3,115 research outputs found
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
Wind reversals in turbulent Rayleigh-Benard convection
The phenomenon of irregular cessation and subsequent reversal of the
large-scale circulation in turbulent Rayleigh-B\'enard convection is
theoretically analysed. The force and thermal balance on a single plume
detached from the thermal boundary layer yields a set of coupled nonlinear
equations, whose dynamics is related to the Lorenz equations. For Prandtl and
Rayleigh numbers in the range and 10^{7} \leq
\Ra \leq 10^{12}, the model has the following features: (i) chaotic reversals
may be exhibited at Ra ; (ii) the Reynolds number based on the
root mean square velocity scales as \Re_{rms} \sim \Ra^{[0.41 ...
0.47]} (depending on Pr), and as
(depending on Ra); and (iii) the mean reversal frequency follows an effective
scaling law \omega / (\nu L^{-2}) \sim \Pr^{-(0.64 \pm 0.01)} \Ra^{0.44 \pm
0.01}. The phase diagram of the model is sketched, and the observed
transitions are discussed.Comment: 4 pages, 5 figure
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
Variational bound on energy dissipation in turbulent shear flow
We present numerical solutions to the extended Doering-Constantin variational
principle for upper bounds on the energy dissipation rate in plane Couette
flow, bridging the entire range from low to asymptotically high Reynolds
numbers. Our variational bound exhibits structure, namely a pronounced minimum
at intermediate Reynolds numbers, and recovers the Busse bound in the
asymptotic regime. The most notable feature is a bifurcation of the minimizing
wavenumbers, giving rise to simple scaling of the optimized variational
parameters, and of the upper bound, with the Reynolds number.Comment: 4 pages, RevTeX, 5 postscript figures are available as one .tar.gz
file from [email protected]
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
Convective intensification of magnetic fields in the quiet Sun
Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field B_e, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field B_p that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealised numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and is characterised by a pattern of vigorous, time-dependent, “granular” motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localised concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than B_e, and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contain ultra-intense magnetic fields that are significantly greater than B_p. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultra-intense fields develop owing to nonlinear interactions between magnetic fields and convection; they cannot be explained in terms of “convective collapse” within a thin flux tube that remains in overall pressure equilibrium with its surroundings
Coherent transport in a two-electron quantum dot molecule
We investigate the dynamics of two interacting electrons confined to a pair
of coupled quantum dots driven by an external AC field. By numerically
integrating the two-electron Schroedinger equation in time, we find that for
certain values of the strength and frequency of the AC field we can cause the
electrons to be localised within the same dot, in spite of the Coulomb
repulsion between them. Reducing the system to an effective two-site model of
Hubbard type and applying Floquet theory leads to a detailed understanding of
this effect. This demonstrates the possibility of using appropriate AC fields
to manipulate entangled states in mesoscopic devices on extremely short
timescales, which is an essential component of practical schemes for quantum
information processing.Comment: 4 pages, 3 figures; the section dealing with the perturbative
treatment of the Floquet states has been substantially expanded to make it
easier to follo
Dynamics of an electron in finite and infinite one dimensional systems in presence of electric field
We study,numerically, the dynamical behavior of an electron in a two site
nonlinear system driven by dc and ac electric field separately. We also study,
numerically, the effect of electric field on single static impurity and
antidimeric dynamical impurity in an infinite 1D chain to find the strength of
the impurities. Analytical arguments for this system have also been given.Comment: File Latex, 8 Figures available on reques
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.
- …