2,077 research outputs found
Exponential distributions of collective flow-event properties in viscous liquid dynamics
We study the statistics of flow events in the inherent dynamics in
supercooled two- and three-dimensional binary Lennard-Jones liquids.
Distributions of changes of the collective quantities energy, pressure and
shear stress become exponential at low temperatures, as does that of the event
"size" . We show how the -distribution controls the
others, while itself following from exponential tails in the distributions of
(1) single particle displacements , involving a Lindemann-like length
and (2) the number of active particles (with ).Comment: Accepter version (PRL
Bethe lattice solution of a model of SAW's with up to 3 monomers per site and no restriction
In the multiple monomers per site (MMS) model, polymeric chains are
represented by walks on a lattice which may visit each site up to K times. We
have solved the unrestricted version of this model, where immediate reversals
of the walks are allowed (RA) for K = 3 on a Bethe lattice with arbitrary
coordination number in the grand-canonical formalism. We found transitions
between a non-polymerized and two polymerized phases, which may be continuous
or discontinuous. In the canonical situation, the transitions between the
extended and the collapsed polymeric phases are always continuous. The
transition line is partly composed by tricritical points and partially by
critical endpoints, both lines meeting at a multicritical point. In the
subspace of the parameter space where the model is related to SASAW's
(self-attracting self-avoiding walks), the collapse transition is tricritical.
We discuss the relation of our results with simulations and previous Bethe and
Husimi lattice calculations for the MMS model found in the literature.Comment: 25 pages, 9 figure
Charge renormalization and phase separation in colloidal suspensions
We explore the effects of counterion condensation on fluid-fluid phase
separation in charged colloidal suspensions. It is found that formation of
double layers around the colloidal particles stabilizes suspensions against
phase separation. Addition of salt, however, produces an instability which, in
principle, can lead to a fluid-fluid separation. The instability, however, is
so weak that it should be impossible to observe a fully equilibrated
coexistence experimentally.Comment: 7 pages, Europhysics Letters (in press
Universal Formulae for Percolation Thresholds
A power law is postulated for both site and bond percolation thresholds. The
formula writes , where is the space
dimension and the coordination number. All thresholds up to are found to belong to only three universality classes. For first two
classes for site dilution while for bond dilution. The last one
associated to high dimensions is characterized by for both sites and
bonds. Classes are defined by a set of value for . Deviations
from available numerical estimates at are within and
for high dimensional hypercubic expansions at . The
formula is found to be also valid for Ising critical temperatures.Comment: 11 pages, latex, 3 figures not include
Elasticity near the vulcanization transition
Signatures of the vulcanization transition--amorphous solidification induced
by the random crosslinking of macromolecules--include the random localization
of a fraction of the particles and the emergence of a nonzero static shear
modulus. A semi-microscopic statistical-mechanical theory is presented of the
latter signature that accounts for both thermal fluctuations and quenched
disorder. It is found (i) that the shear modulus grows continuously from zero
at the transition, and does so with the classical exponent, i.e., with the
third power of the excess cross-link density and, quite surprisingly, (ii) that
near the transition the external stresses do not spoil the spherical symmetry
of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change
Phase Transitions in a Two-Component Site-Bond Percolation Model
A method to treat a N-component percolation model as effective one component
model is presented by introducing a scaled control variable . In Monte
Carlo simulations on , , and simple cubic
lattices the percolation threshold in terms of is determined for N=2.
Phase transitions are reported in two limits for the bond existence
probabilities and . In the same limits, empirical formulas
for the percolation threshold as function of one
component-concentration, , are proposed. In the limit a new
site percolation threshold, , is reported.Comment: RevTeX, 5 pages, 5 eps-figure
Statistical Models on Spherical Geometries
We use a one-dimensional random walk on -dimensional hyper-spheres to
determine the critical behavior of statistical systems in hyper-spherical
geometries. First, we demonstrate the properties of such a walk by studying the
phase diagram of a percolation problem. We find a line of second and first
order phase transitions separated by a tricritical point. Then, we analyze the
adsorption-desorption transition for a polymer growing near the attractive
boundary of a cylindrical cell membrane. We find that the fraction of adsorbed
monomers on the boundary vanishes exponentially when the adsorption energy
decreases towards its critical value.Comment: 8 pages, latex, 2 figures in p
Effects of Impurities in Random Sequential Adsorption on a One-Dimensional Substrate
We have solved the kinetics of random sequential adsorption of linear
-mers on a one-dimensional disordered substrate for the random sequential
adsorption initial condition and for the random initial condition. The jamming
limits at fixed length of linear -mers have a
minimum point at a particular density of the linear -mers impurity for both
cases. The coverage of the surface and the jamming limits are compared to the
results for Monte Carlo simulation. The Monte Carlo results for the jamming
limits are in good agreement with the analytical results. The continuum limits
are derived from the analytical results on lattice substrates.Comment: 9 pages, latex, 1 figure not included, accepted in Phys. Rev.
Kinetics of self-induced aggregation of Brownian particles: non-Markovian and non-Gaussian features
In this paper we have studied a model for self-induced aggregation in
Brownian particle incorporating the non-Markovian and non-Gaussian character of
the associated random noise process. In this model the time evolution of each
individual is guided by an over-damped Langevin equation of motion with a
non-local drift resulting from the local unbalance distributions of the other
individuals. Our simulation result shows that colored nose can induce the
cluster formation even at large noise strength. Another observation is that
critical noise strength grows very rapidly with increase of noise correlation
time for Gaussian noise than non Gaussian one. However, at long time limit the
cluster number in aggregation process decreases with time following a power
law. The exponent in the power law increases remarkable for switching from
Markovian to non Markovian noise process
Competition for hydrogen bond formation in the helix-coil transition and protein folding
The problem of the helix-coil transition of biopolymers in explicit solvents,
like water, with the ability for hydrogen bonding with solvent is addressed
analytically using a suitably modified version of the Generalized Model of
Polypeptide Chains. Besides the regular helix-coil transition, an additional
coil-helix or reentrant transition is also found at lower temperatures. The
reentrant transition arises due to competition between polymer-polymer and
polymer-water hydrogen bonds. The balance between the two types of hydrogen
bonding can be shifted to either direction through changes not only in
temperature, but also by pressure, mechanical force, osmotic stress or other
external influences. Both polypeptides and polynucleotides are considered
within a unified formalism. Our approach provides an explanation of the
experimental difficulty of observing the reentrant transition with pressure;
and underscores the advantage of pulling experiments for studies of DNA.
Results are discussed and compared with those reported in a number of recent
publications with which a significant level of agreement is obtained.Comment: 21 pages, 3 figures, submitted to Phys Rev
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