27,046 research outputs found
Numerical analysis of the master equation
Applied to the master equation, the usual numerical integration methods, such
as Runge-Kutta, become inefficient when the rates associated with various
transitions differ by several orders of magnitude. We introduce an integration
scheme that remains stable with much larger time increments than can be used in
standard methods. When only the stationary distribution is required, a direct
iteration method is even more rapid; this method may be extended to construct
the quasi-stationary distribution of a process with an absorbing state.
Applications to birth-and-death processes reveal gains in efficiency of two or
more orders of magnitude.Comment: 7 pages 3 figure
Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure
In [arXiv:0804.3035] we studied an interacting particle system which can be
also interpreted as a stochastic growth model. This model belongs to the
anisotropic KPZ class in 2+1 dimensions. In this paper we present the results
that are relevant from the perspective of stochastic growth models, in
particular: (a) the surface fluctuations are asymptotically Gaussian on a
sqrt(ln(t)) scale and (b) the correlation structure of the surface is
asymptotically given by the massless field.Comment: 13 pages, 4 figure
No phase transition for Gaussian fields with bounded spins
Let a<b, \Omega=[a,b]^{\Z^d} and H be the (formal) Hamiltonian defined on
\Omega by
H(\eta) = \frac12 \sum_{x,y\in\Z^d} J(x-y) (\eta(x)-\eta(y))^2 where
J:\Z^d\to\R is any summable non-negative symmetric function (J(x)\ge 0 for all
x\in\Z^d, \sum_x J(x)<\infty and J(x)=J(-x)). We prove that there is a unique
Gibbs measure on \Omega associated to H. The result is a consequence of the
fact that the corresponding Gibbs sampler is attractive and has a unique
invariant measure.Comment: 7 page
Measuring Service Quality: The Opinion of Europeans about Utilities
This paper provides a comparative analysis of statistical methods to evaluate the consumer perception about the quality of Services of General Interest. The evaluation of the service quality perceived by users is usually based on Customer Satisfaction Survey data and an ex-post evaluation is then performed. Another approach, consisting in evaluating Consumers preferences, supplies an ex-ante information on Service Quality. Here, the ex-post approach is considered, two non-standard techniques - the Rasch Model and the Nonlinear Principal Component Analysis - are presented and the potential of both methods is discussed. These methods are applied on the Eurobarometer Survey data to assess the consumer satisfaction among European countries and in different years.Service Quality, Eurobarometer, Non Linear Principal Component Analysis, Rasch Analysis, Conjoint Analysis
Competition interfaces and second class particles
The one-dimensional nearest-neighbor totally asymmetric simple exclusion
process can be constructed in the same space as a last-passage percolation
model in Z^2. We show that the trajectory of a second class particle in the
exclusion process can be linearly mapped into the competition interface between
two growing clusters in the last-passage percolation model. Using technology
built up for geodesics in percolation, we show that the competition interface
converges almost surely to an asymptotic random direction. As a consequence we
get a new proof for the strong law of large numbers for the second class
particle in the rarefaction fan and describe the distribution of the asymptotic
angle of the competition interface.Comment: Published at http://dx.doi.org/10.1214/009117905000000080 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the asymmetric zero-range in the rarefaction fan
We consider the one-dimensional asymmetric zero-range process starting from a
step decreasing profile. In the hydrodynamic limit this initial condition leads
to the rarefaction fan of the associated hydrodynamic equation. Under this
initial condition and for totally asymmetric jumps, we show that the weighted
sum of joint probabilities for second class particles sharing the same site is
convergent and we compute its limit. For partially asymmetric jumps we derive
the Law of Large Numbers for the position of a second class particle under the
initial configuration in which all the positive sites are empty, all the
negative sites are occupied with infinitely many first class particles and with
a single second class particle at the origin. Moreover, we prove that among the
infinite characteristics emanating from the position of the second class
particle, this particle chooses randomly one of them. The randomness is given
in terms of the weak solution of the hydrodynamic equation through some sort of
renormalization function. By coupling the zero-range with the exclusion process
we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic
Teukolsky-Starobinsky Identities - a Novel Derivation and Generalizations
We present a novel derivation of the Teukolsky-Starobinsky identities, based
on properties of the confluent Heun functions. These functions define
analytically all exact solutions to the Teukolsky master equation, as well as
to the Regge-Wheeler and Zerilli ones. The class of solutions, subject to
Teukolsky-Starobinsky type of identities is studied. Our generalization of the
Teukolsky-Starobinsky identities is valid for the already studied linear
perturbations to the Kerr and Schwarzschild metrics, as well as for large new
classes of of such perturbations which are explicitly described in the present
article. Symmetry of parameters of confluent Heun's functions is shown to stay
behind the behavior of the known solutions under the change of the sign of
their spin weights. A new efficient recurrent method for calculation of
Starobinsky's constant is described.Comment: 8 pages, LaTeX file, no figures, final versio
A model for multifragmentation in heavy-ion reactions
From an experimental point of view, clear signatures of multifragmentation
have been detected by different experiments. On the other hand, from a
theoretical point of view, many different models, built on the basis of totally
different and often even contrasting assumptions, have been provided to explain
them. In this contribution we show the capabilities and the shortcomings of one
of this models, a QMD code developed by us and coupled to the nuclear
de-excitation module taken from the multipurpose transport and interaction code
FLUKA, in reproducing the multifragmentation observations recently reported by
the INDRA collaboration for the reaction Nb + Mg at a 30 MeV/A projectile
bombarding energy. As far as fragment production is concerned, we also briefly
discuss the isoscaling technique by considering reactions characterized by a
different isospin asymmetry, and we explain how the QMD + FLUKA model can be
applied to obtain information on the slope of isotopic yield ratios, which is
crucially related to the symmetry energy of asymmetric nuclear matter.Comment: 8 pages, 2 figures, Proc. 12th International Conference on Nuclear
Reaction Mechanisms, Varenna, Italy, June 15 - 19 200
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