15,552 research outputs found
Relaxation of the distribution function tails for systems described by Fokker-Planck equations
We study the formation and the evolution of velocity distribution tails for
systems with long-range interactions. In the thermal bath approximation, the
evolution of the distribution function of a test particle is governed by a
Fokker-Planck equation where the diffusion coefficient depends on the velocity.
We extend the theory of Potapenko et al. [Phys. Rev. E, {\bf 56}, 7159 (1997)]
developed for power law potentials to the case of an arbitrary potential of
interaction. We study how the structure and the progression of the front depend
on the behavior of the diffusion coefficient for large velocities. Particular
emphasis is given to the case where the velocity dependence of the diffusion
coefficient is Gaussian. This situation arises in Fokker-Planck equations
associated with one dimensional systems with long-range interactions such as
the Hamiltonian Mean Field (HMF) model and in the kinetic theory of
two-dimensional point vortices in hydrodynamics. We show that the progression
of the front is extremely slow (logarithmic) in that case so that the
convergence towards the equilibrium state is peculiar
Interference in presence of Dissipation
We study a particle on a ring in presence of various dissipative
environments. We develop and solve a variational scheme assuming low frequency
dominance. We analyze our solution within a renormalization group (RG) scheme
to all orders which reproduces a 2 loop RG for the Caldeira-Legget environment.
In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential
in -R^2 where R is the ring's radius. For either a charge or an electric dipole
coupled to a dirty metal we find that the metal induces dissipation, however
the AB amplitude is ~ R^{-2} for large R, as for free particles. Cold atoms
with a large electric dipole may show a crossover between these two behaviors.Comment: 5 pages, added motivations and reference
Controllability and observabiliy of an artificial advection-diffusion problem
In this paper we study the controllability of an artificial
advection-diffusion system through the boundary. Suitable Carleman estimates
give us the observability on the adjoint system in the one dimensional case. We
also study some basic properties of our problem such as backward uniqueness and
we get an intuitive result on the control cost for vanishing viscosity.Comment: 20 pages, accepted for publication in MCSS. DOI:
10.1007/s00498-012-0076-
The X-ray surface brightness distribution from diffuse gas
We use simulations to predict the X-ray surface brightness distribution
arising from hot, cosmologically distributed diffuse gas. The distribution is
computed for two bands: 0.5-2 keV and 0.1-0.4 keV, using a
cosmological-constant dominated cosmology that fits many other observations. We
examine a number of numerical issues such as resolution, simulation volume and
pixel size and show that the predicted mean background is sensitive to
resolution such that higher resolution systematically increases the mean
predicted background. Although this means that we can compute only lower bounds
to the predicted level, these bounds are already quite restrictive. Since the
observed extra-galactic X-ray background is mostly accounted for by compact
sources, the amount of the observed background attributable to diffuse gas is
tightly constrained. We show that without physical processes in addition to
those included in the simulations (such as radiative cooling or
non-gravitational heating), both bands exceed observational limits. In order to
examine the effect of non-gravitational heating we explore a simple modeling of
energy injection and show that substantial amounts of heating are required
(i.e. 5 keV per particle when averaged over all baryons). Finally, we also
compute the distribution of surface brightness on the sky and show that it has
a well-resolved characteristic shape. This shape is substantially modified by
non-gravitational heating and can be used as a probe of such energy injection.Comment: 11 pages, 11 figures, submitted to Ap
Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics
Considerable attention has been paid, in recent years, to the use of networks
in modeling complex real-world systems. Among the many dynamical processes
involving networks, propagation processes -- in which final state can be
obtained by studying the underlying network percolation properties -- have
raised formidable interest. In this paper, we present a bond percolation model
of multitype networks with an arbitrary joint degree distribution that allows
heterogeneity in the edge occupation probability. As previously demonstrated,
the multitype approach allows many non-trivial mixing patterns such as
assortativity and clustering between nodes. We derive a number of useful
statistical properties of multitype networks as well as a general phase
transition criterion. We also demonstrate that a number of previous models
based on probability generating functions are special cases of the proposed
formalism. We further show that the multitype approach, by naturally allowing
heterogeneity in the bond occupation probability, overcomes some of the
correlation issues encountered by previous models. We illustrate this point in
the context of contact network epidemiology.Comment: 10 pages, 5 figures. Minor modifications were made in figures 3, 4
and 5 and in the text. Explanations and references were adde
Force balance and membrane shedding at the Red Blood Cell surface
During the aging of the red-blood cell, or under conditions of extreme
echinocytosis, membrane is shed from the cell plasma membrane in the form of
nano-vesicles. We propose that this process is the result of the
self-adaptation of the membrane surface area to the elastic stress imposed by
the spectrin cytoskeleton, via the local buckling of membrane under increasing
cytoskeleton stiffness. This model introduces the concept of force balance as a
regulatory process at the cell membrane, and quantitatively reproduces the rate
of area loss in aging red-blood cells.Comment: 4 pages, 3 figure
A contiuum model for low temperature relaxation of crystal steps
High and low temperature relaxation of crystal steps are described in a
unified picture, using a continuum model based on a modified expression of the
step free energy. Results are in agreement with experiments and Monte Carlo
simulations of step fluctuations and monolayer cluster diffusion and
relaxation. In an extended model where mass exchange with neighboring terraces
is allowed, step transparency and a low temperature regime for unstable step
meandering are found.Comment: Submitted to Phys.Rev.Let
Anomalous spin density distribution on oxygen and Ru in CaSrRuO: A polarised neutron diffraction study
By means of polarized neutron diffraction in a magnetic field of 7.0 T at 1.6
K an anomalously large magnetization density is observed on the in-plane oxygen
in CaSrRuO. Field-induced moments of different ions are
determined by refinement on the flipping ratios, yielding =
0.346(11) , = 0.076(6) and = 0.009(6)
. The moment on the oxygen arises from the strong hybridization
between the Ru-4d and O-2p orbitals. %The maximum entropy method is used for
the %reconstruction of the magnetization density and reveals a strongly
anisotropic The maximum entropy magnetization density reconstruction reveals a
strongly anisotropic density at the Ru site, consistent with the distribution
of the {\it xy} ( band) {\it d}-orbitals.Comment: 4 pages 3 figure
- …