6,225 research outputs found
Normal edge-colorings of cubic graphs
A normal -edge-coloring of a cubic graph is an edge-coloring with
colors having the additional property that when looking at the set of colors
assigned to any edge and the four edges adjacent it, we have either exactly
five distinct colors or exactly three distinct colors. We denote by
the smallest , for which admits a normal
-edge-coloring. Normal -edge-colorings were introduced by Jaeger in order
to study his well-known Petersen Coloring Conjecture. More precisely, it is
known that proving for every bridgeless cubic graph is
equivalent to proving Petersen Coloring Conjecture and then, among others,
Cycle Double Cover Conjecture and Berge-Fulkerson Conjecture. Considering the
larger class of all simple cubic graphs (not necessarily bridgeless), some
interesting questions naturally arise. For instance, there exist simple cubic
graphs, not bridgeless, with . On the other hand, the known
best general upper bound for was . Here, we improve it by
proving that for any simple cubic graph , which is best
possible. We obtain this result by proving the existence of specific no-where
zero -flows in -edge-connected graphs.Comment: 17 pages, 6 figure
Clustering and Non-Gaussian Behavior in Granular Matter
We investigate the properties of a model of granular matter consisting of
Brownian particles on a line subject to inelastic mutual collisions. This model
displays a genuine thermodynamic limit for the mean values of the energy and
the energy dissipation. When the typical relaxation time associated with
the Brownian process is small compared with the mean collision time
the spatial density is nearly homogeneous and the velocity probability
distribution is gaussian. In the opposite limit one has
strong spatial clustering, with a fractal distribution of particles, and the
velocity probability distribution strongly deviates from the gaussian one.Comment: 4 pages including 3 eps figures, LaTex, added references, corrected
typos, minimally changed contents and abstract, to published in
Phys.Rev.Lett. (tentatively on 28th of October, 1998
Droplet and cluster formation in freely falling granular streams
Particle beams are important tools for probing atomic and molecular
interactions. Here we demonstrate that particle beams also offer a unique
opportunity to investigate interactions in macroscopic systems, such as
granular media. Motivated by recent experiments on streams of grains that
exhibit liquid-like breakup into droplets, we use molecular dynamics
simulations to investigate the evolution of a dense stream of macroscopic
spheres accelerating out of an opening at the bottom of a reservoir. We show
how nanoscale details associated with energy dissipation during collisions
modify the stream's macroscopic behavior. We find that inelastic collisions
collimate the stream, while the presence of short-range attractive interactions
drives structure formation. Parameterizing the collision dynamics by the
coefficient of restitution (i.e., the ratio of relative velocities before and
after impact) and the strength of the cohesive interaction, we map out a
spectrum of behaviors that ranges from gas-like jets in which all grains drift
apart to liquid-like streams that break into large droplets containing hundreds
of grains. We also find a new, intermediate regime in which small aggregates
form by capture from the gas phase, similar to what can be observed in
molecular beams. Our results show that nearly all aspects of stream behavior
are closely related to the velocity gradient associated with vertical free
fall. Led by this observation, we propose a simple energy balance model to
explain the droplet formation process. The qualitative as well as many
quantitative features of the simulations and the model compare well with
available experimental data and provide a first quantitative measure of the
role of attractions in freely cooling granular streams
Large phenotype jumps in biomolecular evolution
By defining the phenotype of a biopolymer by its active three-dimensional
shape, and its genotype by its primary sequence, we propose a model that
predicts and characterizes the statistical distribution of a population of
biopolymers with a specific phenotype, that originated from a given genotypic
sequence by a single mutational event. Depending on the ratio g0 that
characterizes the spread of potential energies of the mutated population with
respect to temperature, three different statistical regimes have been
identified. We suggest that biopolymers found in nature are in a critical
regime with g0 in the range 1-6, corresponding to a broad, but not too broad,
phenotypic distribution resembling a truncated Levy flight. Thus the biopolymer
phenotype can be considerably modified in just a few mutations. The proposed
model is in good agreement with the experimental distribution of activities
determined for a population of single mutants of a group I ribozyme.Comment: to appear in Phys. Rev. E; 7 pages, 6 figures; longer discussion in
VII, new fig.
Demonstration of the Complementarity of One- and Two-Photon Interference
The visibilities of second-order (single-photon) and fourth-order
(two-photon) interference have been observed in a Young's double-slit
experiment using light generated by spontaneous parametric down-conversion and
a photon-counting intensified CCD camera. Coherence and entanglement underlie
one-and two-photon interference, respectively. As the effective source size is
increased, coherence is diminished while entanglement is enhanced, so that the
visibility of single-photon interference decreases while that of two-photon
interference increases. This is the first experimental demonstration of the
complementarity between single- and two-photon interference (coherence and
entanglement) in the spatial domain.Comment: 21 pages, 7 figure
Avalanche statistics of sand heaps
Large scale computer simulations are presented to investigate the avalanche
statistics of sand piles using molecular dynamics. We could show that different
methods of measurement lead to contradicting conclusions, presumably due to
avalanches not reaching the end of the experimental table.Comment: 6 pages, 4 figure
Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime
We model the dynamics of avalanches in granular assemblies in partly filled
rotating cylinders using a mean-field approach. We show that, upon varying the
cylinder angular velocity , the system undergoes a hysteresis cycle
between an intermittent and a continuous flow regimes. In the intermittent flow
regime, and approaching the transition, the avalanche duration exhibits
critical slowing down with a temporal power-law divergence. Upon adding a white
noise term, and close to the transition, the distribution of avalanche
durations is also a power-law. The hysteresis, as well as the statistics of
avalanche durations, are in good qualitative agreement with recent experiments
in partly filled rotating cylinders.Comment: 4 pages, RevTeX 3.0, postscript figures 1, 3 and 4 appended
Temperature scaling in a dense vibro-fluidised granular material
The leading order "temperature" of a dense two dimensional granular material
fluidised by external vibrations is determined. An asymptotic solution is
obtained where the particles are considered to be elastic in the leading
approximation. The velocity distribution is a Maxwell-Boltzmann distribution in
the leading approximation. The density profile is determined by solving the
momentum balance equation in the vertical direction, where the relation between
the pressure and density is provided by the virial equation of state. The
predictions of the present analysis show good agreement with simulation results
at higher densities where theories for a dilute vibrated granular material,
with the pressure-density relation provided by the ideal gas law, are in error.
The theory also predicts the scaling relations of the total dissipation in the
bed reported by McNamara and Luding (PRE v 58, p 813).Comment: ReVTeX (psfrag), 5 pages, 5 figures, Submitted to PR
Breakdown of self-organized criticality
We introduce two sandpile models which show the same behavior of real
sandpiles, that is, an almost self-organized critical behavior for small
systems and the dominance of large avalanches as the system size increases. The
systems become fully self-organized critical, with the critical exponents of
the Bak, Tang and Wiesenfeld model, as the system parameters are changed,
showing that these systems can make a bridge between the well known theoretical
and numerical results and what is observed in real experiments. We find that a
simple mechanism determines the boundary where self-organized can or cannot
exist, which is the presence of local chaos.Comment: 3 pages, 4 figure
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