Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session D7: Rare Events in Physics and Population Dynamics |
Hide Abstracts |
Sponsoring Units: GSNP Chair: Beate Schmittmann, Virginia Polytechnic Institute and State University Room: 407 |
Monday, March 16, 2009 2:30PM - 3:06PM |
D7.00001: Transitions in the Kramers escape rate in classical and quantum field theories Invited Speaker: Daniel Stein Small random fluctuations, either of thermal or quantum origin, are the cause of many important and interesting physical phenomena. These include chemical reactions, nucleation in phase transitions (i.e., the formation of a droplet of one phase within another phase), and the formation of unusual spatially localized states in various condensed matter systems. In all of these, random fluctuations (or ``noise''), no matter how small, eventually drives a physical system from one stable state to another. We discuss how in some classical systems thermally activated hopping over a barrier undergoes a transition as an external parameter such as system size or external field is varied. Its features are similar to those arising when classical activation over a barrier crosses over to quantum tunneling through that barrier as temperature is lowered. This crossover has some (but not all of the) features of a second-order phase transition. We also discuss two timely applications from mesoscopic physics: thermally induced breakup of monovalent metallic nanowires, and stochastic reversal of magnetization in thin ferromagnetic annuli. Each are of interest both from the point of view of fundamental physics and for potential technological applications. [Preview Abstract] |
Monday, March 16, 2009 3:06PM - 3:42PM |
D7.00002: Stochastic predator-prey models: spatial variability enhances species fitness Invited Speaker: Uwe C. Tauber It is now well understood that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. Simulations of spatial stochastic predator-prey systems yield striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. Here, we address the influence of spatially varying reaction rates on a stochastic two-species Lotka-Volterra lattice model. The effects of this quenched randomness on population densities, transient oscillations, spatial correlations, and invasion fronts are investigated through Monte Carlo simulations. We find that spatial variability in the predation rate results in more localized activity patches. Population fluctuations in rare favorable regions in turn cause a remarkable increase in the asymptotic population densities of both predators and prey, and also lead to accelerated front propagation. [Preview Abstract] |
Monday, March 16, 2009 3:42PM - 4:18PM |
D7.00003: Fluctuations in epidemic modeling - disease extinction and control Invited Speaker: Ira Schwartz The analysis of infectious disease fluctuations has recently seen an increasing rise in the use of new tools and models from stochastic dynamics and statistical physics. Examples arise in modeling fluctuations of multi-strain diseases, in modeling adaptive social behavior and its impact on disease fluctuations, and in the analysis of disease extinction in finite population models. Proper stochastic model reduction [1] allows one to predict unobserved fluctuations from observed data in multi-strain models [2]. Degree alteration and power law behavior is predicted in adaptive network epidemic models [3,4]. And extinction rates derived from large fluctuation theory exhibit scaling with respect to distance to the bifurcation point of disease onset with an unusual exponent [5]. In addition to outbreak prediction, another main goal of epidemic modeling is one of eliminating the disease to extinction through various control mechanisms, such as vaccine implementation or quarantine. In this talk, a description will be presented of the fluctuational behavior of several epidemic models and their extinction rates. A general framework and analysis of the effect of non-Gaussian control actuations which enhance the rate to disease extinction will be described. In particular, in it is shown that even in the presence of a small Poisson distributed vaccination program, there is an exponentially enhanced rate to disease extinction. These ideas may lead to improved methods of controlling disease where random vaccinations are prevalent. \\[4pt] Recent papers:\\[0pt] [1] E. Forgoston and I. B. Schwartz, ``Escape Rates in a Stochastic Environment with Multiple Scales,'' arXiv:0809.1345 2008.\\[0pt] [2] L. B. Shaw, L. Billings, I. B. Schwartz, ``Using dimension reduction to improve outbreak predictability of multi-strain diseases,'' J. Math. Bio. {\bf 55}, 1 2007.\\[0pt] [3] L. B. Shaw and I. B. Schwartz, ``Fluctuating epidemics on adaptive networks,'' Physical Review E {\bf 77}, 066101 2008.\\[0pt] [4] L. B. Shaw and I. B. Schwartz, ``Noise induced dynamics in adaptivenetworks with applications to epidemiology,'' arXiv:0807.3455 2008.\\[0pt] [5] M. I. Dykman, I. B. Schwartz, A. S. Landsman, ``Disease Extinction in the Presence of Random Vaccination,'' Phys. Rev. Letts. {\bf 101}, 078101 2008. [Preview Abstract] |
