1,026 research outputs found
Dispersion processes
We study a synchronous dispersion process in which particles are
initially placed at a distinguished origin vertex of a graph . At each time
step, at each vertex occupied by more than one particle at the beginning of
this step, each of these particles moves to a neighbour of chosen
independently and uniformly at random. The dispersion process ends once the
particles have all stopped moving, i.e. at the first step at which each vertex
is occupied by at most one particle.
For the complete graph and star graph , we show that for any
constant , with high probability, if , then the
process finishes in steps, whereas if , then
the process needs steps to complete (if ever). We also show
that an analogous lazy variant of the process exhibits the same behaviour but
for higher thresholds, allowing faster dispersion of more particles.
For paths, trees, grids, hypercubes and Cayley graphs of large enough sizes
(in terms of ) we give bounds on the time to finish and the maximum distance
traveled from the origin as a function of the number of particles
Pahranagat Shear System, Lincoln County, Nevada
The author has identified the following significant results. A structural model which relates strike-slip deformation to Basin Range extensional tectonics was formulated on the basis of analysis and interpreatation of ERTS-1 MSS imagery over southern Lincoln County, Nevada. Study of published geologic data and field reconnaissance of key areas has been conducted to support the ERTS-1 data interpretation. The structural model suggests that a left-lateral strike-slip fault zone, called the Pahranagat Shear System, formed as a transform fault separating two areas of east-west structural extension
On the Distribution of a Second Class Particle in the Asymmetric Simple Exclusion Process
We give an exact expression for the distribution of the position X(t) of a
single second class particle in the asymmetric simple exclusion process (ASEP)
where initially the second class particle is located at the origin and the
first class particles occupy the sites {1,2,...}
Rotation in prominences
We have studied rotation in non-eruptive limb prominences; in most cases dopplergrams could be used to confirm proper motion measurements. In some cases part of the prominence rotates; in the others, the entire body is in rotation. Velocities of 15–75 km s⁻¹ are found. Of fifty-one prominences studied in 1978, five showed rotation
A Fredholm Determinant Representation in ASEP
In previous work the authors found integral formulas for probabilities in the
asymmetric simple exclusion process (ASEP) on the integer lattice. The dynamics
are uniquely determined once the initial state is specified. In this note we
restrict our attention to the case of step initial condition with particles at
the positive integers, and consider the distribution function for the m'th
particle from the left. In the previous work an infinite series of multiple
integrals was derived for this distribution. In this note we show that the
series can be summed to give a single integral whose integrand involves a
Fredholm determinant. We use this determinant representation to derive
(non-rigorously, at this writing) a scaling limit.Comment: 12 Pages. Version 3 includes a scaling conjectur
Multi-shocks in asymmetric simple exclusions processes: Insights from fixed-point analysis of the boundary-layers
The boundary-induced phase transitions in an asymmetric simple exclusion
process with inter-particle repulsion and bulk non-conservation are analyzed
through the fixed points of the boundary layers. This system is known to have
phases in which particle density profiles have different kinds of shocks. We
show how this boundary-layer fixed-point method allows us to gain physical
insights on the nature of the phases and also to obtain several quantitative
results on the density profiles especially on the nature of the boundary-layers
and shocks.Comment: 12 pages, 8 figure
Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights
Many real networks are complex and have power-law vertex degree distribution,
short diameter, and high clustering. We analyze the network model based on
thresholding of the summed vertex weights, which belongs to the class of
networks proposed by Caldarelli et al. (2002). Power-law degree distributions,
particularly with the dynamically stable scaling exponent 2, realistic
clustering, and short path lengths are produced for many types of weight
distributions. Thresholding mechanisms can underlie a family of real complex
networks that is characterized by cooperativeness and the baseline scaling
exponent 2. It contrasts with the class of growth models with preferential
attachment, which is marked by competitiveness and baseline scaling exponent 3.Comment: 5 figure
Spatial Scaling in Model Plant Communities
We present an analytically tractable variant of the voter model that provides
a quantitatively accurate description of beta-diversity (two-point correlation
function) in two tropical forests. The model exhibits novel scaling behavior
that leads to links between ecological measures such as relative species
abundance and the species area relationship.Comment: 10 pages, 3 figure
Duality and phase diagram of one dimensional transport
The observation of duality by Mukherji and Mishra in one dimensional
transport problems has been used to develop a general approach to classify and
characterize the steady state phase diagrams. The phase diagrams are determined
by the zeros of a set of coarse-grained functions without the need of detailed
knowledge of microscopic dynamics. In the process, a new class of
nonequilibrium multicritical points has been identified.Comment: 6 pages, 2 figures (4 eps files
- …