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https://www.readbyqxmd.com/read/28306551/master-equations-and-the-theory-of-stochastic-path-integrals
#1
Markus F Weber, Erwin Frey
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations...
April 2017: Reports on Progress in Physics
https://www.readbyqxmd.com/read/28297849/continuous-time-limits-of-the-utterance-selection-model
#2
Jérôme Michaud
In this paper we derive alternative continuous time limits of the utterance selection model (USM) for language change [G. J. Baxter et al., Phys. Rev. E 73, 046118 (2006)PLEEE81539-375510.1103/PhysRevE.73.046118]. This is motivated by the fact that the Fokker-Planck continuous time limit derived in the original version of the USM is only valid for a small range of parameters. We investigate the consequences of relaxing these constraints on parameters. Using the normal approximation of the multinomial approximation, we derive a continuous time limit of the USM in the form of a weak-noise stochastic differential equation...
February 2017: Physical Review. E
https://www.readbyqxmd.com/read/28243720/extracting-cellular-automaton-rules-from-physical-langevin-equation-models-for-single-and-collective-cell-migration
#3
J M Nava-Sedeño, H Hatzikirou, F Peruani, A Deutsch
Cellular automata (CA) are discrete time, space, and state models which are extensively used for modeling biological phenomena. CA are "on-lattice" models with low computational demands. In particular, lattice-gas cellular automata (LGCA) have been introduced as models of single and collective cell migration. The interaction rule dictates the behavior of a cellular automaton model and is critical to the model's biological relevance. The LGCA model's interaction rule has been typically chosen phenomenologically...
February 27, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28208407/stochastically-gated-local-and-occupation-times-of-a-brownian-particle
#4
Paul C Bressloff
We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected...
January 2017: Physical Review. E
https://www.readbyqxmd.com/read/28208350/l%C3%A3-vy-flights-in-the-presence-of-a-point-sink-of-finite-strength
#5
Deepika Janakiraman
In this paper, the absorption of a particle undergoing Lévy flight in the presence of a point sink of arbitrary strength and position is studied. The motion of such a particle is given by a modified Fokker-Planck equation whose exact solution in the Laplace domain can be described in terms of the Laplace transform of the unperturbed (absence of the sink) Green's function. This solution for the Green's function is a well-studied, generic result which applies to both fractional and usual Fokker-Planck equations alike...
January 2017: Physical Review. E
https://www.readbyqxmd.com/read/28157360/redefining-the-axion-window
#6
Luca Di Luzio, Federico Mescia, Enrico Nardi
A major goal of axion searches is to reach inside the parameter space region of realistic axion models. Currently, the boundaries of this region depend on somewhat arbitrary criteria, and it would be desirable to specify them in terms of precise phenomenological requirements. We consider hadronic axion models and classify the representations R_{Q} of the new heavy quarks Q. By requiring that (i) the Q's are sufficiently short lived to avoid issues with long-lived strongly interacting relics, (ii) no Landau poles are induced below the Planck scale; 15 cases are selected which define a phenomenologically preferred axion window bounded by a maximum (minimum) value of the axion-photon coupling about 2 times (4 times) larger than is commonly assumed...
January 20, 2017: Physical Review Letters
https://www.readbyqxmd.com/read/28157343/critical-number-of-fields-in-stochastic-inflation
#7
Vincent Vennin, Hooshyar Assadullahi, Hassan Firouzjahi, Mahdiyar Noorbala, David Wands
Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary e-folds, which give rise to all correlation functions of primordial curvature perturbations through the stochastic δN formalism. The number of fields is a critical parameter. The probability of exploring arbitrarily large-field regions of the potential becomes nonvanishing when more than two fields are driving inflation...
January 20, 2017: Physical Review Letters
https://www.readbyqxmd.com/read/28089383/-long-term-psychiatric-hospitalizations
#8
L Plancke, A Amariei
BACKGROUND: Long-term hospitalizations in psychiatry raise the question of desocialisation of the patients and the inherent costs. METHODS: Individual indicators were extracted from a medical administrative database containing full-time psychiatric hospitalizations for the period 2011-2013 of people over 16 years old living in the French region of Nord-Pas-de-Calais. We calculated the proportion of people who had experienced a hospitalization with a duration of 292 days or more during the study period...
