3,401 research outputs found
Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases
We prove approach to thermal equilibrium for the fully Hamiltonian dynamics
of a dynamical Lorentz gas, by which we mean an ensemble of particles moving
through a -dimensional array of fixed soft scatterers that each possess an
internal harmonic or anharmonic degree of freedom to which moving particles
locally couple. We establish that the momentum distribution of the moving
particles approaches a Maxwell-Boltzmann distribution at a certain temperature
, provided that they are initially fast and the scatterers are in a
sufficiently energetic but otherwise arbitrary stationary state of their free
dynamics--they need not be in a state of thermal equilibrium. The temperature
to which the particles equilibrate obeys a generalized equipartition
relation, in which the associated thermal energy is equal to
an appropriately defined average of the scatterers' kinetic energy. In the
equilibrated state, particle motion is diffusive
The spatial correlations in the velocities arising from a random distribution of point vortices
This paper is devoted to a statistical analysis of the velocity fluctuations
arising from a random distribution of point vortices in two-dimensional
turbulence. Exact results are derived for the correlations in the velocities
occurring at two points separated by an arbitrary distance. We find that the
spatial correlation function decays extremely slowly with the distance. We
discuss the analogy with the statistics of the gravitational field in stellar
systems.Comment: 37 pages in RevTeX format (no figure); submitted to Physics of Fluid
Electron-Neutrino Bremsstrahlung in Electro-Weak Theory
The electron-neutrino bremsstrahlung process has been considered in the
framework of electro-weak theory. The scattering cross section has been
calculated in the center of mass frame and approximated to extreme relativistic
as well as non-relativistic case. The rate of energy-loss via this type of
bremsstrahlung process has been obtained both in non-degenerate and degenerate
region. The effect of this electron-neutrino bremsstrahlung process in
different ranges of temperature and density characterizing the late stages of
stellar evolution has been discussed. It is found from our study that this
bremsstrahlung process is highly important in the non-degenerate region,
although it might have some significant effect in the extreme relativistic
degenerate region.Comment: 18 pages including 4 figures and 1 table; Published in J. Phys
Quantum phase shift and neutrino oscillations in a stationary, weak gravitational field
A new method based on Synge's world function is developed for determining
within the WKB approximation the gravitationally induced quantum phase shift of
a particle propagating in a stationary spacetime. This method avoids any
calculation of geodesics. A detailed treatment is given for relativistic
particles within the weak field, linear approximation of any metric theory. The
method is applied to the calculation of the oscillation terms governing the
interference of neutrinos considered as a superposition of two eigenstates
having different masses. It is shown that the neutrino oscillations are not
sensitive to the gravitomagnetic components of the metric as long as the spin
contributions can be ignored. Explicit calculations are performed when the
source of the field is a spherical, homogeneous body. A comparison is made with
previous results obtained in Schwarzschild spacetime.Comment: 14 pages, no figure. Enlarged version; added references. In the
Schwarzschild case, our results on the non-radial propagation are compared
with the previous work
Modeling the Parker instability in a rotating plasma screw pinch
We analytically and numerically study the analogue of the Parker (magnetic
buoyancy) instability in a uniformly rotating plasma screw pinch confined in a
cylinder. Uniform plasma rotation is imposed to create a centrifugal
acceleration, which mimics the gravity required for the classical Parker
instability. The goal of this study is to determine how the Parker instability
could be unambiguously identified in a weakly magnetized, rapidly rotating
screw pinch, in which the rotation provides an effective gravity and a radially
varying azimuthal field is controlled to give conditions for which the plasma
is magnetically buoyant to inward motion. We show that an axial magnetic field
is also required to circumvent conventional current driven magnetohydrodynamic
(MHD) instabilities such as the sausage and kink modes that would obscure the
Parker instability. These conditions can be realized in the Madison Plasma
Couette Experiment (MPCX). Simulations are performed using the extended MHD
code NIMROD for an isothermal compressible plasma model. Both linear and
nonlinear regimes of the instability are studied, and the results obtained for
the linear regime are compared with analytical results from a slab geometry.
