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Keramidas Charidakos Ioannis - One of the best experts on this subject based on the ideXlab platform.

  • Applications of Hamiltonian theory to plasma models
    'Aquatic Mammals Journal', 2016
    Co-Authors: Keramidas Charidakos Ioannis
    Abstract:

    Three applications of Hamiltonian Methods in Plasma Physics are presented. The first application is the development of a new, five-field, Hamiltonian gyrofluid model. It is comprised by evolution equations for the ion density, pressure and parallel temperature and electron density and pressure. It contains curvature and compressibility effects. The model is shown to satisfy a conserved energy and a Lie-Poisson bracket for it is given. Casimir invariants are calculated and through them, the normal fields of the system are recovered. Later, the model is linearized and shown to possess modes that are identified with the slab ITG, toroidal ITG and KBM modes. Both an electrostatic and an electromagnetic study are performed. Growth rates and critical parameters for instability are computed and compared to their fluid and kinetic counterparts. The accuracy of the model is shown to be between the fluid and the kinetic results, as was expected. Dissipation is added to the ideal system via the use of non-local terms that mimic Landau damping. The modes of the system are shown to undergo Krein bifurcations and their behavior once dissipation is turned on, strongly suggests that they are negative energy modes. A connection between the marginal stability condition of the ITG mode at high k┴ and the (missing) equation of perpendicular pressure is conjectured opening an interesting possibility for future research. The second application is a method for the derivation of reduced fluid models through the use of an action principle. The importance of the method lies in the fact that since all approximations are made directly at the level of the action, the models that result from the action minimization are guaranteed to retain the Hamiltonian character of their parent-model. The two-fluid action is given in Lagrangian variables and the two-fluid equations of motion are recovered by it's minimization. The Eulerian (field) equations of motion are retrieved through the Lagrange-to-Euler (L-E) map. New, single-fluid variables are defined but instead of being implemented at the level of the equations of motion, they are implemented directly in the action. The action is subjected to approximations. Different approximations lead to different models with the models of Lust, Extended MHD, Hall MHD and electron MHD being retrieved. The passing from Lagrangian to Eulerian variables in the single-fluid description requires a non-trivial modification of the E-L map. A note about the importance of quasineutrality in single-fluid models and its ramifications in the Lagrangian framework is given. Several invariants of the models are calculated via Noethers' Theorem. The third application concerns the imposition of constraints in Hamiltonian systems. Two worked examples of the method of Dirac are presented. The first one is on an electrostatic model which has the Hasegawa-Mima and RMHD as distinct limits. The constraint that leads to the Hasegawa-Mima is investigated. The calculations are demonstrated in detail and the reduced system is produced. A brief discussion of the dispersion relation of the reduced system concludes the first example. The second example is the imposition of quasineutrality and divergence-free current on the bracket of the two-fluid model. The various steps of the method are displayed and the example is completed with the verification that the new bracket satisfies the constraints. The possibility of performing the same calculation with single-fluid variables remains open for future research.Physic

Bruno Tadeu Costa - One of the best experts on this subject based on the ideXlab platform.

  • Lie groupoids and the Noether\'s Theorem in field theory in the hamiltonian approach
    Universidade de São Paulo, 2015
    Co-Authors: Bruno Tadeu Costa
    Abstract:

