4,353 research outputs found
Investigations on finite ideal quantum gases
Recursion formulae of the N-particle partition function, the occupation
numbers and its fluctuations are given using the single-particle partition
function. Exact results are presented for fermions and bosons in a common
one-dimensional harmonic oscillator potential, for the three-dimensional
harmonic oscillator approximations are tested. Applications to excited nuclei
and Bose-Einstein condensation are discussed.Comment: 13 pages, 7 postscript figures, uses 'epsfig.sty'. Submitted to
Physica A. More information available at
http://obelix.physik.uni-osnabrueck.de/~schnack
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
Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics
A numerical method based on Matrix Product Formalism is proposed to study the
phase transitions and shock formation in the Asymmetric Simple Exclusion
Process with open boundaries and parallel dynamics. By working in a canonical
ensemble, where the total number of the particles is being fixed, we find that
the model has a rather non-trivial phase diagram consisting of three different
phases which are separated by second-order phase transition. Shocks may evolve
in the system for special values of the reaction parameters.Comment: 8 pages, 3 figure
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
The scientific evaluation of music content analysis systems: Valid empirical foundations for future real-world impact
We discuss the problem of music content analysis within the formal framework of experimental design
Electron-Ion Interaction Effects in Attosecond Time-Resolved Photoelectron Spectra
Photoionization by attosecond (as) extreme ultraviolet (xuv) pulses into the
laser-dressed continuum of the ionized atom is commonly described in
strong-field approximation (SFA), neglecting the Coulomb interaction between
the emitted photoelectron (PE) and residual ion. By solving the time-dependent
Sch\"{o}dinger equation (TDSE), we identify a temporal shift in
streaked PE spectra, which becomes significant at small PE energies. Within an
eikonal approximation, we trace this shift to the combined action of Coulomb
and laser forces on the released PE, suggesting the experimental and
theoretical scrutiny of their coupling in streaked PE spectra. The initial
state polarization effect by the laser pulse on the xuv streaked spectrum is
also examined.Comment: 9 pages, Accepted by Phys. Rev.
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
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
Finite size corrections to scaling in high Reynolds number turbulence
We study analytically and numerically the corrections to scaling in
turbulence which arise due to the finite ratio of the outer scale of
turbulence to the viscous scale , i.e., they are due to finite size
effects as anisotropic forcing or boundary conditions at large scales. We find
that the deviations \dzm from the classical Kolmogorov scaling of the velocity moments \langle |\u(\k)|^m\rangle \propto k^{-\zeta_m}
decrease like . Our numerics employ a
reduced wave vector set approximation for which the small scale structures are
not fully resolved. Within this approximation we do not find independent
anomalous scaling within the inertial subrange. If anomalous scaling in the
inertial subrange can be verified in the large limit, this supports the
suggestion that small scale structures should be responsible, originating from
viscosity either in the bulk (vortex tubes or sheets) or from the boundary
layers (plumes or swirls)
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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