1,378 research outputs found
Influence of surfactants on the structure of titanium oxide gels : experiments and simulations
We report here on experimental and numerical studies of the influence of
surfactants on mineral gel synthesis. The modification of the gel structure
when the ratios water-precursor and water-surfactant vary is brought to the
fore by fractal dimension measures. A property of {\em polydispersity of the
initial hydrolysis} is proposed to explain these results, and is successfuly
tested through numerical experiments of three dimensional chemically limited
aggregation.Comment: 12 pages, 4 Postscript figures, uses RevTe
Discontinuous percolation transitions in real physical systems
We study discontinuous percolation transitions (PT) in the diffusion-limited
cluster aggregation model of the sol-gel transition as an example of real
physical systems, in which the number of aggregation events is regarded as the
number of bonds occupied in the system. When particles are Brownian, in which
cluster velocity depends on cluster size as with
, a larger cluster has less probability to collide with other
clusters because of its smaller mobility. Thus, the cluster is effectively more
suppressed in growth of its size. Then the giant cluster size increases
drastically by merging those suppressed clusters near the percolation
threshold, exhibiting a discontinuous PT. We also study the tricritical
behavior by controlling the parameter , and the tricritical point is
determined by introducing an asymmetric Smoluchowski equation.Comment: 5 pages, 5 figure
A new conjecture extends the GM law for percolation thresholds to dynamical situations
The universal law for percolation thresholds proposed by Galam and Mauger
(GM) is found to apply also to dynamical situations. This law depends solely on
two variables, the space dimension d and a coordinance numberq. For regular
lattices, q reduces to the usual coordination number while for anisotropic
lattices it is an effective coordination number. For dynamical percolation we
conjecture that the law is still valid if we use the number q_2 of second
nearest neighbors instead of q. This conjecture is checked for the dynamic
epidemic model which considers the percolation phenomenon in a mobile
disordered system. The agreement is good.Comment: 8 pages, latex, 3 figures include
Kinetic Antiferromagnetism in the Triangular Lattice
We show that the motion of a single hole in the infinite Hubbard model
with frustrated hopping leads to weak metallic antiferromagnetism of kinetic
origin. An intimate relationship is demonstrated between the simplest versions
of this problem in 1 and 2 dimensions, and two of the most subtle many body
problems, namely the Heisenberg Bethe ring in 1-d and the 2-dimensional
triangular lattice Heisenberg antiferromagnet.Comment: 10 pages, 2 figures, 5 supplementary figures; Figures fixe
Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction
Experiments on the motion of a particle on an inclined rough plane have
yielded some surprising results. For example, it was found that the frictional
force acting on the ball is viscous, {\it i.e.} proportional to the velocity
rather than the expected square of the velocity. It was also found that, for a
given inclination of the plane, the velocity of the ball scales as a power of
its radius. We present here a one dimensional stochastic model based on the
microscopic equations of motion of the ball, which exhibits the same behaviour
as the experiments. This model yields a mechanism for the origins of the
viscous friction force and the scaling of the velocity with the radius. It also
reproduces other aspects of the phase diagram of the motion which we will
discuss.Comment: 19 pages, latex, 11 postscript figures in separate uuencoded fil
Small Angle Scattering by Fractal Aggregates: A Numerical Investigation of the Crossover Between the Fractal Regime and the Porod Regime
Fractal aggregates are built on a computer using off-lattice cluster-cluster
aggregation models. The aggregates are made of spherical particles of different
sizes distributed according to a Gaussian-like distribution characterised by a
mean and a standard deviation . The wave vector dependent
scattered intensity is computed in order to study the influence of the
particle polydispersity on the crossover between the fractal regime and the
Porod regime. It is shown that, given , the location of the
crossover decreases as increases. The dependence of on
can be understood from the evolution of the shape of the center-to-center
interparticle-distance distribution function.Comment: RevTex, 4 pages + 6 postscript figures, compressed using "uufiles",
published in Phys. Rev. B 50, 1305 (1994
Kondo spin liquid and magnetically long-range ordered states in the Kondo necklace model
A simplified version of the symmetric Kondo lattice model, the Kondo necklace
model, is studied by using a representation of impurity and conduction electron
spins in terms of local Kondo singlet and triplet operators. Within a mean
field theory, a spin gap always appears in the spin triplet excitation spectrum
in 1D, leading to a Kondo spin liquid state for any finite values of coupling
strength (with as hopping and as exchange); in 2D and 3D cubic
lattices the spin gaps are found to vanish continuously around and , respectively, where quantum phase transitions
occur and the Kondo spin liquid state changes into an antiferromagnetically
long-range ordered state. These results are in agreement with variational Monte
Carlo, higher-order series expansion, and recent quantum Monte Carlo
calculations for the symmetric Kondo lattice modelComment: Revtex, four pages, three figures; to be published in Physical Review
B1, 1 July (2000
- …