Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa effect

We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped non-linear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that the upper equilibrium point of the pendulum can become stable even when the noise is white, and the "Kapitsa pendulum" effect is not at work. The stabilization occurs in a strong-noise regime where WKB approximation does not hold.Comment: 4 pages, 7 figure

Velocity fluctuations of noisy reaction fronts propagating into a metastable state: testing theory in stochastic simulations

The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed analytic expression for the front diffusion coefficient in the weak noise limit. Here we test this theory in stochastic simulations involving reacting and diffusing particles on a one-dimensional lattice. We also investigate a small noise-induced systematic shift of the front velocity compared to the prediction from the spatially continuous deterministic reaction-diffusion equation.Comment: 5 pages, 5 figure

Velocity fluctuations of population fronts propagating into metastable states

The position of propagating population fronts fluctuates because of the discreteness of the individuals and stochastic character of processes of birth, death and migration. Here we consider a Markov model of a population front propagating into a metastable state, and focus on the weak noise limit. For typical, small fluctuations the front motion is diffusive, and we calculate the front diffusion coefficient. We also determine the probability distribution of rare, large fluctuations of the front position and, for a given average front velocity, find the most likely population density profile of the front. Implications of the theory for population extinction risk are briefly considered.Comment: 8 pages, 3 figure

Extinction rates of established spatial populations

This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a "refuge" as a Markov process which involves births and deaths on discrete lattice sites and random migrations between neighboring sites. In extinction scenario I the zero population size is a repelling fixed point of the on-site deterministic dynamics. In extinction scenario II the zero population size is an attracting fixed point, corresponding to what is known in ecology as Allee effect. Assuming a large population size, we develop WKB (Wentzel-Kramers-Brillouin) approximation to the master equation. The resulting Hamilton's equations encode the most probable path of the population toward extinction and the mean time to extinction. In the fast-migration limit these equations coincide, up to a canonical transformation, with those obtained, in a different way, by Elgart and Kamenev (2004). We classify possible regimes of population extinction with and without an Allee effect and for different types of refuge and solve several examples analytically and numerically. For a very strong Allee effect the extinction problem can be mapped into the over-damped limit of theory of homogeneous nucleation due to Langer (1969). In this regime, and for very long systems, we predict an optimal refuge size that maximizes the mean time to extinction.Comment: 26 pages including 3 appendices, 16 figure

On population extinction risk in the aftermath of a catastrophic event

We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an example, we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction probability caused by the catastrophe. This quantity is given by the eikonal action computed over "the optimal path" (instanton) of an effective classical Hamiltonian system with a time-dependent Hamiltonian. For a general catastrophe the eikonal equations can be solved numerically. For simple models of catastrophic events analytic solutions can be obtained. One such solution becomes quite simple close to the bifurcation point of the Verhulst model. The eikonal results for the increase in the extinction probability caused by a catastrophe agree well with numerical solutions of the master equation.Comment: 11 pages, 11 figure

A photometricity and extinction monitor at the Apache Point Observatory

An unsupervised software ``robot'' that automatically and robustly reduces and analyzes CCD observations of photometric standard stars is described. The robot measures extinction coefficients and other photometric parameters in real time and, more carefully, on the next day. It also reduces and analyzes data from an all-sky $10 \mu m$ camera to detect clouds; photometric data taken during cloudy periods are automatically rejected. The robot reports its findings back to observers and data analysts via the World-Wide Web. It can be used to assess photometricity, and to build data on site conditions. The robot's automated and uniform site monitoring represents a minimum standard for any observing site with queue scheduling, a public data archive, or likely participation in any future National Virtual Observatory.Comment: accepted for publication in A

Negative velocity fluctuations of pulled reaction fronts

The position of a reaction front, propagating into an unstable state, fluctuates because of the shot noise. What is the probability that the fluctuating front moves considerably slower than its deterministic counterpart? Can the noise arrest the front motion for some time, or even make it move in the wrong direction? We present a WKB theory that assumes many particles in the front region and answers these questions for the microscopic model A->2A, 2A->A and random walk.Comment: 5 pages, 2 figures, revised versio

Hydrodynamic singularities and clustering in a freely cooling inelastic gas

We employ hydrodynamic equations to follow the clustering instability of a freely cooling dilute gas of inelastically colliding spheres into a well-developed nonlinear regime. We simplify the problem by dealing with a one-dimensional coarse-grained flow. We observe that at a late stage of the instability the shear stress becomes negligibly small, and the gas flows solely by inertia. As a result the flow formally develops a finite time singularity, as the velocity gradient and the gas density diverge at some location. We argue that flow by inertia represents a generic intermediate asymptotic of unstable free cooling of dilute inelastic gases.Comment: 4 pages, 4 figure

A nonlinear theory of non-stationary low Mach number channel flows of freely cooling nearly elastic granular gases

We use hydrodynamics to investigate non-stationary channel flows of freely cooling dilute granular gases. We focus on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type in Lagrangian coordinates. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation is exactly soluble, and the solution develops a finite-time density blowup. The heat diffusion, however, becomes important near the attempted singularity. It arrests the density blowup and brings about novel inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. Both the density profile of an ICS, and the characteristic relaxation time towards it are determined by a single dimensionless parameter that describes the relative role of the inelastic energy loss and heat diffusion. At large values of this parameter, the intermediate cooling dynamics proceeds as a competition between low-density regions of the gas. This competition resembles Ostwald ripening: only one hole survives at the end.Comment: 20 pages, 15 figures, final versio

Foraging ecology of black bears in urban environments: guidance for human-bear conflict mitigation

Includes bibliographical references (pages 10-13).Urban environments offer wildlife novel anthropogenic resources that vary spatiotemporally at fine scales. Property damage, economic losses, human injury, or other human-wildlife conflicts can occur when wildlife use these resources; however, few studies have examined urban wildlife resource selection at fine scales to guide conflict mitigation. We studied black bears (Ursus americanus) in the urban area of Aspen, Colorado, USA from 2007 to 2010 to quantify bear foraging on natural and anthropogenic resources and to model factors associated with anthropogenic feeding events. We collected fine-scale spatiotemporal data by tracking GPS-collared bears at 30-min intervals and backtracked to bear locations within 24 hours of use. We used discrete choice models to assess bears' resource selection, modeling anthropogenic feeding (use) and five associated random (availability) locations as a function of attributes related to temporally changing natural (e.g., ripe mast) and human (e.g., garbage) food resources, urban characteristics (e.g., housing density), and land cover characteristics (e.g., distance to riparian area). We backtracked to 2,675 locations used by 24 bears and classified 20% as foraging locations. We found that bears foraged on both natural and anthropogenic food sources in the urban environment, with 77% of feeding events being anthropogenic. We documented inter- and intra-annual foraging patterns in which bears foraged extensively in urban areas when natural food production was poor, then switched to natural food sources when available. These patterns suggest that bears balance energy budgets and individual safety when making foraging decisions. Overwhelmingly, garbage was the main anthropogenic food source that bears used. Selection of foraging sites was not only influenced by presence of garbage but also by proximity to riparian habitat and presence of ripe anthropogenic fruit trees. We found that while 76% of the garbage containers at random locations were bear-resistant, 57% of these bear-resistant containers were not properly secured. We recommend conflict mitigation focus on reducing available garbage and anthropogenic fruit trees, particularly near riparian areas, to make urban environments less energetically beneficial for foraging. Additionally, deploying bear-resistant containers is inadequate without education and proactive enforcement to change human behavior to properly secure garbage and ultimately reduce human-bear conflict.Published with support from the Colorado State University Libraries Open Access Research and Scholarship Fund