2,178 research outputs found
Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
We perform a detailed study of the relaxation towards equilibrium in the
Hamiltonian Mean-Field (HMF) model, a prototype for long-range interactions in
-particle dynamics. In particular, we point out the role played by the
infinity of stationary states of the associated Vlasov dynamics. In this
context, we derive a new general criterion for the stability of any spatially
homogeneous distribution, and compare its analytical predictions with numerical
simulations of the Hamiltonian, finite , dynamics. We then propose and
verify numerically a scenario for the relaxation process, relying on the Vlasov
equation. When starting from a non stationary or a Vlasov unstable stationary
initial state, the system shows initially a rapid convergence towards a stable
stationary state of the Vlasov equation via non stationary states: we
characterize numerically this dynamical instability in the finite system by
introducing appropriate indicators. This first step of the evolution towards
Boltzmann-Gibbs equilibrium is followed by a slow quasi-stationary process,
that proceeds through different stable stationary states of the Vlasov
equation. If the finite system is initialized in a Vlasov stable homogenous
state, it remains trapped in a quasi-stationary state for times that increase
with the nontrivial power law . Single particle momentum distributions
in such a quasi-stationary regime do not have power-law tails, and hence cannot
be fitted by the -exponential distributions derived from Tsallis statistics.Comment: To appear in Physica
The Vlasov equation and the Hamiltonian Mean-Field model
We show that the quasi-stationary states observed in the -particle
dynamics of the Hamiltonian Mean-Field (HMF) model are nothing but Vlasov
stable homogeneous (zero magnetization) states. There is an infinity of Vlasov
stable homogeneous states corresponding to different initial momentum
distributions. Tsallis -exponentials in momentum, homogeneous in angle,
distribution functions are possible, however, they are not special in any
respect, among an infinity of others. All Vlasov stable homogeneous states lose
their stability because of finite effects and, after a relaxation time
diverging with a power-law of the number of particles, the system converges to
the Boltzmann-Gibbs equilibrium
Long-Range Plasmon Assisted Energy Transfer Between Fluorescent Emitters
We demonstrate plasmon assisted energy transfer between fluorophores located
at distances up to m on the top of a thin silver film. Thanks to the
strong confinement and large propagation length of surface plasmon polaritons,
the range of the energy transfer is almost two orders of magnitude larger than
the values reported in the literature so far. The parameters driving the energy
transfer range are thoroughly characterized and are in very good agreement with
theoretically expected values.Comment: 5 pages, 4 figures, accepted for publication in Physical Review
Letter
Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics
We explain the ubiquity and extremely slow evolution of non gaussian
out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means
of traditional kinetic theory. Deriving the Fokker-Planck equation for a test
particle, one also unambiguously explains and predicts striking slow algebraic
relaxation of the momenta autocorrelation, previously found in numerical
simulations. Finally, angular anomalous diffusion are predicted for a large
class of initial distributions. Non Extensive Statistical Mechanics is shown to
be unnecessary for the interpretation of these phenomena
The Power Spectrum, Bias Evolution, and the Spatial Three-Point Correlation Function
We calculate perturbatively the normalized spatial skewness, , and full
three-point correlation function (3PCF), , induced by gravitational
instability of Gaussian primordial fluctuations for a biased tracer-mass
distribution in flat and open cold-dark-matter (CDM) models. We take into
account the dependence on the shape and evolution of the CDM power spectrum,
and allow the bias to be nonlinear and/or evolving in time, using an extension
of Fry's (1996) bias-evolution model. We derive a scale-dependent,
leading-order correction to the standard perturbative expression for in
the case of nonlinear biasing, as defined for the unsmoothed galaxy and
dark-matter fields, and find that this correction becomes large when probing
positive effective power-spectrum indices. This term implies that the inferred
nonlinear-bias parameter, as usually defined in terms of the smoothed density
fields, might depend on the chosen smoothing scale. In general, we find that
the dependence of on the biasing scheme can substantially outweigh that
on the adopted cosmology. We demonstrate that the normalized 3PCF, , is an
ill-behaved quantity, and instead investigate , the variance-normalized
3PCF. The configuration dependence of shows similarly strong
sensitivities to the bias scheme as , but also exhibits significant
dependence on the form of the CDM power spectrum. Though the degeneracy of
with respect to the cosmological parameters and constant linear- and
nonlinear-bias parameters can be broken by the full configuration dependence of
, neither statistic can distinguish well between evolving and non-evolving
bias scenarios. We show that this can be resolved, in principle, by considering
the redshift dependence of .Comment: 41 pages, including 12 Figures. To appear in The Astrophysical
