Relevant bibliographies by topics / Ginzburg-Landau equation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Ginzburg-Landau equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Ginzburg-Landau equation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Ginzburg-Landau equation"

1

CHIRON, DAVID. "BOUNDARY PROBLEMS FOR THE GINZBURG–LANDAU EQUATION." Communications in Contemporary Mathematics 07, no. 05 (October 2005): 597–648. http://dx.doi.org/10.1142/s0219199705001908.

Full text
Abstract:
We provide a study at the boundary for a class of equations including the Ginzburg–Landau equation as well as the equation of travelling waves for the Gross–Pitaevskii model. We prove Clearing-Out results and an orthogonal anchoring condition of the vortex on the boundary for the Ginzburg–Landau equation with magnetic field.
APA, Harvard, Vancouver, ISO, and other styles
2

Adomian, G., and R. E. Meyers. "The Ginzburg-Landau equation." Computers & Mathematics with Applications 29, no. 3 (February 1995): 3–4. http://dx.doi.org/10.1016/0898-1221(94)00222-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Gao, Hongjun, and Keng-Huat Kwek. "Global existence for the generalised 2D Ginzburg-Landau equation." ANZIAM Journal 44, no. 3 (January 2003): 381–92. http://dx.doi.org/10.1017/s1446181100008099.

Full text
Abstract:
AbstractGinzburg-Landau type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics and chemistry. Most work so far has concentrated on Ginzburg-Landau type equations with one spatial variable (1D). In this paper, the authors study a complex generalised Ginzburg-Landau equation with two spatial variables (2D) and fifth-order and cubic terms containing derivatives. Based on detail analysis, sufficient conditions for the existence and uniqueness of global solutions are obtained.
APA, Harvard, Vancouver, ISO, and other styles
4

Li, Xiao-Yu, Yu-Lan Wang, and Zhi-Yuan Li. "Numerical simulation for the fractional-in-space Ginzburg-Landau equation using Fourier spectral method." AIMS Mathematics 8, no. 1 (2022): 2407–18. http://dx.doi.org/10.3934/math.2023124.

Full text
Abstract:
<abstract><p>This paper uses the Fourier spectral method to study the propagation and interaction behavior of the fractional-in-space Ginzburg-Landau equation in different parameters and different fractional derivatives. Comparisons are made between the numerical and the exact solution, and it is found that the Fourier spectral method is a satisfactory and efficient algorithm for capturing the propagation of the fractional-in-space Ginzburg-Landau equation. Experimental findings indicate that the proposed method is easy to implement, effective and convenient in the long-time simulation for solving the proposed model. The influence of the fractional Laplacian operator on the fractional-in-space Ginzburg-Landau equation and some of the propagation behaviors of the 3D fractional-in-space Ginzburg-Landau equation are observed. In Experiment 2, we observe the propagation behaviors of the 3D fractional-in-space Ginzburg-Landau equation which are unlike any that have been previously obtained in numerical studies.</p></abstract>
APA, Harvard, Vancouver, ISO, and other styles
5

Ipsen, M., F. Hynne, and P. G. Sørensen. "Amplitude Equations and Chemical Reaction–Diffusion Systems." International Journal of Bifurcation and Chaos 07, no. 07 (July 1997): 1539–54. http://dx.doi.org/10.1142/s0218127497001217.

Full text
Abstract:
The paper discusses the use of amplitude equations to describe the spatio-temporal dynamics of a chemical reaction–diffusion system based on an Oregonator model of the Belousov–Zhabotinsky reaction. Sufficiently close to a supercritical Hopf bifurcation the reaction–diffusion equation can be approximated by a complex Ginzburg–Landau equation with parameters determined by the original equation at the point of operation considered. We illustrate the validity of this reduction by comparing numerical spiral wave solutions to the Oregonator reaction–diffusion equation with the corresponding solutions to the complex Ginzburg–Landau equation at finite distances from the bifurcation point. We also compare the solutions at a bifurcation point where the systems develop spatio-temporal chaos. We show that the complex Ginzburg–Landau equation represents the dynamical behavior of the reaction–diffusion equation remarkably well, sufficiently far from the bifurcation point for experimental applications to be feasible.
APA, Harvard, Vancouver, ISO, and other styles
6

Barybin, Anatoly A. "Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation." Advances in Condensed Matter Physics 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/425328.

