251 research outputs found
The instability of Alexander-McTague crystals and its implication for nucleation
We show that the argument of Alexander and McTague, that the bcc crystalline
structure is favored in those crystallization processes where the first order
character is not too pronounced, is not correct. We find that any solution that
satisfies the Alexander-McTague condition is not stable. We investigate the
implication of this result for nucleation near the pseudo- spinodal in
near-meanfield systems.Comment: 20 pages, 0 figures, submitted to Physical Review
Dynamic and static properties of the invaded cluster algorithm
Simulations of the two-dimensional Ising and 3-state Potts models at their
critical points are performed using the invaded cluster (IC) algorithm. It is
argued that observables measured on a sub-lattice of size l should exhibit a
crossover to Swendsen-Wang (SW) behavior for l sufficiently less than the
lattice size L, and a scaling form is proposed to describe the crossover
phenomenon. It is found that the energy autocorrelation time tau(l,L) for an
l*l sub-lattice attains a maximum in the crossover region, and a dynamic
exponent z for the IC algorithm is defined according to tau_max ~ L^z.
Simulation results for the 3-state model yield z=.346(.002) which is smaller
than values of the dynamic exponent found for the SW and Wolff algorithms and
also less than the Li-Sokal bound. The results are less conclusive for the
Ising model, but it appears that z<.21 and possibly that tau_max ~ log L so
that z=0 -- similar to previous results for the SW and Wolff algorithms.Comment: 21 pages with 12 figure
Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment
We present a model for diffusion in a molecularly crowded environment. The
model consists of random barriers in percolation network. Random walks in the
presence of slowly moving barriers show normal diffusion for long times, but
anomalous diffusion at intermediate times. The effective exponents for square
distance versus time usually are below one at these intermediate times, but can
be also larger than one for high barrier concentrations. Thus we observe sub-
as well as super-diffusion in a crowded environment.Comment: 8 pages including 4 figure
Monte Carlo study of the magnetic critical properties of the two-dimensional Ising fluid
A two-dimensional fluid of hard spheres each having a spin and
interacting via short-range Ising-like interaction is studied near the second
order phase transition from the paramagnetic gas to the ferromagnetic gas
phase. Monte Carlo simulation technique and the multiple histogram data
analysis were used. By measuring the finite-size behaviour of several different
thermodynamic quantities,we were able to locate the transition and estimate
values of various static critical exponents. The values of exponents
and are close to the ones for the two-dimensional
lattice Ising model. However, our result for the exponent is very
different from the one for the Ising universality class.Comment: 6 pages, 8 figures. To appear in Phys. Rev.
Simulations of grafted polymers in a good solvent
We present improved simulations of three-dimensional self avoiding walks with
one end attached to an impenetrable surface on the simple cubic lattice. This
surface can either be a-thermal, having thus only an entropic effect, or
attractive. In the latter case we concentrate on the adsorption transition, We
find clear evidence for the cross-over exponent to be smaller than 1/2, in
contrast to all previous simulations but in agreement with a re-summed field
theoretic -expansion. Since we use the pruned-enriched Rosenbluth
method (PERM) which allows very precise estimates of the partition sum itself,
we also obtain improved estimates for all entropic critical exponents.Comment: 5 pages with 9 figures included; minor change
Interfacial tension and nucleation in mixtures of colloids and long ideal polymer coils
Mixtures of ideal polymers with hard spheres whose diameters are smaller than
the radius of gyration of the polymer, exhibit extensive immiscibility. The
interfacial tension between demixed phases of these mixtures is estimated, as
is the barrier to nucleation. The barrier is found to scale linearly with the
radius of the polymer, causing it to become large for large polymers. Thus for
large polymers nucleation is suppressed and phase separation proceeds via
spinodal decomposition, as it does in polymer blends.Comment: 4 pages (v2 includes discussion of the scaling of the interfacial
tension along the coexistence curve and its relation to the Ginzburg
criterion
Chaotic scattering through coupled cavities
We study the chaotic scattering through an Aharonov-Bohm ring containing two
cavities. One of the cavities has well-separated resonant levels while the
other is chaotic, and is treated by random matrix theory. The conductance
through the ring is calculated analytically using the supersymmetry method and
the quantum fluctuation effects are numerically investigated in detail. We find
that the conductance is determined by the competition between the mean and
fluctuation parts. The dephasing effect acts on the fluctuation part only. The
Breit-Wigner resonant peak is changed to an antiresonance by increasing the
ratio of the level broadening to the mean level spacing of the random cavity,
and the asymmetric Fano form turns into a symmetric one. For the orthogonal and
symplectic ensembles, the period of the Aharonov-Bohm oscillations is half of
that for regular systems. The conductance distribution function becomes
independent of the ensembles at the resonant point, which can be understood by
the mode-locking mechanism. We also discuss the relation of our results to the
random walk problem.Comment: 13 pages, 9 figures; minor change
Nucleation in Systems with Elastic Forces
Systems with long-range interactions when quenced into a metastable state
near the pseudo-spinodal exhibit nucleation processes that are quite different
from the classical nucleation seen near the coexistence curve. In systems with
long-range elastic forces the description of the nucleation process can be
quite subtle due to the presence of bulk/interface elastic compatibility
constraints. We analyze the nucleation process in a simple 2d model with
elastic forces and show that the nucleation process generates critical droplets
with a different structure than the stable phase. This has implications for
nucleation in many crystal-crystal transitions and the structure of the final
state
Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model
This paper describes the application of finite-size scaling concepts to
domain growth in systems with a non-conserved order parameter. A finite-size
scaling ansatz for the time-dependent order parameter distribution function is
proposed, and tested with extensive Monte-Carlo simulations of domain growth in
the 2-D spin-flip kinetic Ising model. The scaling properties of the
distribution functions serve to elucidate the configurational self-similarity
that underlies the dynamic scaling picture. Moreover, it is demonstrated that
the application of finite-size-scaling techniques facilitates the accurate
determination of the bulk growth exponent even in the presence of strong
finite-size effects, the scale and character of which are graphically exposed
by the order parameter distribution function. In addition it is found that one
commonly used measure of domain size--the scaled second moment of the
magnetisation distribution--belies the full extent of these finite-size
effects.Comment: 13 pages, Latex. Figures available on request. Rep #9401
- …