Journal, Vol. 521, #
Algebraic Correlation Function and Anomalous Diffusion in the HMF model
In the quasi-stationary states of the Hamiltonian Mean-Field model, we
numerically compute correlation functions of momenta and diffusion of angles
with homogeneous initial conditions. This is an example, in a N-body
Hamiltonian system, of anomalous transport properties characterized by non
exponential relaxations and long-range temporal correlations. Kinetic theory
predicts a striking transition between weak anomalous diffusion and strong
anomalous diffusion. The numerical results are in excellent agreement with the
quantitative predictions of the anomalous transport exponents. Noteworthy, also
at statistical equilibrium, the system exhibits long-range temporal
correlations: the correlation function is inversely proportional to time with a
logarithmic correction instead of the usually expected exponential decay,
leading to weak anomalous transport properties
Relaxation times of unstable states in systems with long range interactions
We consider several models with long-range interactions evolving via
Hamiltonian dynamics. The microcanonical dynamics of the basic Hamiltonian Mean
Field (HMF) model and perturbed HMF models with either global anisotropy or an
on-site potential are studied both analytically and numerically. We find that
in the magnetic phase, the initial zero magnetization state remains stable
above a critical energy and is unstable below it. In the dynamically stable
state, these models exhibit relaxation time scales that increase algebraically
with the number of particles, indicating the robustness of the
quasistationary state seen in previous studies. In the unstable state, the
corresponding time scale increases logarithmically in .Comment: Minor change
Cluster physics from joint weak gravitational lensing and Sunyaev-Zel'dovich data
We present a self consistent method to perfom a joint analysis of Sunyaev-Zel'dovich and weak gravitational lensing observation of galaxy clusters. The spatial distribution of the cluster main constituents is described by a perturbative approach. Assuming the hydrostatic equilibrium and the equation of state, we are able to deduce, from observations, maps of projected gas density and gas temperature. The method then naturally entails a X-ray emissivity prediction which can be compared to observed X-ray emissivity maps. When tested on simulated clusters (noise free), this prediction turns out to be in very good agreement with the simulated surface brightness. The simulated and predicted surface brightness images have a correlation coefficient higher than 0.9 and the total flux differ by 0.9 % or 9 % in the two simulated clusters we studied. The method should be easily used on real data in order to provide a physical description of the cluster physics and of its constituents. The tests performed show that we can recover the amount and the spatial distributions of both the baryonic and non-baryonic material with an accuracy better than 10 %. So, in principle, in it might indeed help to alleviate some well known bias affecting, eg baryon fraction measurements
Probability distribution of density fluctuations in the non-linear regime
We present a general procedure for obtaining the present density fluctuation
probability distribution given the statistics of the initial conditions. The
main difficulties faced with regard to this problem are those related to the
non-linear evolution of the density fluctuations and those posed by the fact
that the fields we are interested in are the result of filtering an underlying
field with structure down to scales much smaller than that of filtering. The
solution to the latter problem is discussed here in detail and the solution to
the former is taken from a previous work.
We have checked the procedure for values of the rms density fluctuation as
large as 3/2 and several power spectra and found that it leads to results in
excellent agreement with those obtained in numerical simulations. We also
recover all available exact results from perturbation theory.Comment: Accepted to be published in Ap
On the Unusual Depletions toward Sk 155, or What Are the Small Magellanic Cloud Dust Grains Made of?
The dust in the Small Magellanic Cloud (SMC), an ideal analog of primordial
galaxies at high redshifts, differs markedly from that in the Milky Way by
exhibiting a steeply rising far-ultraviolet extinction curve, an absence of the
2175 Angstrom extinction feature, and a local minimum at ~12 micron in its
infrared emission spectrum, suggesting the lack of ultrasmall carbonaceous
grains (i.e. polycyclic aromatic hydrocarbon molecules) which are ubiquitously
seen in the Milky Way. While current models for the SMC dust all rely heavily
on silicates, recent observations of the SMC sightline toward Sk 155 indicated
that Si and Mg are essentially undepleted and the depletions of Fe range from
mild to severe, suggesting that metallic grains and/or iron oxides, instead of
silicates, may dominate the SMC dust. However, in this Letter we apply the
Kramers-Kronig relation to demonstrate that neither metallic grains nor iron
oxides are capable of accounting for the observed extinction; silicates remain
as an important contributor to the extinction, consistent with current models
for the SMC dust.Comment: 12 pages, 3 figures; The Astrophysical Journal Letters, in pres
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