February 2017: Revue D'épidémiologie et de Santé Publique
https://www.readbyqxmd.com/read/27993627/an-open-loop-approach-to-calculate-noise-induced-transitions
#9
Farzaneh Maleki, Attila Becskei
Bistability permits the co-existence of two distinct cell fates in a population of genetically identical cells. Noise induced transitions between two fates of a bistable system are difficult to calculate due to the intricate interplay between nonlinear dynamics and noise in bistable positive feedback loops. Here we opened multivariable feedback loops at the slowest variable to obtain the open-loop function and the fluctuations in the open-loop output. By the subsequent reclosing of the loop, we calculated the mean first passage time (MFPT) using the Fokker-Planck equation in good agreement with the exact stochastic simulation...
December 18, 2016: Journal of Theoretical Biology
https://www.readbyqxmd.com/read/27967083/time-dependent-probability-density-function-in-cubic-stochastic-processes
#10
Eun-Jin Kim, Rainer Hollerbach
We report time-dependent probability density functions (PDFs) for a nonlinear stochastic process with a cubic force using analytical and computational studies. Analytically, a transition probability is formulated by using a path integral and is computed by the saddle-point solution (instanton method) and a new nonlinear transformation of time. The predicted PDF p(x,t) in general involves a time integral, and useful PDFs with explicit dependence on x and t are presented in certain limits (e.g., in the short and long time limits)...
November 2016: Physical Review. E
https://www.readbyqxmd.com/read/27967014/statistics-of-the-stochastically-forced-lorenz-attractor-by-the-fokker-planck-equation-and-cumulant-expansions
#11
Altan Allawala, J B Marston
We investigate the Fokker-Planck description of the equal-time statistics of the three-dimensional Lorenz attractor with additive white noise. The invariant measure is found by computing the zero (or null) mode of the linear Fokker-Planck operator as a problem of sparse linear algebra. Two variants are studied: a self-adjoint construction of the linear operator and the replacement of diffusion with hyperdiffusion. We also access the low-order statistics of the system by a perturbative expansion in equal-time cumulants...
November 2016: Physical Review. E
https://www.readbyqxmd.com/read/27820827/effect-of-ionic-diffusion-on-extracellular-potentials-in-neural-tissue
#12
Geir Halnes, Tuomo Mäki-Marttunen, Daniel Keller, Klas H Pettersen, Ole A Andreassen, Gaute T Einevoll
Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems...
November 2016: PLoS Computational Biology
https://www.readbyqxmd.com/read/27782504/cdpd-a-new-dissipative-particle-dynamics-method-for-modeling-electrokinetic-phenomena-at-the-mesoscale
#13
Mingge Deng, Zhen Li, Oleg Borodin, George Em Karniadakis
We develop a "charged" dissipative particle dynamics (cDPD) model for simulating mesoscopic electrokinetic phenomena governed by the stochastic Poisson-Nernst-Planck and the Navier-Stokes equations. Specifically, the transport equations of ionic species are incorporated into the DPD framework by introducing extra degrees of freedom and corresponding evolution equations associated with each DPD particle. Diffusion of ionic species driven by the ionic concentration gradient, electrostatic potential gradient, and thermal fluctuations is captured accurately via pairwise fluxes between DPD particles...
October 14, 2016: Journal of Chemical Physics
https://www.readbyqxmd.com/read/27739815/entropy-production-by-active-particles-coupling-of-odd-and-even-functions-of-velocity
#14
Debasish Chaudhuri
Nonequilibrium stochastic dynamics of several active Brownian systems are modeled in terms of nonlinear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for total entropy production in such systems using the Fokker-Planck equation. The result is consistent with the expression for stochastic entropy production in the reservoir that we obtain from probabilities of time-forward and time-reversed trajectories, leading to fluctuation theorems...