Full text
Abstract:
Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary) Ginzburg-Landau equation and Schrödinger's equation for the macroscopic wave function (often called the order parameter) by using the well-known Madelung-Feynman approach to representation of the quantum-mechanical equations in hydrodynamic form. Such an approach has given (a) three different contributions to the resulting chemical potential for the superfluid component, (b) a general hydrodynamic equation of superfluid motion, (c) the continuity equation for superfluid flow with a relaxation term involving the phenomenological parameters and , (d) a new version of the time-dependent Ginzburg-Landau equation for the modulus of the order parameter which takes into account dissipation effects and reflects the charge conservation property for the superfluid component. The conventional Ginzburg-Landau equation also follows from our continuity equation as a particular case of stationarity. All the results obtained are mutually consistent within the scope of the chosen phenomenological description and, being model-neutral, applicable to both the low- and high- superconductors.
APA, Harvard, Vancouver, ISO, and other styles
7

Huang, Chunyan. "On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/607028.

Full text
Abstract:
We study the analytic property of the (generalized) quadratic derivative Ginzburg-Landau equation(1/2⩽α⩽1)in any spatial dimensionn⩾1with rough initial data. For1/2<α⩽1, we prove the analyticity of local solutions to the (generalized) quadratic derivative Ginzburg-Landau equation with large rough initial data in modulation spacesMp,11-2α(1⩽p⩽∞). Forα=1/2, we obtain the analytic regularity of global solutions to the fractional quadratic derivative Ginzburg-Landau equation with small initial data inB˙∞,10(ℝn)∩M∞,10(ℝn). The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroupe-a+it-Δαto overcome the derivative in the nonlinear term.
APA, Harvard, Vancouver, ISO, and other styles
8

Secer, Aydin, and Yasemin Bakir. "Chebyshev wavelet collocation method for Ginzburg-Landau equation." Thermal Science 23, Suppl. 1 (2019): 57–65. http://dx.doi.org/10.2298/tsci180920330s.

Full text
Abstract:
The main aim of this paper is to investigate the efficient Chebyshev wavelet collocation method for Ginzburg-Landau equation. The basic idea of this method is to have the approximation of Chebyshev wavelet series of a non-linear PDE. We demonstrate how to use the method for the numerical solution of the Ginzburg-Landau equation with initial and boundary conditions. For this purpose, we have obtained operational matrix for Chebyshev wavelets. By applying this technique in Ginzburg-Landau equation, the PDE is converted into an algebraic system of non-linear equations and this system has been solved using MAPLE computer algebra system. We demonstrate the validity and applicability of this technique which has been clarified by using an example. Exact solution is compared with an approximate solution. Moreover, Chebyshev wavelet collocation method is found to be acceptable, efficient, accurate and computational for the non-linear or PDE.
APA, Harvard, Vancouver, ISO, and other styles
9

Beaulieu, Anne. "Bounded solutions for an ordinary differential system from the Ginzburg–Landau theory." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 6 (August 14, 2020): 3378–408. http://dx.doi.org/10.1017/prm.2019.68.

Full text
Abstract:
In this paper, we look at a linear system of ordinary differential equations as derived from the two-dimensional Ginzburg–Landau equation. In two cases, it is known that this system admits bounded solutions coming from the invariance of the Ginzburg–Landau equation by translations and rotations. The specific contribution of our work is to prove that in the other cases, the system does not admit any bounded solutions. We show that this bounded solution problem is related to an eigenvalue problem.
APA, Harvard, Vancouver, ISO, and other styles
10

Pascucci, Filippo, Andrea Perali, and Luca Salasnich. "Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions." Condensed Matter 6, no. 4 (December 1, 2021): 49. http://dx.doi.org/10.3390/condmat6040049.

Full text
Abstract:
We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Ginzburg-Landau equation"

1

Liu, Weigang. "A General Study of the Complex Ginzburg-Landau Equation." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90886.

