1,228 research outputs found
Universality in two-dimensional Kardar-Parisi-Zhang growth
We analyze simulations results of a model proposed for etching of a
crystalline solid and results of other discrete models in the 2+1-dimensional
Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W_n of
orders n=2,3,4 of the heights distribution are estimated. Results for the
etching model, the ballistic deposition (BD) model and the
temperature-dependent body-centered restricted solid-on-solid model (BCSOS)
suggest the universality of the absolute value of the skewness S = W_3 /
(W_2)^(3/2) and of the value of the kurtosis Q = W_4 / (W_2)^2 - 3. The sign of
the skewness is the same of the parameter \lambda of the KPZ equation which
represents the process in the continuum limit. The best numerical estimates,
obtained from the etching model, are |S| = 0.26 +- 0.01 and Q = 0.134 +- 0.015.
For this model, the roughness exponent \alpha = 0.383 +- 0.008 is obtained,
accounting for a constant correction term (intrinsic width) in the scaling of
the squared interface width. This value is slightly below previous estimates of
extensive simulations and rules out the proposal of the exact value \alpha=2/5.
The conclusion is supported by results for the ballistic deposition model.
Independent estimates of the dynamical exponent and of the growth exponent are
1.605 <= z <= 1.64 and \beta = 0.229 +- 0.005, respectively, which are
consistent with the relations \alpha + z = 2 and z = \alpha / \beta.Comment: 8 pages, 9 figures, to be published in Phys. Rev.
Fission of a multiphase membrane tube
A common mechanism for intracellular transport is the use of controlled
deformations of the membrane to create spherical or tubular buds. While the
basic physical properties of homogeneous membranes are relatively well-known,
the effects of inhomogeneities within membranes are very much an active field
of study. Membrane domains enriched in certain lipids in particular are
attracting much attention, and in this Letter we investigate the effect of such
domains on the shape and fate of membrane tubes. Recent experiments have
demonstrated that forced lipid phase separation can trigger tube fission, and
we demonstrate how this can be understood purely from the difference in elastic
constants between the domains. Moreover, the proposed model predicts timescales
for fission that agree well with experimental findings
A moving boundary model motivated by electric breakdown: II. Initial value problem
An interfacial approximation of the streamer stage in the evolution of sparks
and lightning can be formulated as a Laplacian growth model regularized by a
'kinetic undercooling' boundary condition. Using this model we study both the
linearized and the full nonlinear evolution of small perturbations of a
uniformly translating circle. Within the linear approximation analytical and
numerical results show that perturbations are advected to the back of the
circle, where they decay. An initially analytic interface stays analytic for
all finite times, but singularities from outside the physical region approach
the interface for , which results in some anomalous relaxation at
the back of the circle. For the nonlinear evolution numerical results indicate
that the circle is the asymptotic attractor for small perturbations, but larger
perturbations may lead to branching. We also present results for more general
initial shapes, which demonstrate that regularization by kinetic undercooling
cannot guarantee smooth interfaces globally in time.Comment: 44 pages, 18 figures, paper submitted to Physica
Analytical Estimate of the Critical Velocity for Vortex Pair Creation in Trapped Bose Condensates
We use a modified Thomas-Fermi approximation to estimate analytically the
critical velocity for the formation of vortices in harmonically trapped BEC. We
compare this analytical estimate to numerical calculations and to recent
experiments on trapped alkali condensates.Comment: 12 page
Crossover from Rate-Equation to Diffusion-Controlled Kinetics in Two-Particle Coagulation
We develop an analytical diffusion-equation-type approximation scheme for the
one-dimensional coagulation reaction A+A->A with partial reaction probability
on particle encounters which are otherwise hard-core. The new approximation
describes the crossover from the mean-field rate-equation behavior at short
times to the universal, fluctuation-dominated behavior at large times. The
approximation becomes quantitatively accurate when the system is initially
close to the continuum behavior, i.e., for small initial density and fast
reaction. For large initial density and slow reaction, lattice effects are
nonnegligible for an extended initial time interval. In such cases our
approximation provides the correct description of the initial mean-field as
well as the asymptotic large-time, fluctuation-dominated behavior. However, the
