19 research outputs found
Multicanonical Simulations of the Tails of the Order-Parameter Distribution of the Two-Dimensional Ising Model
We report multicanonical Monte Carlo simulations of the tails of the
order-parameter distribution of the two-dimensional Ising model for fixed
boundary conditions. Clear numerical evidence for "fat" stretched exponential
tails is found below the critical temperature, indicating the possible presence
of fat tails at the critical temperature.Comment: 4 pages, elsart3.cls (included), 5 postscript figures, author
information under http://www.physik.uni-leipzig.de/index.php?id=2
Continuous time random walk and parametric subordination in fractional diffusion
The well-scaled transition to the diffusion limit in the framework of the
theory of continuous-time random walk (CTRW)is presented starting from its
representation as an infinite series that points out the subordinated character
of the CTRW itself. We treat the CTRW as a combination of a random walk on the
axis of physical time with a random walk in space, both walks happening in
discrete operational time. In the continuum limit we obtain a generally
non-Markovian diffusion process governed by a space-time fractional diffusion
equation. The essential assumption is that the probabilities for waiting times
and jump-widths behave asymptotically like powers with negative exponents
related to the orders of the fractional derivatives. By what we call parametric
subordination, applied to a combination of a Markov process with a positively
oriented L\'evy process, we generate and display sample paths for some special
cases.Comment: 28 pages, 18 figures. Workshop 'In Search of a Theory of Complexity'.
Denton, Texas, August 200
Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation
A detailed study is presented for a large class of uncoupled continuous-time
random walks (CTRWs). The master equation is solved for the Mittag-Leffler
survival probability. The properly scaled diffusive limit of the master
equation is taken and its relation with the fractional diffusion equation is
discussed. Finally, some common objections found in the literature are
thoroughly reviewed.Comment: Preprint version of an already published paper. 8 page
Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations
During the last decade, lattice-Boltzmann (LB) simulations have been improved
to become an efficient tool for determining the permeability of porous media
samples. However, well known improvements of the original algorithm are often
not implemented. These include for example multirelaxation time schemes or
improved boundary conditions, as well as different possibilities to impose a
pressure gradient. This paper shows that a significant difference of the
calculated permeabilities can be found unless one uses a carefully selected
setup. We present a detailed discussion of possible simulation setups and
quantitative studies of the influence of simulation parameters. We illustrate
our results by applying the algorithm to a Fontainebleau sandstone and by
comparing our benchmark studies to other numerical permeability measurements in
the literature.Comment: 14 pages, 11 figure
Fractional calculus and continuous-time finance II: the waiting-time distribution
We complement the theory of tick-by-tick dynamics of financial markets based
on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et
al., and we point out its consistency with the behaviour observed in the
waiting-time distribution for BUND future prices traded at LIFFE, London.Comment: Revised version, 17 pages, 4 figures. Physica A, Vol. 287, No 3-4,
468--481 (2000). Proceedings of the International Workshop on "Economic
Dynamics from the Physics Point of View", Bad-Honnef (Germany), 27-30 March
200
Composite continuous time random walks
Random walks in composite continuous time are introduced. Composite time flow is the product of translational time flow and fractional time flow [see Chem. Phys. 84, 399 (2002)]. The continuum limit of composite continuous time random walks gives a diffusion equation where the infinitesimal generator of time flow is the sum of a first order and a fractional time derivative. The latter is specified as a generalized Riemann-Liouville derivative. Generalized and binomial Mittag-Leffler functions are found as the exact results for waiting time density and mean square displacement
On the Analysis of Spatial Binary Images
This paper deals with the characterization of microscopically heterogeneous, but macroscopically homogeneous spatial structures. A new method is presented which is strictly based on integral-geometric formulae such as Crofton's intersection formulae and Hadwiger's recursive de nition of the Euler number. The corresponding algorithms have clear advantages over other techniques. As an example of application we consider the analysis of spatial digital images produced by means of Computer Assisted Tomo- graphy
Statistical prediction of corrosion front penetration
A statistical method to predict the stochastic evolution of corrosion fronts has been developed. The method is based on recording material loss and maximum front depth. In this paper we introduce the method and test its applicability. In the absence of experimental data we use simulation data from a three-dimensional corrosion model for this test. The corrosion model simulates localized breakdown of a protective oxide layer, hydrolysis of corrosion product and repassivation of the exposed surface. In the long time limit of the model, pits tend to coalesce. For different model parameters the model reproduces corrosion patterns observed in experiment. The statistical prediction method is based in the theory of stochastic processes. It allows the estimation of conditional probability densities for penetration depth, pitting factor, residual lifetimes, and corrosion rates which are of technological interest
Desiderata for Fractional Derivatives and Integrals
The purpose of this brief article is to initiate discussions in this special issue by proposing desiderata for calling an operator a fractional derivative or a fractional integral. Our desiderata are neither axioms nor do they define fractional derivatives or integrals uniquely. Instead they intend to stimulate the field by providing guidelines based on a small number of time honoured and well established criteria