September 2016: Physical Review. E
https://www.readbyqxmd.com/read/27739760/diffusion-in-an-expanding-medium-fokker-planck-equation-green-s-function-and-first-passage-properties
#15
S B Yuste, E Abad, C Escudero
We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in an expanding medium. To this end, we take a conveniently generalized Chapman-Kolmogorov equation as the starting point. We obtain an analytical expression for the Green's function (propagator) and investigate both analytically and numerically how this function and the associated moments behave. We also study first-passage properties in expanding hyperspherical geometries. We show that in all cases the behavior is determined to a great extent by the so-called Brownian conformal time τ(t), which we define via the relation τ[over ̇]=1/a^{2}, where a(t) is the expansion scale factor...
September 2016: Physical Review. E
https://www.readbyqxmd.com/read/27727295/forward-period-analysis-method-of-the-periodic-hamiltonian-system
#16
Pengfei Wang
Using the forward period analysis (FPA), we obtain the period of a Morse oscillator and mathematical pendulum system, with the accuracy of 100 significant digits. From these results, the long-term [0, 1060] (time unit) solutions, ranging from the Planck time to the age of the universe, are computed reliably and quickly with a parallel multiple-precision Taylor series (PMT) scheme. The application of FPA to periodic systems can greatly reduce the computation time of long-term reliable simulations. This scheme provides an efficient way to generate reference solutions, against which long-term simulations using other schemes can be tested...
2016: PloS One
https://www.readbyqxmd.com/read/27715088/how-isotropic-is-the-universe
#17
Daniela Saadeh, Stephen M Feeney, Andrew Pontzen, Hiranya V Peiris, Jason D McEwen
A fundamental assumption in the standard model of cosmology is that the Universe is isotropic on large scales. Breaking this assumption leads to a set of solutions to Einstein's field equations, known as Bianchi cosmologies, only a subset of which have ever been tested against data. For the first time, we consider all degrees of freedom in these solutions to conduct a general test of isotropy using cosmic microwave background temperature and polarization data from Planck. For the vector mode (associated with vorticity), we obtain a limit on the anisotropic expansion of (σ_{V}/H)_{0}<4...
September 23, 2016: Physical Review Letters
https://www.readbyqxmd.com/read/27661676/first-measurements-of-high-frequency-cross-spectra-from-a-pair-of-large-michelson-interferometers
#18
Aaron S Chou, Richard Gustafson, Craig Hogan, Brittany Kamai, Ohkyung Kwon, Robert Lanza, Lee McCuller, Stephan S Meyer, Jonathan Richardson, Chris Stoughton, Raymond Tomlin, Samuel Waldman, Rainer Weiss
Measurements are reported of the cross-correlation of spectra of differential position signals from the Fermilab Holometer, a pair of colocated 39 m long, high power Michelson interferometers with flat broadband frequency response in the MHz range. The instrument obtains sensitivity to high frequency correlated signals far exceeding any previous measurement in a broad frequency band extending beyond the 3.8 MHz inverse light-crossing time of the apparatus. The dominant but uncorrelated shot noise is averaged down over 2×10^{8} independent spectral measurements with 381 Hz frequency resolution to obtain 2...
September 9, 2016: Physical Review Letters
https://www.readbyqxmd.com/read/27643695/high-frequency-nanocapacitor-arrays-concept-recent-developments-and-outlook
#19
Serge G Lemay, Cecilia Laborde, Christophe Renault, Andrea Cossettini, Luca Selmi, Frans P Widdershoven
We have developed a measurement platform for performing high-frequency AC detection at nanoelectrodes. The system consists of 65 536 electrodes (diameter 180 nm) arranged in a sub-micrometer rectangular array. The electrodes are actuated at frequencies up to 50 MHz, and the resulting AC current response at each separately addressable electrode is measured in real time. These capabilities are made possible by fabricating the electrodes on a complementary metal-oxide-semiconductor (CMOS) chip together with the associated control and readout electronics, thus minimizing parasitic capacitance and maximizing the signal-to-noise ratio...
October 18, 2016: Accounts of Chemical Research
https://www.readbyqxmd.com/read/27627294/stochastic-bifurcations-in-a-prototypical-thermoacoustic-system
#20
E A Gopalakrishnan, J Tony, E Sreelekha, R I Sujith
We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise...
August 2016: Physical Review. E
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