34 research outputs found
Critical Binder cumulant in two-dimensional anisotropic Ising models
The Binder cumulant at the phase transition of Ising models on square
lattices with various ferromagnetic nearest and next-nearest neighbour
couplings is determined using mainly Monte Carlo techniques. We discuss the
possibility to relate the value of the critical cumulant in the isotropic,
nearest neighbour and in the anisotropic cases to each other by means of a
scale transformation in rectangular geometry, to pinpoint universal and
nonuniversal features.Comment: 7 pages, 4 figures, submitted to J. Phys.
Number of spanning clusters at the high-dimensional percolation thresholds
A scaling theory is used to derive the dependence of the average number
of spanning clusters at threshold on the lattice size L. This number should
become independent of L for dimensions d<6, and vary as log L at d=6. The
predictions for d>6 depend on the boundary conditions, and the results there
may vary between L^{d-6} and L^0. While simulations in six dimensions are
consistent with this prediction (after including corrections of order loglog
L), in five dimensions the average number of spanning clusters still increases
as log L even up to L = 201. However, the histogram P(k) of the spanning
cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L,
indicating that for sufficiently large L the average will approach a finite
value: a fit of the 5D multiplicity data with a constant plus a simple linear
correction to scaling reproduces the data very well. Numerical simulations for
d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review
Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation
We propose methods for constructing high-quality pseudorandom number
generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit
two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the
information hidden. The single cat map provides the random properties expected
from a good RNG and is hence an appropriate building block for an RNG, although
unnecessary correlations are always present in practice. We show that
introducing hidden variables and introducing rotation in the RNG output,
accompanied with the proper initialization, dramatically suppress these
correlations. We analyze the mechanisms of the single-cat-map correlations
analytically and show how to diminish them. We generalize the Percival-Vivaldi
theory in the case of the ensemble of maps, find the period of the proposed RNG
analytically, and also analyze its properties. We present efficient practical
realizations for the RNGs and check our predictions numerically. We also test
our RNGs using the known stringent batteries of statistical tests and find that
the statistical properties of our best generators are not worse than those of
other best modern generators.Comment: 18 pages, 3 figures, 9 table
Cyclotron enhancement of tunneling
A state of an electron in a quantum wire or a thin film becomes metastable,
when a static electric field is applied perpendicular to the wire direction or
the film surface. The state decays via tunneling through the created potential
barrier. An additionally applied magnetic field, perpendicular to the electric
field, can increase the tunneling decay rate for many orders of magnitude. This
happens, when the state in the wire or the film has a velocity perpendicular to
the magnetic field. According to the cyclotron effect, the velocity rotates
under the barrier and becomes more aligned with the direction of tunneling.
This mechanism can be called cyclotron enhancement of tunneling
Использование flash-технологии в образовательном процессе подготовки инженера-электромеханика
In the article in order to familiarize the use of modern digital technologies in the educational process is an electronic multimedia publication for the study of intelligent displacement sensor. It is based on Flash technology and has traditional construction of educational and methodological nature. The student has the opportunity prepare for the work, since the publication is equipped with a theoretical part, revealing the purpose and tasks, and the order of the work. Using Flash-technology visualizes the constructive construction of the device under study, its phased peration, circuit decisions of device nodes. An explanation of the operation of electronic units is accompanied by a graphic demonstration of the generated, processed and transmitted electronic circuits of electronic signals, reflecting the purpose of the device, namely obtaining a complex of signals proportional to the quality and quantity of the angular or linear movement of moving objects. Such visualization allows you to look “inside” electronic circuits, which is not provided possible in a real object. The scheme of determining the direction of movement (rotation) of an object is especially highlighted. Schemes are given speed measuring devices based on two principles of counting the number of pulses from the output of the displacement sensor. Designed electronic multimedia edition organically fits into the distance learning system as an integral part of the electronic university.