Excitonic transport in static-disordered one dimensional systems is studied in the presence of thermal fluctuations that are described by the Haken-Strobl-Reineker model. For short times, non-diffusive behavior is observed that can be characterized as the free-particle dynamics on the lengthscale bounded by the Anderson localized system. Over longer time scales, the environment-induced dephasing is sufficient to overcome the Anderson localization caused by the disorder and allow for transport to occur which is always seen to be diffusive. In the limiting regimes of weak and strong dephasing quantum master equations are developed, and their respective scaling relations imply the existence of a maximum in the diffusion constant as a function of the dephasing rate that is confirmed numerically. In the weak dephasing regime, it is demonstrated that the diffusion constant is proportional to the square of the localization length which leads to a significant enhancement of the transport rate
Population extinction is of central interest for population dynamics. It may occur from a large rare fluctuation. We find that, in contrast to related large-fluctuation effects like noise-induced interstate switching, quite generally extinction rates in multipopulation systems display fragility, where the height of the effective barrier to be overcome in the fluctuation depends on the system parameters nonanalytically. We show that one of the best-known models of epidemiology, the susceptible-infectious-susceptible model, is fragile to total population fluctuations.
We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007)], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008)], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012)]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.
Many populations in nature are fragmented: they consist of local populations occupying separate patches. A local population is prone to extinction due to the shot noise of birth and death processes. A migrating population from another patch can dramatically delay the extinction. What is the optimal migration rate that minimizes the extinction risk of the whole population? Here we answer this question for a connected network of model habitat patches with different carrying capacities.PACS numbers: 87.23. Cc, 02.50.Ga, 05.10.Gg Many populations in nature are fragmented. Such meta-populations consist of local populations occupying separate habitat patches [1][2][3]. Habitat fragmentation is implicated in the decline and extinction of many endangered species [4]. To mitigate the negative impact of habitat fragmentation, conservation biologists have called for the construction of corridors to facilitate migration between separate habitat patches [5]. Predicting how migration affects population persistence is important for species conservation, especially when the local population size is depressed, and the local populations become prone to extinction because of randomness of the birth and death processes. In this situation, it is of crucial importance to determine the optimal migration rate that maximizes the mean time to extinction (MTE) of the meta-population. This problem has attracted much of attention from ecologists, and has been addressed, for different meta-populations, in experiments and stochastic simulations [6][7][8][9][10][11]. Here we approach this important problem theoretically, for a simple logistic model of stochastic local populations coupled by migration. We analyze rare large fluctuations causing population extinction and show that there is an optimal migration rate that maximizes the MTE of the meta-population. Meta-population model. Mathematical biologists have proposed different types of stochastic metapopulation models. In a widely used class of models the local population distribution, its dynamics within a patch, and its effect on migration are ignored [12][13][14]. We show here that it is a proper account of these features that leads to the qualitatively new effect of the existence of an optimal migration rate.Consider N local populations of particles A located on a connected network of patches i = 1, 2, ..., N . The particles undergo branching A → 2A with rate constant 1 on each patch and annihilation 2A → ∅ with rate constant 1/(κ i K) on patch i. The parameters κ i = O(1), i = 1, 2, . . . , N , describe the disparity among the local carrying capacities κ i K. Each particle can also migrate between connected patches i and j with rate constant µ ij = µ ji . We assume that µ ij = µM ij , where elements of M ij are of order unity.For K ≫ 1 each local population is expected to be long-lived. Still, the shot noise will ultimately drive the whole meta-population to extinction. The MTE of the meta-population, T , is exponentially large in K but finite [11,15]. How does T depend on the charac...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.