4,679 research outputs found
Hawking-like emission in kink-soliton escape from a potential well.
The escape of solitons over a potential barrier is analysed within the framework of a nonlinear Klein–Gordon equation. It is shown that the creation of a kink–antikink pair near the barrier through an internal mode instability can be followed by escape of the kink in a process analogous to Hawking radiation. These results have important implications in a wider context, including stochastic resonance and ratchet systems, which are also discussed
Competition between noise and coupling in the induction of synchronisation.
We apply a Fokker-Planck analysis to investigate the relative influences of coupling strength and noise on the synchronisation of two phase oscillators. We go beyond earlier studies of noise-induced synchronisation (without couplings) and coupling-induced synchronisation (without common noise) to consider both effects together, and we obtain a result that is very different from a straightforward superposition of the effects of each agent acting alone: two regimes are possible depending on which agent is inducing the synchronisation. In each regime, one agent induces and the other hinders the synchronisation. In particular we show that, counterintuitively, coupling can sometimes inhibit synchronisation
Probit models for capture-recapture data subject to imperfect detection, individual heterogeneity and misidentification
As noninvasive sampling techniques for animal populations have become more
popular, there has been increasing interest in the development of
capture-recapture models that can accommodate both imperfect detection and
misidentification of individuals (e.g., due to genotyping error). However,
current methods do not allow for individual variation in parameters, such as
detection or survival probability. Here we develop misidentification models for
capture-recapture data that can simultaneously account for temporal variation,
behavioral effects and individual heterogeneity in parameters. To facilitate
Bayesian inference using our approach, we extend standard probit regression
techniques to latent multinomial models where the dimension and zeros of the
response cannot be observed. We also present a novel Metropolis-Hastings within
Gibbs algorithm for fitting these models using Markov chain Monte Carlo. Using
closed population abundance models for illustration, we re-visit a DNA
capture-recapture population study of black bears in Michigan, USA and find
evidence of misidentification due to genotyping error, as well as temporal,
behavioral and individual variation in detection probability. We also estimate
a salamander population of known size from laboratory experiments evaluating
the effectiveness of a marking technique commonly used for amphibians and fish.
Our model was able to reliably estimate the size of this population and
provided evidence of individual heterogeneity in misidentification probability
that is attributable to variable mark quality. Our approach is more
computationally demanding than previously proposed methods, but it provides the
flexibility necessary for a much broader suite of models to be explored while
properly accounting for uncertainty introduced by misidentification and
imperfect detection. In the absence of misidentification, our probit
formulation also provides a convenient and efficient Gibbs sampler for Bayesian
analysis of traditional closed population capture-recapture data.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS783 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Enlargement of a low-dimensional stochastic web
We consider an archetypal example of a low-dimensional stochastic web, arising in a 1D oscillator driven by a plane wave of a frequency equal or close to a multiple of the oscillator’s natural frequency. We show that the web can be greatly enlarged by the introduction of a slow, very weak, modulation of the wave angle. Generalizations are discussed. An application to electron transport in a nanometre-scale semiconductor superlattice in electric and magnetic fields is suggested
Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths
We consider the Kuramoto model of an ensemble of interacting oscillators
allowing for an arbitrary distribution of frequencies and coupling strengths.
We define a family of traveling wave states as stationary in a rotating frame,
and derive general equations for their parameters. We suggest empirical
stability conditions which, for the case of incoherence, become exact. In
addition to making new theoretical predictions, we show that many earlier
results follow naturally from our general framework. The results are applicable
in scientific contexts ranging from physics to biology.Comment: 5 pages, 1 figur
Energy-optimal steering of transitions through a fractal basin boundary.
We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary. The complicated structure of the paths inside the fractal boundary is determined by a hierarchy of homoclinic original sad- dles. By exploiting an analogy between the control problem and the concept of an optimal fluctuational path, we identify the optimal deterministic control function as being equivalent to the optimal fluctu- ational force obtained from a numerical analysis of the fluctuational transitions between two states
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