В статье в целях ознакомления применения современных цифровых технологий в образовательном процессе приводится электронное мультимедийное издание по изучению интеллектуального датчика перемещения. Оно выполнено на основе Flash-технологии и имеет традиционное построение учебно-методического характера. Обучающийся имеет возможность подготовится к выполнению работы, поскольку издание снабжено теоретической частью, раскрывающей цель и задачи, и порядком выполнения работы. Использование Flash-технологии визуализирует конструктивное построение изучаемого устройства, его поэтапное функционирование, схемные решения узлов устройства. Разъяснение работы электронных блоков сопровождается графической демонстрацией формируемых, обрабатываемых и проходящих по электрическим цепям электронных сигналов, отражающих назначение устройства, а именно получение комплекса сигналов пропорциональных качеству и количеству углового или линейного перемещения движущихся объектов. Такая визуализация позволяет заглянуть «внутрь» электронных схем, что не предоставляется возможным в реальном объекте. Особенно выделена схема определения направления движения (вращения) объекта. Приведены схемы устройств измерения скорости, основанных на двух принципах подсчета количества импульсов с выхода датчика перемещения. Разработанное электронное мультимедийное издание органически вписывается в систему дистанционного обучения как составная часть электронного университета
Fermions and Disorder in Ising and Related Models in Two Dimensions
The aspects of phase transitions in the two-dimensional Ising models modified
by quenched and annealed site disorder are discussed in the framework of
fermionic approach based on the reformulation of the problem in terms of
integrals with anticommuting Grassmann variables.Comment: 11 pages, 1 table, no figures. The discussion is merely based on a
talk given at the International Bogoliubov Conference on Problems of
Theoretical and Mathematical Physics, MIRAS--JINR, Moscow--Dubna, Russia,
August 21--27, 200
A new test for random number generators: Schwinger-Dyson equations for the Ising model
We use a set of Schwinger-Dyson equations for the Ising Model to check
several random number generators. For the model in two and three dimensions, it
is shown that the equations are sensitive tests of bias originated by the
random numbers. The method is almost costless in computer time when added to
any simulation.Comment: 6 pages, 3 figure
Evaporation and fluid dynamics of a sessile drop of capillary size
Theoretical description and numerical simulation of an evaporating sessile
drop are developed. We jointly take into account the hydrodynamics of an
evaporating sessile drop, effects of the thermal conduction in the drop and the
diffusion of vapor in air. A shape of the rotationally symmetric drop is
determined within the quasistationary approximation. Nonstationary effects in
the diffusion of the vapor are also taken into account. Simulation results
agree well with the data of evaporation rate measurements for the toluene drop.
Marangoni forces associated with the temperature dependence of the surface
tension, generate fluid convection in the sessile drop. Our results demonstrate
several dynamical stages of the convection characterized by different number of
vortices in the drop. During the early stage the street of vortices arises near
a surface of the drop and induces a non-monotonic spatial distribution of the
temperature over the drop surface. The initial number of near-surface vortices
in the drop is controlled by the Marangoni cell size which is similar to that
given by Pearson for flat fluid layers. This number quickly decreases with
time, resulting in three bulk vortices in the intermediate stage. The vortices
finally transform into the single convection vortex in the drop, existing
during about 1/2 of the evaporation time.Comment: 23 pages, 12 figure
Ising Universality in Three Dimensions: A Monte Carlo Study
We investigate three Ising models on the simple cubic lattice by means of
Monte Carlo methods and finite-size scaling. These models are the spin-1/2
Ising model with nearest-neighbor interactions, a spin-1/2 model with
nearest-neighbor and third-neighbor interactions, and a spin-1 model with
nearest-neighbor interactions. The results are in accurate agreement with the
hypothesis of universality. Analysis of the finite-size scaling behavior
reveals corrections beyond those caused by the leading irrelevant scaling
field. We find that the correction-to-scaling amplitudes are strongly dependent
on the introduction of further-neighbor interactions or a third spin state. In
a spin-1 Ising model, these corrections appear to be very small. This is very
helpful for the determination of the universal constants of the Ising model.
The renormalization exponents of the Ising model are determined as y_t = 1.587
(2), y_h = 2.4815 (15) and y_i = -0.82 (6). The universal ratio Q =
^2/ is equal to 0.6233 (4) for periodic systems with cubic symmetry.
The critical point of the nearest-neighbor spin-1/2 model is K_c=0.2216546
(10).Comment: 25 pages, uuencoded compressed PostScript file (to appear in Journal
of Physics A
Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters
Percolation models with multiple percolating clusters have attracted much
attention in recent years. Here we use Monte Carlo simulations to study bond
percolation on planar random lattices, duals of random
lattices, and square lattices with free and periodic boundary conditions, in
vertical and horizontal directions, respectively, and with various aspect ratio
. We calculate the probability for the appearance of
percolating clusters, the percolating probabilities, , the average
fraction of lattice bonds (sites) in the percolating clusters,
(), and the probability distribution function for the fraction
of lattice bonds (sites), in percolating clusters of subgraphs with
percolating clusters, (). Using a small number of
nonuniversal metric factors, we find that , ,
(), and () for random lattices, duals
of random lattices, and square lattices have the same universal finite-size
scaling functions. We also find that nonuniversal metric factors are
independent of boundary conditions and aspect ratios.Comment: 15 pages, 11 figure