4,976 research outputs found
Global Persistence Exponent for Critical Dynamics
A `persistence exponent' is defined for nonequilibrium critical
phenomena. It describes the probability, , that the
global order parameter has not changed sign in the time interval following
a quench to the critical point from a disordered state. This exponent is
calculated in mean-field theory, in the limit of the model,
to first order in , and for the 1-d Ising model. Numerical
results are obtained for the 2-d Ising model. We argue that is a new
independent exponent.Comment: 4 pages, revtex, one figur
Non-equilibrium Dynamics Following a Quench to the Critical Point in a Semi-infinite System
We study the non-equilibrium dynamics (purely dissipative and relaxational)
in a semi-infinite system following a quench from the high temperature
disordered phase to its critical temperature. We show that the local
autocorrelation near the surface of a semi-infinite system decays algebraically
in time with a new exponent which is different from the bulk. We calculate this
new non-equilibrium surface exponent in several cases, both analytically and
numerically.Comment: revtex, 9 pages, 2 figures available from the author
On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
Finite-size scaling (FSS) is a standard technique for measuring scaling
exponents in spin glasses. Here we present a critique of this approach,
emphasizing the need for all length scales to be large compared to microscopic
scales. In particular we show that the replacement, in FSS analyses, of the
correlation length by its asymptotic scaling form can lead to apparently good
scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page
Coarsening Dynamics of a One-Dimensional Driven Cahn-Hilliard System
We study the one-dimensional Cahn-Hilliard equation with an additional
driving term representing, say, the effect of gravity. We find that the driving
field has an asymmetric effect on the solution for a single stationary
domain wall (or `kink'), the direction of the field determining whether the
analytic solutions found by Leung [J.Stat.Phys.{\bf 61}, 345 (1990)] are
unique. The dynamics of a kink-antikink pair (`bubble') is then studied. The
behaviour of a bubble is dependent on the relative sizes of a characteristic
length scale , where is the driving field, and the separation, ,
of the interfaces. For the velocities of the interfaces are
negligible, while in the opposite limit a travelling-wave solution is found
with a velocity . For this latter case () a set of
reduced equations, describing the evolution of the domain lengths, is obtained
for a system with a large number of interfaces, and implies a characteristic
length scale growing as . Numerical results for the domain-size
distribution and structure factor confirm this behavior, and show that the
system exhibits dynamical scaling from very early times.Comment: 20 pages, revtex, 10 figures, submitted to Phys. Rev.
Phase separation in an homogeneous shear flow: Morphology, growth laws and dynamic scaling
We investigate numerically the influence of an homogeneous shear flow on the
spinodal decomposition of a binary mixture by solving the Cahn-Hilliard
equation in a two-dimensional geometry. Several aspects of this much studied
problem are clarified. Our numerical data show unambiguously that, in the shear
flow, the domains have on average an elliptic shape. The time evolution of the
three parameters describing this ellipse are obtained for a wide range of shear
rates. For the lowest shear rates investigated, we find the growth laws for the
two principal axis , , while
the mean orientation of the domains with respect to the flow is inversely
proportional to the strain. This implies that when hydrodynamics is neglected a
shear flow does not stop the domain growth process. We investigate also the
possibility of dynamic scaling, and show that only a non trivial form of
scaling holds, as predicted by a recent analytical approach to the case of a
non-conserved order parameter. We show that a simple physical argument may
account for these results.Comment: Version accepted for publication - Physical Review
Non-Markovian Persistence and Nonequilibrium Critical Dynamics
The persistence exponent \theta for the global order parameter, M(t), of a
system quenched from the disordered phase to its critical point describes the
probability, p(t) \sim t^{-\theta}, that M(t) does not change sign in the time
interval t following the quench. We calculate \theta to O(\epsilon^2) for model
A of critical dynamics (and to order \epsilon for model C) and show that at
this order M(t) is a non-Markov process. Consequently, \theta is a new
exponent. The calculation is performed by expanding around a Markov process,
using a simplified version of the perturbation theory recently introduced by
Majumdar and Sire [Phys. Rev. Lett. _77_, 1420 (1996); cond-mat/9604151].Comment: 4 pages, Revtex, no figures, requires multicol.st
Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems
We consider the phase-ordering kinetics of one-dimensional scalar systems.
For attractive long-range () interactions with ,
``Energy-Scaling'' arguments predict a growth-law of the average domain size for all . Numerical results for ,
, and demonstrate both scaling and the predicted growth laws. For
purely short-range interactions, an approach of Nagai and Kawasaki is
asymptotically exact. For this case, the equal-time correlations scale, but the
time-derivative correlations break scaling. The short-range solution also
applies to systems with long-range interactions when , and in that limit the amplitude of the growth law is exactly
calculated.Comment: 19 pages, RevTex 3.0, 8 FIGURES UPON REQUEST, 1549
Electron Impact Excitation Cross Sections for Hydrogen-Like Ions
We present cross sections for electron-impact-induced transitions n --> n' in
hydrogen-like ions C 5+, Ne 9+, Al 12+, and Ar 17+. The cross sections are
computed by Coulomb-Born with exchange and normalization (CBE) method for all
transitions with n < n' < 7 and by convergent close-coupling (CCC) method for
transitions with n 2s and 1s
--> 2p are presented as well. The CCC and CBE cross sections agree to better
than 10% with each other and with earlier close-coupling results (available for
transition 1 --> 2 only). Analytical expression for n --> n' cross sections and
semiempirical formulae are discussed.Comment: RevTeX, 5 pages, 13 PostScript figures, submitted to Phys. Rev.
The coupling between flame surface dynamics and species mass conservation in premixed turbulent combustion
Current flamelot models based on a description of the flame surface dynamics require the closure of two inter-related equations: a transport equation for the mean reaction progress variable, (tilde)c, and a transport equation for the flame surface density, Sigma. The coupling between these two equations is investigated using direct numerical simulations (DNS) with emphasis on the correlation between the turbulent fluxes of (tilde)c, bar(pu''c''), and Sigma, (u'')(sub S)Sigma. Two different DNS databases are used in the present work: a database developed at CTR by A. Trouve and a database developed by C. J. Rutland using a different code. Both databases correspond to statistically one-dimensional premixed flames in isotropic turbulent flow. The run parameters, however, are significantly different, and the two databases correspond to different combustion regimes. It is found that in all simulated flames, the correlation between bar(pu''c'') and (u'')(sub S)Sigma is always strong. The sign, however, of the turbulent flux of (tilde)c or Sigma with respect to the mean gradients, delta(tilde)c/delta(x) or delta(Sigma)/delta(x), is case-dependent. The CTR database is found to exhibit gradient turbulent transport of (tilde)c and Sigma, whereas the Rutland DNS features counter-gradient diffusion. The two databases are analyzed and compared using various tools (a local analysis of the flow field near the flame, a classical analysis of the conservation equation for (tilde)(u''c''), and a thin flame theoretical analysis). A mechanism is then proposed to explain the discrepancies between the two databases and a preliminary simple criterion is derived to predict the occurrence of gradient/counter-gradient turbulent diffusion
Scaling of stiffness energy for 3d +/-J Ising spin glasses
Large numbers of ground states of 3d EA Ising spin glasses are calculated for
sizes up to 10^3 using a combination of a genetic algorithm and Cluster-Exact
Approximation. A detailed analysis shows that true ground states are obtained.
The ground state stiffness (or domain wall) energy D is calculated. A D ~ L^t
behavior with t=0.19(2) is found which strongly indicates that the 3d model has
an equilibrium spin-glass-paramagnet transition for non-zero T_c.Comment: 4 pages, 4 figure
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