31 research outputs found
Friction coefficient of a disk in a sheet of viscous fluid: numerical calculation
We study the class C of (generalized) orthogonal polynomial sequences {Pn(x)}n=0∞ satisfying a recurrence relation of the type Pn(x) = (x − cn)Pn−1(x) − λnPn−2(x), n> 1, where λn ≠0 and the sequence {λn+1/(cncn+1)}n=1∞ constitutes a chain sequence. We obtain a new characterization of C in terms of the moment sequence associated with an orthogonal polynomial sequence, and contribute to the solution of the problem of determining a (signed) orthogonalizing measure for a member of C
Three-dimensional Ising model in the fixed-magnetization ensemble: a Monte Carlo study
We study the three-dimensional Ising model at the critical point in the
fixed-magnetization ensemble, by means of the recently developed geometric
cluster Monte Carlo algorithm. We define a magnetic-field-like quantity in
terms of microscopic spin-up and spin-down probabilities in a given
configuration of neighbors. In the thermodynamic limit, the relation between
this field and the magnetization reduces to the canonical relation M(h).
However, for finite systems, the relation is different. We establish a close
connection between this relation and the probability distribution of the
magnetization of a finite-size system in the canonical ensemble.Comment: 8 pages, 2 Postscript figures, uses RevTe
Diffusive Thermal Dynamics for the Ising Ferromagnet
We introduce a thermal dynamics for the Ising ferromagnet where the energy
variations occurring within the system exhibit a diffusive character typical of
thermalizing agents such as e.g. localized excitations. Time evolution is
provided by a walker hopping across the sites of the underlying lattice
according to local probabilities depending on the usual Boltzmann weight at a
given temperature. Despite the canonical hopping probabilities the walker
drives the system to a stationary state which is not reducible to the canonical
equilibrium state in a trivial way. The system still exhibits a magnetic phase
transition occurring at a finite value of the temperature larger than the
canonical one. The dependence of the model on the density of walkers realizing
the dynamics is also discussed. Interestingly the differences between the
stationary state and the Boltzmann equilibrium state decrease with increasing
number of walkers.Comment: 9 pages, 14 figures. Accepted for publication on PR
Physical tests for Random Numbers in Simulations
We propose three physical tests to measure correlations in random numbers
used in Monte Carlo simulations. The first test uses autocorrelation times of
certain physical quantities when the Ising model is simulated with the Wolff
algorithm. The second test is based on random walks, and the third on blocks of
n successive numbers. We apply the tests to show that recent errors in high
precision simulations using generalized feedback shift register algorithms are
due to short range correlations in random number sequences. We also determine
the length of these correlations.Comment: 16 pages, Post Script file, HU-TFT-94-
Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution
We study equilibrium properties of a catalytically-activated annihilation reaction taking place on a one-dimensional chain of length () in which some segments (placed at random, with mean concentration
) possess special, catalytic properties. Annihilation reaction takes place,
as soon as any two particles land onto two vacant sites at the extremities
of the catalytic segment, or when any particle lands onto a vacant site on
a catalytic segment while the site at the other extremity of this segment is
already occupied by another particle. Non-catalytic segments are inert with
respect to reaction and here two adsorbed particles harmlessly coexist. For
both "annealed" and "quenched" disorder in placement of the catalytic segments,
we calculate exactly the disorder-average pressure per site. Explicit
asymptotic formulae for the particle mean density and the compressibility are
also presented.Comment: AMSTeX, 27 pages + 4 figure