692 research outputs found
Search for universality in one-dimensional ballistic annihilation kinetics
We study the kinetics of ballistic annihilation for a one-dimensional ideal
gas with continuous velocity distribution. A dynamical scaling theory for the
long time behavior of the system is derived. Its validity is supported by
extensive numerical simulations for several velocity distributions. This leads
us to the conjecture that all the continuous velocity distributions \phi(v)
which are symmetric, regular and such that \phi(0) does not vanish, are
attracted in the long time regime towards the same Gaussian distribution and
thus belong to the same universality class. Moreover, it is found that the
particle density decays as n(t)~t^{-\alpha}, with \alpha=0.785 +/- 0.005.Comment: 8 pages, needs multicol, epsf and revtex. 8 postscript figures
included. Submitted to Phys. Rev. E. Also avaiable at
http://mykonos.unige.ch/~rey/publi.html#Secon
Kinetics of ballistic annihilation and branching
We consider a one-dimensional model consisting of an assembly of two-velocity
particles moving freely between collisions. When two particles meet, they
instantaneously annihilate each other and disappear from the system. Moreover
each moving particle can spontaneously generate an offspring having the same
velocity as its mother with probability 1-q. This model is solved analytically
in mean-field approximation and studied by numerical simulations. It is found
that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the
slow dynamics of the system is governed by the coarsening of clusters of
particles having the same velocities, while for q>1/2 the system relaxes
rapidly towards its stationary state characterized by a distribution of small
cluster sizes.Comment: 10 pages, 11 figures, uses multicol, epic, eepic and eepicemu. Also
avaiable at http://mykonos.unige.ch/~rey/pubt.htm
Direct Interactions in Relativistic Statistical Mechanics
Directly interacting particles are considered in the multitime formalism of
predictive relativistic mechanics. When the equations of motion leave a
phase-space volume invariant, it turns out that the phase average of any first
integral, covariantly defined as a flux across a -dimensional surface, is
conserved. The Hamiltonian case is discussed, a class of simple models is
exhibited, and a tentative definition of equilibrium is proposed.Comment: Plain Tex file, 26 page
Multimodel Inference and Multimodel Averaging in Empirical Modeling of Occupational Exposure Levels
Empirical modeling of exposure levels has been popular for identifying exposure determinants in occupational hygiene. Traditional data-driven methods used to choose a model on which to base inferences have typically not accounted for the uncertainty linked to the process of selecting the final model. Several new approaches propose making statistical inferences from a set of plausible models rather than from a single model regarded as best. This paper introduces the multimodel averaging approach described in the monograph by Burnham and Anderson. In their approach, a set of plausible models are defined a priori by taking into account the sample size and previous knowledge of variables influent on exposure levels. The Akaike information criterion is then calculated to evaluate the relative support of the data for each model, expressed as Akaike weight, to be interpreted as the probability of the model being the best approximating model given the model set. The model weights can then be used to rank models, quantify the evidence favoring one over another, perform multimodel prediction, estimate the relative influence of the potential predictors and estimate multimodel-averaged effects of determinants. The whole approach is illustrated with the analysis of a data set of 1500 volatile organic compound exposure levels collected by the Institute for work and health (Lausanne, Switzerland) over 20 years, each concentration having been divided by the relevant Swiss occupational exposure limit and log-transformed before analysis. Multimodel inference represents a promising procedure for modeling exposure levels that incorporates the notion that several models can be supported by the data and permits to evaluate to a certain extent model selection uncertainty, which is seldom mentioned in current practic
Front localization in a ballistic annihilation model
We study the possibility of localization of the front present in a
one-dimensional ballistically-controlled annihilation model in which the two
annihilating species are initially spatially separated. We construct two
different classes of initial conditions, for which the front remains localized.Comment: Using elsart (Elsevier Latex macro) and epsf. 12 Pages, 2 epsf
figures. Submitted to Physica
Comparison of Indices Proposed as Criteria for Assigning Skin Notation