Full text
Abstract:
In this dissertation, I study a nonlinear partial differential equation, the complex Ginzburg-Landau (CGL) equation. I first employed the perturbative field-theoretic renormalization group method to investigate the critical dynamics near the continuous non-equilibrium transition limit in this equation with additive noise. Due to the fact that time translation invariance is broken following a critical quench from a random initial configuration, an independent ``initial-slip'' exponent emerges to describe the crossover temporal window between microscopic time scales and the asymptotic long-time regime. My analytic work shows that to first order in a dimensional expansion with respect to the upper critical dimension, the extracted initial-slip exponent in the complex Ginzburg-Landau equation is identical to that of the equilibrium model A. Subsequently, I studied transient behavior in the CGL through numerical calculations. I developed my own code to numerically solve this partial differential equation on a two-dimensional square lattice with periodic boundary conditions, subject to random initial configurations. Aging phenomena are demonstrated in systems with either focusing and defocusing spiral waves, and the related aging exponents, as well as the auto-correlation exponents, are numerically determined. I also investigated nucleation processes when the system is transiting from a turbulent state to the ``frozen'' state. An extracted finite dimensionless barrier in the deep-quenched case and the exponentially decaying distribution of the nucleation times in the near-transition limit are both suggestive that the dynamical transition observed here is discontinuous. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-SC0002308
Doctor of Philosophy
The complex Ginzburg-Landau equation is one of the most studied nonlinear partial differential equation in the physics community. I study this equation using both analytical and numerical methods. First, I employed the field theory approach to extract the critical initial-slip exponent, which emerges due to the breaking of time translation symmetry and describes the intermediate temporal window between microscopic time scales and the asymptotic long-time regime. I also numerically solved this equation on a two-dimensional square lattice. I studied the scaling behavior in non-equilibrium relaxation processes in situations where defects are interactive but not subject to strong fluctuations. I observed nucleation processes when the system under goes a transition from a strongly fluctuating disordered state to the relatively stable “frozen” state where its dynamics cease. I extracted a finite dimensionless barrier for systems that are quenched deep into the frozen state regime. An exponentially decaying long tail in the nucleation time distribution is found, which suggests a discontinuous transition. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-SC0002308.
APA, Harvard, Vancouver, ISO, and other styles
2

Braun, Robert, and Fred Feudel. "Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation." Universität Potsdam, 1996. http://opus.kobv.de/ubp/volltexte/2007/1409/.

Full text
Abstract:
We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.
APA, Harvard, Vancouver, ISO, and other styles
3

Cruz-Pacheco, Gustavo. "The nonlinear Schroedinger limit of the complex Ginzburg-Landau equation." Diss., The University of Arizona, 1995. http://hdl.handle.net/10150/187238.

Full text
Abstract:
This work consists of a study of the complex Ginzburg-Landau equation (CGL) as a perturbation of the nonlinear Schrodinger equation (NLS) in one dimension under periodic boundary conditions. Using an averaging technique which is similar to a Melnikov method for pde's, necessary conditions are derived for the persistence of NLS solutions under the CGL perturbation. For the traveling wave solutions, these conditions are derived for a general nonlinearity and written explicitly as two equations for the two continuous parameters which determine the NLS traveling wave. It is shown using a Melnikov argument that in this case these two conditions are sufficient provided they satisfy a transversality condition. As a concrete example, the equations for the parameters are solved numerically in the important case of the CGL equation with a cubic nonlinearity. For the case of the CGL equation with a general power nonlinearity, it is proved that the NLS homoclinic orbits to rotating waves are destroyed by the CGL perturbation. Special attention is dedicated to the cubic case. For this nonlinearity, the NLS equation is a completely integrable Hamiltonian system and a much larger family of its solutions can be written explicitly. The necessary conditions for the persistence of the NLS isospectral manifold are written explicitly as a system of equations for the simple periodic eigenvalues. As an example, the conditions for an even genus two solution are written down as a system of three equations with three unknowns.
APA, Harvard, Vancouver, ISO, and other styles
4

Horsch, Karla 1968. "Attractors for Lyapunov cases of the complex Ginzburg-Landau equation." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/282419.