intermediate-time crossover between the two regimes is described only
semiquantitatively.Comment: 21 pages, plain Te
Dynamics of Particles Deposition on a Disordered Substrate: II. Far-from Equilibrium Behavior. -
The deposition dynamics of particles (or the growth of a rigid crystal) on a
disordered substrate at a finite deposition rate is explored. We begin with an
equation of motion which includes, in addition to the disorder, the periodic
potential due to the discrete size of the particles (or to the lattice
structure of the crystal) as well as the term introduced by Kardar, Parisi, and
Zhang (KPZ) to account for the lateral growth at a finite growth rate. A
generating functional for the correlation and response functions of this
process is derived using the approach of Martin, Sigga, and Rose. A consistent
renormalized perturbation expansion to first order in the non-Gaussian
couplings requires the calculation of diagrams up to three loops. To this order
we show, for the first time for this class of models which violates the the
fluctuation-dissipation theorem, that the theory is renormalizable. We find
that the effects of the periodic potential and the disorder decay on very large
scales and asymptotically the KPZ term dominates the behavior. However, strong
non-trivial crossover effects are found for large intermediate scales.Comment: 52 pages & 17 Figs in uucompressed file. UR-CM 94-090
Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models
We investigate the relation between two-time, multi-spin, correlation and
response functions in the non-equilibrium critical dynamics of Ising models in
d=1 and d=2 spatial dimensions. In these non-equilibrium situations, the
fluctuation-dissipation theorem (FDT) is not satisfied. We find FDT
`violations' qualitatively similar to those reported in various glassy
materials, but quantitatively dependent on the chosen observable, in contrast
to the results obtained in infinite-range glass models. Nevertheless, all FDT
violations can be understood by considering separately the contributions from
large wavevectors, which are at quasi-equilibrium and obey FDT, and from small
wavevectors where a generalized FDT holds with a non-trivial limit
fluctuation-dissipation ratio X. In d=1, we get X = 1/2 for spin observables,
which measure the orientation of domains, while X = 0 for observables that are
sensitive to the domain-wall motion. Numerical simulations in d=2 reveal a
unique X = 0.34 for all observables. Measurement protocols for X are discussed
in detail. Our results suggest that the definition of an effective temperature
Teff = T / X for large length scales is generically possible in non-equilibrium
critical dynamics.Comment: 26 pages, 10 figure
Scaling Approach to Calculate Critical Exponents in Anomalous Surface Roughening
We study surface growth models exhibiting anomalous scaling of the local
surface fluctuations. An analytical approach to determine the local scaling
exponents of continuum growth models is proposed. The method allows to predict
when a particular growth model will have anomalous properties () and to calculate the local exponents. Several continuum growth
equations are examined as examples.Comment: RevTeX, 4 pages, no figs. To appear in Phys. Rev. Let
Aggregation with Multiple Conservation Laws
Aggregation processes with an arbitrary number of conserved quantities are
investigated. On the mean-field level, an exact solution for the size
distribution is obtained. The asymptotic form of this solution exhibits
nontrivial ``double'' scaling. While processes with one conserved quantity are
governed by a single scale, processes with multiple conservation laws exhibit
an additional diffusion-like scale. The theory is applied to ballistic
aggregation with mass and momentum conserving collisions and to diffusive
aggregation with multiple species.Comment: 18 pages, te
Elements Discrimination in the Study of Super-Heavy Elements using an Ionization Chamber
Dedicated ionization chamber was built and installed to measure the energy
loss of very heavy nuclei at 2.7 MeV/u produced in fusion reactions in inverse
kinematics (beam of 208Pb). After going through the ionization chamber,
products of reactions on 12C, 18O targets are implanted in a Si detector. Their
identification through their alpha decay chain is ambiguous when their
half-life is short. After calibration with Pb and Th nuclei, the ionization
chamber signal allowed us to resolve these ambiguities. In the search for rare
super-heavy nuclei produced in fusion reactions in inverse or symmetric
kinematics, such a chamber will provide direct information on the nuclear
charge of each implanted nucleus.Comment: submitted to NIMA, 10 pages+4 figures, Latex, uses elsart.cls and
grahpic
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