    Neste trabalho, abordamos o conceito de simetria em teoria de campos, no âmbito hamiltoniano mais precisamente, sua relação com leis de conservação, conforme estabelecida pelo(s) teorema(s) de Noether. Propomos uma visão alternativa àquela normalmente usada na literatura, baseada na substituição de grupos e álgebras de Lie por grupoides e algebroides de Lie. Tradicionalmente, dado um fibrado E de configuração sobre o espaço-tempo M (cujas seções são os campos do modelo sob investigação), simetrias são implementadas pela ação de um grupo de automorfismos de E, ou seja, um subgrupo de Aut(E), no espaço Γ (E) das seções de E, exigindo-se que o funcional ação S seja invariante sob tal ação: neste caso, quando o pertinente subgrupo for de dimensão infinita, surgem graves dificuldades quando queremos tratar de questões de análise e de geometria com rigor matemático. A vantagem principal desta abordagem alternativa provém do fato de que, embora o grupo Aut(E) e, tipicamente, os subgrupos relevantes, assim como o espaço Γ (E), sejam de dimensão infinita, a sua ação é induzida por uma ação de um grupoide de Lie no fibrado pertinente, a qual envolve apenas variedades de dimensão finita e portanto não há qualquer dúvida em relação a questões tais como qual seria a topologia ou estrutura de variedade subjacente ou em qual sentido essa ação deve ser suave. Formulamos o teorema de Noether neste contexto, baseado em uma nova versão da construção da aplicação momento que a cada gerador de simetrias que associa uma (n - 1)-forma sobre J*E cujo pull-back com uma seção de J* E, que é solução das equações de movimento, produz uma (n - 1)-forma sobre o espaço-tempo, a famosa corrente de Noether, que é conservada, ou seja, fechadaIn this thesis, we deal with the concept of symmetry in field theory, in the covariant hamiltonian approach more precisely, its relation with conservation laws, as established by Noethers Theorem(s). We propose an alternative view to that normally used in the literature, based on replacing Lie groups and algebras by Lie groupoids and algebroids. Traditionally, given a configuration bundle E over space-time M (whose sections are the fields of the model under investigation), symmetries are implemented by the action of a group of automorphisms of E, i.e., a subgroup of Aut(E), on the space Γ (E) of sections of E, requiring the action functional S to be invariant under that action: in this case, when the pertinent subgroup has infinite dimension, serious difficulties arise when we want to deal with analytical and geometrical questions with mathematical rigor. The main advantage of this alternative approach comes from the fact that, although the group Aut(E) and, typically, the relevant subgroups, as well as the space Γ (E), are infinite-dimensional, its action is induced by the action of a Lie groupoid in the pertinent bundle, which involves only finite-dimentional manifolds and therefore there is no doubt about questions such as what should be the topology or the underlying manifold structure or in what sense this action should be smooth. We formulate the Noethers Theorem in this context, based on a new version of the construction of the momentum map that associates a (n - 1)-form on J*E to each symmetries generator whose pull-back with a section of J*E, that is solution of the equations of motion, produces a (n - 1)-form on the space-time, the famous Noether current, that is conserved, i.e., close

Shimizu Katsutaro - One of the best experts on this subject based on the ideXlab platform.

  • Proposal for the proper gravitational energy-momentum tensor
    'World Scientific Pub Co Pte Lt', 2017
    Co-Authors: Shimizu Katsutaro
    Abstract:

    We propose a gravitational energy-momentum tensor of the general relativity obtained using Noethers Theorem. It transforms as a tensor under general coordinate transformations. One of the two indices of the gravitational energy-momentum tensor labels a local Lorentz frame that satisfies the energy-momentum conservation law. The energies for a gravitational wave and a Friedmann-Lemaitre--Robertson--Walker universe are calculated as examples.Comment: A discussion on a Schwarzschild black hole is delete

Moreira, Marco Antonio - One of the best experts on this subject based on the ideXlab platform.

  • O conceito de simetria na Física
    'Biblioteca Central da UNB', 2019
    Co-Authors: Moreira, Marco Antonio
    Abstract:

    The idea of symmetry is, initially, approached as part of everyday life and, after, as a central concept in physics. Meanings of the concept of symmetry are presented in the context of physics and examples are given. The relationship between symmetry and conservation laws, as expressed by Noethers Theorem, is emphasized. A significant part of the text is dedicated to the concept of spontaneous symmetry breaking. The aim of this paper is to call attention to the role of symmetry in the construction of physics knowledge.A ideia de simetria é abordada, inicialmente, como parte do cotidiano e depois como um conceito central na Física. São apresentados significados do conceito no contexto da Física e são dados exemplos. É destacada a relação entre simetria e leis de conservação, expressa no teorema de Noether. Boa parte do texto é dedicada ao conceito de quebra espontânea de simetria. A proposta do texto é a de enfatizar o papel da simetria na construção do conhecimento físico

Gibbs, Philip E. - One of the best experts on this subject based on the ideXlab platform.

  • Covariant Energy-Momentum Conservation In General Relativity
    1997
    Co-Authors: Gibbs, Philip E.
    Abstract:

    A covariant formula for conserved currents of energy, momentum and angular-momentum is derived from a general form of Noethers Theorem applied directly to the Einstein-Hilbert action of classical general relativity. Energy conservation in a closed big-bang cosmology is discussed as a special case. Special care is taken to distinguish between kinematic and dynamic expressions.Comment: 12 pages, postscript, no figures, references adde