Full text
Abstract:
A special case of the complex Ginzburg-Landau (CGL) equation possessing a Lyapunov functional is identified. The global attractor of this Lyapunov CGL (LCGL) is studied in one spatial dimension with periodic boundary conditions. The LCGL may be viewed as a dissipative perturbation of the nonlinear Schrodinger equation (NLS), a completely integrable Hamiltonian system. The o-limit sets of the LCGL are identified as compact, connected unions of subsets of the stationary points of the flow. The stationary points do not depend on the strength of the perturbation, and so neither do the o-limit sets. However, the basins of attraction do depend sensitively on the perturbation strength. To determine the stability of the o-limit sets, the global Lyapunov functional is studied. Using the integrable NLS machinery, the second variation of the Lyapunov functional is diagonalized. An analysis of the diagonal elements yields that certain LCGL stationary points are stable. We are able to analyze the basins of attraction for a planar toy problem, which like the LCGL, is a dissipative perturbation of a Hamiltonian system. For this problem, almost every phase point is in a basin of attraction of an asymptotically stable stationary point. As the perturbation tends to zero, these basins become intermingled and the event of a fixed phase point being captured into a particular basin becomes probabilistic. Formulas for computing the probabilities of capture are given. These formulas are substantiated through a formal asymptotic analysis and numerical experiments. Such a probabilistic description of the basins of attraction is not completed for the infinite dimensional LCGL.
APA, Harvard, Vancouver, ISO, and other styles
5

Aguareles, Carrero Maria. "Interaction of spiral waves in the general complex Ginzburg-Landau equation." Doctoral thesis, Universitat Politècnica de Catalunya, 2007. http://hdl.handle.net/10803/5854.

Full text
Abstract:
Molts sistemes físics tenen la propietat que la seva dinàmica ve definida per algun tipus de difussió espaial en competició amb un fenòmen de reacció, com per exemple en el cas de dos components químics que reaccionen al mateix temps que es difon l'un en el si de l'altre. La presència d'aquests dos fenòmens, la difusió i la reacció, sovint dóna lloc a patrons no homogenis de gran riquesa. Els models matemàtics que descriuen aquest tipus de comportament són normalment equacions en derivades parcials les solucions de les quals representen aquests patrons.

En aquesta tesi s'analitza l'equació de Ginzburg-Landau complexa general, que és una equació en derivades parcials de reacció-difusió que s'utilitza sovint com a model matemàtic per a descriure sistemes oscil·latoris en dominis extensos. En particular estudiem els patrons que sorgeixen en el pla quan s'imposa que el grau de Brouwer de la solució no sigui nul. Aquests patrons estan formats per ones de rotació en forma d'espirals, és a dir, les corbes de nivell de la solució formen espirals que emanen dels punts on la funció s'anul·la. Quan la solució s'anul·la només en un punt i per tant només hi ha una espiral, tota la dependència temporal apareix en el terme de freqüència. Així doncs, la funció solució es pot expressar com a funció del radi polar i en termes del seu grau topològic i la freqüència de l'ona. Per tant, aquestes solucions es poden expressar en termes d'un sistema d'equacions diferencials ordinàries. Aquestes solucions només existeixen per una certa freqüència que depèn unívocament dels paràmetres de l'equació i, com a conseqüència i degut a la relació de dispersió entre el nombre d'ones i la freqüència, el nombre d'ones a l'infinit, l'anomenat nombre d'ones asimptòtic, ve també determinat unívocament pels paràmetres. Quan les solucions tenen més d'un zero aïllat la condició sobre el grau de la funció fa que de cada zero sorgeixi una espiral diferent i aquestes es mouen en el pla mantenint la seva estructura local. En aquest treball s'usen tècniques d'anàlisi asimptòtica per trobar equacions del moviment per als centres de les espirals i es troba que aquesta evolució temporal és lenta. En concret, per la distàncies relatives grans entre els centres de les espirals, l'escala de temps per a la seva dinàmica ve donada pel logaritme de l'invers d'aquesta distància. Es demostra que aquestes equacions del moviment són diferents en funció de la relació entre els paràmetres de l'equació de Ginzburg-Landau complexa i la separació entre els centres de les espirals, i que la forma com es passa d'unes equacions a les altres és molt singular. També es demostra que el nombre d'ones asimptòtic per al cas de sistemes amb diverses espirals també està unívocament determinat pels paràmetres però no obstant, el cas de sistemes amb diverses espirals es diferencia del cas d'una única ona en què deixa de ser constant i evoluciona al mateix ritme que la velocitat dels centres de les espirals.
Many physical systems have the property that its dynamics is driven by some kind of spatical diffusion that is in competition with a reaction, like for instance two chemical species that react at the same time that there is a diffusion of each of them into the other. This interplay between reaction and diffusion produce non-homogeneous patterns that can sometimes be very rich. The mathematical models that describe this kind of behaviours are usually nonlinear partial differential equations whose solutions represent these patterns.