Monday, March 16, 2009 4:18PM - 4:54PM |
D7.00004: Forecasting fluctuating outbreaks in seasonally driven epidemics Invited Speaker: Lewi Stone Seasonality is a driving force that has major impact on the spatio-temporal dynamics of natural systems and their populations. This is especially true for the transmission of common infectious diseases such as influenza, measles, chickenpox, and pertussis. Here we gain new insights into the nonlinear dynamics of recurrent diseases through the analysis of the classical seasonally forced SIR epidemic model. Despite many efforts over the last decades, it has been difficult to gain general analytical insights because of the complex synchronization effects that can evolve between the external forcing and the model's natural oscillations. The analysis advanced here attempts to make progress in this direction by focusing on the dynamics of ``skips'' where we identify and predict years in which the epidemic is absent rather than outbreak years. Skipping events are intrinsic to the forced SIR model when parameterised in the chaotic regime. In fact, it is difficult if not impossible to locate realistic chaotic parameter regimes in which outbreaks occur regularly each year. This contrasts with the well known Rossler oscillator whose outbreaks recur regularly but whose amplitude vary chaotically in time (Uniform Phase Chaotic Amplitude oscillations). The goal of the present study is to develop a ``language of skips'' that makes it possible to predict under what conditions the next outbreak is likely to occur, and how many ``skips'' might be expected after any given outbreak. We identify a new threshold effect and give clear analytical conditions that allow accurate predictions. Moreover, the time of occurrence (i.e., phase) of an outbreak proves to be a useful new parameter that carries important epidemiological information. In forced systems, seasonal changes can prevent late-initiating outbreaks (i.e., having high phase) from running to completion. These principles yield forecasting tools that should have relevance for the study of newly emerging and reemerging diseases. [Preview Abstract] |
Monday, March 16, 2009 4:54PM - 5:30PM |
D7.00005: Noise-activated switching and signal amplification in nonlinear resonators, from nanomechanical beams to superconducting striplines Invited Speaker: Eyal Buks A driven nonlinear system operating close to bifurcation, namely, close to transition between different stability zones, is extremely sensitive to external perturbations. This behavior can be exploited for amplifying small signals, and also for noise reduction (squeezing). We experimentally demonstrate these effects using two classes of systems, namely, nanomechanical resonators in the form of doubly clamped beams, and electromagnetic resonators made of superconducting striplines. While a bifurcation between monostable and bistable zones is employed for the first class of resonators, a bifurcation between monostable and astable zones is employed for the second one. In both cases we observe extremely high gain and very strong noise squeezing as we approach bifurcation. While the Duffing-like nonlinearity of the mechanical beams is well understood, the piecewise-linear behavior exhibited by the superconducting stripline resonators is yet not fully accountable. We provide theoretical evidence to support our hypothesis that the underlying mechanism responsible for the observed piecewise-linear behavior is thermal instability in a narrow stripline section (a microbridge), which is integrated into the resonator. A simple theoretical model predicts a rich variety of dynamical effects, including self-sustained oscillations, stochastic resonance, and intermittency between different steadystate and limit-cycle solutions. These effects are experimentally observed by tuning the system close to the zone of astability, where no steadystate response exists. A comparison with theory yields partial agreement. Moreover, in more recent experiments we study a new configuration in which the microbridge is replaced by a superconducting interference device (SQUID) in the form of a loop containing two microbridges. Our preliminary experimental results show that self-sustained oscillations occur also in this configuration. Moreover, the frequency and lineshape of these oscillations exhibit periodicity as a function of externally applied magnetic flux. Further work is needed to theoretically account for the observed behavior. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2019 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700