Based on this comparison, it is found that in a cylindrical pinch the magnetic
buoyancy mechanism dominates at relatively large Mach numbers (M>5), while at
low Mach numbers (M<1) the instability is due to the curvature of magnetic
field lines. At intermediate values of Mach number (1<M<5) the Coriolis force
has a strong stabilizing effect on the plasma. A possible scenario for
experimental demonstration of the Parker instability in MPCX is discussed
Quasinormal ringing of Kerr black holes: The excitation factors
Distorted black holes radiate gravitational waves. In the so-called ringdown
phase radiation is emitted in a discrete set of complex quasinormal
frequencies, whose values depend only on the black hole's mass and angular
momentum. Ringdown radiation could be detectable with large signal-to-noise
ratio by the Laser Interferometer Space Antenna LISA. If more than one mode is
detected, tests of the black hole nature of the source become possible. The
detectability of different modes depends on their relative excitation, which in
turn depends on the cause of the perturbation (i.e. on the initial data). A
``universal'', initial data-independent measure of the relative mode excitation
is encoded in the poles of the Green's function that propagates small
perturbations of the geometry (``excitation factors''). We compute for the
first time the excitation factors for general-spin perturbations of Kerr black
holes. We find that for corotating modes with the excitation factors tend
to zero in the extremal limit, and that the contribution of the overtones
should be more significant when the black hole is fast rotating. We also
present the first analytical calculation of the large-damping asymptotics of
the excitation factors for static black holes, including the Schwarzschild and
Reissner-Nordstrom metrics. This is an important step to determine the
convergence properties of the quasinormal mode expansion.Comment: 33 pages, 9 figures, 7 tables, RevTeX4. v2: Two new figures and minor
changes in the presentation. Matches version in press in Phys. Rev.
Orientational relaxation in a discotic liquid crystal
We investigate orientational relaxation of a model discotic liquid crystal,
consists of disc-like molecules, by molecular dynamics simulations along two
isobars starting from the high temperature isotropic phase. The two isobars
have been so chosen that (A) the phase sequence isotropic (I)-nematic
(N)-columnar (C) appears upon cooling along one of them and (B) the sequence
isotropic (I)-columnar (C) along the other. While the orientational relaxation
in the isotropic phase near the I-N phase transition in system (A) shows a
power law decay at short to intermediate times, such power law relaxation is
not observed in the isotropic phase near the I-C phase boundary in system (B).
In order to understand this difference (the existence or the absence of the
power law decay), we calculated the the growth of the orientational pair
distribution functions (OPDF) near the I-N phase boundary and also near the I-C
phase boundary. We find that OPDF shows a marked growth in long range
correlation as the I-N phase boundary is approached in the I-N-C system (A),
but such a growth is absent in the I-C system, which appears to be consistent
with the result that I-N phase transition in the former is weakly first order
while the the I-C phase transition in the later is not weak. As the system
settles into the nematic phase, the decay of the single-particle second-rank
orientational OTCF follows a pattern that is similar to what is observed with
calamitic liquid crystals and supercooled molecular liquids.Comment: 16 pages and 4 figure
Magnification relations for Kerr lensing and testing Cosmic Censorship
A Kerr black hole with mass parameter m and angular momentum parameter a
acting as a gravitational lens gives rise to two images in the weak field
limit. We study the corresponding magnification relations, namely the signed
and absolute magnification sums and the centroid up to post-Newtonian order. We
show that there are post-Newtonian corrections to the total absolute
magnification and centroid proportional to a/m, which is in contrast to the
spherically symmetric case where such corrections vanish. Hence we also propose
a new set of lensing observables for the two images involving these
corrections, which should allow measuring a/m with gravitational lensing. In
fact, the resolution capabilities needed to observe this for the Galactic black
hole should in principle be accessible to current and near-future
instrumentation. Since a/m >1 indicates a naked singularity, a most interesting
application would be a test of the Cosmic Censorship conjecture. The technique
used to derive the image properties is based on the degeneracy of the Kerr lens
and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple
physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in
Phys. Rev.
Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle
We show that, when a gold nanoparticle is coated by a thin layer of nematic
liquid crystal, the deformation produced by the nanoparticle surface can
enhance the splitting of the nanoparticle surface plasmon. We consider three
plausible liquid crystal director configurations in zero electric field: boojum
pair (north-south pole configuration), baseball (tetrahedral), and homogeneous.
From a calculation using the Discrete Dipole Approximation, we find that the
surface plasmon splitting is largest for the boojum pair, intermediate for the
homogeneous, and smallest for the baseball configuration. The boojum pair
results are in good agreement with experiment. We conclude that the
nanoparticle surface has a strong effect on the director orientation, but,
surprisingly, that this deformation can actually enhance the surface plasmon
splitting.Comment: 5 pages, 3 figures To be published in PR
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