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Clustering and chaos in globally coupled oscillatorsBanaji, Murad January 2001 (has links)
No description available.
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Systèmes elliptiques issus de la modélisation des supraconducteurs / Elliptical systems related to superconductor modelZhang, Peng 05 December 2014 (has links)
Ce travail porte sur des équations aux dérivées partielles issues de la physique mathématique, plus particulièrement sur celles régissant la supraconductivité. Ainsi, la majorité du travail concerne le modèle de Ginzburg-Landau, qui est un modèle macroscopique de supraconducteurs de type-II. Ce travail est divisé en deux parties principales: La première partie se focalise sur l'analyse des vortex du modèle de Ginzburg-Landau en deux dimensions pour les supraconducteurs de type-II, modèle conduisant à une estimation de la variation du nombre de vortex et à l'optimalité du réseau d'Abrikosov parmi les réseaux de Bravais. Nous avons également étudié certains modèles de stuctures des matériaux comme ceux de Lennard-Jones et de Thomas-Fermi. La seconde partie est consacrée à la fonctionnelle de Ginzburg-Landau en dimension $n$. Deux résultats principaux sont obtenus. L'un porte sur l'énergie renormalisée pour les minimiseurs de la fonctionnelle de Ginzburg-Landau. L'autre concerne les limites des solutions de l'équation de Ginzburg-Landau. Ces deux résultats sont fortement reliés aux applications $n$-harmoniques / Our work focus on the elliptic partial differential Equations arising from the mathematical physics, especially from the superconductivity. Therefore most of our work is on the Ginzburg-Landau model, which is a macroscopic model for the type-II superconductors. The work is divided into two big parts : this first part is on the vortices analysis of the Ginzburg-Landau model of Type-II superconductors in 2 dimensions, including the variations of the number of vortices and optimality of Abrikosov lattices among Bravais Lattices. We also have done some work related to the material structure, for example, the Lennard-Jones model and the Thomas-Fermi model. This second part is on the Ginzburg-Landau functional in $n$-dimensional case. Two main results are contained in this part: One is on the renormalized energy for minimizer of $n$-dimensional Ginzburg-Landau functional; The other one is on the limits of solutions to Ginzburg-Landau equations in $n$ dimension. Both of these two results are closely related to the p-harmonic maps
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Estudo computacional de vórtices em discos supercondutores na presença de campo magnético externo e dipolo magnéticoSILVA, Fillipe Cesar Oliveira da 31 July 2015 (has links)
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Previous issue date: 2015-07-31 / CNPq / O avan¸co tecnol´ogico tem permitido a constru¸c˜ao de sistemas supercondutores
de baixas dimensionalidades, da ordem do comprimento de coerˆencia, ξ, e/ou comprimento
de penetra¸c˜ao, λ. Esses sistemas s˜ao chamados de supercondutores mesosc
´opicos, onde se ´e capaz de alcan¸car correntes e campos cr´ıticos mais elevados.
Dependendo do tamanho do supercondutor mesosc´opico, configura¸c˜oes de mol´eculas
de v´ortices s˜ao obtidas tanto experimentalmente, como teoricamente usando a teoria
de GL e a teoria de London. Nesse trabalho, utilizaremos o m´etodo variacional
aplicado `a teoria de Ginzburg-Landau e a teoria de London para estudar v´ortices em
discos supercondutores finos em campo magn´etico externo homogˆeneo e confinados
em um potencial produzido por um dipolo magn´etico, respectivamente.
Estudamos, inicialmente, discos supercondutores mesosc´opicos imersos em um
meio isolante na presen¸ca de um campo magn´etico uniforme perpendicular ao plano
do disco. Desprezamos os efeitos de desmagnetiza¸c˜ao e expandimos o parˆametro de
ordem em fun¸c˜oes ortonormais do operador energia cin´etica. Para a obten¸c˜ao de
v´ortices gigantes, representamos o parˆametro de ordem por apenas uma autofun¸c˜ao.
Para estados de multiv´ortices, o parˆametro de ordem ´e representado como uma expans
˜A
£o de duas autofun¸c˜oes, com vorticidades distintas. Observamos o comportamento
da varia¸c˜ao da energia livre em fun¸c˜ao do campo magn´etico aplicado, para
diversos tamanhos de discos supercondutores, acompanhando seus estados mais favor
´aveis.
Na segunda parte da disserta¸c˜ao, estudamos a disposi¸c˜ao dos v´ortices e antiv´ortices
confinados em um disco supercondutor atrav´es de campo magn´etico n˜ao homogˆeneo gerado por um dipolo magn´etico na dire¸c˜ao do eixo de simetria do disco, que possibilita
a coexistˆencia de v´ortices e antiv´ortices, com diferentes configura¸c˜oes poss´ıveis.
Para obtermos os estados com menor energia dentre as possibildades testadas, utilizamos
como parˆametro de controle trˆes vari´aveis: a distˆancia radial ao eixo de simetria
do dipolo, r0, a altura do dipolo em rela¸c˜ao ao disco, z0, e a magnitude do dipolo
magn´etico, m0. Buscamos o valor da magnitude do dipolo no qual o estado sem
v´ortices deixa de ser o metaest´avel, permitindo a existˆencia de estados com v´ortices.
