716 research outputs found
Algebraic damping in the one-dimensional Vlasov equation
We investigate the asymptotic behavior of a perturbation around a spatially
non homogeneous stable stationary state of a one-dimensional Vlasov equation.
Under general hypotheses, after transient exponential Landau damping, a
perturbation evolving according to the linearized Vlasov equation decays
algebraically with the exponent -2 and a well defined frequency. The
theoretical results are successfully tested against numerical -body
simulations, corresponding to the full Vlasov dynamics in the large limit,
in the case of the Hamiltonian mean-field model. For this purpose, we use a
weighted particles code, which allows us to reduce finite size fluctuations and
to observe the asymptotic decay in the -body simulations.Comment: 26 pages, 8 figures; text slightly modified, references added, typos
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Macroscopic detection of the strong stochasticity threshold in Fermi-Pasta-Ulam chains of oscillators
The largest Lyapunov exponent of a system composed by a heavy impurity
embedded in a chain of anharmonic nearest-neighbor Fermi-Pasta-Ulam oscillators
is numerically computed for various values of the impurity mass . A
crossover between weak and strong chaos is obtained at the same value
of the energy density (energy per degree of freedom)
for all the considered values of the impurity mass . The threshold \epsi
lon_{_T} coincides with the value of the energy density at which a
change of scaling of the relaxation time of the momentum autocorrelation
function of the impurity ocurrs and that was obtained in a previous work ~[M.
Romero-Bastida and E. Braun, Phys. Rev. E {\bf65}, 036228 (2002)]. The complete
Lyapunov spectrum does not depend significantly on the impurity mass . These
results suggest that the impurity does not contribute significantly to the
dynamical instability (chaos) of the chain and can be considered as a probe for
the dynamics of the system to which the impurity is coupled. Finally, it is
shown that the Kolmogorov-Sinai entropy of the chain has a crossover from weak
to strong chaos at the same value of the energy density that the crossover
value of largest Lyapunov exponent. Implications of this result
are discussed.Comment: 6 pages, 5 figures, revtex4 styl
Large deviation techniques applied to systems with long-range interactions
We discuss a method to solve models with long-range interactions in the
microcanonical and canonical ensemble. The method closely follows the one
introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation
techniques. We show how it can be adapted to obtain the solution of a large
class of simple models, which can show ensemble inequivalence. The model
Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free
Electron Laser) state variables. This latter extension gives access to the
comparison with dynamics and to the study of non-equilibri um effects. We treat
both infinite range and slowly decreasing interactions and, in particular, we
present the solution of the alpha-Ising model in one-dimension with
Generalized algebra within a nonextensive statistics
By considering generalized logarithm and exponential functions used in
nonextensive statistics, the four usual algebraic operators : addition,
subtraction, product and division, are generalized. The properties of the
generalized operators are investigated. Some standard properties are preserved,
e.g., associativity, commutativity and existence of neutral elements. On the
contrary, the distributivity law and the opposite element is no more universal
within the generalized algebra.Comment: 11 pages, no figure, TeX. Reports on Mathematical Physics (2003), in
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Consequences of the ion beam irradiation on the chemical durability of thorium phosphate diphosphate â kinetics study
RADIOCHIn the field of the long-term specific immobilization of actinides, thorium phosphate diphosphate (ÎČ-TPD), as potential candidate, must respond to several criteria. Among them, the material must present a good resistance to irradiation and keep its initial good properties such as resistance to aqueous alteration. In order to check this later point, sintered samples of ÎČ-TUPD solid solutions were pre-irradiated with ion beams with various conditions (fluence, stopping power) then submitted to leaching tests in different media (pH, temperature, complexing reagents, flow rate, ...). The normalized dissolution rates depend significantly on the amorphous fraction (increase by a factor of 10â100 between unirradiated and fully amorphized materials). On the contrary, the pre-irradiation of the samples does not affect the kinetic parameters of the dissolution such as the partial order relative to the proton concentration (n = 0.37 ± 0.01 and n = 0.34 ± 0.01 for unirradiated and fully amorphized samples, respectively) and the activation energy of the reaction of dissolution (Eapp = 49 ± 4 kJ molâ1 and Eapp = 42 ± 4 kJ molâ1 for unirradiated and partly amorphized samples (fA < 1), respectively)
Lyapunov exponent of many-particle systems: testing the stochastic approach
The stochastic approach to the determination of the largest Lyapunov exponent
of a many-particle system is tested in the so-called mean-field
XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the
Lyapunov exponent to a few statistical properties of the Hessian matrix of the
interaction, which can be calculated as suitable thermal averages. We have
verified that there is a satisfactory quantitative agreement between theory and
simulations in the disordered phases of the XY models, either with attractive
or repulsive interactions. Part of the success of the theory is due to the
possibility of predicting the shape of the required correlation functions,
because this permits the calculation of correlation times as thermal averages.Comment: 11 pages including 6 figure
Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions
We investigate the ensemble inequivalence of the spherical spin glass model
with nonlinear interactions of polynomial order . This model is solved
exactly for arbitrary and is shown to have first-order phase transitions
between the paramagnetic and spin glass or ferromagnetic phases for .
In the parameter region around the first-order transitions, the solutions give
different results depending on the ensemble used for the analysis. In
particular, we observe that the microcanonical specific heat can be negative
and the phase may not be uniquely determined by the temperature.Comment: 15 pages, 10 figure
The Non--Ergodicity Threshold: Time Scale for Magnetic Reversal
We prove the existence of a non-ergodicity threshold for an anisotropic
classical Heisenberg model with all-to-all couplings. Below the threshold, the
energy surface is disconnected in two components with positive and negative
magnetizations respectively. Above, in a fully chaotic regime, magnetization
changes sign in a stochastic way and its behavior can be fully characterized by
an average magnetization reversal time. We show that statistical mechanics
predicts a phase--transition at an energy higher than the non-ergodicity
threshold. We assess the dynamical relevance of the latter for finite systems
through numerical simulations and analytical calculations. In particular, the
time scale for magnetic reversal diverges as a power law at the ergodicity
threshold with a size-dependent exponent, which could be a signature of the
phenomenon.Comment: 4 pages 4 figure
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