273 research outputs found
Conformal approach to cylindrical DLA
We extend the conformal mapping approach elaborated for the radial Diffusion
Limited Aggregation model (DLA) to the cylindrical geometry. We introduce in
particular a complex function which allows to grow a cylindrical cluster using
as intermediate step a radial aggregate. The grown aggregate exhibits the same
self-affine features of the original cylindrical DLA. The specific choice of
the transformation allows us to study the relationship between the radial and
the cylindrical geometry. In particular the cylindrical aggregate can be seen
as a radial aggregate with particles of size increasing with the radius. On the
other hand the radial aggregate can be seen as a cylindrical aggregate with
particles of size decreasing with the height. This framework, which shifts the
point of view from the geometry to the size of the particles, can open the way
to more quantitative studies on the relationship between radial and cylindrical
DLA.Comment: 16 pages, 8 figure
Viscoelasticity near the gel-point: a molecular dynamics study
We report on extensive molecular dynamics simulations on systems of soft
spheres of functionality f, i.e. particles that are capable of bonding
irreversibly with a maximum of f other particles. These bonds are randomly
distributed throughout the system and imposed with probability p. At a critical
concentration of bonds, p_c approximately equal to 0.2488 for f=6, a gel is
formed and the shear viscosity \eta diverges according to \eta ~ (p_c-p)^{-s}.
We find s is approximately 0.7 in agreement with some experiments and with a
recent theoretical prediction based on Rouse dynamics of phantom chains. The
diffusion constant decreases as the gel point is approached but does not
display a well-defined power law.Comment: 4 pages, 4 figure
Dynamic Scaling of Width Distribution in Edwards--Wilkinson Type Models of Interface Dynamics
Edwards--Wilkinson type models are studied in 1+1 dimensions and the
time-dependent distribution, P_L(w^2,t), of the square of the width of an
interface, w^2, is calculated for systems of size L. We find that, using a flat
interface as an initial condition, P_L(w^2,t) can be calculated exactly and it
obeys scaling in the form _\infty P_L(w^2,t) = Phi(w^2 / _\infty,
t/L^2) where _\infty is the stationary value of w^2. For more complicated
initial states, scaling is observed only in the large- time limit and the
scaling function depends on the initial amplitude of the longest wavelength
mode. The short-time limit is also interesting since P_L(w^2,t) is found to
closely approximate the log-normal distribution. These results are confirmed by
Monte Carlo simulations on a `roof-top' model of surface evolution.Comment: 5 pages, latex, 3 ps figures in a separate files, submitted to
Phys.Rev.
The inelastic Takahashi hard-rod gas
We study a one-dimensional fluid of hard-rods interacting each other via
binary inelastic collisions and a short ranged square-well potential. Upon
tuning the depth and the sign of the well, we investigate the interplay between
dissipation and cohesive or repulsive forces. Molecular dynamics simulations of
the cooling regime indicate that the presence of this simple interparticle
interaction is sufficient to significantly modify the energy dissipation rates
expected by the Haff's law for the free cooling. The simplicity of the model
makes it amenable to an analytical approach based on the Boltzmann-Enskog
transport equation which allows deriving the behaviour of the granular
temperature. Furthermore, in the elastic limit, the model can be solved exactly
to provide a full thermodynamic description. A meaningful theoretical
approximation explaining the properties of the inelastic system in interaction
with a thermal bath can be directly extrapolated from the properties of the
corresponding elastic system, upon a proper re-definition of the relevant
observables. Simulation results both in the cooling and driven regime can be
fairly interpreted according to our theoretical approach and compare rather
well to our predictions.Comment: 14 pages RevTex, 9 eps figure
Phase transitions in the q-voter model with two types of stochastic driving
In this paper we study nonlinear -voter model with stochastic driving on a
complete graph. We investigate two types of stochasticity that, using the
language of social sciences, can be interpreted as different kinds of
nonconformity. From a social point of view, it is very important to distinguish
between two types nonconformity, so called anti-conformity and independence. A
majority of works suggests that these social differences may be completely
irrelevant in terms of microscopic modeling that uses tools of statistical
physics and that both types of nonconformity play the role of so called 'social
temperature'. In this paper we clarify the concept of 'social temperature' and
show that different type of 'noise' may lead to qualitatively different
emergent properties. In particularly, we show that in the model with
anti-conformity the critical value of noise increases with parameter ,
whereas in the model with independence the critical value of noise decreases
with the . Moreover, in the model with anti-conformity the phase transition
is continuous for any value of , whereas in the model with independence the
transition is continuous for and discontinuous for
Phase separation in fluids exposed to spatially periodic external fields
We consider the liquid-vapor type phase transition for fluids confined within
spatially periodic external fields. For a fluid in d=3 dimensions, the periodic
field induces an additional phase, characterized by large density modulations
along the field direction. At the triple point, all three phases (modulated,
vapor, and liquid) coexist. At temperatures slightly above the triple point and
for low (high) values of the chemical potential, two-phase coexistence between
the modulated phase and the vapor (liquid) is observed. We study this
phenomenon using computer simulations and mean-field theory for the Ising
model. The theory shows that, in order for the modulated phase to arise, the
field wavelength must exceed a threshold value. We also find an extremely low
tension of the interface between the modulated phase and the vapor/liquid
phases. The tension is of the order 10^{-4} kB T per squared lattice spacing,
where kB is the Boltzmann constant, and T the temperature. In order to detect
such low tensions, a new simulation method is proposed. We also consider the
case of d=2 dimensions. The modulated phase then does not survive, leading to a
radically different phase diagram.Comment: 11 pages, 14 figure
Phase Transitions in Hexane Monolayers Physisorbed onto Graphite
We report the results of molecular dynamics (MD) simulations of a complete
monolayer of hexane physisorbed onto the basal plane of graphite. At low
temperatures the system forms a herringbone solid. With increasing temperature,
a solid to nematic liquid crystal transition takes place at K
followed by another transition at K into an isotropic fluid.
We characterize the different phases by calculating various order parameters,
coordinate distributions, energetics, spreading pressure and correlation
functions, most of which are in reasonable agreement with available
experimental evidence. In addition, we perform simulations where the
Lennard-Jones interaction strength, corrugation potential strength and dihedral
rigidity are varied in order to better characterize the nature of the two
transitions through. We find that both phase transitions are facilitated by a
``footprint reduction'' of the molecules via tilting, and to a lesser degree
via creation of gauche defects in the molecules.Comment: 18 pages, eps figures embedded, submitted to Phys. Rev.
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