17,567 research outputs found
Mechanism of Magnetic Flux Loss in Molecular Clouds
We investigate the detailed processes working in the drift of magnetic fields
in molecular clouds. To the frictional force, whereby the magnetic force is
transmitted to neutral molecules, ions contribute more than half only at cloud
densities , and charged grains contribute more
than 90% at . Thus grains play a decisive role
in the process of magnetic flux loss. Approximating the flux loss time by
a power law , where is the mean field strength in
the cloud, we find , characteristic to ambipolar diffusion,
only at . At higher densities,
decreases steeply with , and finally at , where magnetic fields
effectively decouple from the gas, is attained, reminiscent of
Ohmic dissipation, though flux loss occurs about 10 times faster than by Ohmic
dissipation. Ohmic dissipation is dominant only at . While ions and electrons drift in the direction of
magnetic force at all densities, grains of opposite charges drift in opposite
directions at high densities, where grains are major contributors to the
frictional force. Although magnetic flux loss occurs significantly faster than
by Ohmic dissipation even at very high densities as , the process going on at high densities is quite different from ambipolar
diffusion in which particles of opposite charges are supposed to drift as one
unit.Comment: 34 pages including 9 postscript figures, LaTex, accepted by
Astrophysical Journal (vol.573, No.1, July 1, 2002
Small Structures via Thermal Instability of Partially Ionized Plasma. I. Condensation Mode
(Shortened) Thermal instability of partially ionized plasma is investigated
by linear perturbation analysis. According to the previous studies under the
one fluid approach, the thermal instability is suppressed due to the magnetic
pressure. However, the previous studies did not precisely consider the effect
of the ion-neutral friction, since they did not treat the flow as two fluid
which is composed of ions and neutrals. Then, we revisit the effect of the
ion-neutral friction of the two fluid to the growth of the thermal instability.
According to our study, (1) The instability which is characterized by the mean
molecular weight of neutrals is suppressed via the ion-neutral friction only
when the magnetic field and the friction are sufficiently strong. The
suppression owing to the friction occurs even along the field line. If the
magnetic field and the friction are not so strong, the instability is not
stabilized. (2) The effect of the friction and the magnetic field is mainly
reduction of the growth rate of the thermal instability of weakly ionized
plasma. (3) The effect of friction does not affect the critical wavelength
lambdaF for the thermal instability. This yields that lambdaF of the weakly
ionized plasma is not enlarged even when the magnetic field exists. We insist
that the thermal instability of the weakly ionized plasma in the magnetic field
can grow up even at the small length scale where the instability under the
assumption of the one fluid plasma can not grow owing to the stabilization by
the magnetic field. (4) The wavelength of the maximum growth rate of the
instability shifts shortward according to the decrement of the growth rate,
because the friction is effective at rather larger scale. Therefore, smaller
structures are expected to appear than those without the ion-neutral friction.Comment: To appear in Ap
Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment: I. Formulation of the Problem and Method of Solution
We formulate the problem of the formation of magnetically supercritical cores
in magnetically subcritical parent molecular clouds, and the subsequent
collapse of the cores to high densities, past the detachment of ions from
magnetic field lines and into the opaque regime. We employ the six-fluid MHD
equations, accounting for the effects of grains (negative, positive and
neutral) including their inelastic collisions with other species. We do not
assume that the magnetic flux is frozen in any of the charged species. We
derive a generalized Ohm's law that explicitly distinguishes between flux
advection (and the associated process of ambipolar diffusion) and Ohmic
dissipation, in order to assess the contribution of each mechanism to the
increase of the mass-to-flux ratio of the central parts of a collapsing core
and possibly to the resolution of the magnetic flux problem of star formation.
We show how our formulation is related to and can be transformed into the
traditional, directional formulation of the generalized Ohm's law, and we
derive formulae for the perpendicular, parallel and Hall conductivities
entering the latter, which include, for the first time, the effect of inelastic
collisions between grains. In addition, we present a general (valid in any
geometry) solution for the velocities of charged species as functions of the
velocity of the neutrals and of the effective flux velocity (which can in turn
be calculated from the dynamics of the system and Faraday's law). The last two
sets of formulae can be adapted for use in any general non-ideal MHD code to
study phenomena beyond star formation in magnetic clouds. The results,
including a detailed parameter study, are presented in two accompanying papers.Comment: 17 pages, emulateapj; accepted for publication in the Astrophysical
Journa
A quantum Monte Carlo study on the superconducting Kosterlitz-Thouless transition of the attractive Hubbard model on a triangular lattice
We study the superconducting Kosterlitz-Thouless transition of the attractive
Hubbard model on a two-dimensional triangular lattice using auxiliary field
quantum Monte Carlo method for system sizes up to sites.
Combining three methods to analyze the numerical data, we find, for the
attractive interaction of , that the transition temperature stays almost
constant within the band filling range of , while it is found to
be much lower in the region.Comment: RevTeX 6 page
Cohomology and Support Varieties for Lie Superalgebras II
In \cite{BKN} the authors initiated a study of the representation theory of
classical Lie superalgebras via a cohomological approach. Detecting subalgebras
were constructed and a theory of support varieties was developed. The dimension
of a detecting subalgebra coincides with the defect of the Lie superalgebra and
the dimension of the support variety for a simple supermodule was conjectured
to equal the atypicality of the supermodule. In this paper the authors compute
the support varieties for Kac supermodules for Type I Lie superalgebras and the
simple supermodules for . The latter result verifies our
earlier conjecture for . In our investigation we also
delineate several of the major differences between Type I versus Type II
classical Lie superalgebras. Finally, the connection between atypicality,
defect and superdimension is made more precise by using the theory of support
varieties and representations of Clifford superalgebras.Comment: 28 pages, the proof of Proposition 4.5.1 was corrected, several other
small errors were fixe
Decay of a coherent scalar disturbance in a turbulent flow
The time evolution of an initially coherent, sinusoidal passive-scalar disturbance is considered when the wavelength q is less than the length scale of the surrounding isotropic turbulent flow. In 64 sup 3 direct numerical simulations a Gaussian prescription for the average scalar amplitude breaks down after a timescale associated with the wavenumber of the disturbance and there is a transition to a new characteristic decay. The Gaussian prescription is given by exp(-(1/2) q-squared w(t)), where a form for w(t), the Lagrangian mean square displacement of a single fluid particle, is proposed. After the transition the decay is given by exp(-t/tau), where tau is the new characteristic timescale. If q k(sub K), then 1/tau = 1/tau(sub D) + 1/tau(sub K), where k(sub K) is the Kolmogorov wavenumber, tau(sub D) is the diffusive timescale and tau(sub K) is the Kolmogorov timescale. An experiment originally proposed by de Gennesis considered in which the evolution of a coherent laser-induced pattern is read by a diffracting laser. The theory of this experiment involves the dispersion of particle pairs, but it is shown that in a certain limit it reduces to the single Fourier-mode problem and can be described in terms of single particle diffusion. The decay of a single mode after the transition in the simulation best describes the experiment
Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)
Let be a
classical Lie superalgebra and be the category of finite
dimensional -supermodules which are completely reducible over the
reductive Lie algebra . In an earlier paper the authors
demonstrated that for any module in the rate of growth of the
minimal projective resolution (i.e., the complexity of ) is bounded by the
dimension of . In this paper we compute the complexity
of the simple modules and the Kac modules for the Lie superalgebra
. In both cases we show that the complexity is related to
the atypicality of the block containing the module.Comment: 32 page
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