In this thesis we focus on an especific reaction-diffusion equation that is the so-called general complex Ginzburg-Landau equation that is used as a model for oscillatory systems in extended domains. In particular we are interested in the type of patterns in the plane that arise when the solutions have a non-vanishing Brouwer degree. These patterns have the property that they exhibit rotating waves in the shape of spirals, which means that the contour lines arrange in the shape of spirals that emerge from the points where the solution vanishes. When the solution vanishes only at one point all the time dependence appears as a frequency term so the solutions can be expressed as a function of the polar radius and in terms of the topological degree of the solution and the frequency of the wave. Therefore, these solutions can be expressed in terms of a system of ordinary differential equations. These solutions do only exist with a given frequency, and as a consequence and due to the existence of a dispresion relation, the wavenumber far from the origin, the so-called asymptotic wavenumber, is also unique. When the solutions have more than one isolated zero, the condition on the degree of the function has the effect of producing several spirals that emerge from the different zeros of the solution. These spirals evolve in time keeping their structure but moving around on the plane. In this work we use asymptotic analysis techniques to derive laws of motion for the centres of the spirals and we show that the time evolution of these patterns is slow and, for large relative separations of the centres of the spirals, the time scale for the their dynamics is logarithmic in the inverse of this distance. These laws of motion are different depending on the relation between the parameters of the complex Ginzburg-Landau equation and the relative separation of the spirals. We show that the way these laws change as the spirals separate or approach is highly singular. We also show that the asymptotic wavenumber in the case of multiple spirals is as well unique and that it evolves in time at the same rate as the velocity of the centres.
APA, Harvard, Vancouver, ISO, and other styles
6

Banaji, Murad. "Clustering and chaos in globally coupled oscillators." Thesis, Queen Mary, University of London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249289.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

SNOUSSI, SEIFEDDINE. "Etude du comportement asymptotique des solutions d'une equation de ginzburg-landau generalisee." Paris 11, 1996. http://www.theses.fr/1996PA112060.

Full text
Abstract:
L'objet de cette these est d'etudier les problemes d'existence locale ou globale de solutions d'un systeme couple d'une equation de ginzburg-landau generalisee et une equation de poisson ainsi qu'a l'etude de leur comportement asymptotique. Ce systeme est considere sur un domaine pouvant etre borne ou non-borne et les donnees initiales sont supposees etre de faible regularite. La premiere partie de cette these est consacree a l'etude du comportement asymptotique et qualitative des solutions de ce systeme quand il est considere sur un ouvert borne de la droite reelle ou du plan. On donnera des resultats d'existence globale ou d'explosion en temps fini. On etablira l'existence d'un attracteur dont on estimera la dimension de hausdorff ou fractale. Enfin, on etudiera les bifurcations de hopf sur un intervalle borne ou sur un ouvert mince du plan. Dans la deuxieme partie de cette these ce systeme sera considere sur un domaine non-borne. Cette partie est composee de deux chapitres. Dans le premier chapitre on etudie l'existence locale ou globale de solutions dans les espaces de sobolev ainsi que dans les espaces de sobolev a poids ayant des donnees initiales de faible regularite et on montrera que ces solutions se regularise en temps et on determinera en outre la nature de leur singularite a l'origine, leur existence globale en temps est aussi etudiee. Dans le deuxieme chapitre on s'interessera a l'etude du comportement asymptotique de ces solutions dans les espaces de sobolev a poids decroissant invariants par translation. On montrera l'existence d'un attracteur global attirant ces solutions dans la metrique des espaces de sobolev a poids
APA, Harvard, Vancouver, ISO, and other styles
8

Sauvageot, Myrto. "Modèle de Ginzburg-Landau : solutions radiales et branches de bifurcation." Paris 6, 2002. http://www.theses.fr/2002PA066548.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Attanasio, Felipe [UNESP]. "Numerical study of the Ginzburg-Landau-Langevin equation: coherent structures and noise perturbation theory." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/92029.