Os resultados mostram uma competi¸c˜ao entre o potencial de confinamento, efeitos
produzidos pela borda do supercondutor e a intera¸c˜ao entre v´ortices, para manter os
v´ortices e antiv´ortices no interior do disco. / Technological breakthroughs have allowed the construction of superconducting
systems in low dimensionalities, which are of the order of the coherence length, ξ,
and/or of the penetration depht, λ. These systems are called mesoscopic superconductors,
which are capable of achieving high critical current and fields. Depending on
the size of the mesoscopic superconducting, configurations of vortices molecules are
obtained either experimentally or theoretically using the GL theory and the theory
of London. In the present work, we apply the variational method to the Ginzburg-
Landau theory and also the London theory to study vortices in thin superconductors
disks submitted to an inhomogeneous magnetic field and confined to a potential produced
by a magnetic dipole, respectively.
We studied initially mesoscopic superconducting disks immersed in a insulation
mean in the presence of a uniform magnetic field which is perpendicular to the plane
of the disk. We neglect the demagnetization effects and expand the order parameter
in orthonormal functions of the kinetic energy operator. To obtain giant vortices,
the order parameter has only one eigenfunction. For multivortex states, the order
parameter consists of two eigenfunctions, with different vorticities. We study the
behaviour of free energy variation due to the applied magnetic field for different sizes
of superconductor disks, and for different vortex states. In the second part
of the dissertation, we study the arrangement of vortices and antivortices in a superconducting
disk submitted to a non-homogeneous magnetic field generated by an
out-plane magnetic dipole, which allows the coexistence of vortices and antivortices
on different configurations. To get the states with lowest energy among the tested possibilities, we used three variables as control parameters: the radial distance from
the disk symmetry axis to the dipole axis of symmetry, r0, the height of the dipole
relative to the disc, z0, and the magnitude of the magnetic dipole, m0. We seek the
value of the magnitude of the dipole in which the state with no vortices ceases to
be the most stable one, allowing the existence of states with vortices. The results
show a competition among the confinement potential, effects produced by the edge
of the superconductor, and the interaction between vortices to keep the vortices and
antivortices within the disc.
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Supercondutividade e a transição de fase supercondutora: Misturas de duas fases na cerâmica (Hg,Re 1223)ELEUTERIO, F. H. S. 15 December 2017 (has links)
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Previous issue date: 2017-12-15 / O foco deste trabalho é a investigação das duas fases intrínsecas de supercondutores estruturais, utilizando como objeto de estudo a resposta magnética e a sua composição granular. Ao investigar a susceptibilidade magnética ac na cerâmica policristalina a base de mercúrio dopada com rênio (Hg0.82Re0.18Ba2Ca2Cu3O8.16) (Hg,Re)-
1223) com o precursor com teor ótimo de oxigênio, pulverizada (reduzida a pó e peneirada) foi possível determinar a temperatura crítica da amostra e observar que ela depende do tamanho de cada do grão. Para a partícula de 20 μm foi encontrada somente uma temperatura crítica de 133K, porém são observadas duas temperaturas críticas (133K e 98 K) ao ser reduzir ainda mais o tamanho da partícula, a uma escala
mesoscópica de 600 nm. Este fato foi elucidado por uma extensão da teoria de Ginzburg-Landau utilizando dois parâmetros de ordem para parametrizar o campo escalar complexo e fazendo a conexão com o modelo microscópico responsável por descrever as peculiaridades destes tipos de grãos.
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Supercondutividade e a transição de fase supercondutora: Misturas de duas fases na cerâmica (Hg,Re 1223)ELEUTERIO, F. H. S. 15 December 2017 (has links)
Made available in DSpace on 2018-08-01T21:59:52Z (GMT). No. of bitstreams: 1
tese_11668_Tese final Fernando Henrique Santos Eleutério - PPGFis20180316-142248.pdf: 1478639 bytes, checksum: 8a421c51018e8816f936d7cac9314677 (MD5)
Previous issue date: 2017-12-15 / O foco deste trabalho é a investigação das duas fases intrínsecas de supercondutores estruturais, utilizando como objeto de estudo a resposta magnética e a sua composição granular. Ao investigar a susceptibilidade magnética ac na cerâmica policristalina a base de mercúrio dopada com rênio (Hg0.82Re0.18Ba2Ca2Cu3O8.16) (Hg,Re)-
1223) com o precursor com teor ótimo de oxigênio, pulverizada (reduzida a pó e peneirada) foi possível determinar a temperatura crítica da amostra e observar que ela depende do tamanho de cada do grão. Para a partícula de 20 μm foi encontrada somente uma temperatura crítica de 133K, porém são observadas duas temperaturas críticas (133K e 98 K) ao ser reduzir ainda mais o tamanho da partícula, a uma escala
mesoscópica de 600 nm. Este fato foi elucidado por uma extensão da teoria de Ginzburg-Landau utilizando dois parâmetros de ordem para parametrizar o campo escalar complexo e fazendo a conexão com o modelo microscópico responsável por descrever as peculiaridades destes tipos de grãos.
