291 research outputs found
The geometry of percolation fronts in two-dimensional lattices with spatially varying densities
Percolation theory is usually applied to lattices with a uniform probability
p that a site is occupied or that a bond is closed. The more general case,
where p is a function of the position x, has received less attention. Previous
studies with long-range spatial variations in p(x) have only investigated cases
where p has a finite, non-zero gradient at the critical point p_c. Here we
extend the theory to two-dimensional cases in which the gradient can change
from zero to infinity. We present scaling laws for the width and length of the
hull (i.e. the boundary of the spanning cluster). We show that the scaling
exponents for the width and the length depend on the shape of p(x), but they
always have a constant ratio 4/3 so that the hull's fractal dimension D=7/4 is
invariant. On this basis, we derive and verify numerically an asymptotic
expression for the probability h(x) that a site at a given distance x from p_c
is on the hull.Comment: 13 pages, 7 figures, to appear in New Journal of Physic
Sheridan Hall: Newspaper, Sheridan - renovation to be done before February 1991
Article from The University Leader with details on the renovation of the old coliseum into a performing arts center and administrative offices.https://scholars.fhsu.edu/sheridan/1022/thumbnail.jp
Consensus time in a voter model with concealed and publicly expressed opinions
The voter model is a simple agent-based model to mimic opinion dynamics in
social networks: a randomly chosen agent adopts the opinion of a randomly
chosen neighbour. This process is repeated until a consensus emerges. Although
the basic voter model is theoretically intriguing, it misses an important
feature of real opinion dynamics: it does not distinguish between an agent's
publicly expressed opinion and her inner conviction. A person may not feel
comfortable declaring her conviction if her social circle appears to hold an
opposing view. Here we introduce the Concealed Voter Model where we add a
second, concealed layer of opinions to the public layer. If an agent's public
and concealed opinions disagree, she can reconcile them by either publicly
disclosing her previously secret point of view or by accepting her public
opinion as inner conviction. We study a complete graph of agents who can choose
from two opinions. We define a martingale that determines the probability
of all agents eventually agreeing on a particular opinion. By analyzing the
evolution of in the limit of a large number of agents, we derive the
leading-order terms for the mean and standard deviation of the consensus time
(i.e. the time needed until all opinions are identical). We thereby give a
precise prediction by how much concealed opinions slow down a consensus.Comment: 21 pages, 6 figures, to appear in J. Stat. Mech. Theory Ex
Sheridan Renovation to be Done Before Fberuary 1991 , Offices, Center, to Move into Sheridan
Several pages of the University Leader from June, 1990 detailing the process of moving into the new Sheridan Hall.https://scholars.fhsu.edu/buildings/2352/thumbnail.jp
Transition from connected to fragmented vegetation across an environmental gradient: scaling laws in ecotone geometry
A change in the environmental conditions across space—for example, altitude or latitude—can cause significant changes in the density of a vegetation type and, consequently, in spatial connectivity. We use spatially explicit simulations to study the transition from connected to fragmented vegetation. A static (gradient percolation) model is compared to dynamic (gradient contact process) models. Connectivity is characterized from the perspective of various species that use this vegetation type for habitat and differ in dispersal or migration range, that is, “step length” across the landscape. The boundary of connected vegetation delineated by a particular step length is termed the “ hull edge.” We found that for every step length and for every gradient, the hull edge is a fractal with dimension 7/4. The result is the same for different spatial models, suggesting that there are universal laws in ecotone geometry. To demonstrate that the model is applicable to real data, a hull edge of fractal dimension 7/4 is shown on a satellite image of a piñon‐juniper woodland on a hillside. We propose to use the hull edge to define the boundary of a vegetation type unambiguously. This offers a new tool for detecting a shift of the boundary due to a climate change
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Stream and vegetative habitat restoration in a spring-fed stream to augment endangered species habitat
Percolation theory suggests some general features in range margins across environmental gradients
The margins within the geographic range of species are often specific in
terms of ecological and evolutionary processes, and can strongly influence the
species' reaction to climate change. One of the frequently observed features at
range margins is fragmentation, caused internally by population dynamics or
externally by the limited availability of suitable habitat sites. We study both
causes, and describe the transition from a connected to a fragmented state
across space by means of a gradient metapopulation model. The main features of
our approach are the following. 1) Inhomogeneities can occur at two spatial
scales: there is a broad-scale gradient, which can be patterned by fine-scale
heterogeneities. The latter is implemented by dispersing a variable number of
small obstacles over the terrain, which can be penetrable or unpenetrable by
the spreading species. 2) We study the occupancy of this terrain in a
steady-state on two temporal scales: in snapshots and by long-term averages.
The simulations reveal some general scaling laws that are applicable in various
environments, independently of the mechanism of fragmentation. The edge of the
connected region (the hull) is a fractal with dimension 7/4. Its width and
length changes with the gradient according to universal scaling laws, that are
characteristic for percolation transitions. The results suggest that
percolation theory is a powerful tool for understanding the structure of range
margins in a broad variety of real-life scenarios, including those in which the
environmental gradient is combined with fine-scale heterogeneity. This provides
a new method for comparing the range margins of different species in various
geographic regions, and monitoring range shifts under climate change.Comment: 17 pages, 5 figure
Intermediate landscape disturbance maximizes metapopulation density
The viability of metapopulations in fragmented landscapes has become a central theme in conservation biology. Landscape fragmentation is increasingly recognized as a dynamical process: in many situations, the quality of local habitats must be expected to undergo continual changes. Here we assess the implications of such recurrent local disturbances for the equilibrium density of metapopulations. Using a spatially explicit lattice model in which the considered metapopulation as well as the underlying landscape pattern change dynamically, we show that equilibrium metapopulation density is maximized at intermediate frequencies of local landscape disturbance. On both sides around this maximum, the metapopulation may go extinct. We show how the position and shape of the intermediate viability maximum is responding to changes in the landscape’s overall habitat quality and the population’s propensity for local extinction. We interpret our findings in terms of a dual effect of intensified landscape disturbances, which on the one hand exterminate local populations and on the other hand enhance a metapopulation’s capacity for spreading between habitat clusters
Introduction to the problem of rocket-powered aircraft performance
An introduction to the problem of determining the fundamental limitations on the performance possibilities of rocket-powered aircraft is presented. Previous material on the subject is reviewed and given in condensed form along with supplementary analyses. Some of the problems discussed are: 1) limiting velocity of a rocket projectile; 2) limiting velocity of a rocket jet; 3) jet efficiency; 4) nozzle characteristics; 5) maximum attainable altitudes; 6) ranges. Formulas are presented relating the performance of a rocket-powered aircraft to basic weight and nozzle dimensional parameters. The use of these formulas is illustrated by their application to the special case of a nonlifting rocket projectile
Theoretical characteristics of two-dimensional supersonic control surfaces
The "Busemann second-order-approximation theory" for the pressure distribution over a two-dimensional airfoil in supersonic flow was used to determine some of the aerodynamic characteristics of uncambered symmetrical parabolic and double-wedge airfoils with leading-edge and trailing-edge flaps. The characteristics presented and discussed in this paper are: flap effectiveness factor, rate of change of hinge-moment coefficient with flap deflection, rate of change of the pitching-moment coefficient with flap deflection, rate of change of the pitching-moment coefficient about the mid chord with flap deflection, and the location of the center of pressure of the airfoil-flap combination
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