Objectives: Skin notations are used as a hazard identification tool to flag chemicals associated with a potential risk related to transdermal penetration. The transparency and rigorousness of the skin notation assignment process have recently been questioned. We compared different approaches proposed as criteria for these notations as a starting point for improving and systematizing current practice. Methods: In this study, skin notations, dermal acute lethal dose 50 in mammals (LD50s) and two dermal risk indices derived from previously published work were compared using the lists of Swiss maximum allowable concentrations (MACs) and threshold limit values (TLVs) from the American Conference of Governmental Industrial Hygienists (ACGIH). The indices were both based on quantitative structure-activity relationship (QSAR) estimation of transdermal fluxes. One index compared the cumulative dose received through skin given specific exposure surface and duration to that received through lungs following inhalation 8 h at the MAC or TLV. The other index estimated the blood level increase caused by adding skin exposure to the inhalation route at kinetic steady state. Dermal-to-other route ratios of LD50 were calculated as secondary indices of dermal penetrability. Results: The working data set included 364 substances. Depending on the subdataset, agreement between the Swiss and ACGIH skin notations varied between 82 and 87%. Chemicals with a skin notation were more likely to have higher dermal risk indices and lower dermal LD50 than chemicals without a notation (probabilities between 60 and 70%). The risk indices, based on cumulative dose and kinetic steady state, respectively, appeared proportional up to a constant independent of chemical-specific properties. They agreed well with dermal LD50s (Spearman correlation coefficients −0.42 to −0.43). Dermal-to-other routes LD50 ratios were moderately associated with QSAR-based transdermal fluxes (Spearman correlation coefficients −0.2 to −0.3). Conclusions: The plausible but variable relationship between current skin notations and the different approaches tested confirm the need to improve current skin notations. QSAR-based risk indices and dermal toxicity data might be successfully integrated in a systematic alternative to current skin notations for detecting chemicals associated with potential dermal risk in the workplac
Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature
The definition of a nonequilibrium temperature through generalized
fluctuation-dissipation relations relies on the independence of the
fluctuation-dissipation temperature from the observable considered. We argue
that this observable independence is deeply related to the uniformity of the
phase-space probability distribution on the hypersurfaces of constant energy.
This property is shown explicitly on three different stochastic models, where
observable-dependence of the fluctuation-dissipation temperature arises only
when the uniformity of the phase-space distribution is broken. The first model
is an energy transport model on a ring, with biased local transfer rules. In
the second model, defined on a fully connected geometry, energy is exchanged
with two heat baths at different temperatures, breaking the uniformity of the
phase-space distribution. Finally, in the last model, the system is connected
to a zero temperature reservoir, and preserves the uniformity of the
phase-space distribution in the relaxation regime, leading to an
observable-independent temperature.Comment: 15 pages, 7 figure
Dynamical real-space renormalization group calculations with a new clustering scheme on random networks
We have defined a new type of clustering scheme preserving the connectivity
of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving
process. Our new clustering scheme performs much better for correlation length
and dynamical critical exponents in high dimensions, where the conventional
Migdal-Kadanoff bond moving scheme breaks down. In two and three dimensions we
find the dynamical critical exponents for the kinetic Ising Model to be z=2.13
and z=2.09, respectively at pure Ising fixed point. These values are in very
good agreement with recent Monte Carlo results. We investigate the phase
diagram and the critical behaviour for randomly bond diluted lattices in d=2
and 3, in the light of this new transformation. We also provide exact
correlation exponent and dynamical critical exponent values on hierarchical
lattices with power-law degree distributions, both in the pure and random
cases.Comment: 8 figure
A renormalization group study of a class of reaction-diffusion model, with particles input
We study a class of reaction-diffusion model extrapolating continuously
between the pure coagulation-diffusion case () and the pure
annihilation-diffusion one () with particles input
() at a rate . For dimension , the dynamics
strongly depends on the fluctuations while, for , the behaviour is
mean-field like. The models are mapped onto a field theory which properties are
studied in a renormalization group approach. Simple relations are found between
the time-dependent correlation functions of the different models of the class.
For the pure coagulation-diffusion model the time-dependent density is found to
be of the form , where
is the diffusion constant. The critical exponent and are
computed to all orders in , where is the dimension of the
system, while the scaling function is computed to second order in
. For the one-dimensional case an exact analytical solution is
provided which predictions are compared with the results of the renormalization
group approach for .Comment: Ten pages, using Latex and IOP macro. Two latex figures. Submitted to
Journal of Physics A. Also available at
http://mykonos.unige.ch/~rey/publi.htm
On the universality of a class of annihilation-coagulation models
A class of -dimensional reaction-diffusion models interpolating
continuously between the diffusion-coagulation and the diffusion-annihilation
models is introduced. Exact relations among the observables of different models
are established. For the one-dimensional case, it is shown how correlations in
the initial state can lead to non-universal amplitudes for time-dependent
particles density.Comment: 18 pages with no figures. Latex file using REVTE
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