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Vortex motion in type II superconductorsRichardson, Giles William January 1995 (has links)
No description available.
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Processos térmicos e estado resistivo em supercondutores mesoscópicos : dinâmica de vórtices e gradiente e difusão térmica estudados usando o teorema da energia livre e o formalismo de Ginzburg-Landau /Duarte, Elwis Carlos Sartorelli. January 2018 (has links)
Orientador: Rafael Zadorosny / Resumo: Este trabalho está estruturado em duas partes. A primeira, envolve o estudo do estado de vórtices e comportamento magnético de um supercondutor mesoscópico submetido a um gradiente térmico. Foi veri cado que a influência de um gradiente térmico altera o estado de vórtice gigante e pode levar a magnetização a ter um comportamento anômalo, o qual depende do parâmetro de Ginzburg-Landau e das temperaturas nas regiões "quente" e "fria". Na segunda parte, abordamos o estado resistivo durante o movimento de um vórtice e durante a dinâmica de par vórtice-antivórtice (V-AV) para os tipos de Abrikosov e Cinemáticos. Estudamos quais parâmetros afetam as propriedades do não equilíbrio e os mecanismos de dissipação presentes no processo de difusão térmica. Para os processos envolvendo vórtice ou V-AV de Abrikosov, os mecanismos de dissipação devido à processos de relaxação contribuem para a maior parte da potência total dissipada e, consequentemente, exercem uma grande contribuição para a variação de temperatura. Por outro lado, para o caso de V-AV cinemáticos, os elétrons normais aparecem como principal mecanismo de dissipação, todavia os processos de relaxação tem uma contribuição considerável para esse caso. Para realizar tais estudos, utilizamos o teorema da energia livre e as equações de Ginzburg- Landau generalizadas. / Abstract: This work is structured in two parts. In the rst one, the vortices states and the magnetic behavior were studied for a mesoscopic superconductor under a thermal gradient. It was veri ed that the thermal gradient changes the giant vortex state and could lead a exotic behavior of the magnetization curve, depending on the parameter and the temperature of the hot and the cold . In the second part, the focus was the resistive state during one vortex motion and during the annihilation process of a vortex-antivortex (V-AV) pair both with Abrikosov and Kinematic types. We de ned which parameters a ect the nonequilibrium proprieties and the dissipative mechanisms present in the thermal di usion processes. For the cases involving a vortex or an Abrikosov's V-AV pair, the dissipative mechanisms due to the relaxation process have the major contribution for the total power dissipated power and consequently, exert great contribuition on the temperature variation. On the other hand, for the case of kinematic V-AV, the normal eletrons rised as the main dissipative mechanism, however relaxation process has a considerable contribuition for this case. To realize such studies, we used the free energy theorem and the generalized Ginzburg-Landau equations. / Doutor
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Existence of Critical Points for the Ginzburg-Landau Functional on Riemannian ManifoldsMesaric, 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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Existence of Critical Points for the Ginzburg-Landau Functional on Riemannian ManifoldsMesaric, 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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A numerical study of steady-state vortex configurations and vortex pinning in type-II superconductorsKim, Sangbum 12 April 2006 (has links)
In part I, a numerical study of the mixed states in a mesoscopic type-II superconducting
cylinder is described. Steady-state configurations and transient behavior of
the magnetic vortices for various values of the applied magnetic field H are presented.
Transitions between different multi-vortex states as H is changed is demonstrated by
abrupt changes in vortex configurations and jumps in the B vs H plot. An efficient
scheme to determine the equilibrium vortex configuration in a mesoscopic system at
any given applied field, not limited to the symmetry of the system, is devised and
demonstrated.
In part II, a superconducting thin film is subject to a non-uniform magnetic field
from a vertical magnetic dipole, consisting of two magnetic monopoles of opposite
charges. For a film with constant thickness and with no pins, it has been found that
the film carries two pairs of vortex-antivortex in the steady state in the imposed
flux range of 2.15 < (Phi)+ < 2.90 (in units of flux quantum) and no vortex at all for
(Phi)+ <= 2.15. Transitions from a superconducting state with 3 pairs of vortex-antivortex
to one with 2 pairs, where a pair of vortex-antivortex annihilates, have been observed
in the pseudo-time sequence. With a perturbation with antidots (holes), vortexantivortex
pair has been created for lower magnetic fluxes down to (Phi)+ = 1.3.
In the sample of size 16(Xi) x 16(Xi), the attraction force between the vortex and
antivortex always dominates over the pinning force, so that they eventually come out
of pins, move toward each other, and annihilate each other. The annihilation rate,
measured with time taken for the annihilation, is reduced noticeably by the increase
of the distance between pins, or the increase in the pin size. A simulation of the
magnetic vortex pinning in the sample of size 32(Xi) x 32(Xi) suggests we are likely to
achieve pinning of the vortex-antivortex pair with the sample size around this and
vortex-antivortex separation of 22(Xi). Using this sample as a template, the maximum
density of pinned vortices achievable is calculates to be about 7.6 x 10^14 vortices/m2
for (Xi) =~ 1.6A°.
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