7,767 research outputs found
The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems
We present a new variational principle for the gyrokinetic system, similar to
the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in
the Eulerian frame and based on constrained variations of the phase space fluid
velocity and particle distribution function. Using a Legendre transform, we
explicitly derive the field theoretic Hamiltonian structure of the system. This
is carried out with a modified Dirac theory of constraints, which is used to
construct meaningful brackets from those obtained directly from
Euler-Poincar\'{e} theory. Possible applications of these formulations include
continuum geometric integration techniques, large-eddy simulation models and
Casimir type stability methods.
[1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)Comment: 36 pages, 1 figur
Lattice Models of Quantum Gravity
Standard Regge Calculus provides an interesting method to explore quantum
gravity in a non-perturbative fashion but turns out to be a CPU-time demanding
enterprise. One therefore seeks for suitable approximations which retain most
of its universal features. The -Regge model could be such a desired
simplification. Here the quadratic edge lengths of the simplicial complexes
are restricted to only two possible values , with
, in close analogy to the ancestor of all lattice theories, the
Ising model. To test whether this simpler model still contains the essential
qualities of the standard Regge Calculus, we study both models in two
dimensions and determine several observables on the same lattice size. In order
to compare expectation values, e.g. of the average curvature or the Liouville
field susceptibility, we employ in both models the same functional integration
measure. The phase structure is under current investigation using mean field
theory and numerical simulation.Comment: 4 pages, 1 figure
The 1981 outburst of the old nova GK Persei
Old nova GK Per was observed in 1981 with the IUE, during its rise, maximum, and subsequent return to minimum. In outburst, GK Per is luminous but much redder than dwarf novae or standard model accretion disks. The observed spectrum can be explained qualitatively with the Ghosh and Lamb (1979) model for the interaction of an accretion disk with the magnetic field of the accreting white dwarf. The N V and He2 are enhanced relative to other emission lines during outburst. This can be understood with photoionization by very soft X-rays having a luminosity comparable to that of the hard X-rays
Z_2-Regge versus Standard Regge Calculus in two dimensions
We consider two versions of quantum Regge calculus. The Standard Regge
Calculus where the quadratic link lengths of the simplicial manifold vary
continuously and the Z_2-Regge Model where they are restricted to two possible
values. The goal is to determine whether the computationally more easily
accessible Z_2 model still retains the universal characteristics of standard
Regge theory in two dimensions. In order to compare observables such as average
curvature or Liouville field susceptibility, we use in both models the same
functional integration measure, which is chosen to render the Z_2-Regge Model
particularly simple. Expectation values are computed numerically and agree
qualitatively for positive bare couplings. The phase transition within the
Z_2-Regge Model is analyzed by mean-field theory.Comment: 21 pages, 16 ps-figures, to be published in Phys. Rev.
Leray and LANS- modeling of turbulent mixing
Mathematical regularisation of the nonlinear terms in the Navier-Stokes
equations provides a systematic approach to deriving subgrid closures for
numerical simulations of turbulent flow. By construction, these subgrid
closures imply existence and uniqueness of strong solutions to the
corresponding modelled system of equations. We will consider the large eddy
interpretation of two such mathematical regularisation principles, i.e., Leray
and LANS regularisation. The Leray principle introduces a {\bfi
smoothed transport velocity} as part of the regularised convective
nonlinearity. The LANS principle extends the Leray formulation in a
natural way in which a {\bfi filtered Kelvin circulation theorem},
incorporating the smoothed transport velocity, is explicitly satisfied. These
regularisation principles give rise to implied subgrid closures which will be
applied in large eddy simulation of turbulent mixing. Comparison with filtered
direct numerical simulation data, and with predictions obtained from popular
dynamic eddy-viscosity modelling, shows that these mathematical regularisation
models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure
ON NON-RIEMANNIAN PARALLEL TRANSPORT IN REGGE CALCULUS
We discuss the possibility of incorporating non-Riemannian parallel transport
into Regge calculus. It is shown that every Regge lattice is locally equivalent
to a space of constant curvature. Therefore well known-concepts of differential
geometry imply the definition of an arbitrary linear affine connection on a
Regge lattice.Comment: 12 pages, Plain-TEX, two figures (available from the author
A Lagrangian kinetic model for collisionless magnetic reconnection
A new fully kinetic system is proposed for modeling collisionless magnetic
reconnection. The formulation relies on fundamental principles in Lagrangian
dynamics, in which the inertia of the electron mean flow is neglected in the
expression of the Lagrangian, rather then enforcing a zero electron mass in the
equations of motion. This is done upon splitting the electron velocity into its
mean and fluctuating parts, so that the latter naturally produce the
corresponding pressure tensor. The model exhibits a new Coriolis force term,
which emerges from a change of frame in the electron dynamics. Then, if the
electron heat flux is neglected, the strong electron magnetization limit yields
a hybrid model, in which the electron pressure tensor is frozen into the
electron mean velocity.Comment: 15 pages, no figures. To Appear in Plasma Phys. Control. Fusio
Mercury Toxicity in Chick Embryos
Mercury accumulating to high levels in animal tissue is generally in the form of methylmercury which is readily absorbed but only slowly eliminated. While methylmercury can be formed by microorganisms in lake bottom sediments and concentrated up the biological food chain, inorganic mercury or its metabolic equivalent is sometimes available to animals
First-order transition in the one-dimensional three-state Potts model with long-range interactions
The first-order phase transition in the three-state Potts model with
long-range interactions decaying as has been examined by
numerical simulations using recently proposed Luijten-Bl\"ote algorithm. By
applying scaling arguments to the interface free energy, the Binder's
fourth-order cumulant, and the specific heat maximum, the change in the
character of the transition through variation of parameter was
studied.Comment: 6 pages (containing 5 figures), to appear in Phys. Rev.
Regge Calculus in Teleparallel Gravity
In the context of the teleparallel equivalent of general relativity, the
Weitzenbock manifold is considered as the limit of a suitable sequence of
discrete lattices composed of an increasing number of smaller an smaller
simplices, where the interior of each simplex (Delaunay lattice) is assumed to
be flat. The link lengths between any pair of vertices serve as independent
variables, so that torsion turns out to be localized in the two dimensional
hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a
vector undergoes a dislocation in relation to its initial position as it is
parallel transported along the perimeter of the dual lattice (Voronoi polygon),
we obtain the discrete analogue of the teleparallel action, as well as the
corresponding simplicial vacuum field equations.Comment: Latex, 10 pages, 2 eps figures, to appear in Class. Quant. Gra
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