Full text
Abstract:
Made available in DSpace on 2014-06-11T19:25:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-02-21Bitstream added on 2014-06-13T19:12:26Z : No. of bitstreams: 1 attanasio_f_me_ift.pdf: 793752 bytes, checksum: 490b63eed4bdd7ec83984c78ac824d6d (MD5)
Nesta Dissertação apresentamos um estudo numéerico em uma dimensão espacial da equação de Ginzburg-Landau-Langevin (GLL), com ênfase na aplicabilidade de um método de perturbação estocástico e na mecânica estatística de defeitos topológicos em modelos de campos escalares reais. Revisamos brevemente conceitos de mecânica estatística de sistemas em equilíbrio e próximos a ele e apresentamos como a equação de GLL pode ser usada em sistemas que exibem transições de fase, na quantização estocástica e no estudo da interação de estruturas coerentes com fônons de origem térmica. Também apresentamos um método perturbativo, denominado teoria de perturbação no ruído (TPR), adequado para situações onde a intensidade do ruído estocástico é fraca. Através de simulações numéricas, investigamos a restauração de uma simetria 'Z IND. 2' quebrada, a aplicabilidade da TPR em uma dimensão e efeitos de temperatura finita numa solução topológica do tipo kink - onde apresentamos novos resultados sobre defeitos de dois kinks
In this Dissertation we present a numerical study of the GinzburgLandau-Langevin (GLL) equation in one spatial dimension, with emphasis on the applicability of a stochastic perturbative method and the statistical mechanics of topological defect structures in field-theoretic models of real scalar fields. We briefly review concepts of equilibrium and near-equilibrium statistical mechanics and present how the GLL equation can be used in systems that exhibit phase transitions, in stochastic quantization and in the study of the interaction of coherent structures with thermal phonons. We also present a perturbative method, named noise perturbation theory (NPT), suitable for situations where the stochastic noise intensity is weak. Through numerical simulations we investigate the restoration of a broken 'Z IND. 2' symmetry, the applicability of the NPT in one dimension and finite temperature effects on a topological kink solution - where we present new results on two-kink defects
APA, Harvard, Vancouver, ISO, and other styles
10

Attanasio, Felipe. "Numerical study of the Ginzburg-Landau-Langevin equation : coherent structures and noise perturbation theory /." São Paulo, 2013. http://hdl.handle.net/11449/92029.

Full text
Abstract:
Orientador: Gastão Inácio Krein
Banca: Raquel Santos Marques de Carvalho
Banca: Ricardo D'Elia Matheus
Resumo: Nesta Dissertação apresentamos um estudo numéerico em uma dimensão espacial da equação de Ginzburg-Landau-Langevin (GLL), com ênfase na aplicabilidade de um método de perturbação estocástico e na mecânica estatística de defeitos topológicos em modelos de campos escalares reais. Revisamos brevemente conceitos de mecânica estatística de sistemas em equilíbrio e próximos a ele e apresentamos como a equação de GLL pode ser usada em sistemas que exibem transições de fase, na quantização estocástica e no estudo da interação de estruturas coerentes com fônons de origem térmica. Também apresentamos um método perturbativo, denominado teoria de perturbação no ruído (TPR), adequado para situações onde a intensidade do ruído estocástico é fraca. Através de simulações numéricas, investigamos a restauração de uma simetria 'Z IND. 2' quebrada, a aplicabilidade da TPR em uma dimensão e efeitos de temperatura finita numa solução topológica do tipo "kink" - onde apresentamos novos resultados sobre defeitos de dois kinks
Abstract: In this Dissertation we present a numerical study of the GinzburgLandau-Langevin (GLL) equation in one spatial dimension, with emphasis on the applicability of a stochastic perturbative method and the statistical mechanics of topological defect structures in field-theoretic models of real scalar fields. We briefly review concepts of equilibrium and near-equilibrium statistical mechanics and present how the GLL equation can be used in systems that exhibit phase transitions, in stochastic quantization and in the study of the interaction of coherent structures with thermal phonons. We also present a perturbative method, named noise perturbation theory (NPT), suitable for situations where the stochastic noise intensity is weak. Through numerical simulations we investigate the restoration of a broken 'Z IND. 2' symmetry, the applicability of the NPT in one dimension and finite temperature effects on a topological "kink" solution - where we present new results on two-kink defects
Mestre
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Ginzburg-Landau equation"

