1,503 research outputs found
Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vaccum
This paper considers the initial boundary problem to the planar compressible
magnetohydrodynamic equations with large initial data and vacuum. The global
existence and uniqueness of large strong solutions are established when the
heat conductivity coefficient satisfies \begin{equation*}
C_{1}(1+\theta^q)\leq \kappa(\theta)\leq C_2(1+\theta^q) \end{equation*} for
some constants , and .Comment: 19pages,some typos are correcte
Electron Inertial Effects on Rapid Energy Redistribution at Magnetic X-points
The evolution of non-potential perturbations to a current-free magnetic
X-point configuration is studied, taking into account electron inertial effects
as well as resistivity. Electron inertia is shown to have a negligible effect
on the evolution of the system whenever the collisionless skin depth is less
than the resistive scale length. Non-potential magnetic field energy in this
resistive MHD limit initially reaches equipartition with flow energy, in
accordance with ideal MHD, and is then dissipated extremely rapidly, on an
Alfvenic timescale that is essentially independent of Lundquist number. In
agreement with resistive MHD results obtained by previous authors, the magnetic
field energy and kinetic energy are then observed to decay on a longer
timescale and exhibit oscillatory behavior, reflecting the existence of
discrete normal modes with finite real frequency. When the collisionless skin
depth exceeds the resistive scale length, the system again evolves initially
according to ideal MHD. At the end of this ideal phase, the field energy decays
typically on an Alfvenic timescale, while the kinetic energy (which is equally
partitioned between ions and electrons in this case) is dissipated on the
electron collision timescale. The oscillatory decay in the energy observed in
the resistive case is absent, but short wavelength structures appear in the
field and velocity profiles, suggesting the possibility of particle
acceleration in oppositely-directed current channels. The model provides a
possible framework for interpreting observations of energy release and particle
acceleration on timescales down to less than a second in the impulsive phase of
solar flares.Comment: 30 pages, 8 figure
Holography and hydrodynamics with weakly broken symmetries
Hydrodynamics is a theory of long-range excitations controlled by equations
of motion that encode the conservation of a set of currents (energy, momentum,
charge, etc.) associated with explicitly realized global symmetries. If a
system possesses additional weakly broken symmetries, the low-energy
hydrodynamic degrees of freedom also couple to a few other "approximately
conserved" quantities with parametrically long relaxation times. It is often
useful to consider such approximately conserved operators and corresponding new
massive modes within the low-energy effective theory, which we refer to as
quasihydrodynamics. Examples of quasihydrodynamics are numerous, with the most
transparent among them hydrodynamics with weakly broken translational symmetry.
Here, we show how a number of other theories, normally not thought of in this
context, can also be understood within a broader framework of
quasihydrodynamics: in particular, the M\"uller-Israel-Stewart theory and
magnetohydrodynamics coupled to dynamical electric fields. While historical
formulations of quasihydrodynamic theories were typically highly
phenomenological, here, we develop a holographic formalism to systematically
derive such theories from a (microscopic) dual gravitational description.
Beyond laying out a general holographic algorithm, we show how the
M\"uller-Israel-Stewart theory can be understood from a dual higher-derivative
gravity theory and magnetohydrodynamics from a dual theory with two-form bulk
fields. In the latter example, this allows us to unambiguously demonstrate the
existence of dynamical photons in the holographic description of
magnetohydrodynamics.Comment: 65 pages, 5 figures. v2: minor changes, more references; v3:
published versio
Stochastic Flux-Freezing and Magnetic Dynamo
We argue that magnetic flux-conservation in turbulent plasmas at high
magnetic Reynolds numbers neither holds in the conventional sense nor is
entirely broken, but instead is valid in a novel statistical sense associated
to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The
latter phenomenon is due to the explosive separation of particles undergoing
turbulent Richardson diffusion, which leads to a breakdown of Laplacian
determinism for classical dynamics. We discuss empirical evidence for
spontaneous stochasticity, including our own new numerical results. We then use
a Lagrangian path-integral approach to establish stochastic flux-freezing for
resistive hydromagnetic equations and to argue, based on the properties of
Richardson diffusion, that flux-conservation must remain stochastic at infinite
magnetic Reynolds number. As an important application of these results we
consider the kinematic, fluctuation dynamo in non-helical, incompressible
turbulence at unit magnetic Prandtl number. We present results on the
Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate
a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of
field-line motion is an essential ingredient of both. We finally consider
briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure
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