2,681 research outputs found
Yang-Lee zeroes for an urn model for the separation of sand
We apply the Yang-Lee theory of phase transitions to an urn model of
separation of sand. The effective partition function of this nonequilibrium
system can be expressed as a polynomial of the size-dependent effective
fugacity . Numerical calculations show that in the thermodynamic limit, the
zeros of the effective partition function are located on the unit circle in the
complex -plane. In the complex plane of the actual control parameter certain
roots converge to the transition point of the model. Thus the Yang-Lee theory
can be applied to a wider class of nonequilibrium systems than those considered
previously.Comment: 4 pages, 3 eps figures include
Extended phase diagram of the Lorenz model
The parameter dependence of the various attractive solutions of the three
variable nonlinear Lorenz model equations for thermal convection in
Rayleigh-B\'enard flow is studied. Its bifurcation structure has commonly been
investigated as a function of r, the normalized Rayleigh number, at fixed
Prandtl number \sigma. The present work extends the analysis to the entire
(r,\sigma) parameter plane. An onion like periodic pattern is found which is
due to the alternating stability of symmetric and non-symmetric periodic
orbits. This periodic pattern is explained by considering non-trivial limits of
large r and \sigma. In addition to the limit which was previously analyzed by
Sparrow, we identify two more distinct asymptotic regimes in which either
\sigma/r or \sigma^2/r is constant. In both limits the dynamics is
approximately described by Airy functions whence the periodicity in parameter
space can be calculated analytically. Furthermore, some observations about
sequences of bifurcations and coexistence of attractors, periodic as well as
chaotic, are reported.Comment: 36 pages, 20 figure
Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros
We present a detailed description of a classification scheme for phase
transitions in finite systems based on the distribution of Fisher zeros of the
canonical partition function in the complex temperature plane. We apply this
scheme to finite Bose-systems in power law traps within a semi-analytic
approach with a continuous one-particle density of states for different values of and to a three dimensional harmonically
confined ideal Bose-gas with discrete energy levels. Our results indicate that
the order of the Bose-Einstein condensation phase transition sensitively
depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small
systems see "http://www.smallsystems.de
Modified semiclassical approximation for trapped Bose gases
A generalization of the semiclassical approximation is suggested allowing for
an essential extension of its region of applicability. In particular, it
becomes possible to describe Bose-Einstein condensation of a trapped gas in
low-dimensional traps and in traps of low confining dimensions, for which the
standard semiclassical approximation is not applicable. The results of the
modified approach are shown to coincide with purely quantum-mechanical
calculations for harmonic traps, including the one-dimensional harmonic trap.
The advantage of the semiclassical approximation is in its simplicity and
generality. Power-law potentials of arbitrary powers are considered. Effective
thermodynamic limit is defined for any confining dimension. The behaviour of
the specific heat, isothermal compressibility, and density fluctuations is
analyzed, with an emphasis on low confining dimensions, where the usual
semiclassical method fails. The peculiarities of the thermodynamic
characteristics in the effective thermodynamic limit are discussed.Comment: Revtex file, 13 page
First Order Phase Transition in a Reaction-Diffusion Model With Open Boundary: The Yang-Lee Theory Approach
A coagulation-decoagulation model is introduced on a chain of length L with
open boundary. The model consists of one species of particles which diffuse,
coagulate and decoagulate preferentially in the leftward direction. They are
also injected and extracted from the left boundary with different rates. We
will show that on a specific plane in the space of parameters, the steady state
weights can be calculated exactly using a matrix product method. The model
exhibits a first-order phase transition between a low-density and a
high-density phase. The density profile of the particles in each phase is
obtained both analytically and using the Monte Carlo Simulation. The two-point
density-density correlation function in each phase has also been calculated. By
applying the Yang-Lee theory we can predict the same phase diagram for the
model. This model is further evidence for the applicability of the Yang-Lee
theory in the non-equilibrium statistical mechanics context.Comment: 10 Pages, 3 Figures, To appear in Journal of Physics A: Mathematical
and Genera
Visualization of Coherent Destruction of Tunneling in an Optical Double Well System
We report on a direct visualization of coherent destruction of tunneling
(CDT) of light waves in a double well system which provides an optical analog
of quantum CDT as originally proposed by Grossmann, Dittrich, Jung, and Hanggi
[Phys. Rev. Lett. {\bf 67}, 516 (1991)]. The driven double well, realized by
two periodically-curved waveguides in an Er:Yb-doped glass, is designed so that
spatial light propagation exactly mimics the coherent space-time dynamics of
matter waves in a driven double-well potential governed by the Schr\"{o}dinger
equation. The fluorescence of Er ions is exploited to image the spatial
evolution of light in the two wells, clearly demonstrating suppression of light
tunneling for special ratios between frequency and amplitude of the driving
field.Comment: final versio
Variable Curvature Slab Molecular Dynamics as a Method to Determine Surface Stress
A thin plate or slab, prepared so that opposite faces have different surface
stresses, will bend as a result of the stress difference. We have developed a
classical molecular dynamics (MD) formulation where (similar in spirit to
constant-pressure MD) the curvature of the slab enters as an additional
dynamical degree of freedom. The equations of motion of the atoms have been
modified according to a variable metric, and an additional equation of motion
for the curvature is introduced. We demonstrate the method to Au surfaces, both
clean and covered with Pb adsorbates, using many-body glue potentials.
Applications to stepped surfaces, deconstruction and other surface phenomena
are under study.Comment: 16 pages, 8 figures, REVTeX, submitted to Physical Review
Transitions and Probes in Turbulent Helium
Previous analysis of a Paris turbulence experiment \cite{zoc94,tab95} shows a
transition at the Taylor Reynolds number \rel \approx 700. Here correlation
function data is analyzed which gives further evidence for this transition. It
is seen in both the power spectrum and in structure function measurements. Two
possible explanations may be offered for this observed transition: that it is
intrinsic to the turbulence flow in this closed box experiment or that it is an
effect of a change in the flow around the anemometer. We particularly examine a
pair of ``probe effects''. The first is a thermal boundary layer which does
exist about the probe and does limit the probe response, particularly at high
frequencies. Arguments based on simulations of the response and upon
observations of dissipation suggests that this effect is only crucial beyond
\rel\approx 2000. The second effect is produced by vortex shedding behind the
probe. This has been seen to produce a large modification in some of the power
spectra for large \rel. It might also complicate the interpretation of the
experimental results. However, there seems to be a remaining range of data for
\rel < 1300 uncomplicated by these effects, and which are thus suggestive of
an intrinsic transition.Comment: uuencoded .ps files. submitted to PRE. 12 figures are sent upon
request to jane wang ([email protected]
Universality in fully developed turbulence
We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70,
3251 (1993)] of highly turbulent flow with Taylor-Reynolds number
up to , employing a reduced wave
vector set method (introduced earlier) to approximately solve the Navier-Stokes
equation. First, also for these extremely high Reynolds numbers ,
the energy spectra as well as the higher moments -- when scaled by the spectral
intensity at the wave number of peak dissipation -- can be described by
{\it one universal} function of for all . Second, the ISR
scaling exponents of this universal function are in agreement with
the 1941 Kolmogorov theory (the better, the large is), as is the
dependence of . Only around viscous damping leads to
slight energy pileup in the spectra, as in the experimental data (bottleneck
phenomenon).Comment: 14 pages, Latex, 5 figures (on request), 3 tables, submitted to Phys.
Rev.
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