1,716 research outputs found
A note on the forced Burgers equation
We obtain the exact solution for the Burgers equation with a time dependent
forcing, which depends linearly on the spatial coordinate. For the case of a
stochastic time dependence an exact expression for the joint probability
distribution for the velocity fields at multiple spatial points is obtained. A
connection with stretched vortices in hydrodynamic flows is discussed.Comment: 10 page
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
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
Clinical practice guidelines: towards better quality guidelines and increased international collaboration
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Exact probability function for bulk density and current in the asymmetric exclusion process
We examine the asymmetric simple exclusion process with open boundaries, a
paradigm of driven diffusive systems, having a nonequilibrium steady state
transition. We provide a full derivation and expanded discussion and digression
on results previously reported briefly in M. Depken and R. Stinchcombe, Phys.
Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for
the joint probability function for the bulk density and current, both for
finite systems, and also in the thermodynamic limit. The resulting distribution
is non-Gaussian, and while the fluctuations in the current are continuous at
the continuous phase transitions, the density fluctuations are discontinuous.
The derivations are done by using the standard operator algebraic techniques,
and by introducing a modified version of the original operator algebra. As a
byproduct of these considerations we also arrive at a novel and very simple way
of calculating the normalization constant appearing in the standard treatment
with the operator algebra. Like the partition function in equilibrium systems,
this normalization constant is shown to completely characterize the
fluctuations, albeit in a very different manner.Comment: 10 pages, 4 figure
Merging and fragmentation in the Burgers dynamics
We explore the noiseless Burgers dynamics in the inviscid limit, the
so-called ``adhesion model'' in cosmology, in a regime where (almost) all the
fluid particles are embedded within point-like massive halos. Following
previous works, we focus our investigations on a ``geometrical'' model, where
the matter evolution within the shock manifold is defined from a geometrical
construction. This hypothesis is at variance with the assumption that the usual
continuity equation holds but, in the inviscid limit, both models agree in the
regular regions. Taking advantage of the formulation of the dynamics of this
``geometrical model'' in terms of Legendre transforms and convex hulls, we
study the evolution with time of the distribution of matter and the associated
partitions of the Lagrangian and Eulerian spaces. We describe how the halo mass
distribution derives from a triangulation in Lagrangian space, while the dual
Voronoi-like tessellation in Eulerian space gives the boundaries of empty
regions with shock nodes at their vertices. We then emphasize that this
dynamics actually leads to halo fragmentations for space dimensions greater or
equal to 2 (for the inviscid limit studied in this article). This is most
easily seen from the properties of the Lagrangian-space triangulation and we
illustrate this process in the two-dimensional (2D) case. In particular, we
explain how point-like halos only merge through three-body collisions while
two-body collisions always give rise to two new massive shock nodes (in 2D).
This generalizes to higher dimensions and we briefly illustrate the
three-dimensional (3D) case. This leads to a specific picture for the
continuous formation of massive halos through successive halo fragmentations
and mergings.Comment: 21 pages, final version published in Phys.Rev.
Statistical Properties of the Final State in One-dimensional Ballistic Aggregation
We investigate the long time behaviour of the one-dimensional ballistic
aggregation model that represents a sticky gas of N particles with random
initial positions and velocities, moving deterministically, and forming
aggregates when they collide. We obtain a closed formula for the stationary
measure of the system which allows us to analyze some remarkable features of
the final `fan' state. In particular, we identify universal properties which
are independent of the initial position and velocity distributions of the
particles. We study cluster distributions and derive exact results for extreme
value statistics (because of correlations these distributions do not belong to
the Gumbel-Frechet-Weibull universality classes). We also derive the energy
distribution in the final state. This model generates dynamically many
different scales and can be viewed as one of the simplest exactly solvable
model of N-body dissipative dynamics.Comment: 19 pages, 5 figures include
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