1,616 research outputs found
Relaxation to thermal equilibrium in the self-gravitating sheet model
We revisit the issue of relaxation to thermal equilibrium in the so-called
"sheet model", i.e., particles in one dimension interacting by attractive
forces independent of their separation. We show that this relaxation may be
very clearly detected and characterized by following the evolution of order
parameters defined by appropriately normalized moments of the phase space
distribution which probe its entanglement in space and velocity coordinates.
For a class of quasi-stationary states which result from the violent relaxation
of rectangular waterbag initial conditions, characterized by their virial ratio
R_0, we show that relaxation occurs on a time scale which (i) scales
approximately linearly in the particle number N, and (ii) shows also a strong
dependence on R_0, with quasi-stationary states from colder initial conditions
relaxing much more rapidly. The temporal evolution of the order parameter may
be well described by a stretched exponential function. We study finally the
correlation of the relaxation times with the amplitude of fluctuations in the
relaxing quasi-stationary states, as well as the relation between temporal and
ensemble averages.Comment: 37 pages, 24 figures; some additional discussion of previous
literature and other minor modifications, final published versio
Canonical solution of a system of long-range interacting rotators on a lattice
The canonical partition function of a system of rotators (classical X-Y
spins) on a lattice, coupled by terms decaying as the inverse of their distance
to the power alpha, is analytically computed. It is also shown how to compute a
rescaling function that allows to reduce the model, for any d-dimensional
lattice and for any alpha<d, to the mean field (alpha=0) model.Comment: Initially submitted to Physical Review Letters: following referees'
Comments it has been transferred to Phys. Rev. E, because of supposed no
general interest. Divided into sections, corrections in (5) and (20),
reference 5 updated. 8 pages 1 figur
Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems
We derive a necessary and sufficient condition of linear dynamical stability
for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF)
model. The condition is expressed by an explicit disequality that has to be
satisfied by the stationary state, and it generalizes the known disequality for
homogeneous stationary states. In addition, we derive analogous disequalities
that express necessary and sufficient conditions of formal stability for the
stationary states. Their usefulness, from the point of view of linear dynamical
stability, is that they are simpler, although they provide only sufficient
criteria of linear stability. We show that for homogeneous stationary states
the relations become equal, and therefore linear dynamical stability and formal
stability become equivalent.Comment: Submitted to Journal of Statistical Mechanics: Theory and Experimen
Canonical Solution of Classical Magnetic Models with Long-Range Couplings
We study the canonical solution of a family of classical spin
models on a generic -dimensional lattice; the couplings between two spins
decay as the inverse of their distance raised to the power , with
. The control of the thermodynamic limit requires the introduction of
a rescaling factor in the potential energy, which makes the model extensive but
not additive. A detailed analysis of the asymptotic spectral properties of the
matrix of couplings was necessary to justify the saddle point method applied to
the integration of functions depending on a diverging number of variables. The
properties of a class of functions related to the modified Bessel functions had
to be investigated. For given , and for any , and lattice
geometry, the solution is equivalent to that of the model, where the
dimensionality and the geometry of the lattice are irrelevant.Comment: Submitted for publication in Journal of Statistical Physic
Stability in microcanonical many-body spin glasses
We generalize the de Almeida-Thouless line for the many-body Ising spin glass
to the microcanonical ensemble and show that it coincides with the canonical
one. This enables us to draw a complete microcanonical phase diagram of this
model
Solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction
We describe a solvable model of a phase oscillator network on a circle with
infinite-range Mexican-hat-type interaction. We derive self-consistent
equations of the order parameters and obtain three non-trivial solutions
characterized by the rotation number. We also derive relevant characteristics
such as the location-dependent distributions of the resultant frequencies of
desynchronized oscillators. Simulation results closely agree with the
theoretical ones
Invariant measures of the 2D Euler and Vlasov equations
We discuss invariant measures of partial differential equations such as the
2D Euler or Vlasov equations. For the 2D Euler equations, starting from the
Liouville theorem, valid for N-dimensional approximations of the dynamics, we
define the microcanonical measure as a limit measure where N goes to infinity.
When only the energy and enstrophy invariants are taken into account, we give
an explicit computation to prove the following result: the microcanonical
measure is actually a Young measure corresponding to the maximization of a
mean-field entropy. We explain why this result remains true for more general
microcanonical measures, when all the dynamical invariants are taken into
account. We give an explicit proof that these microcanonical measures are
invariant measures for the dynamics of the 2D Euler equations. We describe a
more general set of invariant measures, and discuss briefly their stability and
their consequence for the ergodicity of the 2D Euler equations. The extension
of these results to the Vlasov equations is also discussed, together with a
proof of the uniqueness of statistical equilibria, for Vlasov equations with
repulsive convex potentials. Even if we consider, in this paper, invariant
measures only for Hamiltonian equations, with no fluxes of conserved
quantities, we think this work is an important step towards the description of
non-equilibrium invariant measures with fluxes.Comment: 40 page
Rietveld refinement of the mixed boracite Fe1.59Zn1.41B7O13Br
The structural characterization of the new iron–zinc heptaborate bromide with composition Fe1.59Zn1.41B7O13Br, prepared by chemical transport is reported. A rigid-body model with constrained generalized coordinates was defined in order to hold the positions of the B atoms at reasonable interatomic distances that typically would reach unacceptable values because of the weak scattering power of boron. There are three independent sites for the B atoms of which two are tetrahedrally coordinated. The bond-valence sum around the third B atom, located on a threefold rotation axis, was calculated considering two cases of coordination of boron with oxygens: trigonal-planar and tetrahedral. The contribution of the fourth O atom to the bond-valence sum was found to be only 0.06 v.u., indicating the presence of a very weak bond in the right position to have a distorted tetrahedral coordination in favour of the trigonal-planar coordination for the third B atom. X-ray fluorescence (XRF) was used to determinate the Fe/Zn ratio
Identification of distinct lymphocyte subsets responding to subcellular fractions of Mycobacterium bovis bacille calmette-Guerin (BCG)
In order to investigate the ability of Mycobacterium bovis BCG vaccination to induce immune responses toward different classes of mycobacterial antigens and the cell populations involved in such responses, proliferation of distinct human lymphocyte subsets from BCG-vaccinated donors in response to different subcellular fractions of BCG was analysed and compared with that of not sensitized subjects. Proliferation of different cell subsets was evaluated by flow cytometric determination of bromodeoxyuridine incorporated into DNA of dividing cells and simultaneous identification of cell surface markers. Although a certain degree of variability was observed among different donors, after 6 days of in vitro stimulation BCG-vaccinated subjects displayed, as a mean, a stronger blastogenic response to all the classes of antigens compared with non-sensitized ones. PPD, culture filtrates and membrane antigens induced a predominant proliferation of CD4(+) T cells. In contrast, preparations enriched in cytosolic antigens elicited strong proliferation of gamma delta(+) T cells which, as a mean, represented 55% of the proliferating cells. Although to a lesser extent, proliferation of gamma delta(+) T cells was also elicited by preparations enriched in membrane and cell wall antigens. In response to the latter preparation proliferation of CD4(+) T cells and CD16(+)/CD3(-) (natural killer (NK)) cells was observed, as well. In particular, cell wall antigens were found to induce significantly higher levels of proliferation of NK cells compared with all the other classes of antigens
- …