1

Bethuel, Fabrice. Ginzburg-Landau vortices. Boston: Birkhäuser, 1994.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Herbert, Geoffrey M. Stability analysis of the Fisher and Landau-Ginzburg equations. [s.l.]: typescript, 1995.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Hélein, Frédéric, Fabrice Bethuel, and Haïm Brezis. Ginzburg-Landau Vortices. Birkhäuser, 2017.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Helein, Frederic, Haim Brezis, and Fabrice Bethuel. Ginzburg-Landau Vortices. Birkhauser Verlag, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

Full text
Abstract:
Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.
APA, Harvard, Vancouver, ISO, and other styles
6

Tang, Q., and K. H. Hoffmann. Ginzburg-Landau Phase Transition Theory and Superconductivity. Birkhäuser Boston, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

(Editor), Haim Brezis, and Daqian Li (Editor), eds. Ginzburg-landau Vortices (Series in Contemporary Applied Mathematics). World Scientific Publishing Company, 2005.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

Analysis of Ginzburg-Landau Vortices (Progress in Nonlinear Differential Equations & Their Applications). Birkhauser Verlag AG, 2000.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Ginzburg-Landau Phase Transition Theory and Superconductivity (International Series of Numerical Mathematics). Birkhauser, 2001.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Zeitlin, Vladimir. Resonant Wave Interactions and Resonant Excitation of Wave-guide Modes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0012.

Full text
Abstract:
The idea of resonant nonlinear interactions of waves, and of resonant wave triads, is first explained using the example of Rossby waves, and then used to highlight a mechanism of excitation of wave-guide modes, by impinging free waves at the oceanic shelf, and at the equator. Physics and mathematics of the mechanism, which is related to the phenomena of parametric resonance and wave modulation, are explained in detail in both cases. The resulting modulation equations, of Ginzburg–Landau or nonlinear Schrodinger type, are obtained by multi-scale asymptotic expansions and elimination of resonances, after the explanation of this technique. The chapter thus makes a link between geophysical fluid dynamics and other branches of nonlinear physics. A variety of nonlinear phenomena including coherent structure formation is displayed. The resonant excitation of wave-guide modes provides an efficient mechanism of energy transfer to the wave guides from the large to the small.
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Ginzburg-Landau equation"

1

Bethuel, Fabrice, Haïm Brezis, and Frédéric Hélein. "Non-minimizing solutions of the Ginzburg-Landau equation." In Ginzburg-Landau Vortices, 107–36. Boston, MA: Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0287-5_10.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Tarasov, Vasily E. "Fractional Ginzburg-Landau Equation." In Nonlinear Physical Science, 215–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14003-7_9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Sirovich, L., and P. K. Newton. "Ginzburg-Landau Equation: Stability and Bifurcations." In Stability of Time Dependent and Spatially Varying Flows, 276–93. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-4724-1_15.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Tarasov, Vasily E. "Ginzburg-Landau Equation for Fractal Media." In Nonlinear Physical Science, 115–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14003-7_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Ovchinnikov, Yuri, and Israel Sigal. "Ginzburg-Landau equation I. Static vortices." In CRM Proceedings and Lecture Notes, 199–220. Providence, Rhode Island: American Mathematical Society, 1997. http://dx.doi.org/10.1090/crmp/012/16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Pacard, Frank, and Tristan Rivière. "The Ginzburg-Landau Equation in ℂ." In Linear and Nonlinear Aspects of Vortices, 51–71. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1386-4_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Grundland, A. M., J. A. Tuszyński, and P. Winternitz. "Elliptic Function Solutions for Landau-Ginzburg Equation." In Partially Intergrable Evolution Equations in Physics, 583–84. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0591-7_28.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Akhmediev, Nail, and Adrian Ankiewicz. "Solitons of the Complex Ginzburg—Landau Equation." In Springer Series in Optical Sciences, 311–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-540-44582-1_12.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Izadi, Mojtaba, Charles R. Koch, and Stevan S. Dubljevic. "Model Predictive Control of Ginzburg-Landau Equation." In Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 75–90. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-98177-2_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Salerno, Mario, and Fatkhulla Kh Abdullaev. "Discrete Solitons of the Ginzburg-Landau Equation." In Dissipative Optical Solitons, 303–17. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97493-0_14.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Ginzburg-Landau equation"

1

Zaslavsky, George M., and Vasily E. Tarasov. "Fractional Generalization of Ginzburg-Landau and Nonlinear Schroedinger Equations." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84266.

