1,237 research outputs found
Hall drift of axisymmetric magnetic fields in solid neutron-star matter
Hall drift, i. e., transport of magnetic flux by the moving electrons giving
rise to the electrical current, may be the dominant effect causing the
evolution of the magnetic field in the solid crust of neutron stars. It is a
nonlinear process that, despite a number of efforts, is still not fully
understood. We use the Hall induction equation in axial symmetry to obtain some
general properties of nonevolving fields, as well as analyzing the evolution of
purely toroidal fields, their poloidal perturbations, and current-free, purely
poloidal fields. We also analyze energy conservation in Hall instabilities and
write down a variational principle for Hall equilibria. We show that the
evolution of any toroidal magnetic field can be described by Burgers' equation,
as previously found in plane-parallel geometry. It leads to sharp current
sheets that dissipate on the Hall time scale, yielding a stationary field
configuration that depends on a single, suitably defined coordinate. This
field, however, is unstable to poloidal perturbations, which grow as their
field lines are stretched by the background electron flow, as in instabilities
earlier found numerically. On the other hand, current-free poloidal
configurations are stable and could represent a long-lived crustal field
supported by currents in the fluid stellar core.Comment: 8 pages, 5 figure panels; new version with very small correction;
accepted by Astronomy & Astrophysic
Clocked Atom Delivery to a Photonic Crystal Waveguide
Experiments and numerical simulations are described that develop quantitative
understanding of atomic motion near the surfaces of nanoscopic photonic crystal
waveguides (PCWs). Ultracold atoms are delivered from a moving optical lattice
into the PCW. Synchronous with the moving lattice, transmission spectra for a
guided-mode probe field are recorded as functions of lattice transport time and
frequency detuning of the probe beam. By way of measurements such as these, we
have been able to validate quantitatively our numerical simulations, which are
based upon detailed understanding of atomic trajectories that pass around and
through nanoscopic regions of the PCW under the influence of optical and
surface forces. The resolution for mapping atomic motion is roughly 50 nm in
space and 100 ns in time. By introducing auxiliary guided mode (GM) fields that
provide spatially varying AC-Stark shifts, we have, to some degree, begun to
control atomic trajectories, such as to enhance the flux into to the central
vacuum gap of the PCW at predetermined times and with known AC-Stark shifts.
Applications of these capabilities include enabling high fractional filling of
optical trap sites within PCWs, calibration of optical fields within PCWs, and
utilization of the time-dependent, optically dense atomic medium for novel
nonlinear optical experiments
Exact joint density-current probability function for the asymmetric exclusion process
We study the asymmetric exclusion process with open boundaries and derive the
exact form of the joint probability function for the occupation number and the
current through the system. We further consider the thermodynamic limit,
showing that the resulting distribution is non-Gaussian and that the density
fluctuations have a discontinuity at the continuous phase transition, while the
current fluctuations are continuous. The derivations are performed by using the
standard operator algebraic approach, and by the introduction of new operators
satisfying a modified version of the original algebra.Comment: 4 pages, 3 figure
Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process
As a solvable and broadly applicable model system, the totally asymmetric
exclusion process enjoys iconic status in the theory of non-equilibrium phase
transitions. Here, we focus on the time dependence of the total number of
particles on a 1-dimensional open lattice, and its power spectrum. Using both
Monte Carlo simulations and analytic methods, we explore its behavior in
different characteristic regimes. In the maximal current phase and on the
coexistence line (between high/low density phases), the power spectrum displays
algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the
high/low density phases, we find pronounced \emph{oscillations}, which damp
into power laws. This behavior can be understood in terms of driven biased
diffusion with conserved noise in the bulk.Comment: 4 pages, 4 figure
Ellipticals at z=0 from Self-Consistent Hydrodynamical Simulations: Clues on Age Effects in their Stellar Populations
We present results of a study of the stellar age distributions in the sample
of elliptical-like objects (ELOs) identified at z=0 in four simulations
operating in the context of a concordance cosmological model. The simulations
show that the formation of most stars in each ELO of the sample is a
consequence of violent dynamical events, either fast multiclump collapse at
high z, or mergers at lower z. This second way can explain the age spread as
well as the dynamical peculiarities observed in some ellipticals, but its
relative weight is never dominant and decreases as the ELO mass at the halo
scale, , increases, to such an extent that some recent mergers
contributing an important fraction to the total ELO mass can possibly
contribute only a small fraction of new born stars. More massive objects have
older means and narrower spreads in their stellar age distributions than less
massive ones. The ELO sample shows also a tight correlation between
and the central stellar l.o.s. velocity dispersion, . This gives
a trend of the means and spreads of ELO stellar populations with
that is consistent, even quantitatively, with the age effects observationally
detected in the stellar populations of elliptical galaxies. Therefore, these
effects can be explained as the observational manifestation of the intrinsic
correlations found in the ELO sample between and the properties of
the stellar age distribution, on the one hand, and and
, on the other hand. These correlations hint, for the first time,
at a possible way to reconcile age effects in ellipticals, and, particularly,
the increase of ratios with , with the
hierarchical clustering paradigm.Comment: 13 pages, 2 figures, accepted for publication in Astrophysical
Journal Letter
The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension
We extend the previously developed weak noise scheme, applied to the noisy
Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing
interface in arbitrary dimensions. By means of the Cole-Hopf transformation we
show that the growth morphology can be interpreted in terms of dynamically
evolving textures of localized growth modes with superimposed diffusive modes.
In the Cole-Hopf representation the growth modes are static solutions to the
diffusion equation and the nonlinear Schroedinger equation, subsequently
boosted to finite velocity by a Galilei transformation. We discuss the dynamics
of the pattern formation and, briefly, the superimposed linear modes.
Implementing the stochastic interpretation we discuss kinetic transitions and
in particular the properties in the pair mode or dipole sector. We find the
Hurst exponent H=(3-d)/(4-d) for the random walk of growth modes in the dipole
sector. Finally, applying Derrick's theorem based on constrained minimization
we show that the upper critical dimension is d=4 in the sense that growth modes
cease to exist above this dimension.Comment: 27 pages, 19 eps figs, revte
Exact solution of the one-dimensional ballistic aggregation
An exact expression for the mass distribution of the ballistic
aggregation model in one dimension is derived in the long time regime. It is
shown that it obeys scaling with a scaling
function for and for
. Relevance of these results to Burgers turbulence is discussed.Comment: 11 pages, 2 Postscript figure
Power laws and self-similar behavior in negative ionization fronts
We study anode-directed ionization fronts in curved geometries. When the
magnetic effects can be neglected, an electric shielding factor determines the
behavior of the electric field and the charged particle densities. From a
minimal streamer model, a Burgers type equation which governs the dynamics of
the electric shielding factor is obtained. A Lagrangian formulation is then
derived to analyze the ionization fronts. Power laws for the velocity and the
amplitude of streamer fronts are observed numerically and calculated
analytically by using the shielding factor formulation. The phenomenon of
geometrical diffusion is explained and clarified, and a universal self-similar
asymptotic behavior is derived.Comment: 25 pages, 9 figure
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