ambas as hierarquias / The structure of Kac-Moody algebras and its representations constitute a basic ingredient for the construction of integrable hierarchies and its soliton solutions (obtained from the dressing method). Several models within the mKdV and KNS hierarchies are discussed in detail and some new integrable equations, corresponding to negative even grades of the mKdV hierarchy, are proposed. Different solutions and recursion operators are constructed for both hierarchies
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Soluções solitônicas por aproximantes de Padé via método iterativo de Taylor / Solitonic solutions via Pade approximants and an iterative Taylor methodBiazotti, Herbert Antonio 28 September 2018 (has links)
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Sobre as referências
1 VACHASPATI, T. "Kinks and Domain Walls". New York: [s.n.], 2006. (remover aspas)
2 RAJARAMAN, R. "Solitons and Instantons". North-Holland, Amsterdam: [s.n.], 1989. (remover aspas)
Rever paginação de alguns periódicos, pois não há traço indicando o intervalo de páginas
Mais informações acesse o link: http://www2.feg.unesp.br/Home/Biblioteca21/diretrizes-2016.pdf
Agradecemos a compreensão.
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Previous issue date: 2018-09-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Certos sistemas físicos podem ser descritos por uma classe de equações não-lineares. Essas equações descrevem pacotes de onda chamado de sólitons que tem aplicações em diversas áreas, por exemplo, Óptica, Cosmologia, Matéria Condensada e Física de Partículas. Alguns métodos foram desenvolvidos ao longo dos anos para encontrar as soluções dessas equações. Buscaremos essas soluções usando o que chamamos de Método Iterativo de Taylor (MIT), que fornece uma solução aproximada em polinômio de Taylor de forma distinta do que se tem na literatura. Usaremos o MIT para calcular soluções por aproximantes de Padé que são razões entre dois polinômios e fornecem soluções melhores que o polinômio de Taylor que o gerou. Inicialmente resolveremos a equação de um modelo de um campo denominado λφ4 . Em seguida resolveremos um modelo com dois campos escalares acoplados e encontraremos uma solução analítica aproximada em casos onde não existe solução analítica, explorando a diversidade das soluções do modelo. Usando essa abordagem por aproximantes de Padé veremos que há algumas vantagens em relação a outros métodos. / Certain physical systems can be described by a class of non-linear differential equations. Those equations describe wave packets called solitons which have applications in several areas, for example, Optics, Cosmology, Condensed Matter, and Particle Physics. Some methods have been developed over the years to find solutions to these equations. We will look for those solutions using what we call the Taylor Iterative Method (TIM), which provides an approximate solution in terms of a Taylor’s polynomial in a unusual way, regarding the present literature. We will use TIM to calculate solutions by Padé approximants, which are ratios between two polynomials and provide better solutions than the Taylor polynomial itself. We first solve the field equation of a model called λφ4. Then we will solve a model with two coupled scalar fields and find an approximate analytic solution in cases where there is no known analytical solution, exploring the diversity of the solutions of the model. We will see that there are some advantages in using the Padè approximants as compared to other methods / 1586040
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Solitons de Yamabe e métricas CPELeandro Neto, Benedito 24 November 2015 (has links)
Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Programa de Pós-Graduação em Matemática, 2015. / Submitted by Patrícia Nunes da Silva (patricia@bce.unb.br) on 2016-01-26T14:54:49Z
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2015_BeneditoLeandroNeto_Parcial.pdf: 248614 bytes, checksum: aa0e94e4558b4314ccdb73a1bce22eaf (MD5) / Provamos que (anti)self dual solitons gradientes (quasi) Yamabe com curvatura seccional positiva são rotacionais simétricos. Além disso, mostramos que, (anti)self dual solitons gradientes de Yamabe tem uma estrutura de produto torcido muito particular desde que a função potencial não tenha pontos críticos. Consideramos solitons gradientes de Yamabe conformes a espaços pseudo-Euclidianos n-dimensionais. Caracterizamos todos os solitons que são invariantes pela ação de um grupo de translação (n-1)-dimensional e obtemos os solitons tipo estável. Como aplicação, obtemos um exemplo de soliton gradiente de Yamabe estável completo, conforme a um espaço Lorentziano. Investigamos também os pontos críticos do funcional curvatura escalar total restrito a um espaço de métricas com curvatura escalar constante e volume unitátio que denotamos por métricas CPE. Foi conjecturado nos anos 1980 que toda métrica CPE é, necessariamente, Einstein. Provamos que métricas CPE, no caso de dimensão quatro, com tensor W+ harmônico são isométricas à esfera S4 dada uma condição integral. No caso n-dimensional, provamos uma condição necessária e suficiente sobre a norma do gradiente da função potencial para que a métrica CPE seja Einstein. / We prove that an (anti)self dual quasi Yamabe gradient soliton with positive sectional curvature is rotationally symmetric. We also prove that four dimensional (anti) self dual gradient Yamabe soliton has a special warped product structure provided that the potential function has no critical points. We consider gradient Yamabe solitons, conformal to an n-dimensional pseudo-Euclidean space. We characterize all such solitons which are invariant under the action of an (n-1)-dimensional translation group and we obtain the steady solitons. Applications provide an explicit example of a complete steady gradient Yamabe soliton, conformal to the Lorentzian space. We also investigate the critical points of the total scalar curvature functional restricted to space of metrics with constant scalar curvature of unitary volume, for simplicity CPE metrics. It was conjectured in the 1980's that every CPE metric must be Einstein. We prove that a 4-dimensional CPE metric with harmonic tensor W+ must be isometric to a round sphere S4 provided an integral condition is satisfied. We also give a necessary and sufficient condition on the norm of the gradient of the potential function for a CPE metric to be Einstein.
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