4,774 research outputs found
Convective and Rotational Stability of a Dilute Plasma
The stability of a dilute plasma to local convective and rotational
disturbances is examined. A subthermal magnetic field and finite thermal
conductivity along the field lines are included in the analysis. Stability
criteria similar in form to the classical H{\o}iland inequalities are found,
but with angular velocity gradients replacing angular momentum gradients, and
temperature gradients replacing entropy gradients. These criteria are
indifferent to the properties of the magnetic field and to the magnitude of the
thermal conductivity. Angular velocity gradients and temperature gradients are
both free energy sources; it is not surprising that they are directly relevant
to the stability of the gas. Magnetic fields and thermal conductivity provide
the means by which these sources can be tapped. Previous studies have generally
been based upon the classical H{\o}iland criteria, which are inappropriate for
magnetized, dilute astrophysical plasmas. In sharp contrast to recent claims in
the literature, the new stability criteria demonstrate that marginal flow
stability is not a fundamental property of accreting plasmas thought to be
associated with low luminosity X-ray sources.Comment: Final version (Appendix added), 19 pages, 3 figs., AAS LaTEX macros
v4.0. To appear ApJ 1 Dec 200
Lie-Poincare' transformations and a reduction criterion in Landau theory
In the Landau theory of phase transitions one considers an effective
potential whose symmetry group and degree depend on the system
under consideration; generally speaking, is the most general
-invariant polynomial of degree . When such a turns out to be too
complicate for a direct analysis, it is essential to be able to drop
unessential terms, i.e. to apply a simplifying criterion. Criteria based on
singularity theory exist and have a rigorous foundation, but are often very
difficult to apply in practice. Here we consider a simplifying criterion (as
stated by Gufan) and rigorously justify it on the basis of classical
Lie-Poincar\'e theory as far as one deals with fixed values of the control
parameter(s) in the Landau potential; when one considers a range of values, in
particular near a phase transition, the criterion has to be accordingly
partially modified, as we discuss. We consider some specific cases of group
as examples, and study in detail the application to the
Sergienko-Gufan-Urazhdin model for highly piezoelectric perovskites.Comment: 32 pages, no figures. To appear in Annals of Physic
A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow
We present an efficient discontinuous Galerkin scheme for simulation of the
incompressible Navier-Stokes equations including laminar and turbulent flow. We
consider a semi-explicit high-order velocity-correction method for time
integration as well as nodal equal-order discretizations for velocity and
pressure. The non-linear convective term is treated explicitly while a linear
system is solved for the pressure Poisson equation and the viscous term. The
key feature of our solver is a consistent penalty term reducing the local
divergence error in order to overcome recently reported instabilities in
spatially under-resolved high-Reynolds-number flows as well as small time
steps. This penalty method is similar to the grad-div stabilization widely used
in continuous finite elements. We further review and compare our method to
several other techniques recently proposed in literature to stabilize the
method for such flow configurations. The solver is specifically designed for
large-scale computations through matrix-free linear solvers including efficient
preconditioning strategies and tensor-product elements, which have allowed us
to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores.
We validate our code and demonstrate optimal convergence rates with laminar
flows present in a vortex problem and flow past a cylinder and show
applicability of our solver to direct numerical simulation as well as implicit
large-eddy simulation of turbulent channel flow at as well as
.Comment: 28 pages, in preparation for submission to Journal of Computational
Physic
On paths-based criteria for polynomial time complexity in proof-nets
Girard's Light linear logic (LLL) characterized polynomial time in the
proof-as-program paradigm with a bound on cut elimination. This logic relied on
a stratification principle and a "one-door" principle which were generalized
later respectively in the systems L^4 and L^3a. Each system was brought with
its own complex proof of Ptime soundness.
In this paper we propose a broad sufficient criterion for Ptime soundness for
linear logic subsystems, based on the study of paths inside the proof-nets,
which factorizes proofs of soundness of existing systems and may be used for
future systems. As an additional gain, our bound stands for any reduction
strategy whereas most bounds in the literature only stand for a particular
strategy.Comment: Long version of a conference pape
Non-hydrostatic mesoscale atmospheric modeling by the anisotropic mesh adaptive discontinuous Galerkin method
We deal with non-hydrostatic mesoscale atmospheric modeling using the fully
implicit space-time discontinuous Galerkin method in combination with the
anisotropic -mesh adaptation technique. The time discontinuous
approximation allows the treatment of different meshes at different time levels
in a natural way which can significantly reduce the number of degrees of
freedom. The presented approach generates a sequence of triangular meshes
consisting of possible anisotropic elements and varying polynomial
approximation degrees such that the interpolation error is below the given
tolerance and the number of degrees of freedom at each time step is minimal. We
describe the discretization of the problem together with several implementation
issues related to the treatment of boundary conditions, algebraic solver and
adaptive choice of the size of the time steps.The computational performance of
the proposed method is demonstrated on several benchmark problems
Spectral element modeling of three dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core
This paper deals with the spectral element modeling of seismic wave
propagation at the global scale. Two aspects relevant to low-frequency studies
are particularly emphasized. First, the method is generalized beyond the
Cowling approximation in order to fully account for the effects of
self-gravitation. In particular, the perturbation of the gravity field outside
the Earth is handled by a projection of the spectral element solution onto the
basis of spherical harmonics. Second, we propose a new formulation inside the
fluid which allows to account for an arbitrary density stratification. It is
based upon a decomposition of the displacement into two scalar potentials, and
results in a fully explicit fluid-solid coupling strategy. The implementation
of the method is carefully detailed and its accuracy is demonstrated through a
series of benchmark tests.Comment: Sent to Geophysical Journal International on July 29, 200
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