Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session P4: Fluctuations and Rare Events in Physical, Chemical, and Biological Systems |
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Sponsoring Units: GSNP Chair: Mark Dykman, Michigan State University Room: Morial Convention Center 206 |
Wednesday, March 12, 2008 8:00AM - 8:36AM |
P4.00001: Rare events and phase transitions in reaction diffusion systems Invited Speaker: I shall discuss a way to evaluate tails of the probability distribution functions in stochastic reaction-diffusion models. The method is based on the semi-classical treatment of a proper ``quantum'' field theory, which may be associated with reaction-diffusion systems. The same set of ideas may be applied to a classification of non-equilibrium phase transitions, taking place in these models. \newline \newline V. Elgart and A. Kamenev, Classification of phase transitions in reaction--diffusion systems, Phys. Rev. E 74, 041101 (2006). \newline V. Elgart and A. Kamenev, Rare Events Statistics in Reaction--Diffusion Systems, Phys. Rev. E. 70, 041106 (2004). [Preview Abstract] |
Wednesday, March 12, 2008 8:36AM - 9:12AM |
P4.00002: Switching and phase transitions in a parametrically-excited cold atom trap. Invited Speaker: Stochastic dynamics of cold atoms in a modulated magneto-optical atom trap was investigated. The studies focused on the phenomena related to switching between the parametrically excited period-2 states. The rates of single-atom activated transitions were analyzed. When the atom density was increased, there were observed Ising-class phase transitions where the symmetric population of period-2 states was spontaneously broken [1,2]. Anomalous fluctuations in the decay of the unstable state were investigated [3]. \newline \newline [1] Kihwan Kim, Myoung-Sun Heo, Ki-Hwan Lee, Kiyoub Jang, Heung-Ryoul Noh, Doochul Kim, and Wonho Jhe, Phys. Rev. Lett. \textbf{97}, 036104 (2006). \newline [2] Kihwan Kim,. Heung-Ryoul Noh, and Wonho Jhe, Phys. Rev. A, \textbf{71}, 033413 (2005). \newline [3] ``Transient and fluctuation behavior of atomic population at unstable state in parametrically driven magneto-optical trap,'' Myoung-Sun Heo, Yonghee Kim, Heung-Ryoul Noh, Mark Dykman and Wonho Jhe, in preparation. [Preview Abstract] |
Wednesday, March 12, 2008 9:12AM - 9:48AM |
P4.00003: Activation barrier scaling and switching path distribution in a micromechanical parametric oscillator Invited Speaker: Parametrically modulated systems develop multiple coexisting states under sufficiently large drive. In the presence of fluctuations, the system can occasionally overcome the activation barrier and switch from one state to the other, resulting in the phase of oscillation slipping by $\pi$. We study noise-induced switching in a parametrically-driven micromechanical torsional oscillator. Certain properties of the switching are generic to bistable systems, while others are specific to nonequilibrium systems that lack detailed balance. For instance, close to the bifurcation points, the activation barrier for switching is expected to display system-independent scaling. By measuring the rate of random transitions at different fluctuation intensities, we deduce the activation barrier as a function of frequency detuning from the bifurcation points and measure a critical exponent that is in good agreement with theoretical predictions. We also measure the escape trajectories followed by the oscillator, confirming the notion that they form narrow tubes in phase space centered at the most probable escape path. The uphill section of this path is found to be distinct from its time-reversed downhill section, an important property for systems far from thermal equilibrium. Near the saddle point the velocity is significantly diminished and the motion becomes diffusive, leading to strong broadening and increase in height of the probability distribution. Apart from fundamental interest, the sharp change in the oscillation amplitude near the subcritical bifurcation point can provide accurate determination of device parameters. [Preview Abstract] |
Wednesday, March 12, 2008 9:48AM - 10:24AM |
P4.00004: Spectral theory of extreme statistics in birth-death systems Invited Speaker: Statistics of rare events, or large deviations, in chemical reactions and systems of birth-death type have attracted a great deal of interest in many areas of science including cell biochemistry, astrochemistry, epidemiology, population biology, \textit{etc.} Large deviations become of vital importance when discrete (non-continuum) nature of a population of ``particles'' (molecules, bacteria, cells, animals or even humans) and stochastic character of interactions can drive the population to extinction. I will briefly review the novel \textit{spectral method} [1-3] for calculating the extreme statistics of a broad class of birth-death processes and reactions involving a single species. The spectral method combines the probability generating function formalism with the Sturm-Liouville theory of linear differential operators. It involves a controlled perturbative treatment based on a natural large parameter of the problem: the average number of particles/individuals in a stationary or metastable state. For extinction (the first passage) problems the method yields accurate results for the extinction statistics and for the quasi-stationary probability distribution, including the tails, of metastable states. I will demonstrate the power of the method on the example of a branching and annihilation reaction, $A \to\hspace{-2.8mm}\hspace{2mm}2A\,,\,2A \to\hspace{-2.8mm}\hspace{2mm} \emptyset$, representative of a rather general class of processes. \begin{enumerate} \item{M. Assaf and B. Meerson, Phys. Rev. Lett. \textbf{97}, 200602 (2006).} \item{M. Assaf and B. Meerson, Phys. Rev. E \textbf{74}, 041115 (2006).} \item{M. Assaf and B. Meerson, Phys. Rev. E \textbf{75}, 031122 (2007).} \end{enumerate} [Preview Abstract] |
Wednesday, March 12, 2008 10:24AM - 11:00AM |
P4.00005: Strong Fluctuations and Cycling in Biological Systems Invited Speaker: In this talk I describe a mechanism for generating cycles in a large class of ``mesoscale'' biological populations (meaning populations composed of thousands to tens of thousands of units). Cycles are caused by a resonant amplification of the system dynamics triggered by internal noise. I will discuss this mechanism in the context of two classes of simple systems: ecological (e.g. predator-prey, host-pathogen) and biochemical (e.g. small gene regulation networks, modules of metabolic processes). [Predator-Prey Cycles from Resonant Amplification of Demographic Stochasticity, A. J. McKane and T. J. Newman, Physical Review Letters 94, 218102 (2005); Amplified Biochemical Oscillations in Cellular Systems, A. J. McKane, J. Nagy, T. J. Newman, and M. Stefanini, Journal of Statistical Physics 128, 165:191 (2007).] [Preview Abstract] |
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