Full text
Abstract:
The fractional generalization of the Ginzburg-Landau equation is derived from the variational Euler-Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some different forms of the fractional Ginzburg-Landau equation or nonlinear Schro¨dinger equation with fractional derivatives are presented. The Agrawal variational principle and its generalization have been applied.
APA, Harvard, Vancouver, ISO, and other styles
2

Brand, Helmut R., Orazio Descalzi, and Jaime Cisternas. "Hole Solutions in the Cubic Complex Ginzburg-Landau Equation versus Holes in the Cubic-Quintic Complex Ginzburg-Landau Equation." In NONEQUILIBRIUM STATISTICAL MECHANICS AND NONLINEAR PHYSICS: XV Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics. AIP, 2007. http://dx.doi.org/10.1063/1.2746737.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

FURSIKOV, A. V. "ANALYTICITY OF STABLE INVARIANT MANIFOLDS FOR GINZBURG-LANDAU EQUATION." In Applied Analysis and Differential Equations - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708229_0009.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Saitoh, Kuniyasu, and Hisao Hayakawa. "Time dependent Ginzburg-Landau equation for sheared granular flow." In 28TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4769651.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Guo, Shan, Chao Xu, and Xuemin Tu. "Parameter estimation for Ginzburg-Landau equation via implicit sampling." In 2016 American Control Conference (ACC). IEEE, 2016. http://dx.doi.org/10.1109/acc.2016.7526490.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Li, Jing, and Zhixiong Zhang. "Complex Ginzburg-Landau equation with boundary control and observation." In 2016 2nd International Conference on Control Science and Systems Engineering (ICCSSE). IEEE, 2016. http://dx.doi.org/10.1109/ccsse.2016.7784365.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Xiang, Chunhuan, and Honglei Wang. "An approximate method for solving complex Ginzburg-Landau equation." In 2018 8th International Conference on Manufacturing Science and Engineering (ICMSE 2018). Paris, France: Atlantis Press, 2018. http://dx.doi.org/10.2991/icmse-18.2018.111.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Bazhenov, M., M. Rabinovich, and L. Rubchinsky. "Time periodic spatial disorder in a complex Ginzburg–Landau equation." In Chaotic, fractal, and nonlinear signal processing. AIP, 1996. http://dx.doi.org/10.1063/1.51051.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

BARASHENKOV, I. V., and S. D. CROSS. "LOCALISED SOLUTIONS OF THE PARAMETRICALLY DRIVEN COMPLEX GINZBURG-LANDAU EQUATION." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810175_0043.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

GARZÓN, R., and V. VALENTE. "NUMERICAL EXPERIMENTS ON THE CONTROLLABILITY OF THE GINZBURG-LANDAU EQUATION." In Proceedings of the European Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812706874_0009.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Ginzburg-Landau equation"

1

Takac, P. Dynamics on the attractor for the complex Ginzburg-Landau equation. Office of Scientific and Technical Information (OSTI), August 1994. http://dx.doi.org/10.2172/10174640.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Vernov, Sergey Yu. Construction of Elliptic Solutions to the Quintic Complex One-dimensional Ginzburg–Landau Equation. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-322-333.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Fleckinger-Pelle, J., H. G. Kaper, and P. Takac. Dynamics of the Ginzburg-Landau equations of superconductivity. Office of Scientific and Technical Information (OSTI), August 1997. http://dx.doi.org/10.2172/516027.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Coskun, E., and M. K. Kwong. Parallel solution of the time-dependent Ginzburg-Landau equations and other experiences using BlockComm-Chameleon and PCN on the IBM SP, Intel iPSC/860, and clusters of workstations. Office of Scientific and Technical Information (OSTI), September 1995. http://dx.doi.org/10.2172/266722.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Ginzburg-Landau equation' for particular source types:
Journal articles Dissertations / Theses
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography