Nanoscale mapping of heterogeneity of the polarization reversal in lead-free relaxor–ferroelectric ceramic composites

DOE PAGES

Gobeljic, D.; Shvartsman, V. V.; Belianinov, A.; ...

2016-01-05

Relaxor/ferroelectric ceramic/ceramic composites have shown to be promising in generating large electromechanical strain at moderate electric fields. However, the mechanisms of polarization and strain coupling between grains of different nature in the composites remain unclear. To rationalize the coupling mechanisms we performed advanced piezoresponse force microscopy (PFM) studies of 0.92BNT-0.06BT-0.02KNN/0.93BNT-0.07BT (ergodic/non-ergodic relaxor) composites. PFM is able to distinguish grains of different phases by characteristic domain patterns. Polarization switching has been probed locally, on a sub-grain scale. k-Means clustering analysis applied to arrays of local hysteresis loops reveals variations of polarization switching characteristics between the ergodic and non-ergodic relaxor grains. Here,more » we report a different set of switching parameters for grains in the composites as opposed to the pure phase samples. These results confirm ceramic/ceramic composites to be a viable approach to tailor the piezoelectric properties and optimize the macroscopic electromechanical characteristics.« less

A simple condition for uniqueness of the absolutely continuous ergodic measure and its application to economic models

NASA Astrophysics Data System (ADS)

Sato, Kenji; Yano, Makoto

2012-09-01

Unique existence of the absolutely continuous ergodic measure, or existence of ergodic chaos (in a strong sense), has been considered important in economics since it explains the mechanism underlying economic fluctuations. In the present study, a simple sufficient condition for ergodic chaos is proved and applied to economic models.

Weak ergodicity of population evolution processes.

PubMed

Inaba, H

1989-10-01

The weak ergodic theorems of mathematical demography state that the age distribution of a closed population is asymptotically independent of the initial distribution. In this paper, we provide a new proof of the weak ergodic theorem of the multistate population model with continuous time. The main tool to attain this purpose is a theory of multiplicative processes, which was mainly developed by Garrett Birkhoff, who showed that ergodic properties generally hold for an appropriate class of multiplicative processes. First, we construct a general theory of multiplicative processes on a Banach lattice. Next, we formulate a dynamical model of a multistate population and show that its evolution operator forms a multiplicative process on the state space of the population. Subsequently, we investigate a sufficient condition that guarantees the weak ergodicity of the multiplicative process. Finally, we prove the weak and strong ergodic theorems for the multistate population and resolve the consistency problem.

Ergodicity of the generalized lemon billiards

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jingyu; Mohr, Luke; Zhang, Hong-Kun, E-mail: hongkun@math.umass.edu

2013-12-15

In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.

Ergodicity and model quality in template-restrained canonical and temperature/Hamiltonian replica exchange coarse-grained molecular dynamics simulations of proteins.

PubMed

Karczyńska, Agnieszka S; Czaplewski, Cezary; Krupa, Paweł; Mozolewska, Magdalena A; Joo, Keehyoung; Lee, Jooyoung; Liwo, Adam

2017-12-05

Molecular simulations restrained to single or multiple templates are commonly used in protein-structure modeling. However, the restraints introduce additional barriers, thus impairing the ergodicity of simulations, which can affect the quality of the resulting models. In this work, the effect of restraint types and simulation schemes on ergodicity and model quality was investigated by performing template-restrained canonical molecular dynamics (MD), multiplexed replica-exchange molecular dynamics, and Hamiltonian replica exchange molecular dynamics (HREMD) simulations with the coarse-grained UNRES force field on nine selected proteins, with pseudo-harmonic log-Gaussian (unbounded) or Lorentzian (bounded) restraint functions. The best ergodicity was exhibited by HREMD. It has been found that non-ergodicity does not affect model quality if good templates are used to generate restraints. However, when poor-quality restraints not covering the entire protein are used, the improved ergodicity of HREMD can lead to significantly improved protein models. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Detection of ɛ-ergodicity breaking in experimental data—A study of the dynamical functional sensibility

NASA Astrophysics Data System (ADS)

Loch-Olszewska, Hanna; Szwabiński, Janusz

2018-05-01

The ergodicity breaking phenomenon has already been in the area of interest of many scientists, who tried to uncover its biological and chemical origins. Unfortunately, testing ergodicity in real-life data can be challenging, as sample paths are often too short for approximating their asymptotic behaviour. In this paper, the authors analyze the minimal lengths of empirical trajectories needed for claiming the ɛ-ergodicity based on two commonly used variants of an autoregressive fractionally integrated moving average model. The dependence of the dynamical functional on the parameters of the process is studied. The problem of choosing proper ɛ for ɛ-ergodicity testing is discussed with respect to especially the variation of the innovation process and the data sample length, with a presentation on two real-life examples.

Detection of ε-ergodicity breaking in experimental data-A study of the dynamical functional sensibility.

PubMed

Loch-Olszewska, Hanna; Szwabiński, Janusz

2018-05-28

The ergodicity breaking phenomenon has already been in the area of interest of many scientists, who tried to uncover its biological and chemical origins. Unfortunately, testing ergodicity in real-life data can be challenging, as sample paths are often too short for approximating their asymptotic behaviour. In this paper, the authors analyze the minimal lengths of empirical trajectories needed for claiming the ε-ergodicity based on two commonly used variants of an autoregressive fractionally integrated moving average model. The dependence of the dynamical functional on the parameters of the process is studied. The problem of choosing proper ε for ε-ergodicity testing is discussed with respect to especially the variation of the innovation process and the data sample length, with a presentation on two real-life examples.

Diversity Performance Analysis on Multiple HAP Networks.

PubMed

Dong, Feihong; Li, Min; Gong, Xiangwu; Li, Hongjun; Gao, Fengyue

2015-06-30

One of the main design challenges in wireless sensor networks (WSNs) is achieving a high-data-rate transmission for individual sensor devices. The high altitude platform (HAP) is an important communication relay platform for WSNs and next-generation wireless networks. Multiple-input multiple-output (MIMO) techniques provide the diversity and multiplexing gain, which can improve the network performance effectively. In this paper, a virtual MIMO (V-MIMO) model is proposed by networking multiple HAPs with the concept of multiple assets in view (MAV). In a shadowed Rician fading channel, the diversity performance is investigated. The probability density function (PDF) and cumulative distribution function (CDF) of the received signal-to-noise ratio (SNR) are derived. In addition, the average symbol error rate (ASER) with BPSK and QPSK is given for the V-MIMO model. The system capacity is studied for both perfect channel state information (CSI) and unknown CSI individually. The ergodic capacity with various SNR and Rician factors for different network configurations is also analyzed. The simulation results validate the effectiveness of the performance analysis. It is shown that the performance of the HAPs network in WSNs can be significantly improved by utilizing the MAV to achieve overlapping coverage, with the help of the V-MIMO techniques.

Efficiency bounds for nonequilibrium heat engines

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehta, Pankaj; Polkovnikov, Anatoli, E-mail: asp@bu.edu

2013-05-15

We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodicmore » engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples. -- Highlights: ► Derived efficiency bounds for heat engines working with a single reservoir. ► Analyzed both ergodic and non-ergodic engines. ► Showed that non-ergodic engines can be more efficient. ► Extended fundamental thermodynamic relation to arbitrary nonequilibrium processes.« less

Ergodicity in natural earthquake fault networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tiampo, K. F.; Rundle, J. B.; Holliday, J.

2007-06-15

Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C. D. Ferguson, W. Klein, and J. B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibriumlike systems with statistically stationary dynamics over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K. F.more » Tiampo, J. B. Rundle, W. Klein, J. S. Sa Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. We analyze the seismicity of three naturally occurring earthquake fault networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity and that, while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Ergodicity in this application not only requires that the system be stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages in studying their spatiotemporal evolution.« less

On the analogues of Szegő's theorem for ergodic operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirsch, W; Pastur, L A

2015-01-31

Szegő's theorem on the asymptotic behaviour of the determinants of large Toeplitz matrices is generalized to the class of ergodic operators. The generalization is formulated in terms of a triple consisting of an ergodic operator and two functions, the symbol and the test function. It is shown that in the case of the one-dimensional discrete Schrödinger operator with random ergodic or quasiperiodic potential and various choices of the symbol and the test function this generalization leads to asymptotic formulae which have no analogues in the situation of Toeplitz operators. Bibliography: 22 titles.

Ergodic Transition in a Simple Model of the Continuous Double Auction

PubMed Central

Radivojević, Tijana; Anselmi, Jonatha; Scalas, Enrico

2014-01-01

We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen. PMID:24558377

Ergodic transition in a simple model of the continuous double auction.

PubMed

Radivojević, Tijana; Anselmi, Jonatha; Scalas, Enrico

2014-01-01

We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen.

A statistical evaluation of non-ergodic variogram estimators

USGS Publications Warehouse

Curriero, F.C.; Hohn, M.E.; Liebhold, A.M.; Lele, S.R.

2002-01-01

Geostatistics is a set of statistical techniques that is increasingly used to characterize spatial dependence in spatially referenced ecological data. A common feature of geostatistics is predicting values at unsampled locations from nearby samples using the kriging algorithm. Modeling spatial dependence in sampled data is necessary before kriging and is usually accomplished with the variogram and its traditional estimator. Other types of estimators, known as non-ergodic estimators, have been used in ecological applications. Non-ergodic estimators were originally suggested as a method of choice when sampled data are preferentially located and exhibit a skewed frequency distribution. Preferentially located samples can occur, for example, when areas with high values are sampled more intensely than other areas. In earlier studies the visual appearance of variograms from traditional and non-ergodic estimators were compared. Here we evaluate the estimators' relative performance in prediction. We also show algebraically that a non-ergodic version of the variogram is equivalent to the traditional variogram estimator. Simulations, designed to investigate the effects of data skewness and preferential sampling on variogram estimation and kriging, showed the traditional variogram estimator outperforms the non-ergodic estimators under these conditions. We also analyzed data on carabid beetle abundance, which exhibited large-scale spatial variability (trend) and a skewed frequency distribution. Detrending data followed by robust estimation of the residual variogram is demonstrated to be a successful alternative to the non-ergodic approach.

Estimating Ergodic Capacity of Cooperative Analog Relaying under Different Adaptive Source Transmission Techniques

DTIC Science & Technology

2011-08-01

component in an airborne platform. Authorized licensed use limited to: ROME AFB. Downloaded on August 05,2010 at 14:47:37 UTC from IEEE Xplore ...UTC from IEEE Xplore . Restrictions apply. 2 . (7) For instance, it is not difficult to show that the MGF of for Nakagami-m fading with i.n.d fading...August 05,2010 at 14:47:37 UTC from IEEE Xplore . Restrictions apply. 3 ditions. Once again, using integration by parts, (14) can be concisely expressed

Are there ergodic limits to evolution? Ergodic exploration of genome space and convergence.

PubMed

McLeish, Tom C B

2015-12-06

We examine the analogy between evolutionary dynamics and statistical mechanics to include the fundamental question of ergodicity-the representative exploration of the space of possible states (in the case of evolution this is genome space). Several properties of evolutionary dynamics are identified that allow a generalization of the ergodic dynamics, familiar in dynamical systems theory, to evolution. Two classes of evolved biological structure then arise, differentiated by the qualitative duration of their evolutionary time scales. The first class has an ergodicity time scale (the time required for representative genome exploration) longer than available evolutionary time, and has incompletely explored the genotypic and phenotypic space of its possibilities. This case generates no expectation of convergence to an optimal phenotype or possibility of its prediction. The second, more interesting, class exhibits an evolutionary form of ergodicity-essentially all of the structural space within the constraints of slower evolutionary variables have been sampled; the ergodicity time scale for the system evolution is less than the evolutionary time. In this case, some convergence towards similar optima may be expected for equivalent systems in different species where both possess ergodic evolutionary dynamics. When the fitness maximum is set by physical, rather than co-evolved, constraints, it is additionally possible to make predictions of some properties of the evolved structures and systems. We propose four structures that emerge from evolution within genotypes whose fitness is induced from their phenotypes. Together, these result in an exponential speeding up of evolution, when compared with complete exploration of genomic space. We illustrate a possible case of application and a prediction of convergence together with attaining a physical fitness optimum in the case of invertebrate compound eye resolution.

Quantifying non-ergodic dynamics of force-free granular gases.

PubMed

Bodrova, Anna; Chechkin, Aleksei V; Cherstvy, Andrey G; Metzler, Ralf

2015-09-14

Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient ε. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of ε on the impact velocity of particles.

Quantum Ergodicity and L p Norms of Restrictions of Eigenfunctions

NASA Astrophysics Data System (ADS)

Hezari, Hamid

2018-02-01

We prove an analogue of Sogge's local L p estimates for L p norms of restrictions of eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions one can get improvements of the results of Burq-Gérard-Tzvetkov, Hu, and Chen-Sogge. The improvements are logarithmic on negatively curved manifolds (without boundary) and by o(1) for manifolds (with or without boundary) with ergodic geodesic flows. In the case of ergodic billiards with piecewise smooth boundary, we get o(1) improvements on L^∞ estimates of Cauchy data away from a shrinking neighborhood of the corners, and as a result using the methods of Ghosh et al., Jung and Zelditch, Jung and Zelditch, we get that the number of nodal domains of 2-dimensional ergodic billiards tends to infinity as λ \\to ∞. These results work only for a full density subsequence of any given orthonormal basis of eigenfunctions. We also present an extension of the L p estimates of Burq-Gérard-Tzvetkov, Hu, Chen-Sogge for the restrictions of Dirichlet and Neumann eigenfunctions to compact submanifolds of the interior of manifolds with piecewise smooth boundary. This part does not assume ergodicity on the manifolds.

Granular Contact Forces: Proof of "Self-Ergodicity" by Generalizing Boltzmann's Stosszahlansatz and H Theorem

NASA Technical Reports Server (NTRS)

Metzger, Philip T.

2006-01-01

Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann's stosszahlansatz (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann's H functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is self-ergodic. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized H Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling.

Ergodicity, configurational entropy and free energy in pigment solutions and plant photosystems: influence of excited state lifetime.

PubMed

Jennings, Robert C; Zucchelli, Giuseppe

2014-01-01

We examine ergodicity and configurational entropy for a dilute pigment solution and for a suspension of plant photosystem particles in which both ground and excited state pigments are present. It is concluded that the pigment solution, due to the extreme brevity of the excited state lifetime, is non-ergodic and the configurational entropy approaches zero. Conversely, due to the rapid energy transfer among pigments, each photosystem is ergodic and the configurational entropy is positive. This decreases the free energy of the single photosystem pigment array by a small amount. On the other hand, the suspension of photosystems is non-ergodic and the configurational entropy approaches zero. The overall configurational entropy which, in principle, includes contributions from both the single excited photosystems and the suspension which contains excited photosystems, also approaches zero. Thus the configurational entropy upon photon absorption by either a pigment solution or a suspension of photosystem particles is approximately zero. Copyright © 2014 Elsevier B.V. All rights reserved.

Moments distributions of single dye molecule spectra in a low-temperature polymer: Analysis of system ergodicity

NASA Astrophysics Data System (ADS)

Anikushina, T. A.; Naumov, A. V.

2013-12-01

This article demonstrates the principal advantages of the technique for analysis of the long-term spectral evolution of single molecules (SM) in the study of the microscopic nature of the dynamic processes in low-temperature polymers. We performed the detailed analysis of the spectral trail of single tetra-tert-butylterrylene (TBT) molecule in an amorphous polyisobutylene matrix, measured over 5 hours at T = 7K. It has been shown that the slow temporal dynamics is in qualitative agreement with the standard model of two-level systems and stochastic sudden-jump model. At the same time the distributions of the first four moments (cumulants) of the spectra of the selected SM measured at different time points were found not consistent with the standard theory prediction. It was considered as evidence that in a given time interval the system is not ergodic

Analysis of multiuser mixed RF/FSO relay networks for performance improvements in Cloud Computing-Based Radio Access Networks (CC-RANs)

NASA Astrophysics Data System (ADS)

Alimi, Isiaka A.; Monteiro, Paulo P.; Teixeira, António L.

2017-11-01

The key paths toward the fifth generation (5G) network requirements are towards centralized processing and small-cell densification systems that are implemented on the cloud computing-based radio access networks (CC-RANs). The increasing recognitions of the CC-RANs can be attributed to their valuable features regarding system performance optimization and cost-effectiveness. Nevertheless, realization of the stringent requirements of the fronthaul that connects the network elements is highly demanding. In this paper, considering the small-cell network architectures, we present multiuser mixed radio-frequency/free-space optical (RF/FSO) relay networks as feasible technologies for the alleviation of the stringent requirements in the CC-RANs. In this study, we use the end-to-end (e2e) outage probability, average symbol error probability (ASEP), and ergodic channel capacity as the performance metrics in our analysis. Simulation results show the suitability of deployment of mixed RF/FSO schemes in the real-life scenarios.

Generalized continued fractions and ergodic theory

NASA Astrophysics Data System (ADS)

Pustyl'nikov, L. D.

2003-02-01

In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest.

Diversity Performance Analysis on Multiple HAP Networks

PubMed Central

Dong, Feihong; Li, Min; Gong, Xiangwu; Li, Hongjun; Gao, Fengyue

2015-01-01

One of the main design challenges in wireless sensor networks (WSNs) is achieving a high-data-rate transmission for individual sensor devices. The high altitude platform (HAP) is an important communication relay platform for WSNs and next-generation wireless networks. Multiple-input multiple-output (MIMO) techniques provide the diversity and multiplexing gain, which can improve the network performance effectively. In this paper, a virtual MIMO (V-MIMO) model is proposed by networking multiple HAPs with the concept of multiple assets in view (MAV). In a shadowed Rician fading channel, the diversity performance is investigated. The probability density function (PDF) and cumulative distribution function (CDF) of the received signal-to-noise ratio (SNR) are derived. In addition, the average symbol error rate (ASER) with BPSK and QPSK is given for the V-MIMO model. The system capacity is studied for both perfect channel state information (CSI) and unknown CSI individually. The ergodic capacity with various SNR and Rician factors for different network configurations is also analyzed. The simulation results validate the effectiveness of the performance analysis. It is shown that the performance of the HAPs network in WSNs can be significantly improved by utilizing the MAV to achieve overlapping coverage, with the help of the V-MIMO techniques. PMID:26134102

Are atmospheric surface layer flows ergodic?

NASA Astrophysics Data System (ADS)

Higgins, Chad W.; Katul, Gabriel G.; Froidevaux, Martin; Simeonov, Valentin; Parlange, Marc B.

2013-06-01

The transposition of atmospheric turbulence statistics from the time domain, as conventionally sampled in field experiments, is explained by the so-called ergodic hypothesis. In micrometeorology, this hypothesis assumes that the time average of a measured flow variable represents an ensemble of independent realizations from similar meteorological states and boundary conditions. That is, the averaging duration must be sufficiently long to include a large number of independent realizations of the sampled flow variable so as to represent the ensemble. While the validity of the ergodic hypothesis for turbulence has been confirmed in laboratory experiments, and numerical simulations for idealized conditions, evidence for its validity in the atmospheric surface layer (ASL), especially for nonideal conditions, continues to defy experimental efforts. There is some urgency to make progress on this problem given the proliferation of tall tower scalar concentration networks aimed at constraining climate models yet are impacted by nonideal conditions at the land surface. Recent advancements in water vapor concentration lidar measurements that simultaneously sample spatial and temporal series in the ASL are used to investigate the validity of the ergodic hypothesis for the first time. It is shown that ergodicity is valid in a strict sense above uniform surfaces away from abrupt surface transitions. Surprisingly, ergodicity may be used to infer the ensemble concentration statistics of a composite grass-lake system using only water vapor concentration measurements collected above the sharp transition delineating the lake from the grass surface.

Mixing, ergodicity and slow relaxation phenomena

NASA Astrophysics Data System (ADS)

Costa, I. V. L.; Vainstein, M. H.; Lapas, L. C.; Batista, A. A.; Oliveira, F. A.

2006-11-01

Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation-dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed.

A new approach to measuring tortuosity

NASA Astrophysics Data System (ADS)

Wert, Amanda; Scott, Sherry E.

2012-03-01

The detection and measurement of the tortuosity - i.e. the bending and winding - of vessels has been shown to be potentially useful in the assessment of cancer progression and treatment response. Although several metrics for tortuosity are used, no single one measure is able to capture all types of tortuosity. This report presents a new multiscale technique for measuring vessel tortuosity. The approach is based on a method - called the ergodicity defect - which gives a scale-dependent measure of deviation from ergodicity. Ergodicity is a concept that captures the manner in which trajectories or signals sample the space; thus, ergodicity and vessel tortuosity both involve the notion of how a signal samples space. Here we begin to explore this connection. We first apply the ergodicity defect tortuosity measure to both 2D and 3D synthetic data in order to demonstrate the response of the method to three types of tortuosity observed in clinical patterns. We then implement the technique on segmented vessels extracted from brain tumor MRA images. Results indicate that the method can be effectively used to detect and measure several types of vessel tortuosity.

An Estimation of the Logarithmic Timescale in Ergodic Dynamics

NASA Astrophysics Data System (ADS)

Gomez, Ignacio S.

An estimation of the logarithmic timescale in quantum systems having an ergodic dynamics in the semiclassical limit, is presented. The estimation is based on an extension of the Krieger’s finite generator theorem for discretized σ-algebras and using the time rescaling property of the Kolmogorov-Sinai entropy. The results are in agreement with those obtained in the literature but with a simpler mathematics and within the context of the ergodic theory. Moreover, some consequences of the Poincaré’s recurrence theorem are also explored.

Uncountably many maximizing measures for a dense subset of continuous functions

NASA Astrophysics Data System (ADS)

Shinoda, Mao

2018-05-01

Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given ‘performance’ function. For a continuous self-map of a compact metric space and a dense set of continuous functions, we show the existence of uncountably many ergodic maximizing measures. We also show that, for a topologically mixing subshift of finite type and a dense set of continuous functions there exist uncountably many ergodic maximizing measures with full support and positive entropy.

In Vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules

NASA Astrophysics Data System (ADS)

Jeon, Jae-Hyung; Tejedor, Vincent; Burov, Stas; Barkai, Eli; Selhuber-Unkel, Christine; Berg-Sørensen, Kirstine; Oddershede, Lene; Metzler, Ralf

2011-01-01

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

Ergodic theory and experimental visualization of chaos in 3D flows

NASA Astrophysics Data System (ADS)

Sotiropoulos, Fotis; Mezic, Igor

2000-11-01

In his motivation for the ergodic hypothesis Gibbs invoked an analogy with fluid mixing: “…Yet no fact is more familiar to us than that stirring tends to bring a liquid to a state of uniform mixture, or uniform densities of its components…”. Although proof of the ergodic hypothesis is possible only for the simplest of systems using methods from ergodic theory, the use of the hypothesis has led to many accurate predictions in statistical mechanics. The problem of fluid mixing, however, turned out to be considerably more complicated than Gibbs envisioned. Chaotic advection can indeed lead to efficient mixing even in non-turbulent flows, but many non-mixed islands are known to persist within well-mixed regions. In numerical studies, Poincaré maps can be used to reveal the structure of such islands but their visualization in the laboratory requires laborious experimental procedures and is possible only for certain types of flows. Here we propose the first non-intrusive, simple to implement, and generally applicable technique for constructing experimental Poincaré maps and apply it to a steady, 3D, vortex breakdown bubble. We employ standard laser-induced fluorescence (LIF) and construct Poincaré maps by time averaging a sufficiently long sequence of instantaneous LIF images. We also show that ergodic theory methods provide a rigorous theoretical justification for this approach whose main objective is to reveal the non-ergodic regions of the flow.

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levnajić, Zoran; Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, California 93106; Mezić, Igor

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone,more » and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.« less

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.

PubMed

Levnajić, Zoran; Mezić, Igor

2015-05-01

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.

Self-averaging and weak ergodicity breaking of diffusion in heterogeneous media

NASA Astrophysics Data System (ADS)

Russian, Anna; Dentz, Marco; Gouze, Philippe

2017-08-01

Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency Rn, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in q ≥2 dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.

Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

NASA Astrophysics Data System (ADS)

van Lith, Janneke

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic. This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.

Possible ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing

NASA Astrophysics Data System (ADS)

Mukherjee, Sudip; Rajak, Atanu; Chakrabarti, Bikas K.

2018-02-01

We explore the behavior of the order parameter distribution of the quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamiltonian at finite temperatures and that at zero temperature obtained using the exact diagonalization method. Our numerical results indicate the existence of a low- but finite-temperature quantum-fluctuation-dominated ergodic region along with the classical fluctuation-dominated high-temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has nonvanishing value everywhere in the thermodynamic limit, indicating nonergodicity. We also show that the average annealing time for convergence (to a low-energy level of the model, within a small error range) becomes system size independent for annealing down through the (quantum-fluctuation-dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite-size scaling-type behavior for the extent of the ergodic region is also addressed.

Quantum ergodicity in the SYK model

NASA Astrophysics Data System (ADS)

Altland, Alexander; Bagrets, Dmitry

2018-05-01

We present a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an ergodic long time regime (describable by random matrix theory). These modes, which play a role conceptually similar to the diffusion modes of dirty metals, carry quantum numbers which we identify as the generators of the Clifford algebra: each of the 2N different products that can be formed from N Majorana operators defines one effective mode. The competition between a decay rate quickly growing in the order of the product and a density of modes exponentially growing in the same parameter explains the characteristics of the system's approach to the ergodic long time regime. We probe this dynamics through various spectral correlation functions and obtain favorable agreement with existing numerical data.

Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Metzler, Ralf

2014-01-14

Single particle traces are standardly evaluated in terms of time averages of the second moment of the position time series r(t). For ergodic processes, one can interpret such results in terms of the known theories for the corresponding ensemble averaged quantities. In anomalous diffusion processes, that are widely observed in nature over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking), and these time averages may no longer be interpreted in terms of ensemble theories. Here we detail some recent results on weakly non-ergodic systems with respect to the time averagedmore » mean squared displacement, the inherent irreproducibility of individual measurements, and methods to determine the exact underlying stochastic process. We also address the phenomenon of ageing, the dependence of physical observables on the time span between initial preparation of the system and the start of the measurement.« less

Ergodicity bounds for birth-death processes with particularities

NASA Astrophysics Data System (ADS)

Zeifman, Alexander I.; Satin, Yacov; Korotysheva, Anna; Shilova, Galina; Kiseleva, Ksenia; Korolev, Victor Yu.; Bening, Vladimir E.; Shorgin, Sergey Ya.

2016-06-01

We introduce an inhomogeneous birth-death process with birth rates λk(t), death rates µk(t), and possible transitions to/from zero with rates βk(t), rk(t) respectively, and obtain ergodicity bounds for this process.

Ergodicity of a singly-thermostated harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, William Graham; Sprott, Julien Clinton; Hoover, Carol Griswold

2016-03-01

Although Nosé's thermostated mechanics is formally consistent with Gibbs' canonical ensemble, the thermostated Nosé-Hoover (harmonic) oscillator, with its mean kinetic temperature controlled, is far from ergodic. Much of its phase space is occupied by regular conservative tori. Oscillator ergodicity has previously been achieved by controlling two oscillator moments with two thermostat variables. Here we use computerized searches in conjunction with visualization to find singly-thermostated motion equations for the oscillator which are consistent with Gibbs' canonical distribution. Such models are the simplest able to bridge the gap between Gibbs' statistical ensembles and Newtonian single-particle dynamics.

Revisitation of the dipole tracer test for heterogeneous porous formations

NASA Astrophysics Data System (ADS)

Zech, Alraune; D'Angelo, Claudia; Attinger, Sabine; Fiori, Aldo

2018-05-01

In this paper, a new analytical solution for interpreting dipole tests in heterogeneous media is derived by associating the shape of the tracer breakthrough curve with the log-conductivity variance. It is presented how the solution can be used for interpretation of dipole field test in view of geostatistical aquifer characterization on three illustrative examples. The analytical solution for the tracer breakthrough curve at the pumping well in a dipole tracer test is developed by considering a perfectly stratified formation. The analysis is carried out making use of the travel time of a generic solute particle, from the injection to the pumping well. Injection conditions are adapted to different possible field setting. Solutions are presented for resident and flux proportional injection mode as well as for an instantaneous pulse of solute and continuous solute injections. The analytical form of the solution allows a detailed investigation on the impact of heterogeneity, the tracer input conditions and ergodicity conditions at the well. The impact of heterogeneity manifests in a significant spreading of solute particles that increases the natural tendency to spreading induced by the dipole setup. Furthermore, with increasing heterogeneity the number of layers needed to reach ergodic conditions become larger. Thus, dipole test in highly heterogeneous aquifers might take place under non-ergodic conditions giving that the log-conductivity variance is underestimated. The method is a promising geostatistical analyzing tool being the first analytical solution for dipole tracer test analysis taking heterogeneity of hydraulic conductivity into account.

Hierarchical layered and semantic-based image segmentation using ergodicity map

NASA Astrophysics Data System (ADS)

Yadegar, Jacob; Liu, Xiaoqing

2010-04-01

Image segmentation plays a foundational role in image understanding and computer vision. Although great strides have been made and progress achieved on automatic/semi-automatic image segmentation algorithms, designing a generic, robust, and efficient image segmentation algorithm is still challenging. Human vision is still far superior compared to computer vision, especially in interpreting semantic meanings/objects in images. We present a hierarchical/layered semantic image segmentation algorithm that can automatically and efficiently segment images into hierarchical layered/multi-scaled semantic regions/objects with contextual topological relationships. The proposed algorithm bridges the gap between high-level semantics and low-level visual features/cues (such as color, intensity, edge, etc.) through utilizing a layered/hierarchical ergodicity map, where ergodicity is computed based on a space filling fractal concept and used as a region dissimilarity measurement. The algorithm applies a highly scalable, efficient, and adaptive Peano- Cesaro triangulation/tiling technique to decompose the given image into a set of similar/homogenous regions based on low-level visual cues in a top-down manner. The layered/hierarchical ergodicity map is built through a bottom-up region dissimilarity analysis. The recursive fractal sweep associated with the Peano-Cesaro triangulation provides efficient local multi-resolution refinement to any level of detail. The generated binary decomposition tree also provides efficient neighbor retrieval mechanisms for contextual topological object/region relationship generation. Experiments have been conducted within the maritime image environment where the segmented layered semantic objects include the basic level objects (i.e. sky/land/water) and deeper level objects in the sky/land/water surfaces. Experimental results demonstrate the proposed algorithm has the capability to robustly and efficiently segment images into layered semantic objects/regions with contextual topological relationships.

Ergodicity of two hard balls in integrable polygons

NASA Astrophysics Data System (ADS)

Bálint, Péter; Troubetzkoy, Serge

2004-11-01

We prove the hyperbolicity, ergodicity and thus the Bernoulli property of two hard balls in one of the following four polygons: the square, the equilateral triangle, the 45°-45°-90° triangle or the 30°-60°-90° triangle.

Are there ergodic limits to evolution? Ergodic exploration of genome space and convergence

PubMed Central

McLeish, Tom C. B.

2015-01-01

We examine the analogy between evolutionary dynamics and statistical mechanics to include the fundamental question of ergodicity—the representative exploration of the space of possible states (in the case of evolution this is genome space). Several properties of evolutionary dynamics are identified that allow a generalization of the ergodic dynamics, familiar in dynamical systems theory, to evolution. Two classes of evolved biological structure then arise, differentiated by the qualitative duration of their evolutionary time scales. The first class has an ergodicity time scale (the time required for representative genome exploration) longer than available evolutionary time, and has incompletely explored the genotypic and phenotypic space of its possibilities. This case generates no expectation of convergence to an optimal phenotype or possibility of its prediction. The second, more interesting, class exhibits an evolutionary form of ergodicity—essentially all of the structural space within the constraints of slower evolutionary variables have been sampled; the ergodicity time scale for the system evolution is less than the evolutionary time. In this case, some convergence towards similar optima may be expected for equivalent systems in different species where both possess ergodic evolutionary dynamics. When the fitness maximum is set by physical, rather than co-evolved, constraints, it is additionally possible to make predictions of some properties of the evolved structures and systems. We propose four structures that emerge from evolution within genotypes whose fitness is induced from their phenotypes. Together, these result in an exponential speeding up of evolution, when compared with complete exploration of genomic space. We illustrate a possible case of application and a prediction of convergence together with attaining a physical fitness optimum in the case of invertebrate compound eye resolution. PMID:26640648

Preserving the Boltzmann ensemble in replica-exchange molecular dynamics.

PubMed

Cooke, Ben; Schmidler, Scott C

2008-10-28

We consider the convergence behavior of replica-exchange molecular dynamics (REMD) [Sugita and Okamoto, Chem. Phys. Lett. 314, 141 (1999)] based on properties of the numerical integrators in the underlying isothermal molecular dynamics (MD) simulations. We show that a variety of deterministic algorithms favored by molecular dynamics practitioners for constant-temperature simulation of biomolecules fail either to be measure invariant or irreducible, and are therefore not ergodic. We then show that REMD using these algorithms also fails to be ergodic. As a result, the entire configuration space may not be explored even in an infinitely long simulation, and the simulation may not converge to the desired equilibrium Boltzmann ensemble. Moreover, our analysis shows that for initial configurations with unfavorable energy, it may be impossible for the system to reach a region surrounding the minimum energy configuration. We demonstrate these failures of REMD algorithms for three small systems: a Gaussian distribution (simple harmonic oscillator dynamics), a bimodal mixture of Gaussians distribution, and the alanine dipeptide. Examination of the resulting phase plots and equilibrium configuration densities indicates significant errors in the ensemble generated by REMD simulation. We describe a simple modification to address these failures based on a stochastic hybrid Monte Carlo correction, and prove that this is ergodic.

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

NASA Astrophysics Data System (ADS)

von Kleist, Max; Schütte, Christof; Zhang, Wei

2018-02-01

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.

Special ergodic theorems and dynamical large deviations

NASA Astrophysics Data System (ADS)

Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav

2012-11-01

Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.

Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics

NASA Astrophysics Data System (ADS)

Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol

2015-09-01

The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.

Giant room-temperature electrostrictive coefficients in lead-free relaxor ferroelectric ceramics by compositional tuning

NASA Astrophysics Data System (ADS)

Ullah, Aman; Gul, Hafiza Bushra; Ullah, Amir; Sheeraz, Muhammad; Bae, Jong-Seong; Jo, Wook; Ahn, Chang Won; Kim, Ill Won; Kim, Tae Heon

2018-01-01

A thermotropic phase boundary between non-ergodic and ergodic relaxor phases is tuned in lead-free Bi1/2Na1/2TiO3-based ceramics through a structural transition driven by compositional modification (usually named as "morphotropic approach"). The substitution of Bi(Ni1/2Ti1/2)O3 for Bi1/2(Na0.78K0.22)1/2TiO3 induces a transition from tetragonal to "metrically" cubic phase and thereby, the ergodic relaxor ferroelectric phase becomes predominant at room temperature. A shift of the transition temperature (denoted as TF-R) in the non-ergodic-to-ergodic phase transition is corroborated via temperature-dependent dielectric permittivity and loss measurements. By monitoring the chemical composition dependence of polarization-electric field and strain-electric field hysteresis loops, it is possible to track the critical concentration of Bi(Ni1/2Ti1/2)O3 where the (1 - x)Bi0.5(Na0.78K0.22)0.5TiO3-xBi(Ni0.5Ti0.5)O3 ceramic undergoes the phase transition around room temperature. At the Bi(Ni0.5Ti0.5)O3 content of x = 0.050, the highest room-temperature electrostrictive coefficient of 0.030 m4/C2 is achieved with no hysteretic characteristic, which can foster the realization of actual electrostrictive devices with high operational efficiency at room temperature.

Competitive agents in a market: Statistical physics of the minority game

NASA Astrophysics Data System (ADS)

Sherrington, David

2007-10-01

A brief review is presented of the minority game, a simple frustrated many-body system stimulated by considerations of a market of competitive speculative agents. Its cooperative behaviour exhibits phase transitions and both ergodic and non-ergodic regimes. It provides novel challenges to statistical physics, reminiscent of those of mean-field spin glasses.

Ergodicity convergence test suggests telomere motion obeys fractional dynamics

NASA Astrophysics Data System (ADS)

Kepten, E.; Bronshtein, I.; Garini, Y.

2011-04-01

Anomalous diffusion, observed in many biological processes, is a generalized description of a wide variety of processes, all obeying the same law of mean-square displacement. Identifying the basic mechanisms of these observations is important for deducing the nature of the biophysical systems measured. We implement a previously suggested method for distinguishing between fractional Langevin dynamics, fractional Brownian motion, and continuous time random walk based on the ergodic nature of the data. We apply the method together with the recently suggested P-variation test and the displacement correlation to the lately measured dynamics of telomeres in the nucleus of mammalian cells and find strong evidence that the telomeres motion obeys fractional dynamics. The ergodic dynamics are observed experimentally to fit fractional Brownian or Langevin dynamics.

Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures

NASA Astrophysics Data System (ADS)

Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J.

2016-06-01

We give explicit C 1-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with one-dimensional center and positive topological entropy on which the center Lyapunov exponent vanishes uniformly. The conditions of the criterion are met on a C 1-dense and open subset of the set of diffeomorphisms having a robust cycle. As a corollary, there exists a C 1-open and dense subset of the set of non-Anosov robustly transitive diffeomorphisms consisting of systems with nonhyperbolic ergodic measures with positive entropy. The criterion is based on a notion of a blender defined dynamically in terms of strict invariance of a family of discs.

Principle of Parsimony, Fake Science, and Scales

NASA Astrophysics Data System (ADS)

Yeh, T. C. J.; Wan, L.; Wang, X. S.

2017-12-01

Considering difficulties in predicting exact motions of water molecules, and the scale of our interests (bulk behaviors of many molecules), Fick's law (diffusion concept) has been created to predict solute diffusion process in space and time. G.I. Taylor (1921) demonstrated that random motion of the molecules reach the Fickian regime in less a second if our sampling scale is large enough to reach ergodic condition. Fick's law is widely accepted for describing molecular diffusion as such. This fits the definition of the parsimony principle at the scale of our concern. Similarly, advection-dispersion or convection-dispersion equation (ADE or CDE) has been found quite satisfactory for analysis of concentration breakthroughs of solute transport in uniformly packed soil columns. This is attributed to the solute is often released over the entire cross-section of the column, which has sampled many pore-scale heterogeneities and met the ergodicity assumption. Further, the uniformly packed column contains a large number of stationary pore-size heterogeneity. The solute thus reaches the Fickian regime after traveling a short distance along the column. Moreover, breakthrough curves are concentrations integrated over the column cross-section (the scale of our interest), and they meet the ergodicity assumption embedded in the ADE and CDE. To the contrary, scales of heterogeneity in most groundwater pollution problems evolve as contaminants travel. They are much larger than the scale of our observations and our interests so that the ergodic and the Fickian conditions are difficult. Upscaling the Fick's law for solution dispersion, and deriving universal rules of the dispersion to the field- or basin-scale pollution migrations are merely misuse of the parsimony principle and lead to a fake science ( i.e., the development of theories for predicting processes that can not be observed.) The appropriate principle of parsimony for these situations dictates mapping of large-scale heterogeneities as detailed as possible and adapting the Fick's law for effects of small-scale heterogeneity resulting from our inability to characterize them in detail.

Persistence and ergodicity of a stochastic single species model with Allee effect under regime switching

NASA Astrophysics Data System (ADS)

Yu, Xingwang; Yuan, Sanling; Zhang, Tonghua

2018-06-01

Allee effect can interact with environment stochasticity and is active when population numbers are small. Our goal of this paper is to investigate such effect on population dynamics. More precisely, we develop and investigate a stochastic single species model with Allee effect under regime switching. We first prove the existence of global positive solution of the model. Then, we perform the survival analysis to seek sufficient conditions for the extinction, non-persistence in mean, persistence in mean and stochastic permanence. By constructing a suitable Lyapunov function, we show that the model is positive recurrent and ergodic. Our results indicate that the regime switching can suppress the extinction of the species. Finally, numerical simulations are carried out to illustrate the obtained theoretical results, where a real-life example is also discussed showing the inclusion of Allee effect in the model provides a better match to the data.

Chaotic attractors and physical measures for some density dependent Leslie population models

NASA Astrophysics Data System (ADS)

Ugarcovici, Ilie; Weiss, Howard

2007-12-01

Following ecologists' discoveries, mathematicians have begun studying extensions of the ubiquitous age structured Leslie population model that allow some survival probabilities and/or fertility rates to depend on population densities. These nonlinear extensions commonly exhibit very complicated dynamics: through computer studies, some authors have discovered robust Hénon-like strange attractors in several families. Population biologists and demographers frequently wish to average a function over many generations and conclude that the average is independent of the initial population distribution. This type of 'ergodicity' seems to be a fundamental tenet in population biology. In this paper we develop the first rigorous ergodic theoretic framework for density dependent Leslie population models. We study two generation models with Ricker and Hassell (recruitment type) fertility terms. We prove that for some parameter regions these models admit a chaotic (ergodic) attractor which supports a unique physical probability measure. This physical measure, having full Lebesgue measure basin, satisfies in the strongest possible sense the population biologist's requirement for ergodicity in their population models. We use the celebrated work of Wang and Young 2001 Commun. Math. Phys. 218 1-97, and our results are the first applications of their method to biology, ecology or demography.

Equilibration of energy in slow–fast systems

PubMed Central

Shah, Kushal; Gelfreich, Vassili; Rom-Kedar, Vered

2017-01-01

Ergodicity is a fundamental requirement for a dynamical system to reach a state of statistical equilibrium. However, in systems with several characteristic timescales, the ergodicity of the fast subsystem impedes the equilibration of the whole system because of the presence of an adiabatic invariant. In this paper, we show that violation of ergodicity in the fast dynamics can drive the whole system to equilibrium. To show this principle, we investigate the dynamics of springy billiards, which are mechanical systems composed of a small particle bouncing elastically in a bounded domain, where one of the boundary walls has finite mass and is attached to a linear spring. Numerical simulations show that the springy billiard systems approach equilibrium at an exponential rate. However, in the limit of vanishing particle-to-wall mass ratio, the equilibration rates remain strictly positive only when the fast particle dynamics reveal two or more ergodic components for a range of wall positions. For this case, we show that the slow dynamics of the moving wall can be modeled by a random process. Numerical simulations of the corresponding springy billiards and their random models show equilibration with similar positive rates. PMID:29183966

Collision-induced evaporation of water clusters and contribution of momentum transfer

NASA Astrophysics Data System (ADS)

Calvo, Florent; Berthias, Francis; Feketeová, Linda; Abdoul-Carime, Hassan; Farizon, Bernadette; Farizon, Michel

2017-05-01

The evaporation of water molecules from high-velocity argon atoms impinging on protonated water clusters has been computationally investigated using molecular dynamics simulations with the reactive OSS2 potential to model water clusters and the ZBL pair potential to represent their interaction with the projectile. Swarms of trajectories and an event-by-event analysis reveal the conditions under which a specific number of molecular evaporation events is found one nanosecond after impact, thereby excluding direct knockout events from the analysis. These simulations provide velocity distributions that exhibit two main features, with a major statistical component arising from a global redistribution of the collision energy into intermolecular degrees of freedom, and another minor but non-ergodic feature at high velocities. The latter feature is produced by direct impacts on the peripheral water molecules and reflects a more complete momentum transfer. These two components are consistent with recent experimental measurements and confirm that electronic processes are not explicitly needed to explain the observed non-ergodic behavior. Contribution to the Topical Issue "Dynamics of Systems at the Nanoscale", edited by Andrey Solov'yov and Andrei Korol.

Ergodicity, Maximum Entropy Production, and Steepest Entropy Ascent in the Proofs of Onsager's Reciprocal Relations

NASA Astrophysics Data System (ADS)

Benfenati, Francesco; Beretta, Gian Paolo

2018-04-01

We show that to prove the Onsager relations using the microscopic time reversibility one necessarily has to make an ergodic hypothesis, or a hypothesis closely linked to that. This is true in all the proofs of the Onsager relations in the literature: from the original proof by Onsager, to more advanced proofs in the context of linear response theory and the theory of Markov processes, to the proof in the context of the kinetic theory of gases. The only three proofs that do not require any kind of ergodic hypothesis are based on additional hypotheses on the macroscopic evolution: Ziegler's maximum entropy production principle (MEPP), the principle of time reversal invariance of the entropy production, or the steepest entropy ascent principle (SEAP).

Ergodic actions of SμU(2) on C∗-algebras from II1 subfactors

NASA Astrophysics Data System (ADS)

Pinzari, Claudia; Roberts, John E.

2010-03-01

To a proper inclusion N⊂M of II factors of finite Jones index [M:N], we associate an ergodic C∗-action of the quantum group SμU(2) (or more generally of certain groups Ao(F)). The higher relative commutant N'∩M can be identified with the spectral space of the rth tensor power u of the defining representation of the quantum group. The index and the deformation parameter are related by -1≤μ<0 and [M:N]=|μ+μ-1|. This ergodic action may be thought of as a virtual subgroup of SμU(2) in the sense of Mackey arising from the tensor category generated by the N-bimodule NMN. μ is negative as NMN is a real bimodule.

Analyzing the dynamics of cell cycle processes from fixed samples through ergodic principles

PubMed Central

Wheeler, Richard John

2015-01-01

Tools to analyze cyclical cellular processes, particularly the cell cycle, are of broad value for cell biology. Cell cycle synchronization and live-cell time-lapse observation are widely used to analyze these processes but are not available for many systems. Simple mathematical methods built on the ergodic principle are a well-established, widely applicable, and powerful alternative analysis approach, although they are less widely used. These methods extract data about the dynamics of a cyclical process from a single time-point “snapshot” of a population of cells progressing through the cycle asynchronously. Here, I demonstrate application of these simple mathematical methods to analysis of basic cyclical processes—cycles including a division event, cell populations undergoing unicellular aging, and cell cycles with multiple fission (schizogony)—as well as recent advances that allow detailed mapping of the cell cycle from continuously changing properties of the cell such as size and DNA content. This includes examples using existing data from mammalian, yeast, and unicellular eukaryotic parasite cell biology. Through the ongoing advances in high-throughput cell analysis by light microscopy, electron microscopy, and flow cytometry, these mathematical methods are becoming ever more important and are a powerful complementary method to traditional synchronization and time-lapse cell cycle analysis methods. PMID:26543196

Singularities and non-hyperbolic manifolds do not coincide

NASA Astrophysics Data System (ADS)

Simányi, Nándor

2013-06-01

We consider the billiard flow of elastically colliding hard balls on the flat ν-torus (ν ⩾ 2), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann-Sinai ergodic hypothesis.

Quantifying nonergodicity in nonautonomous dissipative dynamical systems: An application to climate change

NASA Astrophysics Data System (ADS)

Drótos, Gábor; Bódai, Tamás; Tél, Tamás

2016-08-01

In nonautonomous dynamical systems, like in climate dynamics, an ensemble of trajectories initiated in the remote past defines a unique probability distribution, the natural measure of a snapshot attractor, for any instant of time, but this distribution typically changes in time. In cases with an aperiodic driving, temporal averages taken along a single trajectory would differ from the corresponding ensemble averages even in the infinite-time limit: ergodicity does not hold. It is worth considering this difference, which we call the nonergodic mismatch, by taking time windows of finite length for temporal averaging. We point out that the probability distribution of the nonergodic mismatch is qualitatively different in ergodic and nonergodic cases: its average is zero and typically nonzero, respectively. A main conclusion is that the difference of the average from zero, which we call the bias, is a useful measure of nonergodicity, for any window length. In contrast, the standard deviation of the nonergodic mismatch, which characterizes the spread between different realizations, exhibits a power-law decrease with increasing window length in both ergodic and nonergodic cases, and this implies that temporal and ensemble averages differ in dynamical systems with finite window lengths. It is the average modulus of the nonergodic mismatch, which we call the ergodicity deficit, that represents the expected deviation from fulfilling the equality of temporal and ensemble averages. As an important finding, we demonstrate that the ergodicity deficit cannot be reduced arbitrarily in nonergodic systems. We illustrate via a conceptual climate model that the nonergodic framework may be useful in Earth system dynamics, within which we propose the measure of nonergodicity, i.e., the bias, as an order-parameter-like quantifier of climate change.

Broken Ergodicity in Ideal, Homogeneous, Incompressible Turbulence

NASA Technical Reports Server (NTRS)

Morin, Lee; Shebalin, John; Fu, Terry; Nguyen, Phu; Shum, Victor

2010-01-01

We discuss the statistical mechanics of numerical models of ideal homogeneous, incompressible turbulence and their relevance for dissipative fluids and magnetofluids. These numerical models are based on Fourier series and the relevant statistical theory predicts that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. However, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We explain this phenomena in terms of broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We review the theoretical basis of broken ergodicity, apply it to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence, and show new results from simulations using GPU (graphical processing unit) computers.

Ergodicity Breaking in Geometric Brownian Motion

NASA Astrophysics Data System (ADS)

Peters, O.; Klein, W.

2013-03-01

Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by nonergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this Letter, we study the effects of diversification using the concept of ergodicity breaking.

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.

Information, Consistent Estimation and Dynamic System Identification.

DTIC Science & Technology

1976-11-01

Washington,DC 232129 Tj-CUOSITORING AGENCY NAMIE 6 AOORESS(lI dittevmet Itroo CuooottaaII Offics) IS.- SECURITY CLASS. (of this *.part) SCHEDULE ’B...representative model from a given model set, applicable to infinite and even non-compact model sets. S-UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAOrj(*whe...ergodicity. For a thorough development of ergodic theory the reader is referred to, e.g., Doob [1953], Halmos [1956] and Chacon and Ornstein [1959

Dephasing Catastrophe in 4-ε Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase.

PubMed

Liao, Yunxiang; Foster, Matthew S

2018-06-08

In two dimensions, dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in d=4-ε dimensions, and find a nontrivial fixed point corresponding to a temperature T^{*}∼ε>0 where the dephasing time diverges. Assuming that this fixed point survives to ε=2, we associate it with a possible instability of the ergodic phase. Our approach may open a new line of attack against the problem of the ergodic to many-body-localized phase transition in d>1 spatial dimensions.

Dephasing Catastrophe in 4 -ɛ Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase

NASA Astrophysics Data System (ADS)

Liao, Yunxiang; Foster, Matthew S.

2018-06-01

In two dimensions, dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in d =4 -ɛ dimensions, and find a nontrivial fixed point corresponding to a temperature T*˜ɛ >0 where the dephasing time diverges. Assuming that this fixed point survives to ɛ =2 , we associate it with a possible instability of the ergodic phase. Our approach may open a new line of attack against the problem of the ergodic to many-body-localized phase transition in d >1 spatial dimensions.

Ergodic model for the expansion of spherical nanoplasmas.

PubMed

Peano, F; Coppa, G; Peinetti, F; Mulas, R; Silva, L O

2007-06-01

Recently, the collisionless expansion of spherical nanoplasmas has been analyzed with a new ergodic model, clarifying the transition from hydrodynamiclike to Coulomb-explosion regimes, and providing accurate laws for the relevant features of the phenomenon. A complete derivation of the model is presented here. The important issue of the self-consistent initial conditions is addressed by analyzing the initial charging transient due to the electron expansion, in the approximation of immobile ions. A comparison among different kinetic models for the expansion is presented, showing that the ergodic model provides a simplified description, which retains the essential information on the electron distribution, in particular, the energy spectrum. Results are presented for a wide range of initial conditions (determined from a single dimensionless parameter), in excellent agreement with calculations from the exact Vlasov-Poisson theory, thus providing a complete and detailed characterization of all the stages of the expansion.

Passive runaway electron suppression in tokamak disruptions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, H. M.; Helander, P.; Boozer, A. H.

2013-07-15

Runaway electrons created in disruptions pose a serious problem for tokamaks with large current. It would be desirable to have a runaway electron suppression method which is passive, i.e., a method that does not rely on an uncertain disruption prediction system. One option is to let the large electric field inherent in the disruption drive helical currents in the wall. This would create ergodic regions in the plasma and increase the runaway losses. Whether these regions appear at a suitable time and place to affect the formation of the runaway beam depends on disruption parameters, such as electron temperature andmore » density. We find that it is difficult to ergodize the central plasma before a beam of runaway current has formed. However, the ergodic outer region will make the Ohmic current profile contract, which can lead to instabilities that yield large runaway electron losses.« less

The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

NASA Technical Reports Server (NTRS)

Meyer, C. D., Jr.

1979-01-01

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

NASA Astrophysics Data System (ADS)

Li, Lei; Liu, Jian-Guo; Lu, Jianfeng

2017-10-01

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.

Power-law decay exponents: A dynamical criterion for predicting thermalization

NASA Astrophysics Data System (ADS)

Távora, Marco; Torres-Herrera, E. J.; Santos, Lea F.

2017-01-01

From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior ∝t-γ of the survival probability at long times. We show that the value of the power-law exponent γ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: γ ≥2 and γ <1 . Exponents γ ≥2 imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with γ <1 emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

Spectra of random operators with absolutely continuous integrated density of states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rio, Rafael del, E-mail: delrio@iimas.unam.mx, E-mail: delriomagia@gmail.com

2014-04-15

The structure of the spectrum of random operators is studied. It is shown that if the density of states measure of some subsets of the spectrum is zero, then these subsets are empty. In particular follows that absolute continuity of the integrated density of states implies singular spectra of ergodic operators is either empty or of positive measure. Our results apply to Anderson and alloy type models, perturbed Landau Hamiltonians, almost periodic potentials, and models which are not ergodic.

Speckle dynamics under ergodicity breaking

NASA Astrophysics Data System (ADS)

Sdobnov, Anton; Bykov, Alexander; Molodij, Guillaume; Kalchenko, Vyacheslav; Jarvinen, Topias; Popov, Alexey; Kordas, Krisztian; Meglinski, Igor

2018-04-01

Laser speckle contrast imaging (LSCI) is a well-known and versatile approach for the non-invasive visualization of flows and microcirculation localized in turbid scattering media, including biological tissues. In most conventional implementations of LSCI the ergodic regime is typically assumed valid. However, most composite turbid scattering media, especially biological tissues, are non-ergodic, containing a mixture of dynamic and static centers of light scattering. In the current study, we examined the speckle contrast in different dynamic conditions with the aim of assessing limitations in the quantitative interpretation of speckle contrast images. Based on a simple phenomenological approach, we introduced a coefficient of speckle dynamics to quantitatively assess the ratio of the dynamic part of a scattering medium to the static one. The introduced coefficient allows one to distinguish real changes in motion from the mere appearance of static components in the field of view. As examples of systems with static/dynamic transitions, thawing and heating of Intralipid samples were studied by the LSCI approach.

Tracking single Kv2.1 channels in live cells reveals anomalous subdiffusion and ergodicity breaking

NASA Astrophysics Data System (ADS)

Weigel, Aubrey; Simon, Blair; Tamkun, Michael; Krapf, Diego

2011-03-01

The dynamic organization of the plasma membrane is responsible for essential cellular processes, such as receptor trafficking and signaling. By studying the dynamics of transmembrane proteins a greater understanding of these processes as a whole can be achieved. It is broadly observed that the diffusion pattern of membrane protein displays anomalous subdiffusion. However, the mechanisms responsible for this behavior are not yet established. We explore the dynamics of the voltage gated potassium channel Kv2.1 by using single-particle tracking. We analyze Kv2.1 channel trajectories in terms of the time and ensemble distributions of square displacements. Our results reveal that all Kv2.1 channels experience anomalous subdiffusion and we observe that the Kv2.1 diffusion pattern is non-ergodic. We further investigated the role of the actin cytoskeleton in these channel dynamics by applying actin depolymerizing drugs. It is seen that with the breakdown of the actin cytoskeleton the Kv2.1 channel trajectories recover ergodicity.

Revealing nonergodic dynamics in living cells from a single particle trajectory

NASA Astrophysics Data System (ADS)

Lanoiselée, Yann; Grebenkov, Denis S.

2016-05-01

We propose the improved ergodicity and mixing estimators to identify nonergodic dynamics from a single particle trajectory. The estimators are based on the time-averaged characteristic function of the increments and can thus capture additional information on the process as compared to the conventional time-averaged mean-square displacement. The estimators are first investigated and validated for several models of anomalous diffusion, such as ergodic fractional Brownian motion and diffusion on percolating clusters, and nonergodic continuous-time random walks and scaled Brownian motion. The estimators are then applied to two sets of earlier published trajectories of mRNA molecules inside live Escherichia coli cells and of Kv2.1 potassium channels in the plasma membrane. These statistical tests did not reveal nonergodic features in the former set, while some trajectories of the latter set could be classified as nonergodic. Time averages along such trajectories are thus not representative and may be strongly misleading. Since the estimators do not rely on ensemble averages, the nonergodic features can be revealed separately for each trajectory, providing a more flexible and reliable analysis of single-particle tracking experiments in microbiology.

Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fishman, S., E-mail: fishman@physics.technion.ac.il; Soffer, A., E-mail: soffer@math.rutgers.edu

2016-07-15

We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.

A recurrence-weighted prediction algorithm for musical analysis

NASA Astrophysics Data System (ADS)

Colucci, Renato; Leguizamon Cucunuba, Juan Sebastián; Lloyd, Simon

2018-03-01

Forecasting the future behaviour of a system using past data is an important topic. In this article we apply nonlinear time series analysis in the context of music, and present new algorithms for extending a sample of music, while maintaining characteristics similar to the original piece. By using ideas from ergodic theory, we adapt the classical prediction method of Lorenz analogues so as to take into account recurrence times, and demonstrate with examples, how the new algorithm can produce predictions with a high degree of similarity to the original sample.

Structural analysis of vibroacoustical processes

NASA Technical Reports Server (NTRS)

Gromov, A. P.; Myasnikov, L. L.; Myasnikova, Y. N.; Finagin, B. A.

1973-01-01

The method of automatic identification of acoustical signals, by means of the segmentation was used to investigate noises and vibrations in machines and mechanisms, for cybernetic diagnostics. The structural analysis consists of presentation of a noise or vibroacoustical signal as a sequence of segments, determined by the time quantization, in which each segment is characterized by specific spectral characteristics. The structural spectrum is plotted as a histogram of the segments, also as a relation of the probability density of appearance of a segment to the segment type. It is assumed that the conditions of ergodic processes are maintained.

Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2016-11-01

We introduce a class of discrete random-walk model driven by global memory effects. At any time, the right-left transitions depend on the whole previous history of the walker, being defined by an urnlike memory mechanism. The characteristic function is calculated in an exact way, which allows us to demonstrate that the ensemble of realizations is ballistic. Asymptotically, each realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature, the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long-time regime, they remain random objects. While their average over realizations recovers the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment, an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.

Fluctuations around equilibrium laws in ergodic continuous-time random walks.

PubMed

Schulz, Johannes H P; Barkai, Eli

2015-06-01

We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.

Evaluating gambles using dynamics

NASA Astrophysics Data System (ADS)

Peters, O.; Gell-Mann, M.

2016-02-01

Gambles are random variables that model possible changes in wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. Expectation value maximizers are defined as rational in economics, but expectation values are only meaningful in the presence of ensembles or in systems with ergodic properties, whereas decision-makers have no access to ensembles, and the variables representing wealth in the usual growth models do not have the relevant ergodic properties. Simultaneously addressing the shortcomings of utility and those of expectations, we propose to evaluate gambles by averaging wealth growth over time. No utility function is needed, but a dynamic must be specified to compute time averages. Linear and logarithmic "utility functions" appear as transformations that generate ergodic observables for purely additive and purely multiplicative dynamics, respectively. We highlight inconsistencies throughout the development of decision theory, whose correction clarifies that our perspective is legitimate. These invalidate a commonly cited argument for bounded utility functions.

Chaos, ergodic convergence, and fractal instability for a thermostated canonical harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.; Isbister, Dennis J.

2001-02-01

The authors thermostat a qp harmonic oscillator using the two additional control variables ζ and ξ to simulate Gibbs' canonical distribution. In contrast to the motion of purely Hamiltonian systems, the thermostated oscillator motion is completely ergodic, covering the full four-dimensional \\{q,p,ζ,ξ\\} phase space. The local Lyapunov spectrum (instantaneous growth rates of a comoving corotating phase-space hypersphere) exhibits singularities like those found earlier for Hamiltonian chaos, reinforcing the notion that chaos requires kinetic-as opposed to statistical-study, both at and away from equilibrium. The exponent singularities appear to have a fractal character.

Analyzing the dynamics of cell cycle processes from fixed samples through ergodic principles.

PubMed

Wheeler, Richard John

2015-11-05

Tools to analyze cyclical cellular processes, particularly the cell cycle, are of broad value for cell biology. Cell cycle synchronization and live-cell time-lapse observation are widely used to analyze these processes but are not available for many systems. Simple mathematical methods built on the ergodic principle are a well-established, widely applicable, and powerful alternative analysis approach, although they are less widely used. These methods extract data about the dynamics of a cyclical process from a single time-point "snapshot" of a population of cells progressing through the cycle asynchronously. Here, I demonstrate application of these simple mathematical methods to analysis of basic cyclical processes--cycles including a division event, cell populations undergoing unicellular aging, and cell cycles with multiple fission (schizogony)--as well as recent advances that allow detailed mapping of the cell cycle from continuously changing properties of the cell such as size and DNA content. This includes examples using existing data from mammalian, yeast, and unicellular eukaryotic parasite cell biology. Through the ongoing advances in high-throughput cell analysis by light microscopy, electron microscopy, and flow cytometry, these mathematical methods are becoming ever more important and are a powerful complementary method to traditional synchronization and time-lapse cell cycle analysis methods. © 2015 Wheeler. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

space and time in ergodic gemorphology

NASA Astrophysics Data System (ADS)

Seyed Ebrahimi, S.

2009-04-01

Epistemological perspectives rank among the main factors contributing to word coinage in scientific literature. New words come into existence as new epistemological fields evolve (Sack1992). Each field, however, tends to impose its own interpretation on the words associated with it. To illustrate the point, certain words retain formal structure and relate to the same subject area, but can nonetheless be employed in totally different epistemological fields. The semantic content undergoes a drastic change in each case. Granted that numerous theoretical stances can be identified within the discipline of geomorphology, acquaintance with the semantic content of certain words should help toward a more realistic understanding of what the theorists and practitioners in this field have in mind. This paper, which is based on an analysis of these three theoretical positions aims to highlight the importance of the semantic content of the term equilibrium as utilized in ergodic geomorphology, and the ways in which it is construed from different viewpoints. For this purpose, the authors have of necessity availed themselves of dated sources, rather than up-to-date ones. The paper also argues that familiarity with concepts such as these will ensure a better grasp of the paradigms in question.

Local conditional entropy in measure for covers with respect to a fixed partition

NASA Astrophysics Data System (ADS)

Romagnoli, Pierre-Paul

2018-05-01

In this paper we introduce two measure theoretical notions of conditional entropy for finite measurable covers conditioned to a finite measurable partition and prove that they are equal. Using this we state a local variational principle with respect to the notion of conditional entropy defined by Misiurewicz (1976 Stud. Math. 55 176–200) for the case of open covers. This in particular extends the work done in Romagnoli (2003 Ergod. Theor. Dynam. Syst. 23 1601–10), Glasner and Weiss (2006 Handbook of Dynamical Systems vol 1B (Amsterdam: Elsevier)) and Huang et al (2006 Ergod. Theor. Dynam. Syst. 26 219–45).

Dynamically induced many-body localization

NASA Astrophysics Data System (ADS)

Choi, Soonwon; Abanin, Dmitry A.; Lukin, Mikhail D.

2018-03-01

We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, we demonstrate that the Hamiltonian of a weakly disordered ergodic spin system can be effectively engineered, by using sufficiently fast coherent controls, to yield a stable MBL phase, which in turn completely suppresses the energy absorption from external control field. Our results imply that a broad class of existing many-body systems can be used to probe nonequilibrium phases of matter for a long time, limited only by coupling to external environment.

Quantitative quasiperiodicity

NASA Astrophysics Data System (ADS)

Das, Suddhasattwa; Saiki, Yoshitaka; Sander, Evelyn; Yorke, James A.

2017-11-01

The Birkhoff ergodic theorem concludes that time averages, i.e. Birkhoff averages, B_N( f):=Σn=0N-1 f(x_n)/N of a function f along a length N ergodic trajectory (x_n) of a function T converge to the space average \\int f dμ , where μ is the unique invariant probability measure. Convergence of the time average to the space average is slow. We use a modified average of f(x_n) by giving very small weights to the ‘end’ terms when n is near 0 or N-1 . When (x_n) is a trajectory on a quasiperiodic torus and f and T are C^∞ , our weighted Birkhoff average (denoted \

A semigroup approach to the strong ergodic theorem of the multistate stable population process.

PubMed

Inaba, H

1988-01-01

"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE) excerpt

Decryption of pure-position permutation algorithms.

PubMed

Zhao, Xiao-Yu; Chen, Gang; Zhang, Dan; Wang, Xiao-Hong; Dong, Guang-Chang

2004-07-01

Pure position permutation image encryption algorithms, commonly used as image encryption investigated in this work are unfortunately frail under known-text attack. In view of the weakness of pure position permutation algorithm, we put forward an effective decryption algorithm for all pure-position permutation algorithms. First, a summary of the pure position permutation image encryption algorithms is given by introducing the concept of ergodic matrices. Then, by using probability theory and algebraic principles, the decryption probability of pure-position permutation algorithms is verified theoretically; and then, by defining the operation system of fuzzy ergodic matrices, we improve a specific decryption algorithm. Finally, some simulation results are shown.

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulated Serratia marcescens

PubMed Central

Bogdan, Paul; Wei, Guopeng; Marculescu, Radu; Zhuang, Jiang; Carlsen, Rika Wright; Sitti, Metin

2017-01-01

To add to the current state of knowledge about bacterial swimming dynamics, in this paper, we study the fractal swimming dynamics of populations of Serratia marcescens bacteria both in vitro and in silico, while accounting for realistic conditions like volume exclusion, chemical interactions, obstacles and distribution of chemoattractant in the environment. While previous research has shown that bacterial motion is non-ergodic, we demonstrate that, besides the non-ergodicity, the bacterial swimming dynamics is multi-fractal in nature. Finally, we demonstrate that the multi-fractal characteristic of bacterial dynamics is strongly affected by bacterial density and chemoattractant concentration. PMID:28804259

Electric Field-Induced Large Strain in Ni/Sb-co Doped (Bi0.5Na0.5) TiO3-Based Lead-Free Ceramics

NASA Astrophysics Data System (ADS)

Li, Liangliang; Hao, Jigong; Xu, Zhijun; Li, Wei; Chu, Ruiqing

2018-02-01

Lead-free piezoelectric ceramics (Bi0.5Na0.5)0.935Ba0.065Ti1- x (Ni0.5Sb0.5) x O3 (BNBT6.5- xNS) have been fabricated using conventional solid sintering technique. The effect of (Ni, Sb) doping on the phase structure and electrical properties of BNBT6.5 ceramics were systematically investigated. Results show that the addition of (Ni, Sb) destroyed the ferroelectric long-range order of BNBT6.5 and shifted the ferroelectric-relaxor transition temperature ( T F-R) down to room temperature. Thus, this process induced an ergodic relaxor phase at zero field in samples with x = 0.005. Under the electric field, the ergodic relaxor phase could reversibly transform to ferroelectric phase, which promotes the strain response with peak value of 0.38% (at 80 kV/cm, corresponding to d 33 * = 479 pm/V) at x = 0.005. Temperature-dependent measurements of both polarization and strain confirmed that the large strain originated from a reversible field-induced ergodic relaxor to ferroelectric phase transformation. The proposed material exhibits potential for nonlinear actuators.

Ergodicity, hidden bias and the growth rate gain

NASA Astrophysics Data System (ADS)

Rochman, Nash D.; Popescu, Dan M.; Sun, Sean X.

2018-05-01

Many single-cell observables are highly heterogeneous. A part of this heterogeneity stems from age-related phenomena: the fact that there is a nonuniform distribution of cells with different ages. This has led to a renewed interest in analytic methodologies including use of the ‘von Foerster equation’ for predicting population growth and cell age distributions. Here we discuss how some of the most popular implementations of this machinery assume a strong condition on the ergodicity of the cell cycle duration ensemble. We show that one common definition for the term ergodicity, ‘a single individual observed over many generations recapitulates the behavior of the entire ensemble’ is implied by the other, ‘the probability of observing any state is conserved across time and over all individuals’ in an ensemble with a fixed number of individuals but that this is not true when the ensemble is growing. We further explore the impact of generational correlations between cell cycle durations on the population growth rate. Finally, we explore the ‘growth rate gain’—the phenomenon that variations in the cell cycle duration leads to an improved population-level growth rate—in this context. We highlight that, fundamentally, this effect is due to asymmetric division.

Making sense of snapshot data: ergodic principle for clonal cell populations

PubMed Central

2017-01-01

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations. PMID:29187636

Making sense of snapshot data: ergodic principle for clonal cell populations.

PubMed

Thomas, Philipp

2017-11-01

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations. © 2017 The Author(s).

Statistical characterization of discrete conservative systems: The web map

NASA Astrophysics Data System (ADS)

Ruiz, Guiomar; Tirnakli, Ugur; Borges, Ernesto P.; Tsallis, Constantino

2017-10-01

We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional SB G[p (x ) ] =-k ∫d x p (x ) lnp (x ) . In contrast, possible ergodicity breakdown and transitory sticky dynamical behavior drag the map into the realm of generalized q statistics, based on the nonadditive entropic functional Sq[p (x ) ] =k 1/-∫d x [p(x ) ] q q -1 (q ∈R ;S1=SB G ). We statistically describe the system (probability distribution of the sum of successive iterates, sensitivity to the initial condition, and entropy production per unit time) for typical values of the parameter that controls the ergodicity of the map. For small (large) values of the external parameter K , we observe q -Gaussian distributions with q =1.935 ⋯ (Gaussian distributions), like for the standard map. In contrast, for intermediate values of K , we observe a different scenario, due to the fractal structure of the trajectories embedded in the chaotic sea. Long-standing non-Gaussian distributions are characterized in terms of the kurtosis and the box-counting dimension of chaotic sea.

Fuzzy fractals, chaos, and noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zardecki, A.

1997-05-01

To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the conceptmore » of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.« less

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior

PubMed Central

da Cunha, C. R.; Mineharu, M.; Matsunaga, M.; Matsumoto, N.; Chuang, C.; Ochiai, Y.; Kim, G.-H.; Watanabe, K.; Taniguchi, T.; Ferry, D. K.; Aoki, N.

2016-01-01

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene. PMID:27609184

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior.

PubMed

da Cunha, C R; Mineharu, M; Matsunaga, M; Matsumoto, N; Chuang, C; Ochiai, Y; Kim, G-H; Watanabe, K; Taniguchi, T; Ferry, D K; Aoki, N

2016-09-09

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene.

Constructing local integrals of motion in the many-body localized phase

NASA Astrophysics Data System (ADS)

Chandran, Anushya; Kim, Isaac H.; Vidal, Guifre; Abanin, Dmitry A.

2015-02-01

Many-body localization provides a generic mechanism of ergodicity breaking in quantum systems. In contrast to conventional ergodic systems, many-body-localized (MBL) systems are characterized by extensively many local integrals of motion (LIOM), which underlie the absence of transport and thermalization in these systems. Here we report a physically motivated construction of local integrals of motion in the MBL phase. We show that any local operator (e.g., a local particle number or a spin-flip operator), evolved with the system's Hamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such operators have a clear physical meaning, describing the response of the MBL system to a local perturbation. In particular, when a local operator represents a density of some globally conserved quantity, the corresponding LIOM describes how this conserved quantity propagates through the MBL phase. Being uniquely defined and experimentally measurable, these LIOMs provide a natural tool for characterizing the properties of the MBL phase, in both experiments and numerical simulations. We demonstrate the latter by numerically constructing an extensive set of LIOMs in the MBL phase of a disordered spin-chain model. We show that the resulting LIOMs are quasilocal and use their decay to extract the localization length and establish the location of the transition between the MBL and ergodic phases.

Stochastic methods for analysis of power flow in electric networks

NASA Astrophysics Data System (ADS)

1982-09-01

The modeling and effects of probabilistic behavior on steady state power system operation were analyzed. A solution to the steady state network flow equations which adhere both to Kirchoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques was obtained. The development of sound techniques for producing meaningful data to serve as input is examined. Electric demand modeling, equipment failure analysis, and algorithm development are investigated. Two major development areas are described: a decomposition of stochastic processes which gives stationarity, ergodicity, and even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.

Characterization of microstructure, viscoelasticity, heterogeneity and ergodicity in pectin-laponite-CTAB-calcium nanocomposite hydrogels.

PubMed

Joshi, Nidhi; Rawat, Kamla; Bohidar, H B

2016-01-20

In order to customize the viscoelastic properties of pectin gels, it is necessary to work on a composite platform. Herein, the gelation kinetics, and viscoelastic characterization of anionic polysaccharide pectin dispersion prepared in presence of nanoclay laponite are reported using dynamic light scattering and rheology measurements. The ratio Rg/Rh (Rg and Rh are radius of gyration and hydrodynamic radius respectively) determined from light scattering data revealed the presence of random coils of pectin chains inside the gel matrix. When nanoclay laponite was added to the pectin chains solution, two-phase separation was noticed instantaneously. Therefore, the surfactant cetyltrimethylammonium bromide [CTAB] was added to exfoliate the clay platelets in the dispersion, and also in its gel phase. The exfoliating agent cetyltrimethylammonium bromide ([CTAB]≈ cmc/10) helped to enhance the homogeneity and stability of the pectin-clay sols and gels. The storage and loss moduli (G' and G") of the composite gel changed significantly as function of nanoclay laponite content for concentration up to 0.03% (w/v) causing the softening of the gels (gel strength reduced by close to 50%) compared to pectin-calcium gel. However, as the concentration of nanoclay laponite was maintained between 0.01% and 0.03% (w/v), the gel rigidity (G') recovered by 30% (35-45 Pa). The transition from ergodic to non-ergodic state occurred during sol-gel transition owing to the presence of the nanoclay laponite. The gelation time was not too different from the ergodicity breaking time. Thus, the presence of nanoclay laponite in such minute concentration is shown to cause considerable change in the thermo-physical property of the composite gels. This material property modulation will facilitate designing of soft gels having storage modulus continuously varying in the wide range of 10-70 Pa while keeping the gelation temperature mostly unaltered. Copyright © 2015 Elsevier Ltd. All rights reserved.

Investigation of an HMM/ANN hybrid structure in pattern recognition application using cepstral analysis of dysarthric (distorted) speech signals.

PubMed

Polur, Prasad D; Miller, Gerald E

2006-10-01

Computer speech recognition of individuals with dysarthria, such as cerebral palsy patients requires a robust technique that can handle conditions of very high variability and limited training data. In this study, application of a 10 state ergodic hidden Markov model (HMM)/artificial neural network (ANN) hybrid structure for a dysarthric speech (isolated word) recognition system, intended to act as an assistive tool, was investigated. A small size vocabulary spoken by three cerebral palsy subjects was chosen. The effect of such a structure on the recognition rate of the system was investigated by comparing it with an ergodic hidden Markov model as a control tool. This was done in order to determine if this modified technique contributed to enhanced recognition of dysarthric speech. The speech was sampled at 11 kHz. Mel frequency cepstral coefficients were extracted from them using 15 ms frames and served as training input to the hybrid model setup. The subsequent results demonstrated that the hybrid model structure was quite robust in its ability to handle the large variability and non-conformity of dysarthric speech. The level of variability in input dysarthric speech patterns sometimes limits the reliability of the system. However, its application as a rehabilitation/control tool to assist dysarthric motor impaired individuals holds sufficient promise.

Asymptotic behaviors of a cell-to-cell HIV-1 infection model perturbed by white noise

NASA Astrophysics Data System (ADS)

Liu, Qun

2017-02-01

In this paper, we analyze a mathematical model of cell-to-cell HIV-1 infection to CD4+ T cells perturbed by stochastic perturbations. First of all, we investigate that there exists a unique global positive solution of the system for any positive initial value. Then by using Lyapunov analysis methods, we study the asymptotic property of this solution. Moreover, we discuss whether there is a stationary distribution for this system and if it owns the ergodic property. Numerical simulations are presented to illustrate the theoretical results.

A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pesin, Y.; Weiss, H.

1997-01-01

In this paper we establish the complete multifractal formalism for equilibrium measures for Holder continuous conformal expanding maps and expanding Markov Moran-like geometric constructions. Examples include Markov maps of an interval, beta transformations of an interval, rational maps with hyperbolic Julia sets, and conformal total endomorphisms. We also construct a Holder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex, and hence the multifractal formalism fails.

Three dimensional cross-correlation dynamic light scattering by non-ergodic turbid media.

PubMed

Haro-Pérez, C; Ojeda-Mendoza, G J; Rojas-Ochoa, L F

2011-06-28

We investigate dynamic light scattering by non-ergodic turbid media with an adapted version of the method proposed by Pusey and van Megen [Physica A 157, 705 (1989)]. Our formulation follows the derivation of the original method by extending it to the three dimensional cross-correlation scheme (3DDLS). The main finding is an expression to obtain the dynamic structure factor from light scattering that takes into account the system turbidity and the peculiarities of the 3D geometry. From 3DDLS measurements in well-controlled solid-like systems of different turbidity, we confirm that our results can be interpreted reasonably well by the theoretical approach described here. Good agreement is found with earlier reported results on similar systems.

Periodically driven ergodic and many-body localized quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ponte, Pedro; Department of Physics and Astronomy, University of Waterloo, ON N2L 3G1; Chandran, Anushya

2015-02-15

We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disorderedmore » spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.« less

Unusual strain glassy phase in Fe doped Ni2Mn1.5In0.5

NASA Astrophysics Data System (ADS)

Nevgi, R.; Priolkar, K. R.

2018-01-01

Fe doped Ni2Mn1.5In0.5, particularly, Ni2Mn1.4Fe0.1In0.5, despite having an incommensurate, modulated 7M martensitic structure at room temperature exhibits frequency dependent behavior of storage modulus and loss which obeys the Vogel-Fulcher law as well as shows ergodicity breaking between zero field cooled and field cooled strain measurements just above the transition temperature. Both frequency dependence and ergodicity breaking are characteristics of a strain glassy phase and occur due to the presence of strain domains which are large enough to present signatures of long range martensitic order in diffraction but are non-interacting with other strain domains due to the presence of Fe impurities.

Natural Divertor Spherical Tokamak Plasmas with bean shape and ergodic limiter

NASA Astrophysics Data System (ADS)

Ribeiro, Celso; Herrera, Julio; Chavez, Esteban; Tritz, Kevin

2013-10-01

The former spherical tokamak (ST) MEDUSA (Madison EDUcation Small Aspect.ratio tokamak, R < 0.14 m, a < 0.10 m, BT < 0.5T, Ip < 40 kA, 3 ms pulse) is being recommissioned in Costa Rica Institute of Technology. The main objectives of the MEDUSA-CR project are training and to clarify several issues in relevant physics for conventional and mainly STs, including beta studies in bean-shaped ST plasmas, transport, heating and current drive via Alfvén wave, and natural divertor STs with ergodic magnetic limiter. We report here improvements in the self-consistency of these equilibrium comparisons and a preliminary study of their MHD stability beta limits. VIE-ITCR, IAEA-CRP contract 17592, National Instruments of Costa Rica.

Ergodicity breaking and ageing of underdamped Brownian dynamics with quenched disorder

NASA Astrophysics Data System (ADS)

Guo, Wei; Li, Yong; Song, Wen-Hua; Du, Lu-Chun

2018-03-01

The dynamics of an underdamped Brownian particle moving in one-dimensional quenched disorder under the action of an external force is investigated. Within the tailored parameter regime, the transiently anomalous diffusion and ergodicity breaking, spanning several orders of magnitude in time, have been obtained. The ageing nature of the system weakens as the dissipation of the system increases for other given parameters. Its origin is ascribed to the highly local heterogeneity of the disorder. Two kinds of approximations (in the stationary state), respectively, for large bias and large damping are derived. These results may be helpful in further understanding the nontrivial response of nonlinear dynamics, and also have potential applications to experiments and activities of biological processes.

Symmetry breaking, mixing, instability, and low-frequency variability in a minimal Lorenz-like system.

PubMed

Lucarini, Valerio; Fraedrich, Klaus

2009-08-01

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec(-1)) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f(3/2) power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Integrability versus Thermalizability in Isolated Quantum Systems

NASA Astrophysics Data System (ADS)

Olshanii, Maxim

2012-02-01

The purpose of this presentation is to assess the status of our understanding of the transition from integrability to thermalizability in isolated quantum systems. In Classical Mechanics, the boundary stripe between the two is relatively sharp: its integrability edge is marked by the appearance of finite Lyapunov's exponents that further converge to a unique value when the ergodicity edge is reached. Classical ergodicity is a universal property: if a system is ergodic, then every observable attains its microcanonical value in the infinite time average over the trajectory. On the contrary, in Quantum Mechanics, Lyapunov's exponents are always zero. Furthermore, since quantum dynamics necessarily invokes coherent superpositions of eigenstates of different energy, projectors to the eigenstates become more relevant; those in turn never thermalize. All of the above indicates that in quantum many-body systems, (a) the integrability-thermalizability transition is smooth, and (b) the degree of thermalizability is not absolute like in classical mechanics, but it is relative to the class of observables of interest. In accordance with these observations, we propose a concrete measure of the degree of quantum thermalizability, consistent with the expected empirical manifestations of it. As a practical application of this measure, we devise a unified recipe for choosing an optimal set of conserved quantities to govern the after-relaxation values of observables, in both integrable quantum systems and in quantum systems in between integrable and thermalizable.

Bi-Exact Groups, Strongly Ergodic Actions and Group Measure Space Type III Factors with No Central Sequence

NASA Astrophysics Data System (ADS)

Houdayer, Cyril; Isono, Yusuke

2016-12-01

We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras {M = B rtimes Γ} arising from arbitrary actions {Γ \\curvearrowright B} of bi-exact discrete groups (e.g. free groups) on amenable von Neumann algebras. We prove a spectral gap rigidity result for the central sequence algebra {N' \\cap M^ω} of any nonamenable von Neumann subalgebra with normal expectation {N subset M}. We use this result to show that for any strongly ergodic essentially free nonsingular action {Γ \\curvearrowright (X, μ)} of any bi-exact countable discrete group on a standard probability space, the corresponding group measure space factor {L^∞(X) rtimes Γ} has no nontrivial central sequence. Using recent results of Boutonnet et al. (Local spectral gap in simple Lie groups and applications, 2015), we construct, for every {0 < λ ≤ 1}, a type {III_λ} strongly ergodic essentially free nonsingular action {F_∞ \\curvearrowright (X_λ, μ_λ)} of the free group {{F}_∞} on a standard probability space so that the corresponding group measure space type {III_λ} factor {L^∞(X_λ, μ_λ) rtimes F_∞} has no nontrivial central sequence by our main result. In particular, we obtain the first examples of group measure space type {III} factors with no nontrivial central sequence.

Broken Ergodicity in MHD Turbulence in a Spherical Domain

NASA Technical Reports Server (NTRS)

Shebalin, John V.; wang, Yifan

2011-01-01

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

The generalized Lyapunov theorem and its application to quantum channels

NASA Astrophysics Data System (ADS)

Burgarth, Daniel; Giovannetti, Vittorio

2007-05-01

We give a simple and physically intuitive necessary and sufficient condition for a map acting on a compact metric space to be mixing (i.e. infinitely many applications of the map transfer any input into a fixed convergency point). This is a generalization of the 'Lyapunov direct method'. First we prove this theorem in topological spaces and for arbitrary continuous maps. Finally we apply our theorem to maps which are relevant in open quantum systems and quantum information, namely quantum channels. In this context, we also discuss the relations between mixing and ergodicity (i.e. the property that there exists only a single input state which is left invariant by a single application of the map) showing that the two are equivalent when the invariant point of the ergodic map is pure.

Effective ergodicity breaking in an exclusion process with varying system length

NASA Astrophysics Data System (ADS)

Schultens, Christoph; Schadschneider, Andreas; Arita, Chikashi

2015-09-01

Stochastic processes of interacting particles in systems with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the exclusive queueing process that can be viewed as a one-dimensional exclusion process with varying length, by introducing Langmuir kinetics. This process can be interpreted as an effective model for a queue that interacts with other queues by allowing incoming and leaving of customers in the bulk. We find surprising indications for breaking of ergodicity in a certain parameter regime, where the asymptotic growth behavior depends on the initial length. We show that a random walk with site-dependent hopping probabilities exhibits qualitatively the same behavior.

Structure of chaotic magnetic field lines in IR-T1 tokamak due to ergodic magnetic limiter

NASA Astrophysics Data System (ADS)

Ahmadi, S.; Salar Elahi, A.; Ghorannevis, M.

2018-03-01

In this paper we have studied an Ergodic Magnetic Limiter (EML) based chaotic magnetic field for transport control in the edge plasma of IR-T1 tokamak. The resonance created by the EML causes perturbation of the equilibrium field line in tokamak and as a result, the field lines are chaotic in the vicinity of the dimerized island chains. Transport barriers are formed in the chaotic field line and actually observe in tokamak with reverse magnetic shear. We used area-preserving non-twist (and twist) Poincaré maps to describe the formation of transport barriers, which are actually features of Hamiltonian systems. This transport barrier is useful in reducing radial diffusion of the field line and thus improving the plasma confinement.

Kinetic control of the coverage of oil droplets by DNA-functionalized colloids

PubMed Central

Joshi, Darshana; Bargteil, Dylan; Caciagli, Alessio; Burelbach, Jerome; Xing, Zhongyang; Nunes, André S.; Pinto, Diogo E. P.; Araújo, Nuno A. M.; Brujic, Jasna; Eiser, Erika

2016-01-01

We report a study of reversible adsorption of DNA-coated colloids on complementary functionalized oil droplets. We show that it is possible to control the surface coverage of oil droplets using colloidal particles by exploiting the fact that, during slow adsorption, compositional arrest takes place well before structural arrest occurs. As a consequence, we can prepare colloid-coated oil droplets with a “frozen” degree of loading but with fully ergodic colloidal dynamics on the droplets. We illustrate the equilibrium nature of the adsorbed colloidal phase by exploring the quasi–two-dimensional phase behavior of the adsorbed colloids under the influence of depletion interactions and present simulations of a simple model that illustrates the nature of the compositional arrest and the structural ergodicity. PMID:27532053

Many-body delocalization with random vector potentials

NASA Astrophysics Data System (ADS)

Cheng, Chen; Mondaini, Rubem

2016-11-01

We study the ergodic properties of excited states in a model of interacting fermions in quasi-one-dimensional chains subjected to a random vector potential. In the noninteracting limit, we show that arbitrarily small values of this complex off-diagonal disorder trigger localization for the whole spectrum; the divergence of the localization length in the single-particle basis is characterized by a critical exponent ν which depends on the energy density being investigated. When short-range interactions are included, the localization is lost, and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields.

Statistical Mechanics of Turbulent Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

MHD Turbulence and Magnetic Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Central limit theorem for recurrent random walks on a strip with bounded potential

NASA Astrophysics Data System (ADS)

Dolgopyat, D.; Goldsheid, I.

2018-07-01

We prove that the recurrent random walk (RW) in random environment (RE) on a strip in bounded potential satisfies the central limit theorem (CLT). The key ingredients of the proof are the analysis of the invariant measure equation and construction of a linearly growing martingale for walks in bounded potential. Our main result implies a complete classification of recurrent i.i.d. RWRE on the strip. Namely the walk either exhibits the Sinai behaviour in the sense that converges, as , to a (random) limit (the Sinai law) or, it satisfies the CLT. Another application of our main result is the CLT for the quasiperiodic environments with Diophantine frequencies in the recurrent case. We complement this result by proving that in the transient case the CLT holds for all uniquely ergodic environments. We also investigate the algebraic structure of the environments satisfying the CLT. In particular, we show that there exists a collection of proper algebraic subvarieties in the space of transition probabilities, such that: • If RE is stationary and ergodic and the transition probabilities are con-centrated on one of subvarieties from our collection then the CLT holds. • If the environment is i.i.d then the above condition is also necessary forthe CLT. All these results are valid for one-dimensional RWRE with bounded jumps as a particular case of the strip model.

Phase-space networks of geometrically frustrated systems.

PubMed

Han, Yilong

2009-11-01

We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.

Psychological methodology will change profoundly due to the necessity to focus on intra-individual variation.

PubMed

Molenaar, Peter C M

2007-03-01

I am in general agreement with Toomela's (Integrative Psychological and Behavioral Science doi:10.1007/s12124-007-9004-0, 2007) plea for an alternative psychological methodology inspired by his description of the German-Austrian orientation. I will argue, however, that this alternative methodology has to be based on the classical ergodic theorems, using state-of-the-art statistical time series analysis of intra-individual variation as its main tool. Some more specific points made by Toomela will be criticized, while for others a more extreme elaboration along the lines indicated by Toomela is proposed.

Scattering General Analysis; ANALISIS GENERAL DE LA DISPERSION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tixaire, A.G.

1962-01-01

A definition of scattering states is given. It is shown that such states must belong to the absolutely continuous part of the spectrum of the total hamiltonian whenever scattering systems are considered. Such embedding may be proper unless the quantum system is physically admissible. The Moller wave operators are analyzed using Abel- and Cesaro-limit theoretical arguments. Von Neumann s ergodic theorem is partially generalized. A rigorous derivation of the Gell-Mann and Goldberger and Lippmann and Schwinger equations is obtained by making use of results on spectral theory, wave function, and eigendifferential concepts contained. (auth)

Optimal state points of the subadditive ergodic theorem

NASA Astrophysics Data System (ADS)

Dai, Xiongping

2011-05-01

Let T\\colon (X,\\mathscr{B},\\mu)\\rightarrow(X,\\mathscr{B},\\mu) be an ergodic measure-preserving Borel measurable transformation of a separable metric space X that is not necessarily compact, and suppose that \\{\\varphi_n\\}_{n\\ge1}\\colon X\\rightarrow{R}\\cup\\{-\\infty\\} is a T-subadditive sequence of \\mathscr{B} -measurable upper-bounded functions. In this paper, we prove that, if the sets D_{\\varphi_n} of phivn-discontinuities are of μ-measure 0 for all n >= 1 and if the growth rates \\[ \\begin{equation*} {\\bvarphi}^*(x):=\\limsup_{n\\to+\\infty}\\frac{1}{n}\\varphi_n(x)<0\\tqs for \\mu-a.e. x\\in X, \\end{equation*} \\] then bold varphi*(x) < 0 for all points x in the basin BT(μ) of (T, μ). We apply this to considering the Oseledets regular points.

Robustness of Many-Body Localization in the Presence of Dissipation

NASA Astrophysics Data System (ADS)

Levi, Emanuele; Heyl, Markus; Lesanovsky, Igor; Garrahan, Juan P.

2016-06-01

Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system—an interacting fermionic chain subject to quenched disorder—in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.

Supervised self-organization of homogeneous swarms using ergodic projections of Markov chains.

PubMed

Chattopadhyay, Ishanu; Ray, Asok

2009-12-01

This paper formulates a self-organization algorithm to address the problem of global behavior supervision in engineered swarms of arbitrarily large population sizes. The swarms considered in this paper are assumed to be homogeneous collections of independent identical finite-state agents, each of which is modeled by an irreducible finite Markov chain. The proposed algorithm computes the necessary perturbations in the local agents' behavior, which guarantees convergence to the desired observed state of the swarm. The ergodicity property of the swarm, which is induced as a result of the irreducibility of the agent models, implies that while the local behavior of the agents converges to the desired behavior only in the time average, the overall swarm behavior converges to the specification and stays there at all times. A simulation example illustrates the underlying concept.

A method for determining the weak statistical stationarity of a random process

NASA Technical Reports Server (NTRS)

Sadeh, W. Z.; Koper, C. A., Jr.

1978-01-01

A method for determining the weak statistical stationarity of a random process is presented. The core of this testing procedure consists of generating an equivalent ensemble which approximates a true ensemble. Formation of an equivalent ensemble is accomplished through segmenting a sufficiently long time history of a random process into equal, finite, and statistically independent sample records. The weak statistical stationarity is ascertained based on the time invariance of the equivalent-ensemble averages. Comparison of these averages with their corresponding time averages over a single sample record leads to a heuristic estimate of the ergodicity of a random process. Specific variance tests are introduced for evaluating the statistical independence of the sample records, the time invariance of the equivalent-ensemble autocorrelations, and the ergodicity. Examination and substantiation of these procedures were conducted utilizing turbulent velocity signals.

A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming.

PubMed

Liu, Jing; Duan, Yongrui; Sun, Min

2017-01-01

This paper introduces a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers (ADMM), and which extends the feasible set of the relaxation factor α of the generalized ADMM to the infinite interval [Formula: see text]. Under the conditions that the objective function is convex and the solution set is nonempty, we establish the convergence results of the proposed method, including the global convergence, the worst-case [Formula: see text] convergence rate in both the ergodic and the non-ergodic senses, where k denotes the iteration counter. Numerical experiments to decode a sparse signal arising in compressed sensing are included to illustrate the efficiency of the new method.

A Markovian model market—Akerlof's lemons and the asymmetry of information

NASA Astrophysics Data System (ADS)

Tilles, Paulo F. C.; Ferreira, Fernando F.; Francisco, Gerson; Pereira, Carlos de B.; Sarti, Flavia M.

2011-07-01

In this work we study an agent based model to investigate the role of asymmetric information degrees for market evolution. This model is quite simple and may be treated analytically since the consumers evaluate the quality of a certain good taking into account only the quality of the last good purchased plus her perceptive capacity β. As a consequence, the system evolves according to a stationary Markov chain. The value of a good offered by the firms increases along with quality according to an exponent α, which is a measure of the technology. It incorporates all the technological capacity of the production systems such as education, scientific development and techniques that change the productivity rates. The technological level plays an important role to explain how the asymmetry of information may affect the market evolution in this model. We observe that, for high technological levels, the market can detect adverse selection. The model allows us to compute the maximum asymmetric information degree before the market collapses. Below this critical point the market evolves during a limited period of time and then dies out completely. When β is closer to 1 (symmetric information), the market becomes more profitable for high quality goods, although high and low quality markets coexist. The maximum asymmetric information level is a consequence of an ergodicity breakdown in the process of quality evaluation.

Matchmaker, Matchmaker, Make Me a Match: Migration of Populations via Marriages in the Past

NASA Astrophysics Data System (ADS)

Lee, Sang Hoon; Ffrancon, Robyn; Abrams, Daniel M.; Kim, Beom Jun; Porter, Mason A.

2014-10-01

The study of human mobility is both of fundamental importance and of great potential value. For example, it can be leveraged to facilitate efficient city planning and improve prevention strategies when faced with epidemics. The newfound wealth of rich sources of data—including banknote flows, mobile phone records, and transportation data—has led to an explosion of attempts to characterize modern human mobility. Unfortunately, the dearth of comparable historical data makes it much more difficult to study human mobility patterns from the past. In this paper, we present an analysis of long-term human migration, which is important for processes such as urbanization and the spread of ideas. We demonstrate that the data record from Korean family books (called "jokbo") can be used to estimate migration patterns via marriages from the past 750 years. We apply two generative models of long-term human mobility to quantify the relevance of geographical information to human marriage records in the data, and we find that the wide variety in the geographical distributions of the clans poses interesting challenges for the direct application of these models. Using the different geographical distributions of clans, we quantify the "ergodicity" of clans in terms of how widely and uniformly they have spread across Korea, and we compare these results to those obtained using surname data from the Czech Republic. To examine population flow in more detail, we also construct and examine a population-flow network between regions. Based on the correlation between ergodicity and migration in Korea, we identify two different types of migration patterns: diffusive and convective. We expect the analysis of diffusive versus convective effects in population flows to be widely applicable to the study of mobility and migration patterns across different cultures.

Understanding the impact of Light cone effect on the EoR/CD 21-cm power spectrum

NASA Astrophysics Data System (ADS)

Datta, Kanan K.; Mondal, Rajesh; Ghara, Raghunath; Bharadwaj, Somnath; Choudhury, T. Roy

2018-05-01

Redshifted HI 21-cm signal from the cosmic dawn and epoch of reionization evolve considerably along the LoS. We study the impact of this evolution (so called the light cone effect) on the HI 21-cm power spectrum. It is found that the LC effect has a significant impact on the 3D power spectrum and the change could be up to a factor of few. The LC effect is particularly strong during the cosmic dawn near the `peaks' and `dips' in the power spectrum when plotted with redshift. We also show that the 3D power spectrum, which could fully describe ergodic and periodic signal, losses out some information regarding the second order statistics of the signal as the EoR/CD 21-cm signal is non-ergodic and non-periodic along the line of sight. We show that the multi-frequency angular power spectrum (MAPS) \\ell (\

Temporal correlation functions of concentration fluctuations: an anomalous case.

PubMed

Lubelski, Ariel; Klafter, Joseph

2008-10-09

We calculate, within the framework of the continuous time random walk (CTRW) model, multiparticle temporal correlation functions of concentration fluctuations (CCF) in systems that display anomalous subdiffusion. The subdiffusion stems from the nonstationary nature of the CTRW waiting times, which also lead to aging and ergodicity breaking. Due to aging, a system of diffusing particles tends to slow down as time progresses, and therefore, the temporal correlation functions strongly depend on the initial time of measurement. As a consequence, time averages of the CCF differ from ensemble averages, displaying therefore ergodicity breaking. We provide a simple example that demonstrates the difference between these two averages, a difference that might be amenable to experimental tests. We focus on the case of ensemble averaging and assume that the preparation time of the system coincides with the starting time of the measurement. Our analytical calculations are supported by computer simulations based on the CTRW model.

Surface-induced dissociation of methanol cations: A non-ergodic process

DOE PAGES

Shukla, Anil K.

2017-09-01

Here, dissociation of methanol molecular cations, CH 3OH +, to CH 2OH + on collision with a self-assembled monolayer surface of fluorinated alkyl thiol on gold 111 crystal has been studied at 12.5 eV collision energy. Two energetically and spatially distinct processes contribute to the dissociation process: one involving loss of very large amount of energy approaching the initial kinetic energy of the primary ions with scattering of fragment ions over a broad angular range between surface normal and surface parallel while the second process results from small amount of energy loss with fragment ions scattered over a narrow angularmore » range close to the surface parallel. There is a third process with relatively small contribution to total dissociation whose characteristics are very similar to the low energy loss process. Finally, these results demonstrate that surface-induced dissociation of methanol cations via hydrogen loss is non-ergodic.« less

Reformulation of time-convolutionless mode-coupling theory near the glass transition

NASA Astrophysics Data System (ADS)

Tokuyama, Michio

2017-10-01

The time-convolutionless mode-coupling theory (TMCT) recently proposed is reformulated under the condition that one of two approximations, which have been used to formulate the original TMCT in addition to the MCT approximations done on a derivation of nonlinear memory function in terms of the intermediate-scattering function, is not employed because it causes unphysical results for intermediate times. The improved TMCT equation is then derived consistently under another approximation. It is first checked that the ergodic to non-ergodic transition obtained by a new equation is exactly the same as that obtained by an old one because the long-time dynamics of both equations coincides with each other. However, it is emphasized that a difference between them appears in the intermediate-time dynamics of physical quantities. Such a difference is explored numerically in the dynamics of a non-Gaussian parameter by employing the Percus-Yevick static structure factor to calculate the nonlinear memory function.

Surface-induced dissociation of methanol cations: A non-ergodic process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shukla, Anil K.

Here, dissociation of methanol molecular cations, CH 3OH +, to CH 2OH + on collision with a self-assembled monolayer surface of fluorinated alkyl thiol on gold 111 crystal has been studied at 12.5 eV collision energy. Two energetically and spatially distinct processes contribute to the dissociation process: one involving loss of very large amount of energy approaching the initial kinetic energy of the primary ions with scattering of fragment ions over a broad angular range between surface normal and surface parallel while the second process results from small amount of energy loss with fragment ions scattered over a narrow angularmore » range close to the surface parallel. There is a third process with relatively small contribution to total dissociation whose characteristics are very similar to the low energy loss process. Finally, these results demonstrate that surface-induced dissociation of methanol cations via hydrogen loss is non-ergodic.« less

Production model in the conditions of unstable demand taking into account the influence of trading infrastructure: Ergodicity and its application

NASA Astrophysics Data System (ADS)

Obrosova, N. K.; Shananin, A. A.

2015-04-01

A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by an attempt to analyze the problems of functioning of low competitive macroeconomic structures. The model is formalized in the form of a Bellman equation, for which a closed-form solution is found. The stochastic process of product stock variations is proved to be ergodic and its final probability distribution is found. Expressions for the average production load and the average product stock are found by analyzing the stochastic process. A system of model equations relating the model variables to official statistical parameters is derived. The model is identified using data from the Fiat and KAMAZ companies. The influence of the credit interest rate on the firm market value assessment and the production load level are analyzed using comparative statics methods.

Large data series: Modeling the usual to identify the unusual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Downing, D.J.; Fedorov, V.V.; Lawkins, W.F.

{open_quotes}Standard{close_quotes} approaches such as regression analysis, Fourier analysis, Box-Jenkins procedure, et al., which handle a data series as a whole, are not useful for very large data sets for at least two reasons. First, even with computer hardware available today, including parallel processors and storage devices, there are no effective means for manipulating and analyzing gigabyte, or larger, data files. Second, in general it can not be assumed that a very large data set is {open_quotes}stable{close_quotes} by the usual measures, like homogeneity, stationarity, and ergodicity, that standard analysis techniques require. Both reasons dictate the necessity to use {open_quotes}local{close_quotes} data analysismore » methods whereby the data is segmented and ordered, where order leads to a sense of {open_quotes}neighbor,{close_quotes} and then analyzed segment by segment. The idea of local data analysis is central to the study reported here.« less

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects

PubMed Central

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity. PMID:27010993

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.

PubMed

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.

Flow and transport in digitized images of Berea sandstone: ergodicity, stationarity and upscaling

NASA Astrophysics Data System (ADS)

Puyguiraud, A.; Dentz, M.; Gouze, P.

2017-12-01

We perform Stokes flow simulations on digitized images of a Berea sandstone sample obtained through micro-tomography imaging and segmentation processes. We obtain accurate information on the transport using a streamline reconstruction algorithm which uses the velocity field obtained from the flow simulation as input data. This technique is based on the method proposed by Pollock (Groundwater, 1988) but employs a quadratic interpolation near the rock mesh cells of the domain similarly to Mostaghimi et al. (SPE, 2012). This allows an accurate resolution of the velocity field near the solid interface which plays an important role on the transport characteristics, such as the probability density of first arrival times and the growth of the mean squared displacement, among others, which exhibit non-Fickian behavior. We analyze Lagrangian and Eulerian velocity statistics and their relation, and then focus on the ergodicity and the stationarity properties of the transport.We analyze the temporal evolution of Lagrangian velocity statistics for different injection conditions, and findd quick convergence to a limiting velocity distribution, indicating the transport to be near-stationary. The equivalence between velocity samplings within and across streamlines, as well as the independency of the statistics on the number of sampled streamlines, lead as to conclude that the transport may be modeled as ergodic.These characteristics then allow us to upscale the 3-dimensional simulations using a 1-dimensional Continuous Time Random Walk model. This model, parametrized by the velocity results and the characteristic correlation length obtained from the above mentioned simulations, is able to efficiently reproduce the results and to predict larger scale behaviors.

Symmetry, Statistics and Structure in MHD Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2007-01-01

Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.

On the Study of Cognitive Bidirectional Relaying with Asymmetric Traffic Demands

NASA Astrophysics Data System (ADS)

Ji, Xiaodong

2015-05-01

In this paper, we consider a cognitive radio network scenario, where two primary users want to exchange information with each other and meanwhile, one secondary node wishes to send messages to a cognitive base station. To meet the target quality of service (QoS) of the primary users and raise the communication opportunity of the secondary nodes, a cognitive bidirectional relaying (BDR) scheme is examined. First, system outage probabilities of conventional direct transmission and BDR schemes are presented. Next, a new system parameter called operating region is defined and calculated, which indicates in which position a secondary node can be a cognitive relay to assist the primary users. Then, a cognitive BDR scheme is proposed, giving a transmission protocol along with a time-slot splitting algorithm between the primary and secondary transmissions. Information-theoretic metric of ergodic capacity is studied for the cognitive BDR scheme to evaluate its performance. Simulation results show that with the proposed scheme, the target QoS of the primary users can be guaranteed, while increasing the communication opportunity for the secondary nodes.

Wireless Energy Harvesting Two-Way Relay Networks with Hardware Impairments.

PubMed

Peng, Chunling; Li, Fangwei; Liu, Huaping

2017-11-13

This paper considers a wireless energy harvesting two-way relay (TWR) network where the relay has energy-harvesting abilities and the effects of practical hardware impairments are taken into consideration. In particular, power splitting (PS) receiver is adopted at relay to harvests the power it needs for relaying the information between the source nodes from the signals transmitted by the source nodes, and hardware impairments is assumed suffered by each node. We analyze the effect of hardware impairments [-20]on both decode-and-forward (DF) relaying and amplify-and-forward (AF) relaying networks. By utilizing the obtained new expressions of signal-to-noise-plus-distortion ratios, the exact analytical expressions of the achievable sum rate and ergodic capacities for both DF and AF relaying protocols are derived. Additionally, the optimal power splitting (OPS) ratio that maximizes the instantaneous achievable sum rate is formulated and solved for both protocols. The performances of DF and AF protocols are evaluated via numerical results, which also show the effects of various network parameters on the system performance and on the OPS ratio design.

Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion

NASA Astrophysics Data System (ADS)

Majda, Andrew J.; Tong, Xin T.

2016-10-01

Turbulence in idealized geophysical flows is a very rich and important topic. The anisotropic effects of explicit deterministic forcing, dispersive effects from rotation due to the β -plane and F-plane, and topography together with random forcing all combine to produce a remarkable number of realistic phenomena. These effects have been studied through careful numerical experiments in the truncated geophysical models. These important results include transitions between coherent jets and vortices, and direct and inverse turbulence cascades as parameters are varied, and it is a contemporary challenge to explain these diverse statistical predictions. Here we contribute to these issues by proving with full mathematical rigor that for any values of the deterministic forcing, the β - and F-plane effects and topography, with minimal stochastic forcing, there is geometric ergodicity for any finite Galerkin truncation. This means that there is a unique smooth invariant measure which attracts all statistical initial data at an exponential rate. In particular, this rigorous statistical theory guarantees that there are no bifurcations to multiple stable and unstable statistical steady states as geophysical parameters are varied in contrast to claims in the applied literature. The proof utilizes a new statistical Lyapunov function to account for enstrophy exchanges between the statistical mean and the variance fluctuations due to the deterministic forcing. It also requires careful proofs of hypoellipticity with geophysical effects and uses geometric control theory to establish reachability. To illustrate the necessity of these conditions, a two-dimensional example is developed which has the square of the Euclidean norm as the Lyapunov function and is hypoelliptic with nonzero noise forcing, yet fails to be reachable or ergodic.

Temporal behavior of the effective diffusion coefficients for transport in heterogeneous saturated aquifers

NASA Astrophysics Data System (ADS)

Suciu, N.; Vamos, C.; Vereecken, H.; Vanderborght, J.; Hardelauf, H.

2003-04-01

When the small scale transport is modeled by a Wiener process and the large scale heterogeneity by a random velocity field, the effective coefficients, Deff, can be decomposed as sums between the local coefficient, D, a contribution of the random advection, Dadv, and a contribution of the randomness of the trajectory of plume center of mass, Dcm: Deff=D+Dadv-Dcm. The coefficient Dadv is similar to that introduced by Taylor in 1921, and more recent works associate it with the thermodynamic equilibrium. The ``ergodic hypothesis'' says that over large time intervals Dcm vanishes and the effect of the heterogeneity is described by Dadv=Deff-D. In this work we investigate numerically the long time behavior of the effective coefficients as well as the validity of the ergodic hypothesis. The transport in every realization of the velocity field is modeled with the Global Random Walk Algorithm, which is able to track as many particles as necessary to achieve a statistically reliable simulation of the process. Averages over realizations are further used to estimate mean coefficients and standard deviations. In order to remain in the frame of most of the theoretical approaches, the velocity field was generated in a linear approximation and the logarithm of the hydraulic conductivity was taken to be exponential decaying correlated with variance equal to 0.1. Our results show that even in these idealized conditions, the effective coefficients tend to asymptotic constant values only when the plume travels thousands of correlations lengths (while the first order theories usually predict Fickian behavior after tens of correlations lengths) and that the ergodicity conditions are still far from being met.

Single-Station Sigma for the Iranian Strong Motion Stations

NASA Astrophysics Data System (ADS)

Zafarani, H.; Soghrat, M. R.

2017-11-01

In development of ground motion prediction equations (GMPEs), the residuals are assumed to have a log-normal distribution with a zero mean and a standard deviation, designated as sigma. Sigma has significant effect on evaluation of seismic hazard for designing important infrastructures such as nuclear power plants and dams. Both aleatory and epistemic uncertainties are involved in the sigma parameter. However, ground-motion observations over long time periods are not available at specific sites and the GMPEs have been derived using observed data from multiple sites for a small number of well-recorded earthquakes. Therefore, sigma is dominantly related to the statistics of the spatial variability of ground motion instead of temporal variability at a single point (ergodic assumption). The main purpose of this study is to reduce the variability of the residuals so as to handle it as epistemic uncertainty. In this regard, it is tried to partially apply the non-ergodic assumption by removing repeatable site effects from total variability of six GMPEs driven from the local, Europe-Middle East and worldwide data. For this purpose, we used 1837 acceleration time histories from 374 shallow earthquakes with moment magnitudes ranging from M w 4.0 to 7.3 recorded at 370 stations with at least two recordings per station. According to estimated single-station sigma for the Iranian strong motion stations, the ratio of event-corrected single-station standard deviation ( Φ ss) to within-event standard deviation ( Φ) is about 0.75. In other words, removing the ergodic assumption on site response resulted in 25% reduction of the within-event standard deviation that reduced the total standard deviation by about 15%.

Ground Motion Uncertainty and Variability (single-station sigma): Insights from Euroseistest, Greece

NASA Astrophysics Data System (ADS)

Ktenidou, O. J.; Roumelioti, Z.; Abrahamson, N. A.; Cotton, F.; Pitilakis, K.

2014-12-01

Despite recent improvements in networks and data, the global aleatory uncertainty (sigma) in GMPEs is still large. One reason is the ergodic approach, where we combine data in space to make up for lack of data in time. By estimating the systematic site response, we can make site-specific GMPEs and use a lower, site-specific uncertainty: single-station sigma. In this study we use the EUROSEISTEST database (http://euroseisdb.civil.auth.gr), which has two distinct advantages: good existing knowledge of site conditions at all stations, and careful relocation of the recorded events. Constraining the site and source parameters as best we can, we minimise the within- and between-events components of the global, ergodic sigma. Following that, knowledge of the site response from empirical and theoretical approaches permits us to move on to single-station sigma. The variability per site is not clearly correlated to the site class. We show that in some cases knowledge of Vs30 is not sufficient, and that site-specific data are needed to capture the response, possibly due to 2D/3D effects from complex geometry. Our values of single-station sigma are low compared to the literature. This may be due to the good ray coverage we have in all directions for small, nearby records. Indeed, our single-station sigma values are similar to published single-path values, which means that they may correspond to a fully -rather than partially- non-ergodic approach. We find larger ground motion variability for short distances and small magnitudes. This may be related to the uncertainty in the depth affecting nearby records more, or to stress drop and causing trade-offs between the source and site terms for small magnitudes.

Nonequilibrium viscosity of glass

NASA Astrophysics Data System (ADS)

Mauro, John C.; Allan, Douglas C.; Potuzak, Marcel

2009-09-01

Since glass is a nonequilibrium material, its properties depend on both composition and thermal history. While most prior studies have focused on equilibrium liquid viscosity, an accurate description of nonequilibrium viscosity is essential for understanding the low temperature dynamics of glass. Departure from equilibrium occurs as a glass-forming system is cooled through the glass transition range. The glass transition involves a continuous breakdown of ergodicity as the system gradually becomes trapped in a subset of the available configurational phase space. At very low temperatures a glass is perfectly nonergodic (or “isostructural”), and the viscosity is described well by an Arrhenius form. However, the behavior of viscosity during the glass transition range itself is not yet understood. In this paper, we address the problem of glass viscosity using the enthalpy landscape model of Mauro and Loucks [Phys. Rev. B 76, 174202 (2007)] for selenium, an elemental glass former. To study a wide range of thermal histories, we compute nonequilibrium viscosity with cooling rates from 10-12 to 1012K/s . Based on these detailed landscape calculations, we propose a simplified phenomenological model capturing the essential physics of glass viscosity. The phenomenological model incorporates an ergodicity parameter that accounts for the continuous breakdown of ergodicity at the glass transition. We show a direct relationship between the nonequilibrium viscosity parameters and the fragility of the supercooled liquid. The nonequilibrium viscosity model is validated against experimental measurements of Corning EAGLE XG™ glass. The measurements are performed using a specially designed beam-bending apparatus capable of accurate nonequilibrium viscosity measurements up to 1016Pas . Using a common set of parameters, the phenomenological model provides an accurate description of EAGLE XG™ viscosity over the full range of measured temperatures and fictive temperatures.

On the implications of the classical ergodic theorems: analysis of developmental processes has to focus on intra-individual variation.

PubMed

Molenaar, Peter C M

2008-01-01

It is argued that general mathematical-statistical theorems imply that standard statistical analysis techniques of inter-individual variation are invalid to investigate developmental processes. Developmental processes have to be analyzed at the level of individual subjects, using time series data characterizing the patterns of intra-individual variation. It is shown that standard statistical techniques based on the analysis of inter-individual variation appear to be insensitive to the presence of arbitrary large degrees of inter-individual heterogeneity in the population. An important class of nonlinear epigenetic models of neural growth is described which can explain the occurrence of such heterogeneity in brain structures and behavior. Links with models of developmental instability are discussed. A simulation study based on a chaotic growth model illustrates the invalidity of standard analysis of inter-individual variation, whereas time series analysis of intra-individual variation is able to recover the true state of affairs. (c) 2007 Wiley Periodicals, Inc.

Rheological observation of glassy dynamics of dilute polymer solutions near the coil-stretch transition in elongational flows.

PubMed

Sridhar, T; Nguyen, D A; Prabhakar, R; Prakash, J Ravi

2007-04-20

It has long been conjectured that the macroscopic dynamics of dilute polymer solutions may exhibit a glasslike slowdown caused by ergodicity breaking, in the vicinity of the coil-stretch transition in elongational flows. We report experimental observations using a filament stretching rheometer that confirm the existence of such glassy states. It is observed that different time-dependent elongational strain-rate profiles lead to a pronounced history dependence and aging effects within a narrow range of strain rates. The results have a direct bearing on the analysis and design of processes employing dilute polymer solutions, such as ink-jet printing, surface coating, and turbulent-drag reduction.

Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation

PubMed Central

Spiechowicz, Jakub; Łuczka, Jerzy; Hänggi, Peter

2016-01-01

We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases. PMID:27492219

Nanoprobe diffusion in entangled polymer solutions: Linear vs. unconcatenated ring chains

NASA Astrophysics Data System (ADS)

Nahali, Negar; Rosa, Angelo

2018-05-01

We employ large-scale molecular dynamics computer simulations to study the problem of nanoprobe diffusion in entangled solutions of linear polymers and unknotted and unconcatenated circular (ring) polymers. By tuning both the diameter of the nanoprobe and the density of the solution, we show that nanoprobes of diameter smaller than the entanglement distance (tube diameter) of the solution display the same (Rouse-like) behavior in solutions of both polymer architectures. Instead, nanoprobes with larger diameters appear to diffuse markedly faster in solutions of rings than in solutions of linear chains. Finally, by analysing the distribution functions of spatial displacements, we find that nanoprobe motion in rings' solutions shows both Gaussian and ergodic behaviors, in all regimes considered, while, in solutions of linear chains, nanoprobes exceeding the size of the tube diameter show a transition to non-Gaussian and non-ergodic motion. Our results emphasize the role of chain architecture in the motion of nanoprobes dispersed in polymer solutions.

Non-thermalization in trapped atomic ion spin chains

NASA Astrophysics Data System (ADS)

Hess, P. W.; Becker, P.; Kaplan, H. B.; Kyprianidis, A.; Lee, A. C.; Neyenhuis, B.; Pagano, G.; Richerme, P.; Senko, C.; Smith, J.; Tan, W. L.; Zhang, J.; Monroe, C.

2017-10-01

Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Non-thermalization in trapped atomic ion spin chains.

PubMed

Hess, P W; Becker, P; Kaplan, H B; Kyprianidis, A; Lee, A C; Neyenhuis, B; Pagano, G; Richerme, P; Senko, C; Smith, J; Tan, W L; Zhang, J; Monroe, C

2017-12-13

Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'. © 2017 The Author(s).

Nonadditive entropy Sq and nonextensive statistical mechanics: Applications in geophysics and elsewhere

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2012-06-01

The celebrated Boltzmann-Gibbs (BG) entropy, S BG = -kΣi p i ln p i, and associated statistical mechanics are essentially based on hypotheses such as ergodicity, i.e., when ensemble averages coincide with time averages. This dynamical simplification occurs in classical systems (and quantum counterparts) whose microscopic evolution is governed by a positive largest Lyapunov exponent (LLE). Under such circumstances, relevant microscopic variables behave, from the probabilistic viewpoint, as (nearly) independent. Many phenomena exist, however, in natural, artificial and social systems (geophysics, astrophysics, biophysics, economics, and others) that violate ergodicity. To cover a (possibly) wide class of such systems, a generalization (nonextensive statistical mechanics) of the BG theory was proposed in 1988. This theory is based on nonadditive entropies such as S_q = kfrac{{1 - sumnolimits_i {p_i^q } }} {{q - 1}}left( {S_1 = S_{BG} } right). Here we comment some central aspects of this theory, and briefly review typical predictions, verifications and applications in geophysics and elsewhere, as illustrated through theoretical, experimental, observational, and computational results.

Stability and instability towards delocalization in many-body localization systems

NASA Astrophysics Data System (ADS)

De Roeck, Wojciech; Huveneers, François

2017-04-01

We propose a theory that describes quantitatively the (in)stability of fully many-body localization (MBL) systems due to ergodic, i.e., delocalized, grains, that can be, for example, due to disorder fluctuations. The theory is based on the ETH hypothesis and elementary notions of perturbation theory. The main idea is that we assume as much chaoticity as is consistent with conservation laws. The theory describes correctly—even without relying on the theory of local integrals of motion (LIOM)—the MBL phase in one dimension at strong disorder. It yields an explicit and quantitative picture of the spatial boundary between localized and ergodic systems. We provide numerical evidence for this picture. When the theory is taken to its extreme logical consequences, it predicts that the MBL phase is destabilised in the long time limit whenever (1) interactions decay slower than exponentially in d =1 and (2) always in d >1 . Finer numerics is required to assess these predictions.

A model relating radiated power and impurity concentrations during Ne, N and Ar injection in Tore Supra

NASA Astrophysics Data System (ADS)

Hogan, J.; Demichelis, C.; Monier-Garbet, P.; Guirlet, R.; Hess, W.; Schunke, B.

2000-10-01

A model combining the MIST (core symmetric) and BBQ (SOL asymmetric) codes is used to study the relation between impurity density and radiated power for representative cases from Tore Supra experiments on strong radiation regimes using the ergodic divertor. Transport predictions of external radiation are compared with observation to estimate the absolute impurity density. BBQ provides the incoming distribution of recycling impurity charge states for the radial transport calculation. The shots studied use the ergodic divertor and high ICRH power. Power is first applied and then the extrinsic impurity (Ne, N or Ar) is injected. Separate time dependent intrinsic (C and O) impurity transport calculations match radiation levels before and during the high power and impurity injection phases. Empirical diffusivities are sought to reproduce the UV (CV R, I lines), CVI Lya, OVIII Lya, Zeff, and horizontal bolometer data. The model has been used to calculate the relative radiative efficiency (radiated power / extrinsically contributed electron) for the sample database.

Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

PubMed

Jeon, Jae-Hyung; Metzler, Ralf

2010-02-01

Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

On the continuing relevance of Mandelbrot's non-ergodic fractional renewal models of 1963 to 1967

NASA Astrophysics Data System (ADS)

Watkins, Nicholas W.

2017-12-01

The problem of "1/f" noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, "1/f" noise and LRD, concepts which are often treated as equivalent. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Random walk to a nonergodic equilibrium concept

NASA Astrophysics Data System (ADS)

Bel, G.; Barkai, E.

2006-01-01

Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a δ function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.

Many-body delocalization with random vector potentials

NASA Astrophysics Data System (ADS)

Cheng, Chen; Mondaini, Rubem

In this talk we present the ergodic properties of excited states in a model of interacting fermions in quasi-one dimensional chains subjected to a random vector potential. In the non-interacting limit, we show that arbitrarily small values of this complex off-diagonal disorder triggers localization for the whole spectrum; the divergence of the localization length in the single particle basis is characterized by a critical exponent ν which depends on the energy density being investigated. However, when short-ranged interactions are included, the localization is lost and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields. This research is financially supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. U1530401 and 11674021). RM also acknowledges support from NSFC (Grant No. 11650110441).

When Time Makes a Difference: Addressing Ergodicity and Complexity in Education

ERIC Educational Resources Information Center

Koopmans, Matthijs

2015-01-01

The detection of complexity in behavioral outcomes often requires an estimation of their variability over a prolonged time spectrum to assess processes of stability and transformation. Conventional scholarship typically relies on time-independent measures, "snapshots", to analyze those outcomes, assuming that group means and their…

Coherence Properties of Strongly Interacting Atomic Vapors in Waveguides

DTIC Science & Technology

2011-12-31

lattice in the mean-field regime [22]. There the goal was to repeat, for our system, the Chirikiov-lzrailev program for Fermi- Pasta -Ulam chain and...define a typical deviation from ergodicity), we introduce a geometric structure— based on the Frobenius or Hilbert-Schmidt inner product—to the space of

Topics in quantum chaos

NASA Astrophysics Data System (ADS)

Jordan, Andrew Noble

2002-09-01

In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

A performance analysis of ensemble averaging for high fidelity turbulence simulations at the strong scaling limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makarashvili, Vakhtang; Merzari, Elia; Obabko, Aleksandr

We analyze the potential performance benefits of estimating expected quantities in large eddy simulations of turbulent flows using true ensembles rather than ergodic time averaging. Multiple realizations of the same flow are simulated in parallel, using slightly perturbed initial conditions to create unique instantaneous evolutions of the flow field. Each realization is then used to calculate statistical quantities. Provided each instance is sufficiently de-correlated, this approach potentially allows considerable reduction in the time to solution beyond the strong scaling limit for a given accuracy. This study focuses on the theory and implementation of the methodology in Nek5000, a massively parallelmore » open-source spectral element code.« less

A performance analysis of ensemble averaging for high fidelity turbulence simulations at the strong scaling limit

DOE PAGES

Makarashvili, Vakhtang; Merzari, Elia; Obabko, Aleksandr; ...

2017-06-07

We analyze the potential performance benefits of estimating expected quantities in large eddy simulations of turbulent flows using true ensembles rather than ergodic time averaging. Multiple realizations of the same flow are simulated in parallel, using slightly perturbed initial conditions to create unique instantaneous evolutions of the flow field. Each realization is then used to calculate statistical quantities. Provided each instance is sufficiently de-correlated, this approach potentially allows considerable reduction in the time to solution beyond the strong scaling limit for a given accuracy. This study focuses on the theory and implementation of the methodology in Nek5000, a massively parallelmore » open-source spectral element code.« less

Sequential evaporation of water molecules from protonated water clusters: measurement of the velocity distributions of the evaporated molecules and statistical analysis.

PubMed

Berthias, F; Feketeová, L; Abdoul-Carime, H; Calvo, F; Farizon, B; Farizon, M; Märk, T D

2018-06-22

Velocity distributions of neutral water molecules evaporated after collision induced dissociation of protonated water clusters H+(H2O)n≤10 were measured using the combined correlated ion and neutral fragment time-of-flight (COINTOF) and velocity map imaging (VMI) techniques. As observed previously, all measured velocity distributions exhibit two contributions, with a low velocity part identified by statistical molecular dynamics (SMD) simulations as events obeying the Maxwell-Boltzmann statistics and a high velocity contribution corresponding to non-ergodic events in which energy redistribution is incomplete. In contrast to earlier studies, where the evaporation of a single molecule was probed, the present study is concerned with events involving the evaporation of up to five water molecules. In particular, we discuss here in detail the cases of two and three evaporated molecules. Evaporation of several water molecules after CID can be interpreted in general as a sequential evaporation process. In addition to the SMD calculations, a Monte Carlo (MC) based simulation was developed allowing the reconstruction of the velocity distribution produced by the evaporation of m molecules from H+(H2O)n≤10 cluster ions using the measured velocity distributions for singly evaporated molecules as the input. The observed broadening of the low-velocity part of the distributions for the evaporation of two and three molecules as compared to the width for the evaporation of a single molecule results from the cumulative recoil velocity of the successive ion residues as well as the intrinsically broader distributions for decreasingly smaller parent clusters. Further MC simulations were carried out assuming that a certain proportion of non-ergodic events is responsible for the first evaporation in such a sequential evaporation series, thereby allowing to model the entire velocity distribution.

A Manifesto on Psychology as Idiographic Science: Bringing the Person Back into Scientific Psychology, This Time Forever

ERIC Educational Resources Information Center

Molenaar, Peter C. M.

2004-01-01

Psychology is focused on variation between cases (interindividual variation). Results thus obtained are considered to be generalizable to the understanding and explanation of variation within single cases (intraindividual variation). It is indicated, however, that the direct consequences of the classical ergodic theorems for psychology and…

A Proposal for Research on Complex Media, Imagining and Uncertainty Quantification

DTIC Science & Technology

2013-11-26

demonstration that the Green’s function for wave propagation in an ergodic cavity can be recovered exactly by cross correlation of signals at two points...the continuation of a project in which we have developed autofocus methods based on a phase space formulation ( Wigner transform) of the array data and

From localization to anomalous diffusion in the dynamics of coupled kicked rotors

NASA Astrophysics Data System (ADS)

Notarnicola, Simone; Iemini, Fernando; Rossini, Davide; Fazio, Rosario; Silva, Alessandro; Russomanno, Angelo

2018-02-01

We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N -coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N -dimensional Anderson model. The thermodynamic limit N →∞ , in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N ≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.

A fast ergodic algorithm for generating ensembles of equilateral random polygons

NASA Astrophysics Data System (ADS)

Varela, R.; Hinson, K.; Arsuaga, J.; Diao, Y.

2009-03-01

Knotted structures are commonly found in circular DNA and along the backbone of certain proteins. In order to properly estimate properties of these three-dimensional structures it is often necessary to generate large ensembles of simulated closed chains (i.e. polygons) of equal edge lengths (such polygons are called equilateral random polygons). However finding efficient algorithms that properly sample the space of equilateral random polygons is a difficult problem. Currently there are no proven algorithms that generate equilateral random polygons with its theoretical distribution. In this paper we propose a method that generates equilateral random polygons in a 'step-wise uniform' way. We prove that this method is ergodic in the sense that any given equilateral random polygon can be generated by this method and we show that the time needed to generate an equilateral random polygon of length n is linear in terms of n. These two properties make this algorithm a big improvement over the existing generating methods. Detailed numerical comparisons of our algorithm with other widely used algorithms are provided.

A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

NASA Astrophysics Data System (ADS)

Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

2018-06-01

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω}. An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

Ideas of Flat and Curved Space in History of Physics

NASA Astrophysics Data System (ADS)

Berezin, Alexander A.

2006-04-01

Since ``everything which is not prohibited is compulsory'' (assigned to Gell-Mann) we can postulate infinite flat Cartesian N-dimensional (N: any integer) space-time (ST) as embedding for any curved ST. Ergodicity raises quest of whether total number of inflationary and/or Everett bubbles (mini-verses) is finite, countably infinite (aleph-zero) or uncountably infinite (aleph-one). Are these bubbles form Gaussian distribution or form some non-random subsetting? Perhaps, communication between mini-verses (idea of D.Deutsch) can be facilitated by a kind of minimax non-local dynamics akin to Fermat principle? (Minimax Principle in Bubble Cosmology). Even such classical effects as magnetism and polarization have some non-local features. Can we go below the Planck length to perhaps Compton wavelength of our ``Hubble's bubble'' (h/Mc = 10 to minus 95 m, if M = 10 to 54 kg)? When talking about time loops and ergodicity (eternal return paradigm) is there some hysterisis in the way quantum states are accessed in ``forward'' or ``reverse'' direction? (reverse direction implies backward causality of J.Wheeler and/or Aristotelian final causation).

Linking density functional and mode coupling models for supercooled liquids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Premkumar, Leishangthem; Bidhoodi, Neeta; Das, Shankar P.

2016-03-28

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicitymore » transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.« less

A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

NASA Astrophysics Data System (ADS)

Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

2018-01-01

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω} . An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

On the distribution of saliency.

PubMed

Berengolts, Alexander; Lindenbaum, Michael

2006-12-01

Detecting salient structures is a basic task in perceptual organization. Saliency algorithms typically mark edge-points with some saliency measure, which grows with the length and smoothness of the curve on which these edge-points lie. Here, we propose a modified saliency estimation mechanism that is based on probabilistically specified grouping cues and on curve length distributions. In this framework, the Shashua and Ullman saliency mechanism may be interpreted as a process for detecting the curve with maximal expected length. Generalized types of saliency naturally follow. We propose several specific generalizations (e.g., gray-level-based saliency) and rigorously derive the limitations on generalized saliency types. We then carry out a probabilistic analysis of expected length saliencies. Using ergodicity and asymptotic analysis, we derive the saliency distributions associated with the main curves and with the rest of the image. We then extend this analysis to finite-length curves. Using the derived distributions, we derive the optimal threshold on the saliency for discriminating between figure and background and bound the saliency-based figure-from-ground performance.

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

NASA Astrophysics Data System (ADS)

Boros, Endre; Elbassioni, Khaled; Gurvich, Vladimir; Makino, Kazuhisa

In this paper, we consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V = V B ∪ V W ∪ V R , E), with local rewards r: E to { R}, and three types of vertices: black V B , white V W , and random V R . The game is played by two players, White and Black: When the play is at a white (black) vertex v, White (Black) selects an outgoing arc (v,u). When the play is at a random vertex v, a vertex u is picked with the given probability p(v,u). In all cases, Black pays White the value r(v,u). The play continues forever, and White aims to maximize (Black aims to minimize) the limiting mean (that is, average) payoff. It was recently shown in [7] that BWR-games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games (SSG's), stochastic parity games, and Markov decision processes. In this paper, we give a new algorithm for solving BWR-games in the ergodic case, that is when the optimal values do not depend on the initial position. Our algorithm solves a BWR-game by reducing it, using a potential transformation, to a canonical form in which the optimal strategies of both players and the value for every initial position are obvious, since a locally optimal move in it is optimal in the whole game. We show that this algorithm is pseudo-polynomial when the number of random nodes is constant. We also provide an almost matching lower bound on its running time, and show that this bound holds for a wider class of algorithms. Let us add that the general (non-ergodic) case is at least as hard as SSG's, for which no pseudo-polynomial algorithm is known.

Local and global approaches to the problem of Poincaré recurrences. Applications in nonlinear dynamics

NASA Astrophysics Data System (ADS)

Anishchenko, V. S.; Boev, Ya. I.; Semenova, N. I.; Strelkova, G. I.

2015-07-01

We review rigorous and numerical results on the statistics of Poincaré recurrences which are related to the modern development of the Poincaré recurrence problem. We analyze and describe the rigorous results which are achieved both in the classical (local) approach and in the recently developed global approach. These results are illustrated by numerical simulation data for simple chaotic and ergodic systems. It is shown that the basic theoretical laws can be applied to noisy systems if the probability measure is ergodic and stationary. Poincaré recurrences are studied numerically in nonautonomous systems. Statistical characteristics of recurrences are analyzed in the framework of the global approach for the cases of positive and zero topological entropy. We show that for the positive entropy, there is a relationship between the Afraimovich-Pesin dimension, Lyapunov exponents and the Kolmogorov-Sinai entropy either without and in the presence of external noise. The case of zero topological entropy is exemplified by numerical results for the Poincare recurrence statistics in the circle map. We show and prove that the dependence of minimal recurrence times on the return region size demonstrates universal properties for the golden and the silver ratio. The behavior of Poincaré recurrences is analyzed at the critical point of Feigenbaum attractor birth. We explore Poincaré recurrences for an ergodic set which is generated in the stroboscopic section of a nonautonomous oscillator and is similar to a circle shift. Based on the obtained results we show how the Poincaré recurrence statistics can be applied for solving a number of nonlinear dynamics issues. We propose and illustrate alternative methods for diagnosing effects of external and mutual synchronization of chaotic systems in the context of the local and global approaches. The properties of the recurrence time probability density can be used to detect the stochastic resonance phenomenon. We also discuss how the fractal dimension of chaotic attractors can be estimated using the Poincaré recurrence statistics.

Dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2017-03-01

In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.

The three-body problem and equivariant Riemannian geometry

NASA Astrophysics Data System (ADS)

Alvarez-Ramírez, M.; García, A.; Meléndez, J.; Reyes-Victoria, J. G.

2017-08-01

We study the planar three-body problem with 1/r2 potential using the Jacobi-Maupertuis metric, making appropriate reductions by Riemannian submersions. We give a different proof of the Gaussian curvature's sign and the completeness of the space reported by Montgomery [Ergodic Theory Dyn. Syst. 25, 921-947 (2005)]. Moreover, we characterize the geodesics contained in great circles.

Interacting with an artificial partner: modeling the role of emotional aspects.

PubMed

Cattinelli, Isabella; Goldwurm, Massimiliano; Borghese, N Alberto

2008-12-01

In this paper we introduce a simple model based on probabilistic finite state automata to describe an emotional interaction between a robot and a human user, or between simulated agents. Based on the agent's personality, attitude, and nature, and on the emotional inputs it receives, the model will determine the next emotional state displayed by the agent itself. The probabilistic and time-varying nature of the model yields rich and dynamic interactions, and an autonomous adaptation to the interlocutor. In addition, a reinforcement learning technique is applied to have one agent drive its partner's behavior toward desired states. The model may also be used as a tool for behavior analysis, by extracting high probability patterns of interaction and by resorting to the ergodic properties of Markov chains.

Texture Analysis of Chaotic Coupled Map Lattices Based Image Encryption Algorithm

NASA Astrophysics Data System (ADS)

Khan, Majid; Shah, Tariq; Batool, Syeda Iram

2014-09-01

As of late, data security is key in different enclosures like web correspondence, media frameworks, therapeutic imaging, telemedicine and military correspondence. In any case, a large portion of them confronted with a few issues, for example, the absence of heartiness and security. In this letter, in the wake of exploring the fundamental purposes of the chaotic trigonometric maps and the coupled map lattices, we have presented the algorithm of chaos-based image encryption based on coupled map lattices. The proposed mechanism diminishes intermittent impact of the ergodic dynamical systems in the chaos-based image encryption. To assess the security of the encoded image of this scheme, the association of two nearby pixels and composition peculiarities were performed. This algorithm tries to minimize the problems arises in image encryption.

The spectral method and the central limit theorem for general Markov chains

NASA Astrophysics Data System (ADS)

Nagaev, S. V.

2017-12-01

We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.

A Nonlinear Transfer Operator Theorem

NASA Astrophysics Data System (ADS)

Pollicott, Mark

2017-02-01

In recent papers, Kenyon et al. (Ergod Theory Dyn Syst 32:1567-1584 2012), and Fan et al. (C R Math Acad Sci Paris 349:961-964 2011, Adv Math 295:271-333 2016) introduced a form of non-linear thermodynamic formalism based on solutions to a non-linear equation using matrices. In this note we consider the more general setting of Hölder continuous functions.

James Clerk Maxwell and the Kinetic Theory of Gases: A Review Based on Recent Historical Studies

ERIC Educational Resources Information Center

Brush, Stephen G.

1971-01-01

Maxwell's four major papers and some shorter publications relating to kinetic theory and statistical mechanics are discussed in the light of subsequent research. Reviews Maxwell's ideas on such topics as velocity, distribution law, the theory of heat conduction, the mechanism of the radiometer effect, the ergodic hypothesis, and his views on the…

Electric-field-temperature phase diagram of Mn-doped Bi{sub 0.5}(Na{sub 0.9}K{sub 0.1}){sub 0.5}TiO{sub 3} ceramics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ehara, Yoshitaka, E-mail: Ehara@ceramics.tu-darmstadt.de; Novak, Nikola; Yasui, Shintaro

2015-12-28

An electric field–temperature (E-T) phase diagram for a lead-free 0.5 mol. % Mn-doped Bi(Na{sub 0.1}K{sub 0.9})TiO{sub 3} ceramics was investigated. The x-ray diffraction, dielectric and polarization measurements revealed relaxor behavior and were used to characterize the stability regions of the non-ergodic relaxor, ergodic relaxor and electric field induced ferroelectric states. As indicated by the polarization–current density profiles, transformation between two electric fields, induced ferroelectric states with opposite polarization direction arise via a two-step process through an intermediate relaxor state. Interplay between the ferroelectric state conversion and intermediate relaxor state is governed by the dynamics of polarization relaxation. The presented E-T phase diagrammore » revealed the effects of the applied electric field and temperature on stability regions. This is of special interest since the Bi{sub 0.5}(Na{sub 0.1}K{sub 0.9}){sub 0.5}TiO{sub 3} ceramics were proposed as a potential piezoceramic material.« less

Multipoint entanglement in disordered systems

NASA Astrophysics Data System (ADS)

Magán, Javier M.; Paganelli, Simone; Oganesyan, Vadim

2017-02-01

We develop an approach to characterize excited states of disordered many-body systems using spatially resolved structures of entanglement. We show that the behavior of the mutual information (MI) between two parties of a many-body system can signal a qualitative difference between thermal and localized phases - MI is finite in insulators while it approaches zero in the thermodynamic limit in the ergodic phase. Related quantities, such as the recently introduced Codification Volume (CV), are shown to be suitable to quantify the correlation length of the system. These ideas are illustrated using prototypical non-interacting wavefunctions of localized and extended particles and then applied to characterize states of strongly excited interacting spin chains. We especially focus on evolution of spatial structure of quantum information between high temperature diffusive and many-body localized (MBL) phases believed to exist in these models. We study MI as a function of disorder strength both averaged over the eigenstates and in time-evolved product states drawn from continuously deformed family of initial states realizable experimentally. As expected, spectral and time-evolved averages coincide inside the ergodic phase and differ significantly outside. We also highlight dispersion among the initial states within the localized phase - some of these show considerable generation and delocalization of quantum information.

Dynamics of hot random quantum spin chains: from anyons to Heisenberg spins

NASA Astrophysics Data System (ADS)

Parameswaran, Siddharth; Potter, Andrew; Vasseur, Romain

2015-03-01

We argue that the dynamics of the random-bond Heisenberg spin chain are ergodic at infinite temperature, in contrast to the many-body localized behavior seen in its random-field counterpart. First, we show that excited-state real-space renormalization group (RSRG-X) techniques suffer from a fatal breakdown of perturbation theory due to the proliferation of large effective spins that grow without bound. We repair this problem by deforming the SU (2) symmetry of the Heisenberg chain to its `anyonic' version, SU(2)k , where the growth of effective spins is truncated at spin S = k / 2 . This enables us to construct a self-consistent RSRG-X scheme that is particularly simple at infinite temperature. Solving the flow equations, we compute the excited-state entanglement and show that it crosses over from volume-law to logarithmic scaling at a length scale ξk ~eαk3 . This reveals that (a) anyon chains have random-singlet-like excited states for any finite k; and (b) ergodicity is restored in the Heisenberg limit k --> ∞ . We acknowledge support from the Quantum Materials program of LBNL (RV), the Gordon and Betty Moore Foundation (ACP), and UC Irvine startup funds (SAP).

Transport in the barrier billiard

NASA Astrophysics Data System (ADS)

Saberi Fathi, S. M.; Ettoumi, W.; Courbage, M.

2016-06-01

We investigate transport properties of an ensemble of particles moving inside an infinite periodic horizontal planar barrier billiard. A particle moves among bars and elastically reflects on them. The motion is a uniform translation along the bars' axis. When the tangent of the incidence angle, α , is fixed and rational, the second moment of the displacement along the orthogonal axis at time n , , is either bounded or asymptotic to K n2 , when n →∞ . For irrational α , the collision map is ergodic and has a family of weakly mixing observables, the transport is not ballistic, and autocorrelation functions decay only in time average, but may not decay for a family of irrational α 's. An exhaustive numerical computation shows that the transport may be superdiffusive or subdiffusive with various rates or bounded strongly depending on the values of α . The variety of transport behaviors sounds reminiscent of well-known behavior of conservative systems. Considering then an ensemble of particles with nonfixed α , the system is nonergodic and certainly not mixing and has anomalous diffusion with self-similar space-time properties. However, we verified that such a system decomposes into ergodic subdynamics breaking self-similarity.

Ergodicity of the Stochastic Nosé-Hoover Heat Bath

NASA Astrophysics Data System (ADS)

Wei Chung Lo,; Baowen Li,

2010-07-01

We numerically study the ergodicity of the stochastic Nosé-Hoover heat bath whose formalism is based on the Markovian approximation for the Nosé-Hoover equation [J. Phys. Soc. Jpn. 77 (2008) 103001]. The approximation leads to a Langevin-like equation driven by a fluctuating dissipative force and multiplicative Gaussian white noise. The steady state solution of the associated Fokker-Planck equation is the canonical distribution. We investigate the dynamics of this method for the case of (i) free particle, (ii) nonlinear oscillators and (iii) lattice chains. We derive the Fokker-Planck equation for the free particle and present approximate analytical solution for the stationary distribution in the context of the Markovian approximation. Numerical simulation results for nonlinear oscillators show that this method results in a Gaussian distribution for the particles velocity. We also employ the method as heat baths to study nonequilibrium heat flow in one-dimensional Fermi-Pasta-Ulam (FPU-β) and Frenkel-Kontorova (FK) lattices. The establishment of well-defined temperature profiles are observed only when the lattice size is large. Our results provide numerical justification for such Markovian approximation for classical single- and many-body systems.

Quasi-equilibria in reduced Liouville spaces.

PubMed

Halse, Meghan E; Dumez, Jean-Nicolas; Emsley, Lyndon

2012-06-14

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.

Relay-aided free-space optical communications using α - μ distribution over atmospheric turbulence channels with misalignment errors

NASA Astrophysics Data System (ADS)

Upadhya, Abhijeet; Dwivedi, Vivek K.; Singh, G.

2018-06-01

In this paper, we have analyzed the performance of dual hop radio frequency (RF)/free-space optical (FSO) fixed gain relay environment confined by atmospheric turbulence induced fading channel over FSO link and modeled using α - μ distribution. The RF hop of the amplify-and-forward scheme undergoes the Rayleigh fading and the proposed system model also considers the pointing error effect on the FSO link. A novel and accurate mathematical expression of the probability density function for a FSO link experiencing α - μ distributed atmospheric turbulence in the presence of pointing error is derived. Further, we have presented analytical expressions of outage probability and bit error rate in terms of Meijer-G function. In addition to this, a useful and mathematically tractable closed-form expression for the end-to-end ergodic capacity of the dual hop scheme in terms of bivariate Fox's H function is derived. The atmospheric turbulence, misalignment errors and various binary modulation schemes for intensity modulation on optical wireless link are considered to yield the results. Finally, we have analyzed each of the three performance metrics for high SNR in order to represent them in terms of elementary functions and the achieved analytical results are supported by computer-based simulations.

The Effects of Land Surface Heating And Roughness Elements on the Structure and Scaling Laws of Atmospheric Boundary Layer Turbulence

NASA Astrophysics Data System (ADS)

Ghannam, Khaled

The atmospheric boundary-layer is the lowest 500-2000 m of the Earth's atmosphere where much of human life and ecosystem services reside. This layer responds to land surface (e.g. buoyancy and roughness elements) and slowly evolving free tropospheric (e.g. temperature and humidity lapse rates) conditions that arguably mediate and modulate biosphere-atmosphere interactions. Such response often results in spatially- and temporally-rich turbulence scales that continue to be the subject of inquiry given their significance to a plethora of applications in environmental sciences and engineering. The work here addresses key aspects of boundary layer turbulence with a focus on the role of roughness elements (vegetation canopies) and buoyancy (surface heating) in modifying the well-studied picture of shear-dominated wall-bounded turbulence. A combination of laboratory channel experiments, field experiments, and numerical simulations are used to explore three distinct aspects of boundary layer turbulence. These are: • The concept of ergodicity in turbulence statistics within canopies: It has been long-recognized that homogeneous and stationary turbulence is ergodic, but less is known about the effects of inhomogeneity introduced by the presence of canopies on the turbulence statistics. A high resolution (temporal and spatial) flume experiment is used here to test the convergence of the time statistics of turbulent scalar concentrations to their ensemble (spatio-temporal) counterpart. The findings indicate that within-canopy scalar statistics have a tendency to be ergodic, mostly in shallow layers (close to canopy top) where the sweeping flow events appear to randomize the statistics. Deeper layers within the canopy are dominated by low-dimensional (quasi-deterministic) von Karman vortices that tend to break ergodicity. • Scaling laws of turbulent velocity spectra and structure functions in near-surface atmospheric turbulence: the existence of a logarithmic scaling in the structure function of the longitudinal and vertical velocity components is examined using five experimental data sets that span the roughness sub-layer above vegetation canopies, the atmospheric surface-layer above a lake and a grass field, and an open channel experiment. The results indicate that close to the wall/surface, this scaling exists in the longitudinal velocity structure function only, with the vertical velocity counterpart exhibiting a much narrower extent of this range due to smaller separation of scales. Phenomenological aspects of the large-scale eddies show that the length scale formed by the friction velocity and energy dissipation acts as a dominant similarity length scale in collapsing experimental data at different heights, mainly due to the imbalance between local production and dissipation of turbulence kinetic energy. • Nonlocal heat transport in the convective atmospheric boundary-layer: Failure of the mean gradient-diffusion (K-theory) in the convective boundary-layer is explored. Using large eddy simulation runs for the atmospheric boundary layer spanning weakly to strongly convective conditions, a generic diagnostic framework that encodes the role of third-order moments in nonlocal heat transport is developed and tested. The premise is that these nonlocal effects are responsible for the inherent asymmetry in vertical transport, and hence the necessary non-Gaussian nature of the joint probability density function (JPDF) of vertical velocity and potential temperature must account for these effects. Conditional sampling (quadrant analysis) of this function and the imbalance between the flow mechanisms of ejections and sweeps are used to characterize this asymmetry, which is then linked to the third-order moments using a cumulant-discard method for the Gram-Charlier expansion of the JPDF. The connection between the ejection-sweep events and the third-order moments shows that the concepts of bottom-up/top-down diffusion, or updraft/downdraft models, are accounted for by various quadrants of this joint probability density function. To this end, future research directions that build upon this work are also discussed.

Semantic Context Detection Using Audio Event Fusion

NASA Astrophysics Data System (ADS)

Chu, Wei-Ta; Cheng, Wen-Huang; Wu, Ja-Ling

2006-12-01

Semantic-level content analysis is a crucial issue in achieving efficient content retrieval and management. We propose a hierarchical approach that models audio events over a time series in order to accomplish semantic context detection. Two levels of modeling, audio event and semantic context modeling, are devised to bridge the gap between physical audio features and semantic concepts. In this work, hidden Markov models (HMMs) are used to model four representative audio events, that is, gunshot, explosion, engine, and car braking, in action movies. At the semantic context level, generative (ergodic hidden Markov model) and discriminative (support vector machine (SVM)) approaches are investigated to fuse the characteristics and correlations among audio events, which provide cues for detecting gunplay and car-chasing scenes. The experimental results demonstrate the effectiveness of the proposed approaches and provide a preliminary framework for information mining by using audio characteristics.

Ergodicity of Traffic Flow with Constant Penetration Rate for Traffic Monitoring via Floating Vehicle Technique

NASA Astrophysics Data System (ADS)

Gunawan, Fergyanto E.; Abbas, Bahtiar S.; Atmadja, Wiedjaja; Yoseph Chandra, Fajar; Agung, Alexander AS; Kusnandar, Erwin

2014-03-01

Traffic congestion in Asian megacities has become extremely worse, and any means to lessen the congestion level is urgently needed. Building an efficient mass transportation system is clearly necessary. However, implementing Intelligent Transportation Systems (ITS) have also been demonstrated effective in various advanced countries. Recently, the floating vehicle technique (FVT), an ITS implementation, has become cost effective to provide real-time traffic information with proliferation of the smartphones. Although many publications have discussed various issues related to the technique, none of them elaborates the discrepancy of a single floating car data (FCD) and the associated fleet data. This work addresses the issue based on an analysis of Sugiyama et al's experimental data. The results indicate that there is an optimum averaging time interval such that the estimated velocity by the FVT reasonably representing the traffic velocity.

Nonergodic property of the space-time coupled CTRW: Dependence on the long-tailed property and correlation

NASA Astrophysics Data System (ADS)

Liu, Jian; Li, Baohe; Chen, Xiaosong

2018-02-01

The space-time coupled continuous time random walk model is a stochastic framework of anomalous diffusion with many applications in physics, geology and biology. In this manuscript the time averaged mean squared displacement and nonergodic property of a space-time coupled continuous time random walk model is studied, which is a prototype of the coupled continuous time random walk presented and researched intensively with various methods. The results in the present manuscript show that the time averaged mean squared displacements increase linearly with lag time which means ergodicity breaking occurs, besides, we find that the diffusion coefficient is intrinsically random which shows both aging and enhancement, the analysis indicates that the either aging or enhancement phenomena are determined by the competition between the correlation exponent γ and the waiting time's long-tailed index α.

Dynamics of a stochastic HIV-1 infection model with logistic growth

NASA Astrophysics Data System (ADS)

Jiang, Daqing; Liu, Qun; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed; Xia, Peiyan

2017-03-01

This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HIV-1 infection model. Then we obtain sufficient conditions for extinction of the infection. The stationary distribution shows that the infection can become persistent in vivo.

Vision-Based Autonomous Sensor-Tasking in Uncertain Adversarial Environments

DTIC Science & Technology

2015-01-02

motion segmentation and change detection in crowd behavior. In particular we investigated Finite Time Lyapunov Exponents, Perron Frobenius Operator and...deformation tensor [11]. On the other hand, eigenfunctions of, the Perron Frobenius operator can be used to detect Almost Invariant Sets (AIS) which are... Perron Frobenius operator. Finally, Figure 1.12d shows the ergodic partitions (EP) obtained based on the eigenfunctions of the Koopman operator

A classification of large amplitude oscillations of a spring-pendulum system

NASA Technical Reports Server (NTRS)

Broucke, R.

1977-01-01

We present a detailed classification of large amplitude oscillations of a non-integrable autonomous system with two degrees of freedom: the spring pendulum system. The classification is made with the method of invariant curves. The results show the importance of three types of motion: periodic, quasi-periodic and semi-ergodic. The numerical results are given for nine different values of the energy constant.

Nonlinear dynamics and predictability in the atmospheric sciences

NASA Technical Reports Server (NTRS)

Ghil, M.; Kimoto, M.; Neelin, J. D.

1991-01-01

Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.

Brief Communication: Understanding disasters and early-warning systems

NASA Astrophysics Data System (ADS)

Castaños, H.; Lomnitz, C.

2014-08-01

This paper discusses some methodological questions on understanding disasters. Destructive earthquakes continue to claim thousands of lives. Tsunamis may be caused by recoil of the upper plate. Darwin's twin-epicenter hypothesis is applied to a theory of tsunamis. The ergodicity hypothesis may help estimating the return periods of extremely rare events. A social science outline on the causation of the Tôhoku nuclear disaster is provided.

Brief Communication: Understanding disasters and early-warning systems

NASA Astrophysics Data System (ADS)

Castaños, H.; Lomnitz, C.

2014-12-01

This paper discusses some methodological questions on understanding disasters. Destructive earthquakes continue to claim thousands of lives. Tsunamis may be caused by recoil of the upper plate. Darwin's twin-epicenter hypothesis is applied to a theory of tsunamis. The ergodicity hypothesis may help to estimate the return periods of extremely rare events. A social science outline on the causation of the Tôhoku nuclear disaster is provided.

Stationary conditions for stochastic differential equations

NASA Technical Reports Server (NTRS)

Adomian, G.; Walker, W. W.

1972-01-01

This is a preliminary study of possible necessary and sufficient conditions to insure stationarity in the solution process for a stochastic differential equation. It indirectly sheds some light on ergodicity properties and shows that the spectral density is generally inadequate as a statistical measure of the solution. Further work is proceeding on a more general theory which gives necessary and sufficient conditions in a form useful for applications.

O the Derivation of the Schroedinger Equation from Stochastic Mechanics.

NASA Astrophysics Data System (ADS)

Wallstrom, Timothy Clarke

The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schrodinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time -integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p^{t} (x,y) > cp(y), and this result is applied to show that the set of spin-1over2 diffusions is uniformly ergodic. In stochastic mechanics, the Bopp-Haag-Dankel diffusions on IR^3times SO(3) are used to represent particles with spin. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp -Haag-Dankel diffusions onto IR^3 converge to a Markovian limit process. This conjecture is proved for the spin-1over2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schrodinger equation, and that there are solutions to the Schrodinger equation which do not satisfy the Guerra-Morato Lagrangian variational principle. These observations are shown to apply equally to other existing formulations of stochastic mechanics, and it is argued that these difficulties represent fundamental inadequacies in the physical foundation of stochastic mechanics.

A statistical mechanical model of economics

NASA Astrophysics Data System (ADS)

Lubbers, Nicholas Edward Williams

Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth vi condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex microstructure effects to develop high-performance materials, but general microstructure quantification is an unsolved problem. Motivated by statistical physics, I envision microstructure as a low-dimensional manifold, and construct this manifold by leveraging multiple machine learning approaches including transfer learning, dimensionality reduction, and computer vision breakthroughs with convolutional neural networks.

Phase transition of Boolean networks with partially nested canalizing functions

NASA Astrophysics Data System (ADS)

Jansen, Kayse; Matache, Mihaela Teodora

2013-07-01

We generate the critical condition for the phase transition of a Boolean network governed by partially nested canalizing functions for which a fraction of the inputs are canalizing, while the remaining non-canalizing inputs obey a complementary threshold Boolean function. Past studies have considered the stability of fully or partially nested canalizing functions paired with random choices of the complementary function. In some of those studies conflicting results were found with regard to the presence of chaotic behavior. Moreover, those studies focus mostly on ergodic networks in which initial states are assumed equally likely. We relax that assumption and find the critical condition for the sensitivity of the network under a non-ergodic scenario. We use the proposed mathematical model to determine parameter values for which phase transitions from order to chaos occur. We generate Derrida plots to show that the mathematical model matches the actual network dynamics. The phase transition diagrams indicate that both order and chaos can occur, and that certain parameters induce a larger range of values leading to order versus chaos. The edge-of-chaos curves are identified analytically and numerically. It is shown that the depth of canalization does not cause major dynamical changes once certain thresholds are reached; these thresholds are fairly small in comparison to the connectivity of the nodes.

Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf

2017-09-01

There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

Disordered crystals from first principles I: Quantifying the configuration space

NASA Astrophysics Data System (ADS)

Kühne, Thomas D.; Prodan, Emil

2018-04-01

This work represents the first chapter of a project on the foundations of first-principle calculations of the electron transport in crystals at finite temperatures. We are interested in the range of temperatures, where most electronic components operate, that is, room temperature and above. The aim is a predictive first-principle formalism that combines ab-initio molecular dynamics and a finite-temperature Kubo-formula for homogeneous thermodynamic phases. The input for this formula is the ergodic dynamical system (Ω , G , dP) defining the thermodynamic crystalline phase, where Ω is the configuration space for the atomic degrees of freedom, G is the space group acting on Ω and dP is the ergodic Gibbs measure relative to the G-action. The present work develops an algorithmic method for quantifying (Ω , G , dP) from first principles. Using the silicon crystal as a working example, we find the Gibbs measure to be extremely well characterized by a multivariate normal distribution, which can be quantified using a small number of parameters. The latter are computed at various temperatures and communicated in the form of a table. Using this table, one can generate large and accurate thermally-disordered atomic configurations to serve, for example, as input for subsequent simulations of the electronic degrees of freedom.

The genealogical decomposition of a matrix population model with applications to the aggregation of stages.

PubMed

Bienvenu, François; Akçay, Erol; Legendre, Stéphane; McCandlish, David M

2017-06-01

Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units. Copyright © 2017 Elsevier Inc. All rights reserved.

The significance of heterogeneity of evolving scales to transport in porous formations

NASA Astrophysics Data System (ADS)

Dagan, Gedeon

1994-12-01

Flow takes place in a heterogeneous formation of spatially variable conductivity, which is modeled as a stationary space random function. To model the variability at the regional scale, the formation is viewed as one of a two-dimensional, horizontal structure. A constant head gradient is applied on the formation boundary such that the flow is uniform in the mean. A plume of inert solute is injected at t = 0 in a volume V0. Under ergodic conditions the plume centroid moves with the constant, mean flow velocity U, and a longitudinal macrodispersion coefficient dL may be defined as half of the time rate of change of the plume second spatial moment with respect to the centroid. For a log-conductivity covariance CY of finite integral scale I, at first order in the variance σY2 and for a travel distance L = Ut ≫ I, dL → σY2UI and transport is coined as Fickian. Ergodicity of the moments is ensured if l ≫ I, where l is the initial plume scale. Some field observations have suggested that heterogeneity may be of evolving scales and that the macrodispersion coefficient may grow with L without reaching a constant limit (anomalous diffusion). To model such a behavior, previous studies have assumed that CY is stationary but of unbounded integral scale with CY ˜ arβ (-1 < β < 0) for large lag r. Under ergodic conditions, it was found that asymptotically dL ˜ aUL1+β, i.e., non-Fickian behavior and anomalous dispersion. The present study claims that an ergodic behavior is not possible for a given finite plume of initial size l, since the basic requirement that l ≫ I cannot be satisfied for CY of unbounded scale. For instance, the centroid does not move any more with U but is random (Figure 1), owing to the large-scale heterogeneity. In such a situation the actual effective dispersion coefficient DL is defined as half the rate of change of the mean second spatial moment with respect to the plume centroid in each realization. This is the accessible entity in a given experiment. We show that in contrast with dL, the behavior of DL is controlled by l and it has the Fickian limit DL ˜ aUl1+β (Figure 3). We also discuss the case in which Y is of stationary increments and is characterized by its variogram γy. Then U and dL can be defined only if γY is truncated (equivalently, an "infrared cutoff" is carried out in the spectrum of Y). However, for a bounded U it is shown that DL depends only on γY. Furthermore, for γY = arβ, DL ˜ aUl2Lβ-1; i.e., dispersion is Fickian for 0 < β < 1, whereas for 1 < β < 2, transport is non-Fickian. Since β < 2, DL cannot grow faster than L = Ut. This is in contrast with a recently proposed model (Neuman, 1990) in which the dispersion coefficient is independent of the plume size and it grows approximately like L1.5.

A methodology for stochastic analysis of share prices as Markov chains with finite states.

PubMed

Mettle, Felix Okoe; Quaye, Enoch Nii Boi; Laryea, Ravenhill Adjetey

2014-01-01

Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data.

Chaos based video encryption using maps and Ikeda time delay system

NASA Astrophysics Data System (ADS)

Valli, D.; Ganesan, K.

2017-12-01

Chaos based cryptosystems are an efficient method to deal with improved speed and highly secured multimedia encryption because of its elegant features, such as randomness, mixing, ergodicity, sensitivity to initial conditions and control parameters. In this paper, two chaos based cryptosystems are proposed: one is the higher-dimensional 12D chaotic map and the other is based on the Ikeda delay differential equation (DDE) suitable for designing a real-time secure symmetric video encryption scheme. These encryption schemes employ a substitution box (S-box) to diffuse the relationship between pixels of plain video and cipher video along with the diffusion of current input pixel with the previous cipher pixel, called cipher block chaining (CBC). The proposed method enhances the robustness against statistical, differential and chosen/known plain text attacks. Detailed analysis is carried out in this paper to demonstrate the security and uniqueness of the proposed scheme.

Topological order, entanglement, and quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Mazáč, Dalimil; Hamma, Alioscia

2012-09-01

We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement-deconfinement transitions in the corresponding Z2 gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed.

Nonlinear Filtering in High Dimension

DTIC Science & Technology

2014-06-02

portion of this thesis deals with controlling the distance between conditional distributions in high dimension, we present a few elementary lemmas that...ergodicity. 14 Chapter 2 Preliminaries This chapter is devoted to introducing some elementary concepts and facts in prob- ability theory that will be...measurable space (E,E) to R̄ := [−∞,+∞], or a subset of it, is E-measurable it if is measurable relative to E and the Borel σ- algebra on R̄. We write

Extended applications of track irregularity probabilistic model and vehicle-slab track coupled model on dynamics of railway systems

NASA Astrophysics Data System (ADS)

Xu, Lei; Zhai, Wanming; Gao, Jianmin

2017-11-01

Track irregularities are inevitably in a process of stochastic evolution due to the uncertainty and continuity of wheel-rail interactions. For depicting the dynamic behaviours of vehicle-track coupling system caused by track random irregularities thoroughly, it is a necessity to develop a track irregularity probabilistic model to simulate rail surface irregularities with ergodic properties on amplitudes, wavelengths and probabilities, and to build a three-dimensional vehicle-track coupled model by properly considering the wheel-rail nonlinear contact mechanisms. In the present study, the vehicle-track coupled model is programmed by combining finite element method with wheel-rail coupling model firstly. Then, in light of the capability of power spectral density (PSD) in characterising amplitudes and wavelengths of stationary random signals, a track irregularity probabilistic model is presented to reveal and simulate the whole characteristics of track irregularity PSD. Finally, extended applications from three aspects, that is, extreme analysis, reliability analysis and response relationships between dynamic indices, are conducted to the evaluation and application of the proposed models.

Data Encoding using Periodic Nano-Optical Features

NASA Astrophysics Data System (ADS)

Vosoogh-Grayli, Siamack

Successful trials have been made through a designed algorithm to quantize, compress and optically encode unsigned 8 bit integer values in the form of images using Nano optical features. The periodicity of the Nano-scale features (Nano-gratings) have been designed and investigated both theoretically and experimentally to create distinct states of variation (three on states and one off state). The use of easy to manufacture and machine readable encoded data in secured authentication media has been employed previously in bar-codes for bi-state (binary) models and in color barcodes for multiple state models. This work has focused on implementing 4 states of variation for unit information through periodic Nano-optical structures that separate an incident wavelength into distinct colors (variation states) in order to create an encoding system. Compared to barcodes and magnetic stripes in secured finite length storage media the proposed system encodes and stores more data. The benefits of multiple states of variation in an encoding unit are 1) increased numerically representable range 2) increased storage density and 3) decreased number of typical set elements for any ergodic or semi-ergodic source that emits these encoding units. A thorough investigation has targeted the effects of the use of multi-varied state Nano-optical features on data storage density and consequent data transmission rates. The results show that use of Nano-optical features for encoding data yields a data storage density of circa 800 Kbits/in2 via the implementation of commercially available high resolution flatbed scanner systems for readout. Such storage density is far greater than commercial finite length secured storage media such as Barcode family with maximum practical density of 1kbits/in2 and highest density magnetic stripe cards with maximum density circa 3 Kbits/in2. The numerically representable range of the proposed encoding unit for 4 states of variation is [0 255]. The number of typical set elements for an ergodic source emitting the optical encoding units compared to a bi-state encoding unit (bit) shows a 36 orders of magnitude decrease for the error probability interval of [0 0.01]. The algorithms for the proposed encoding system have been implemented in MATLAB and the Nano-optical structures have been fabricated using Electron Beam Lithography on optical medium.

The Entropy of Non-Ergodic Complex Systems — a Derivation from First Principles

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Hanel, Rudolf

In information theory the 4 Shannon-Khinchin1,2 (SK) axioms determine Boltzmann Gibbs entropy, S -∑i pilog pi, as the unique entropy. Physics is different from information in the sense that physical systems can be non-ergodic or non-Markovian. To characterize such strongly interacting, statistical systems - complex systems in particular - within a thermodynamical framework it might be necessary to introduce generalized entropies. A series of such entropies have been proposed in the past decades. Until now the understanding of their fundamental origin and their deeper relations to complex systems remains unclear. To clarify the situation we note that non-ergodicity explicitly violates the fourth SK axiom. We show that by relaxing this axiom the entropy generalizes to, S ∑i Γ(d + 1, 1 - c log pi), where Γ is the incomplete Gamma function, and c and d are scaling exponents. All recently proposed entropies compatible with the first 3 SK axioms appear to be special cases. We prove that each statistical system is uniquely characterized by the pair of the two scaling exponents (c, d), which defines equivalence classes for all systems. The corresponding distribution functions are special forms of Lambert-W exponentials containing, as special cases, Boltzmann, stretched exponential and Tsallis distributions (power-laws) - all widely abundant in nature. This derivation is the first ab initio justification for generalized entropies. We next show how the phasespace volume of a system is related to its generalized entropy, and provide a concise criterion when it is not of Boltzmann-Gibbs type but assumes a generalized form. We show that generalized entropies only become relevant when the dynamically (statistically) relevant fraction of degrees of freedom in a system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen. Systems governed by generalized entropies are therefore systems whose phasespace volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for accelerating random walks, and a spin system on a constant-conectancy network. We argue that generalized entropies should be relevant for self-organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.

Observation time scale, free-energy landscapes, and molecular symmetry

PubMed Central

Wales, David J.; Salamon, Peter

2014-01-01

When structures that interconvert on a given time scale are lumped together, the corresponding free-energy surface becomes a function of the observation time. This view is equivalent to grouping structures that are connected by free-energy barriers below a certain threshold. We illustrate this time dependence for some benchmark systems, namely atomic clusters and alanine dipeptide, highlighting the connections to broken ergodicity, local equilibrium, and “feasible” symmetry operations of the molecular Hamiltonian. PMID:24374625

Non-equilibrium theory of arrested spinodal decomposition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olais-Govea, José Manuel; López-Flores, Leticia; Medina-Noyola, Magdaleno

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible relaxation [P. E. Ramŕez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010); 82, 061504 (2010)] is applied to the description of the non-equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermodynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whosemore » high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass transition and from above by the spinodal dynamic arrest line, we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the formation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system.« less

Describing Directional Cell Migration with a Characteristic Directionality Time

PubMed Central

Loosley, Alex J.; O’Brien, Xian M.; Reichner, Jonathan S.; Tang, Jay X.

2015-01-01

Many cell types can bias their direction of locomotion by coupling to external cues. Characteristics such as how fast a cell migrates and the directedness of its migration path can be quantified to provide metrics that determine which biochemical and biomechanical factors affect directional cell migration, and by how much. To be useful, these metrics must be reproducible from one experimental setting to another. However, most are not reproducible because their numerical values depend on technical parameters like sampling interval and measurement error. To address the need for a reproducible metric, we analytically derive a metric called directionality time, the minimum observation time required to identify motion as directionally biased. We show that the corresponding fit function is applicable to a variety of ergodic, directionally biased motions. A motion is ergodic when the underlying dynamical properties such as speed or directional bias do not change over time. Measuring the directionality of nonergodic motion is less straightforward but we also show how this class of motion can be analyzed. Simulations are used to show the robustness of directionality time measurements and its decoupling from measurement errors. As a practical example, we demonstrate the measurement of directionality time, step-by-step, on noisy, nonergodic trajectories of chemotactic neutrophils. Because of its inherent generality, directionality time ought to be useful for characterizing a broad range of motions including intracellular transport, cell motility, and animal migration. PMID:25992908

Microcanonical Szilárd engines beyond the quasistatic regime

NASA Astrophysics Data System (ADS)

Acconcia, Thiago V.; Bonança, Marcus V. S.

2017-12-01

We discuss the possibility of extracting energy from a single thermal bath using microcanonical Szilárd engines operating in finite time. This extends previous works on the topic which are restricted to the quasistatic regime. The feedback protocol is implemented based on linear response predictions of the excess work. It is claimed that the underlying mechanism leading to energy extraction does not violate Liouville's theorem and preserves ergodicity throughout the cycle. We illustrate our results with several examples including an exactly solvable model.

Microcanonical Szilárd engines beyond the quasistatic regime.

PubMed

Acconcia, Thiago V; Bonança, Marcus V S

2017-12-01

We discuss the possibility of extracting energy from a single thermal bath using microcanonical Szilárd engines operating in finite time. This extends previous works on the topic which are restricted to the quasistatic regime. The feedback protocol is implemented based on linear response predictions of the excess work. It is claimed that the underlying mechanism leading to energy extraction does not violate Liouville's theorem and preserves ergodicity throughout the cycle. We illustrate our results with several examples including an exactly solvable model.

Equality of the Spectral and Dynamical Definitions of Reflection

NASA Astrophysics Data System (ADS)

Breuer, Jonathan; Ryckman, Eric; Simon, Barry

2010-04-01

For full-line Jacobi matrices, Schrödinger operators, and CMV matrices, we show that being reflectionless, in the sense of the well-known property of m-functions, is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to x = -∞ as t → -∞ goes entirely to x = ∞ as t → ∞. This allows us to settle a conjecture of Deift and Simon from 1983 regarding ergodic Jacobi matrices.

Sharp Estimates in Ruelle Theorems for Matrix Transfer Operators

NASA Astrophysics Data System (ADS)

Campbell, J.; Latushkin, Y.

A matrix coefficient transfer operator , on the space of -sections of an m-dimensional vector bundle over n-dimensional compact manifold is considered. The spectral radius of is estimated bya; and the essential spectral radius by Here is the set of ergodic f-invariant measures, and for is the measure-theoretic entropy of f, is the largest Lyapunov exponent of the cocycle over f generated by , and is the smallest Lyapunov exponent of the differential of f.

Research in Stochastic Processes.

DTIC Science & Technology

1984-10-01

Handbook of Statistics, Volume 5: Time Series in Time Domain, E.J. Hannan, P.R. Krishnaiah and M.M. Rao, eds., North Holland, 1984, to appear. 5. J.A...designs for time series." S. Cambanis, Handbook of Statistics. Volume 5: Time Series in Time Domain, E.J. Hannan, P.R. Krishnaiah and M.M. Rao, eds... Krishnaiah and M.M. Rao, eds., North Holland, 1984, to appear. 59. "Ergodic properties of stationary stable processes." S. Cambanis, C.D. Hardin, and A

The uncertainty principle and quantum chaos

NASA Technical Reports Server (NTRS)

Chirikov, Boris V.

1993-01-01

The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.

Physical models of polarization mode dispersion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Menyuk, C.R.; Wai, P.K.A.

The effect of randomly varying birefringence on light propagation in optical fibers is studied theoretically in the parameter regime that will be used for long-distance communications. In this regime, the birefringence is large and varies very rapidly in comparison to the nonlinear and dispersive scale lengths. We determine the polarization mode dispersion, and we show that physically realistic models yield the same result for polarization mode dispersion as earlier heuristic models that were introduced by Poole. We also prove an ergodic theorem.

2d Granular Gas in Knudsen Regime and in Microgravity Excited by Vibration: Velocity and Position Distributions

NASA Astrophysics Data System (ADS)

Hou, M.; Liu, R.; Li, Y.; Lu, K.; Garrabos, Y.; Evesque, P.

2009-06-01

Dynamics of quasi-2d dissipative granular gas is studied in microgravity condition (of the order of 10-4 g) in the limit of Knudsen regime. The gas, made of 4 spheres, is confined in a square cell enforced to follow linear sinusoidal vibration in ten different vibration modes. The trajectory of one of the particles is tracked and reconstructed from the 2-hour video data. From statistical analysis, we find that (i) loss due to wall friction is small, (ii) trajectory looks ergodic in space, and (iii) distribution ρ(v) of speed follows an exponential distribution, i.e. ρ(v)≈exp(-v/vxo,yo), with vxo,yo being a characteristic velocity along a direction parallel (y) or perpendicular (x) to vibration direction. This law deviates strongly from the Boltzmann distribution of speed in molecular gas. Comparisons of this result with previous measurements in earth environment, and what was found in 3d cell [1] performed in 10-2 g environment are given.

Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents.

PubMed

Hua, Zhongyun; Yi, Shuang; Zhou, Yicong; Li, Chengqing; Wu, Yue

2018-02-01

Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an -dimensional ( -D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic -D Cat matrices iteratively and then constructs the final -D Cat matrix by performing similarity transformation on one basic -D Cat matrix by the other. Given any number of positive LEs, it can generate an -D HCM with desired hyperchaotic complexity. Two illustrative examples of -D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct -D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity.

Superfluidity and Chaos in low dimensional circuits

PubMed Central

Arwas, Geva; Vardi, Amichay; Cohen, Doron

2015-01-01

The hallmark of superfluidity is the appearance of “vortex states” carrying a quantized metastable circulating current. Considering a unidirectional flow of particles in a ring, at first it appears that any amount of scattering will randomize the velocity, as in the Drude model, and eventually the ergodic steady state will be characterized by a vanishingly small fluctuating current. However, Landau and followers have shown that this is not always the case. If elementary excitations (e.g. phonons) have higher velocity than that of the flow, simple kinematic considerations imply metastability of the vortex state: the energy of the motion cannot dissipate into phonons. On the other hand if this Landau criterion is violated the circulating current can decay. Below we show that the standard Landau and Bogoliubov superfluidity criteria fail in low-dimensional circuits. Proper determination of the superfluidity regime-diagram must account for the crucial role of chaos, an ingredient missing from the conventional stability analysis. Accordingly, we find novel types of superfluidity, associated with irregular or chaotic or breathing vortex states. PMID:26315272

Towards simulating and quantifying the light-cone EoR 21-cm signal

NASA Astrophysics Data System (ADS)

Mondal, Rajesh; Bharadwaj, Somnath; Datta, Kanan K.

2018-02-01

The light-cone (LC) effect causes the Epoch of Reionization (EoR) 21-cm signal T_b (\\hat{n}, ν ) to evolve significantly along the line-of-sight (LoS) direction ν. In the first part of this paper, we present a method to properly incorporate the LC effect in simulations of the EoR 21-cm signal that includes peculiar velocities. Subsequently, we discuss how to quantify the second-order statistics of the EoR 21-cm signal in the presence of the LC effect. We demonstrate that the 3D power spectrum P(k) fails to quantify the entire information because it assumes the signal to be ergodic and periodic, whereas the LC effect breaks these conditions along the LoS. Considering a LC simulation centred at redshift 8 where the mean neutral fraction drops from 0.65 to 0.35 across the box, we find that P(k) misses out ˜ 40 per cent of the information at the two ends of the 17.41 MHz simulation bandwidth. The multifrequency angular power spectrum (MAPS) C_{ℓ}(ν_1,ν_2) quantifies the statistical properties of T_b (\\hat{n}, ν ) without assuming the signal to be ergodic and periodic along the LoS. We expect this to quantify the entire statistical information of the EoR 21-cm signal. We apply MAPS to our LC simulation and present preliminary results for the EoR 21-cm signal.

The emergent Copenhagen interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

Hollowood, Timothy J.

2014-05-01

We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.

A laboratory study of nonlinear changes in the directionality of extreme seas

NASA Astrophysics Data System (ADS)

Latheef, M.; Swan, C.; Spinneken, J.

2017-03-01

This paper concerns the description of surface water waves, specifically nonlinear changes in the directionality. Supporting calculations are provided to establish the best method of directional wave generation, the preferred method of directional analysis and the inputs on which such a method should be based. These calculations show that a random directional method, in which the phasing, amplitude and direction of propagation of individual wave components are chosen randomly, has benefits in achieving the required ergodicity. In terms of analysis procedures, the extended maximum entropy principle, with inputs based upon vector quantities, produces the best description of directionality. With laboratory data describing the water surface elevation and the two horizontal velocity components at a single point, several steep sea states are considered. The results confirm that, as the steepness of a sea state increases, the overall directionality of the sea state reduces. More importantly, it is also shown that the largest waves become less spread or more unidirectional than the sea state as a whole. This provides an important link to earlier descriptions of deterministic wave groups produced by frequency focusing, helps to explain recent field observations and has important practical implications for the design of marine structures and vessels.

Markov chain model for demersal fish catch analysis in Indonesia

NASA Astrophysics Data System (ADS)

Firdaniza; Gusriani, N.

2018-03-01

As an archipelagic country, Indonesia has considerable potential fishery resources. One of the fish resources that has high economic value is demersal fish. Demersal fish is a fish with a habitat in the muddy seabed. Demersal fish scattered throughout the Indonesian seas. Demersal fish production in each Indonesia’s Fisheries Management Area (FMA) varies each year. In this paper we have discussed the Markov chain model for demersal fish yield analysis throughout all Indonesia’s Fisheries Management Area. Data of demersal fish catch in every FMA in 2005-2014 was obtained from Directorate of Capture Fisheries. From this data a transition probability matrix is determined by the number of transitions from the catch that lie below the median or above the median. The Markov chain model of demersal fish catch data was an ergodic Markov chain model, so that the limiting probability of the Markov chain model can be determined. The predictive value of demersal fishing yields was obtained by calculating the combination of limiting probability with average catch results below the median and above the median. The results showed that for 2018 and long-term demersal fishing results in most of FMA were below the median value.

Derivation of the spin-glass order parameter from stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Crisanti, A.; Picco, M.; Ritort, F.

2018-05-01

A fluctuation relation is derived to extract the order parameter function q (x ) in weakly ergodic systems. The relation is based on measuring and classifying entropy production fluctuations according to the value of the overlap q between configurations. For a fixed value of q , entropy production fluctuations are Gaussian distributed allowing us to derive the quasi-FDT so characteristic of aging systems. The theory is validated by extracting the q (x ) in various types of glassy models. It might be generally applicable to other nonequilibrium systems and experimental small systems.

Entropy, Ergodicity, and Stem Cell Multipotency

NASA Astrophysics Data System (ADS)

Ridden, Sonya J.; Chang, Hannah H.; Zygalakis, Konstantinos C.; MacArthur, Ben D.

2015-11-01

Populations of mammalian stem cells commonly exhibit considerable cell-cell variability. However, the functional role of this diversity is unclear. Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that the observed dynamics naturally lie close to a critical state, thereby producing a diverse population that is able to respond rapidly to environmental changes. We propose an information-theoretic interpretation of these results that views cellular multipotency as an instance of maximum entropy statistical inference.

Long Time Quantum Evolution of Observables on Cusp Manifolds

NASA Astrophysics Data System (ADS)

Bonthonneau, Yannick

2016-04-01

The Eisenstein functions {E(s)} are some generalized eigenfunctions of the Laplacian on manifolds with cusps. We give a version of Quantum Unique Ergodicity for them, for {|{I}s| to ∞} and {R}s to d/2} with {{R}s - d/2 ≥ log log |{I}s| / log |{I}s|}. For the purpose of the proof, we build a semi-classical quantization procedure for finite volume manifolds with hyperbolic cusps, adapted to a geometrical class of symbols. We also prove an Egorov Lemma until Ehrenfest times on such manifolds.

Periodic Solution and Stationary Distribution of Stochastic Predator-Prey Models with Higher-Order Perturbation

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing

2018-04-01

In this paper, two stochastic predator-prey models with general functional response and higher-order perturbation are proposed and investigated. For the nonautonomous periodic case of the system, by using Khasminskii's theory of periodic solution, we show that the system admits a nontrivial positive T-periodic solution. For the system disturbed by both white and telegraph noises, sufficient conditions for positive recurrence and the existence of an ergodic stationary distribution to the solutions are established. The existence of stationary distribution implies stochastic weak stability to some extent.

Time's arrow: A numerical experiment

NASA Astrophysics Data System (ADS)

Fowles, G. Richard

1994-04-01

The dependence of time's arrow on initial conditions is illustrated by a numerical example in which plane waves produced by an initial pressure pulse are followed as they are multiply reflected at internal interfaces of a layered medium. Wave interactions at interfaces are shown to be analogous to the retarded and advanced waves of point sources. The model is linear and the calculation is exact and demonstrably time reversible; nevertheless the results show most of the features expected of a macroscopically irreversible system, including the approach to the Maxwell-Boltzmann distribution, ergodicity, and concomitant entropy increase.

Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979

NASA Technical Reports Server (NTRS)

Helleman, R. H. G.

1980-01-01

Papers were presented on turbulence, ergodic and integrable behavior, chaotic maps and flows, chemical and fully developed turbulence, and strange attractors. Specific attention was given to measures describing a turbulent flow, stochastization and collapse of vortex systems, a subharmonic route to turbulent convection, and weakly nonlinear turbulence in a rotating convection layer. The Korteweg-de Vries and Hill equations, plasma transport in three dimensions, a horseshoe in the dynamics of a forced beam, and the explosion of strange attractors exhibited by Duffing's equation were also considered.

Optimal harvesting of a stochastic delay logistic model with Lévy jumps

NASA Astrophysics Data System (ADS)

Qiu, Hong; Deng, Wenmin

2016-10-01

The optimal harvesting problem of a stochastic time delay logistic model with Lévy jumps is considered in this article. We first show that the model has a unique global positive solution and discuss the uniform boundedness of its pth moment with harvesting. Then we prove that the system is globally attractive and asymptotically stable in distribution under our assumptions. Furthermore, we obtain the existence of the optimal harvesting effort by the ergodic method, and then we give the explicit expression of the optimal harvesting policy and maximum yield.

Diffusive mixing and Tsallis entropy

DOE PAGES

O'Malley, Daniel; Vesselinov, Velimir V.; Cushman, John H.

2015-04-29

Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis q-entropy, which is non-additive, was developed as an alternative to the classical entropy for systems which are non-ergodic. A generalization of Brownian motion is provided that maximizes the Tsallis entropy rather than the Boltzmann-Gibbs entropy. This process is driven by a Brownian measure with a random diffusion coefficient. In addition, the distribution of this coefficient is derived as a function of q for 1 < q < 3. Applications to transport in porous media are considered.

Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier

NASA Astrophysics Data System (ADS)

Erdős, L.; Tuyen, D. Q.

1990-06-01

We consider a multidimensional system consisting of a particle of mass M and radius r (molecule), surrounded by an infinite ideal gas of point particles of mass m (atoms). The molecule is confined to the unit ball and interacts with its boundary ( barrier) via elastic collision, while the atoms are not affected by the boundary. We obtain convergence to equilibrium for the molecule from almost every initial distribution on its position and velocity. Furthermore, we prove that the infinite composite system of the molecule and the atoms is Bernoulli.

Dynamics of a stochastic cell-to-cell HIV-1 model with distributed delay

NASA Astrophysics Data System (ADS)

Ji, Chunyan; Liu, Qun; Jiang, Daqing

2018-02-01

In this paper, we consider a stochastic cell-to-cell HIV-1 model with distributed delay. Firstly, we show that there is a global positive solution of this model before exploring its long-time behavior. Then sufficient conditions for extinction of the disease are established. Moreover, we obtain sufficient conditions for the existence of an ergodic stationary distribution of the model by constructing a suitable stochastic Lyapunov function. The stationary distribution implies that the disease is persistent in the mean. Finally, we provide some numerical examples to illustrate theoretical results.

Decentralized learning in Markov games.

PubMed

Vrancx, Peter; Verbeeck, Katja; Nowé, Ann

2008-08-01

Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies.

Why many polymers are so fragile: A new perspective

DOE PAGES

Dalle-Ferrier, C.; Kisliuk, A.; Hong, L.; ...

2016-10-21

Many polymers exhibit much steeper temperature dependence of their structural relaxation time (higher fragility) than liquids of small molecules, and the mechanism of this unusually high fragility in polymers remains a puzzle. To reveal additional hints for understanding the underlying mechanism, we analyzed correlation of many properties of polymers to their fragility on example of model polymer polystyrene with various molecular weights (MWs). Here, we demonstrate that these correlations work for short chains (oligomers), but fail progressively with increase in MW. Our surprising discovery is that the steepness of the temperature dependence (fragility) of the viscosity that is determined bymore » chain relaxation follows the correlations at all molecular weights. These results suggest that the molecular level relaxation still follows the behavior usual for small molecules even in polymers, and its fragility (chain fragility) falls in the range usual for molecular liquids. It is the segmental relaxation that has this unusually high fragility. We also speculate that many polymers cannot reach an ergodic state on the time scale of segmental dynamics due to chain connectivity and rigidity. This leads to sharper decrease in accessible configurational entropy upon cooling and results in steeper temperature dependence of segmental relaxation. Our proposed scenario provides a new important insight into the specifics of polymer dynamics: the role of ergodicity time and length scale. At the end, we suggest that a similar scenario can be applicable also to other molecular systems with slow intra-molecular degrees of freedom and to chemically complex systems where the time scale of chemical fluctuations can be longer than the time scale of structural relaxation.« less

Why many polymers are so fragile: A new perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dalle-Ferrier, C.; Kisliuk, A.; Hong, L.

Many polymers exhibit much steeper temperature dependence of their structural relaxation time (higher fragility) than liquids of small molecules, and the mechanism of this unusually high fragility in polymers remains a puzzle. To reveal additional hints for understanding the underlying mechanism, we analyzed correlation of many properties of polymers to their fragility on example of model polymer polystyrene with various molecular weights (MWs). Here, we demonstrate that these correlations work for short chains (oligomers), but fail progressively with increase in MW. Our surprising discovery is that the steepness of the temperature dependence (fragility) of the viscosity that is determined bymore » chain relaxation follows the correlations at all molecular weights. These results suggest that the molecular level relaxation still follows the behavior usual for small molecules even in polymers, and its fragility (chain fragility) falls in the range usual for molecular liquids. It is the segmental relaxation that has this unusually high fragility. We also speculate that many polymers cannot reach an ergodic state on the time scale of segmental dynamics due to chain connectivity and rigidity. This leads to sharper decrease in accessible configurational entropy upon cooling and results in steeper temperature dependence of segmental relaxation. Our proposed scenario provides a new important insight into the specifics of polymer dynamics: the role of ergodicity time and length scale. At the end, we suggest that a similar scenario can be applicable also to other molecular systems with slow intra-molecular degrees of freedom and to chemically complex systems where the time scale of chemical fluctuations can be longer than the time scale of structural relaxation.« less

The Quest for the Ultimate Anisotropic Banach Space

NASA Astrophysics Data System (ADS)

Baladi, Viviane

2017-02-01

We present a new scale U^{t,s}_p (s<-t<0 and 1≤p <∞) of anisotropic Banach spaces, defined via Paley-Littlewood, on which the transfer operator L_g φ = (g \\cdot φ) circ T^{-1} associated to a hyperbolic dynamical system T has good spectral properties. When p=1 and t is an integer, the spaces are analogous to the "geometric" spaces B^{t,|s+t|} considered by Gouëzel and Liverani (Ergod Theory Dyn Syst 26:189-217, 2006). When p>1 and -1+1/p

Quantifying time-of-flight-resolved optical field dynamics in turbid media with interferometric near-infrared spectroscopy (iNIRS) (Conference Presentation)

NASA Astrophysics Data System (ADS)

Borycki, Dawid; Kholiqov, Oybek; Zhou, Wenjun; Srinivasan, Vivek J.

2017-03-01

Sensing and imaging methods based on the dynamic scattering of coherent light, including laser speckle, laser Doppler, and diffuse correlation spectroscopy quantify scatterer motion using light intensity (speckle) fluctuations. The underlying optical field autocorrelation (OFA), rather than being measured directly, is typically inferred from the intensity autocorrelation (IA) through the Siegert relationship, by assuming that the scattered field obeys Gaussian statistics. In this work, we demonstrate interferometric near-infrared spectroscopy (iNIRS) for measurement of time-of-flight (TOF) resolved field and intensity autocorrelations in fluid tissue phantoms and in vivo. In phantoms, we find a breakdown of the Siegert relationship for short times-of-flight due to a contribution from static paths whose optical field does not decorrelate over experimental time scales, and demonstrate that eliminating such paths by polarization gating restores the validity of the Siegert relationship. Inspired by these results, we developed a method, called correlation gating, for separating the OFA into static and dynamic components. Correlation gating enables more precise quantification of tissue dynamics. To prove this, we show that iNIRS and correlation gating can be applied to measure cerebral hemodynamics of the nude mouse in vivo using dynamically scattered (ergodic) paths and not static (non-ergodic) paths, which may not be impacted by blood. More generally, correlation gating, in conjunction with TOF resolution, enables more precise separation of diffuse and non-diffusive contributions to OFA than is possible with TOF resolution alone. Finally, we show that direct measurements of OFA are statistically more efficient than indirect measurements based on IA.

Finite Beta Boundary Magnetic Fields of NCSX

NASA Astrophysics Data System (ADS)

Grossman, A.; Kaiser, T.; Mioduszewski, P.

2004-11-01

The magnetic field between the plasma surface and wall of the National Compact Stellarator (NCSX), which uses quasi-symmetry to combine the best features of the tokamak and stellarator in a configuration of low aspect ratio is mapped via field line tracing in a range of finite beta in which part of the rotational transform is generated by the bootstrap current. We adopt the methodology developed for W7-X, in which an equilibrium solution is computed by an inverse equilibrium solver based on an energy minimizing variational moments code, VMEC2000[1], which solves directly for the shape of the flux surfaces given the external coils and their currents as well as a bootstrap current provided by a separate transport calculation. The VMEC solution and the Biot-Savart vacuum fields are coupled to the magnetic field solver for finite-beta equilibrium (MFBE2001)[2] code to determine the magnetic field on a 3D grid over a computational domain. It is found that the edge plasma is more stellarator-like, with a complex 3D structure, and less like the ordered 2D symmetric structure of a tokamak. The field lines make a transition from ergodically covering a surface to ergodically covering a volume, as the distance from the last closed magnetic surface is increased. The results are compared with the PIES[3] calculations. [1] S.P. Hirshman et al. Comput. Phys. Commun. 43 (1986) 143. [2] E. Strumberger, et al. Nucl. Fusion 42 (2002) 827. [3] A.H. Reiman and H.S. Greenside, Comput. Phys. Commun. 43, 157 (1986).

Meaningful interpretation of subdiffusive measurements in living cells (crowded environment) by fluorescence fluctuation microscopy.

PubMed

Baumann, Gerd; Place, Robert F; Földes-Papp, Zeno

2010-08-01

In living cell or its nucleus, the motions of molecules are complicated due to the large crowding and expected heterogeneity of the intracellular environment. Randomness in cellular systems can be either spatial (anomalous) or temporal (heterogeneous). In order to separate both processes, we introduce anomalous random walks on fractals that represented crowded environments. We report the use of numerical simulation and experimental data of single-molecule detection by fluorescence fluctuation microscopy for detecting resolution limits of different mobile fractions in crowded environment of living cells. We simulate the time scale behavior of diffusion times tau(D)(tau) for one component, e.g. the fast mobile fraction, and a second component, e.g. the slow mobile fraction. The less the anomalous exponent alpha the higher the geometric crowding of the underlying structure of motion that is quantified by the ratio of the Hausdorff dimension and the walk exponent d(f)/d(w) and specific for the type of crowding generator used. The simulated diffusion time decreases for smaller values of alpha # 1 but increases for a larger time scale tau at a given value of alpha # 1. The effect of translational anomalous motion is substantially greater if alpha differs much from 1. An alpha value close to 1 contributes little to the time dependence of subdiffusive motions. Thus, quantitative determination of molecular weights from measured diffusion times and apparent diffusion coefficients, respectively, in temporal auto- and crosscorrelation analyses and from time-dependent fluorescence imaging data are difficult to interpret and biased in crowded environments of living cells and their cellular compartments; anomalous dynamics on different time scales tau must be coupled with the quantitative analysis of how experimental parameters change with predictions from simulated subdiffusive dynamics of molecular motions and mechanistic models. We first demonstrate that the crowding exponent alpha also determines the resolution of differences in diffusion times between two components in addition to photophysical parameters well-known for normal motion in dilute solution. The resolution limit between two different kinds of single molecule species is also analyzed under translational anomalous motion with broken ergodicity. We apply our theoretical predictions of diffusion times and lower limits for the time resolution of two components to fluorescence images in human prostate cancer cells transfected with GFP-Ago2 and GFP-Ago1. In order to mimic heterogeneous behavior in crowded environments of living cells, we need to introduce so-called continuous time random walks (CTRW). CTRWs were originally performed on regular lattice. This purely stochastic molecule behavior leads to subdiffusive motion with broken ergodicity in our simulations. For the first time, we are able to quantitatively differentiate between anomalous motion without broken ergodicity and anomalous motion with broken ergodicity in time-dependent fluorescence microscopy data sets of living cells. Since the experimental conditions to measure a selfsame molecule over an extended period of time, at which biology is taken place, in living cells or even in dilute solution are very restrictive, we need to perform the time average over a subpopulation of different single molecules of the same kind. For time averages over subpopulations of single molecules, the temporal auto- and crosscorrelation functions are first found. Knowing the crowding parameter alpha for the cell type and cellular compartment type, respectively, the heterogeneous parameter gamma can be obtained from the measurements in the presence of the interacting reaction partner, e.g. ligand, with the same alpha value. The product alpha x gamma = gamma is not a simple fitting parameter in the temporal auto- and two-color crosscorrelation functions because it is related to the proper physical models of anomalous (spatial) and heterogeneous (temporal) randomness in cellular systems.We have already derived an analytical solution gamma for in the special case of gamma = 3/2. In the case of two-color crosscorrelation or/and two-color fluorescence imaging (co-localization experiments), the second component is also a two-color species gr, for example a different molecular complex with an additional ligand. Here, we first show that plausible biological mechanisms from FCS/ FCCS and fluorescence imaging in living cells are highly questionable without proper quantitative physical models of subdiffusive motion and temporal randomness. At best, such quantitative FCS/ FCCS and fluorescence imaging data are difficult to interpret under crowding and heterogeneous conditions. It is challenging to translate proper physical models of anomalous (spatial) and heterogeneous (temporal) randomness in living cells and their cellular compartments like the nucleus into biological models of the cell biological process under study testable by single-molecule approaches. Otherwise, quantitative FCS/FCCS and fluorescence imaging measurements in living cells are not well described and cannot be interpreted in a meaningful way.

Stochastic analysis of multiphase flow in porous media: II. Numerical simulations

NASA Astrophysics Data System (ADS)

Abin, A.; Kalurachchi, J. J.; Kemblowski, M. W.; Chang, C.-M.

1996-08-01

The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, α. These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter α. The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.

Exact Results for the Nonergodicity of d -Dimensional Generalized Lévy Walks

NASA Astrophysics Data System (ADS)

Albers, Tony; Radons, Günter

2018-03-01

We provide analytical results for the ensemble-averaged and time-averaged squared displacement, and the randomness of the latter, in the full two-dimensional parameter space of the d -dimensional generalized Lévy walk introduced by Shlesinger et al. [Phys. Rev. Lett. 58, 1100 (1987), 10.1103/PhysRevLett.58.1100]. In certain regions of the parameter plane, we obtain surprising results such as the divergence of the mean-squared displacements, the divergence of the ergodicity breaking parameter despite a finite mean-squared displacement, and subdiffusion which appears superdiffusive when one only considers time averages.

Observations on the Proper Orthogonal Decomposition

NASA Technical Reports Server (NTRS)

Berkooz, Gal

1992-01-01

The Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L(2) optimal sense. It is used in diverse disciplines from image processing to turbulence. Recently the P.O.D. is receiving much attention as a tool for studying dynamics of systems in infinite dimensional space. This paper reviews the mathematical fundamentals of this theory. Also included are results on the span of the eigenfunction basis, a geometric corollary due to Chebyshev's inequality and a relation between the P.O.D. symmetry and ergodicity.

On the number of infinite geodesics and ground states in disordered systems

NASA Astrophysics Data System (ADS)

Wehr, Jan

1997-04-01

We study first-passage percolation models and their higher dimensional analogs—models of surfaces with random weights. We prove that under very general conditions the number of lines or, in the second case, hypersurfaces which locally minimize the sum of the random weights is with probability one equal to 0 or with probability one equal to +∞. As corollaries we show that in any dimension d≥2 the number of ground states of an Ising ferromagnet with random coupling constants equals (with probability one) 2 or +∞. Proofs employ simple large-deviation estimates and ergodic arguments.

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-10-01

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s < 1, the disease of stochastic autonomous SVIR model will die out exponentially; if R˜0s > 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

The Shock and Vibration Bulletin: Proceedings on the Symposium on ShocK and Vibration (52nd) Held in New Orleans, Louisiana on 26-28 October 1981. Part 4. Fatigue and Random Loading Control, Isolation and Damping

DTIC Science & Technology

1982-05-01

functions for every ergodic ensemble or process, but this frequency for each time-acceleration involves in principle a different kind data input, but...geometries Journal Phys. E: Sci. Instrum. 14, (solid and hollow) are different . 202-207. 5. CONCLUSION It has been shown in principle that tests with a...Center, Huntsville, AL SPACE SIIUI’LE SOLID ROCKE FIOOSTEIt WATER ENTRY CAVITY COLLAPSE LOADS I. T. Keefe and E. A. Rawls , Chrysler Corporation, Slidell

Faithful actions of locally compact quantum groups on classical spaces

NASA Astrophysics Data System (ADS)

Goswami, Debashish; Roy, Sutanu

2017-07-01

We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141-160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well.

Calibration of a universal indicated turbulence system

NASA Technical Reports Server (NTRS)

Chapin, W. G.

1977-01-01

Theoretical and experimental work on a Universal Indicated Turbulence Meter is described. A mathematical transfer function from turbulence input to output indication was developed. A random ergodic process and a Gaussian turbulence distribution were assumed. A calibration technique based on this transfer function was developed. The computer contains a variable gain amplifier to make the system output independent of average velocity. The range over which this independence holds was determined. An optimum dynamic response was obtained for the tubulation between the system pitot tube and pressure transducer by making dynamic response measurements for orifices of various lengths and diameters at the source end.

Spatiotemporal chaos of fractional order logistic equation in nonlinear coupled lattices

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; Wang, Xing-Yuan; Liu, Li-Yan; He, Yi; Liu, Jia

2017-11-01

We investigate a new spatiotemporal dynamics with fractional order differential logistic map and spatial nonlinear coupling. The spatial nonlinear coupling features such as the higher percentage of lattices in chaotic behaviors for most of parameters and none periodic windows in bifurcation diagrams are held, which are more suitable for encryptions than the former adjacent coupled map lattices. Besides, the proposed model has new features such as the wider parameter range and wider range of state amplitude for ergodicity, which contributes a wider range of key space when applied in encryptions. The simulations and theoretical analyses are developed in this paper.

Conformational sampling enhancement of replica exchange molecular dynamics simulations using swarm particle intelligence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamberaj, Hiqmet, E-mail: hkamberaj@ibu.edu.mk

In this paper, we present a new method based on swarm particle social intelligence for use in replica exchange molecular dynamics simulations. In this method, the replicas (representing the different system configurations) are allowed communicating with each other through the individual and social knowledge, in additional to considering them as a collection of real particles interacting through the Newtonian forces. The new method is based on the modification of the equations of motion in such way that the replicas are driven towards the global energy minimum. The method was tested for the Lennard-Jones clusters of N = 4,  5, andmore » 6 atoms. Our results showed that the new method is more efficient than the conventional replica exchange method under the same practical conditions. In particular, the new method performed better on optimizing the distribution of the replicas among the thermostats with time and, in addition, ergodic convergence is observed to be faster. We also introduce a weighted histogram analysis method allowing analyzing the data from simulations by combining data from all of the replicas and rigorously removing the inserted bias.« less

Transient aging in fractional Brownian and Langevin-equation motion.

PubMed

Kursawe, Jochen; Schulz, Johannes; Metzler, Ralf

2013-12-01

Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on t(a) is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.

Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment

NASA Astrophysics Data System (ADS)

Zhao, Yu; Yuan, Sanling

2017-07-01

As well known that the sudden environmental shocks and toxicant can affect the population dynamics of fish species, a mechanistic understanding of how sudden environmental change and toxicant influence the optimal harvesting policy requires development. This paper presents the optimal harvesting of a stochastic two-species competitive model with Lévy noise in a polluted environment, where the Lévy noise is used to describe the sudden climate change. Due to the discontinuity of the Lévy noise, the classical optimal harvesting methods based on the explicit solution of the corresponding Fokker-Planck equation are invalid. The object of this paper is to fill up this gap and establish the optimal harvesting policy. By using of aggregation and ergodic methods, the approximation of the optimal harvesting effort and maximum expectation of sustainable yields are obtained. Numerical simulations are carried out to support these theoretical results. Our analysis shows that the Lévy noise and the mean stress measure of toxicant in organism may affect the optimal harvesting policy significantly.

Conformational sampling enhancement of replica exchange molecular dynamics simulations using swarm particle intelligence

NASA Astrophysics Data System (ADS)

Kamberaj, Hiqmet

2015-09-01

In this paper, we present a new method based on swarm particle social intelligence for use in replica exchange molecular dynamics simulations. In this method, the replicas (representing the different system configurations) are allowed communicating with each other through the individual and social knowledge, in additional to considering them as a collection of real particles interacting through the Newtonian forces. The new method is based on the modification of the equations of motion in such way that the replicas are driven towards the global energy minimum. The method was tested for the Lennard-Jones clusters of N = 4, 5, and 6 atoms. Our results showed that the new method is more efficient than the conventional replica exchange method under the same practical conditions. In particular, the new method performed better on optimizing the distribution of the replicas among the thermostats with time and, in addition, ergodic convergence is observed to be faster. We also introduce a weighted histogram analysis method allowing analyzing the data from simulations by combining data from all of the replicas and rigorously removing the inserted bias.

Many-body localization-delocalization transition in the quantum Sherrington-Kirkpatrick model

NASA Astrophysics Data System (ADS)

Mukherjee, Sudip; Nag, Sabyasachi; Garg, Arti

2018-04-01

We analyze the many-body localization- (MBL) to-delocalization transition in the Sherrington-Kirkpatrick (SK) model of Ising spin glass in the presence of a transverse field Γ . Based on energy-resolved analysis, which is of relevance for a closed quantum system, we show that the quantum SK model has many-body mobility edges separating the MBL phase, which is nonergodic and nonthermal, from the delocalized phase, which is ergodic and thermal. The range of the delocalized regime increases with an increase in the strength of Γ , and eventually for Γ larger than ΓCP the entire many-body spectrum is delocalized. We show that the Renyi entropy is almost independent of the system size in the MBL phase while the delocalized phase shows extensive Renyi entropy. We further obtain the spin-glass transition curve in the energy density ɛ -Γ plane from the collapse of the eigenstate spin susceptibility. We demonstrate that in most of the parameter regime, the spin-glass transition occurs close to the MBL transition, indicating that the spin-glass phase is nonergodic and nonthermal while the paramagnetic phase is delocalized and thermal.

Slow relaxation dynamics of clogs in a vibrated granular silo.

PubMed

Guerrero, B V; Pugnaloni, L A; Lozano, C; Zuriguel, I; Garcimartín, A

2018-04-01

We experimentally explore the vibration-induced unclogging of arches halting the flow in a two-dimensional silo. The endurance of arches is determined by carrying out a survival analysis of their breaking times. By analyzing the dynamics of two morphological variables, we demonstrate that arches evolve toward less regular structures and it seems that there may exist a certain degree of irregularity that the arch reaches before collapsing. Moreover, we put forward that σ (the standard deviation of all angles between consecutive beads) describes faithfully the morphological evolution of the arch. Focusing on long-lasting arches, we study σ calculating its two-time autocorrelation function and its mean-squared displacement. In particular, the apparent logarithmic increase of the correlation and the decrease of the mean-squared displacement of σ when the waiting time is increased reveal a slowing down of the dynamics. This behavior is a clear hallmark of aging phenomena and confirms the lack of ergodicity in the unclogging dynamics. Our findings provide new insights on how an arch tends to destabilize and how the probability that it breaks with a long sustained vibration decreases with time.

Slow relaxation dynamics of clogs in a vibrated granular silo

NASA Astrophysics Data System (ADS)

Guerrero, B. V.; Pugnaloni, L. A.; Lozano, C.; Zuriguel, I.; Garcimartín, A.

2018-04-01

We experimentally explore the vibration-induced unclogging of arches halting the flow in a two-dimensional silo. The endurance of arches is determined by carrying out a survival analysis of their breaking times. By analyzing the dynamics of two morphological variables, we demonstrate that arches evolve toward less regular structures and it seems that there may exist a certain degree of irregularity that the arch reaches before collapsing. Moreover, we put forward that σ (the standard deviation of all angles between consecutive beads) describes faithfully the morphological evolution of the arch. Focusing on long-lasting arches, we study σ calculating its two-time autocorrelation function and its mean-squared displacement. In particular, the apparent logarithmic increase of the correlation and the decrease of the mean-squared displacement of σ when the waiting time is increased reveal a slowing down of the dynamics. This behavior is a clear hallmark of aging phenomena and confirms the lack of ergodicity in the unclogging dynamics. Our findings provide new insights on how an arch tends to destabilize and how the probability that it breaks with a long sustained vibration decreases with time.

Transmembrane protein CD93 diffuses by a continuous time random walk.

NASA Astrophysics Data System (ADS)

Goiko, Maria; de Bruyn, John; Heit, Bryan

Molecular motion within the cell membrane is a poorly-defined process. In this study, we characterized the diffusion of the transmembrane protein CD93. By careful analysis of the dependence of the ensemble-averaged mean squared displacement (EA-MSD, r2) on time t and the ensemble-averaged, time-averaged MSD (EA-TAMSD, δ2) on lag time τ and total measurement time T, we showed that the motion of CD93 is well-described by a continuous-time random walk (CTRW). CD93 tracks were acquired using single particle tracking. The tracks were classified as confined or free, and the behavior of the MSD analyzed. EA-MSDs of both populations grew non-linearly with t, indicative of anomalous diffusion. Their EA-TAMSDs were found to depend on both τ and T, indicating non-ergodicity. Free molecules had r2 tα and δ2 (τ /T 1 - α) , with α 0 . 5 , consistent with a CTRW. Mean maximal excursion analysis supported this result. Confined CD93 had r2 t0 and δ2 (τ / T) α , with α 0 . 3 , consistent with a confined CTRW. CTRWs are described by a series of random jumps interspersed with power-law distributed waiting times, and may arise due to the interactions of CD93 with the endocytic machinery. NSERC.

Multimodal corridor and capacity analysis manual. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1998-12-31

This report presents the results of research carried out under NCHRP Project 8-31, Long-Term Availability of Multimodal Corridor Capacity. The report is presented as a manual on multimodal corridor and capacity analysis. Because transportation-system and corridor capacity for freight and passengers is critical for meeting current and future transportation demand, this manual will provide much needed assistance to a wide range of practitioners, particularly those engaged in performance analysis, capacity management, needs studies, systems planning, and corridor development planning--including major investment studies. It provides information regarding capacity analysis approaches for highways, rail, pipelines, and waterways and presents available options formore » enhancing corridor capacity and performance through various strategies such as new capacity development, freeing up unused capacity, or control of travel demand. Evaluation methods for these options are included.« less

Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models

PubMed Central

Grün, Sonja; Helias, Moritz

2017-01-01

Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition. PMID:28968396

Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models.

PubMed

Rostami, Vahid; Porta Mana, PierGianLuca; Grün, Sonja; Helias, Moritz

2017-10-01

Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition.

A characterization of linearly repetitive cut and project sets

NASA Astrophysics Data System (ADS)

Haynes, Alan; Koivusalo, Henna; Walton, James

2018-02-01

For the development of a mathematical theory which can be used to rigorously investigate physical properties of quasicrystals, it is necessary to understand regularity of patterns in special classes of aperiodic point sets in Euclidean space. In one dimension, prototypical mathematical models for quasicrystals are provided by Sturmian sequences and by point sets generated by substitution rules. Regularity properties of such sets are well understood, thanks mostly to well known results by Morse and Hedlund, and physicists have used this understanding to study one dimensional random Schrödinger operators and lattice gas models. A key fact which plays an important role in these problems is the existence of a subadditive ergodic theorem, which is guaranteed when the corresponding point set is linearly repetitive. In this paper we extend the one-dimensional model to cut and project sets, which generalize Sturmian sequences in higher dimensions, and which are frequently used in mathematical and physical literature as models for higher dimensional quasicrystals. By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with cubical windows. We also prove that these are precisely the collection of such sets which satisfy subadditive ergodic theorems. The results are explicit enough to allow us to apply them to known classical models, and to construct linearly repetitive cut and project sets in all pairs of dimensions and codimensions in which they exist. Research supported by EPSRC grants EP/L001462, EP/J00149X, EP/M023540. HK also gratefully acknowledges the support of the Osk. Huttunen foundation.

Crowding Induces Complex Ergodic Diffusion and Dynamic Elongation of Large DNA Molecules

PubMed Central

Chapman, Cole D.; Gorczyca, Stephanie; Robertson-Anderson, Rae M.

2015-01-01

Despite the ubiquity of molecular crowding in living cells, the effects of crowding on the dynamics of genome-sized DNA are poorly understood. Here, we track single, fluorescent-labeled large DNA molecules (11, 115 kbp) diffusing in dextran solutions that mimic intracellular crowding conditions (0–40%), and determine the effects of crowding on both DNA mobility and conformation. Both DNAs exhibit ergodic Brownian motion and comparable mobility reduction in all conditions; however, crowder size (10 vs. 500 kDa) plays a critical role in the underlying diffusive mechanisms and dependence on crowder concentration. Surprisingly, in 10-kDa dextran, crowder influence saturates at ∼20% with an ∼5× drop in DNA diffusion, in stark contrast to exponentially retarded mobility, coupled to weak anomalous subdiffusion, with increasing concentration of 500-kDa dextran. Both DNAs elongate into lower-entropy states (compared to random coil conformations) when crowded, with elongation states that are gamma distributed and fluctuate in time. However, the broadness of the distribution of states and the time-dependence and length scale of elongation length fluctuations depend on both DNA and crowder size with concentration having surprisingly little impact. Results collectively show that mobility reduction and coil elongation of large crowded DNAs are due to a complex interplay between entropic effects and crowder mobility. Although elongation and initial mobility retardation are driven by depletion interactions, subdiffusive dynamics, and the drastic exponential slowing of DNA, up to ∼300×, arise from the reduced mobility of larger crowders. Our results elucidate the highly important and widely debated effects of cellular crowding on genome-sized DNA. PMID:25762333

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

NASA Astrophysics Data System (ADS)

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

2018-05-01

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 +1 dimensions. We have found that, close to the ground state E ≈0 , discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N , which we compute analytically and numerically, grows exponentially with N for E ≈0 . However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈0 , the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first O (N ) eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N . Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor g (t ), obtained from the connected two-level correlation function of the unfolded spectrum, decays as 1 /t2 for times shorter but comparable to the Thouless time with g (0 ) related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

Formation of Low Symmetry Ordered Phases in Block Polymer Melts

NASA Astrophysics Data System (ADS)

Bates, Frank

Until recently the phase behavior of asymmetric AB diblock copolymers in the melt state was universally accepted as a solved problem: spherical domains packed on a body centered cubic (BCC) lattice. Recent experiments with low molecular weight diblocks have upended this picture, beginning with the discovery of the Frank-Kasper sigma phase in poly(isoprene)- b-poly(lactide) (PI-PLA) followed recently by the identification of a dodecagonal quasicrystal phase (DDQC) as a metastable state that evolves from the supercooled disordered liquid. Self-consistent mean-field theory shows that introducing conformational asymmetry (bA >bB where b is the statistical segment length) opens a window in the phase portrait at fA <<1/2 that supports the formation of various low symmetry ordered phases. However, contrary to the widely accepted mean-field picture, the disordered state near the order-disorder transition (ODT) is highly structured and rapid cooling of this micellar fluid several tens of degrees below the ODT temperature arrests macromolecular chain exchange transitioning the material from an ergodic to non-ergodic state. We have explored the evolution of order following such temperature quenches and during subsequent reheating using synchrotron small-angle X-ray scattering (SAXS) revealing surprising analogies with the behavior of metal alloys. This presentation will associate the formation of ordered low symmetry phases with the concept of sphericity, the tendency for the self-assembled nanoparticles to be spherical in competition with the constraints imposed by periodic and aperiodic packing without voids and subject to the condition of incompressibility. Supported by NSF-DMR-1104368. This work was conducted in collaboration with Kyungtae Kim, Morgan Schulze, Akash Arora, Ronald Lewis, Timothy Gillard, Sangwoo Lee, Kevin Dorfman and Marc Hillmyer.

A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks

PubMed Central

Khammash, Mustafa

2014-01-01

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. PMID:24968191

Thermodynamic phase transitions for Pomeau-Manneville maps

NASA Astrophysics Data System (ADS)

Venegeroles, Roberto

2012-08-01

We study phase transitions in the thermodynamic description of Pomeau-Manneville intermittent maps from the point of view of infinite ergodic theory, which deals with diverging measure dynamical systems. For such systems, we use a distributional limit theorem to provide both a powerful tool for calculating thermodynamic potentials as also an understanding of the dynamic characteristics at each instability phase. In particular, topological pressure and Rényi entropy are calculated exactly for such systems. Finally, we show the connection of the distributional limit theorem with non-Gaussian fluctuations of the algorithmic complexity proposed by Gaspard and Wang [Proc. Natl. Acad. Sci. USA10.1073/pnas.85.13.4591 85, 4591 (1988)].

The threshold of a stochastic avian-human influenza epidemic model with psychological effect

NASA Astrophysics Data System (ADS)

Zhang, Fengrong; Zhang, Xinhong

2018-02-01

In this paper, a stochastic avian-human influenza epidemic model with psychological effect in human population and saturation effect within avian population is investigated. This model describes the transmission of avian influenza among avian population and human population in random environments. For stochastic avian-only system, persistence in the mean and extinction of the infected avian population are studied. For the avian-human influenza epidemic system, sufficient conditions for the existence of an ergodic stationary distribution are obtained. Furthermore, a threshold of this stochastic model which determines the outcome of the disease is obtained. Finally, numerical simulations are given to support the theoretical results.

Blessing and curse of chaos in numerical turbulence simulations

NASA Astrophysics Data System (ADS)

Lee, Jon

1994-03-01

Because of the trajectory instability, time reversal is not possible beyond a certain evolution time and hence the time irreversibility prevails under the finite-accuracy trajectory computation. This therefore provides a practical reconciliation of the dynamic reversibility and macroscopic irreversibility (blessing of chaos). On the other hand, the trajectory instability is also responsible for a limited evolution time, so that finite-accuracy computation would yield a pseudo-orbit which is totally unrelated to the true trajectory (curse of chaos). For the inviscid 2D flow, however, we can accurately compute the long- time average of flow quantities with a pseudo-orbit by invoking the ergodic theorem.

Comment on "Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua".

PubMed

Felderhof, B U

2013-08-01

Recently, a critical test of the Navier-Stokes-Fourier equations for compressible fluid continua was proposed [H. Brenner, Phys. Rev. E 87, 013014 (2013)]. It was shown that the equations of bivelocity hydrodynamics imply that a compressible fluid in an isolated rotating circular cylinder attains a nonequilibrium steady state with a nonuniform temperature increasing radially with distance from the axis. We demonstrate that statistical mechanical arguments, involving Hamiltonian dynamics and ergodicity due to irregularity of the wall, lead instead to a thermal equilibrium state with uniform temperature. This is the situation to be expected in experiment.

Mixing properties of the one-atom maser

NASA Astrophysics Data System (ADS)

Bruneau, Laurent

2014-06-01

We study the relaxation properties of the quantized electromagnetic field in a cavity under repeated interactions with single two-level atoms, so-called one-atom maser. We improve the ergodic results obtained in Bruneau and Pillet (J Stat Phys 134(5-6):1071-1095, 2009) and prove that, whenever the atoms are initially distributed according to the canonical ensemble at temperature , all the invariant states are mixing. Under some non-resonance condition this invariant state is known to be thermal equilibirum at some renormalized temperature and we prove that the mixing is then arbitrarily slow, in other words that there is no lower bound on the relaxation speed.

Ranking and clustering of nodes in networks with smart teleportation

NASA Astrophysics Data System (ADS)

Lambiotte, R.; Rosvall, M.

2012-05-01

Random teleportation is a necessary evil for ranking and clustering directed networks based on random walks. Teleportation enables ergodic solutions, but the solutions must necessarily depend on the exact implementation and parametrization of the teleportation. For example, in the commonly used PageRank algorithm, the teleportation rate must trade off a heavily biased solution with a uniform solution. Here we show that teleportation to links rather than nodes enables a much smoother trade-off and effectively more robust results. We also show that, by not recording the teleportation steps of the random walker, we can further reduce the effect of teleportation with dramatic effects on clustering.

Optimal control strategy for an impulsive stochastic competition system with time delays and jumps

NASA Astrophysics Data System (ADS)

Liu, Lidan; Meng, Xinzhu; Zhang, Tonghua

2017-07-01

Driven by both white and jump noises, a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of two species are established. In addition, we obtain that the system is asymptotically stable in distribution by using ergodic method. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of differential equations. Finally, some numerical simulations are provided to illustrate the theoretical results.

The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

NASA Astrophysics Data System (ADS)

Giordano, C. M.; Cincotta, P. M.

2018-05-01

In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S', estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S' coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.

An accelerated proximal augmented Lagrangian method and its application in compressive sensing.

PubMed

Sun, Min; Liu, Jing

2017-01-01

As a first-order method, the augmented Lagrangian method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable's subproblem to make it more implementable. In this paper, we propose an accelerated PALM with indefinite proximal regularization (PALM-IPR) for convex programming with linear constraints, which generalizes the proximal terms from semi-definite to indefinite. Under mild assumptions, we establish the worst-case [Formula: see text] convergence rate of PALM-IPR in a non-ergodic sense. Finally, numerical results show that our new method is feasible and efficient for solving compressive sensing.

Quantum memories and Landauer's principle

NASA Astrophysics Data System (ADS)

Alicki, Robert

2011-10-01

Two types of arguments concerning (im)possibility of constructing a scalable, exponentially stable quantum memory equipped with Hamiltonian controls are discussed. The first type concerns ergodic properties of open Kitaev models which are considered as promising candidates for such memories. It is shown that, although the 4D Kitaev model provides stable qubit observables, the Hamiltonian control is not possible. The thermodynamical approach leads to the new proposal of the revised version of Landauer's principle and suggests that the existence of quantum memory implies the existence of the perpetuum mobile of the second kind. Finally, a discussion of the stability property of information and its implications is presented.

Markov Chain Ontology Analysis (MCOA)

PubMed Central

2012-01-01

Background Biomedical ontologies have become an increasingly critical lens through which researchers analyze the genomic, clinical and bibliographic data that fuels scientific research. Of particular relevance are methods, such as enrichment analysis, that quantify the importance of ontology classes relative to a collection of domain data. Current analytical techniques, however, remain limited in their ability to handle many important types of structural complexity encountered in real biological systems including class overlaps, continuously valued data, inter-instance relationships, non-hierarchical relationships between classes, semantic distance and sparse data. Results In this paper, we describe a methodology called Markov Chain Ontology Analysis (MCOA) and illustrate its use through a MCOA-based enrichment analysis application based on a generative model of gene activation. MCOA models the classes in an ontology, the instances from an associated dataset and all directional inter-class, class-to-instance and inter-instance relationships as a single finite ergodic Markov chain. The adjusted transition probability matrix for this Markov chain enables the calculation of eigenvector values that quantify the importance of each ontology class relative to other classes and the associated data set members. On both controlled Gene Ontology (GO) data sets created with Escherichia coli, Drosophila melanogaster and Homo sapiens annotations and real gene expression data extracted from the Gene Expression Omnibus (GEO), the MCOA enrichment analysis approach provides the best performance of comparable state-of-the-art methods. Conclusion A methodology based on Markov chain models and network analytic metrics can help detect the relevant signal within large, highly interdependent and noisy data sets and, for applications such as enrichment analysis, has been shown to generate superior performance on both real and simulated data relative to existing state-of-the-art approaches. PMID:22300537

Markov Chain Ontology Analysis (MCOA).

PubMed

Frost, H Robert; McCray, Alexa T

2012-02-03

Biomedical ontologies have become an increasingly critical lens through which researchers analyze the genomic, clinical and bibliographic data that fuels scientific research. Of particular relevance are methods, such as enrichment analysis, that quantify the importance of ontology classes relative to a collection of domain data. Current analytical techniques, however, remain limited in their ability to handle many important types of structural complexity encountered in real biological systems including class overlaps, continuously valued data, inter-instance relationships, non-hierarchical relationships between classes, semantic distance and sparse data. In this paper, we describe a methodology called Markov Chain Ontology Analysis (MCOA) and illustrate its use through a MCOA-based enrichment analysis application based on a generative model of gene activation. MCOA models the classes in an ontology, the instances from an associated dataset and all directional inter-class, class-to-instance and inter-instance relationships as a single finite ergodic Markov chain. The adjusted transition probability matrix for this Markov chain enables the calculation of eigenvector values that quantify the importance of each ontology class relative to other classes and the associated data set members. On both controlled Gene Ontology (GO) data sets created with Escherichia coli, Drosophila melanogaster and Homo sapiens annotations and real gene expression data extracted from the Gene Expression Omnibus (GEO), the MCOA enrichment analysis approach provides the best performance of comparable state-of-the-art methods. A methodology based on Markov chain models and network analytic metrics can help detect the relevant signal within large, highly interdependent and noisy data sets and, for applications such as enrichment analysis, has been shown to generate superior performance on both real and simulated data relative to existing state-of-the-art approaches.

Deterministic or Probabilistic - Robustness or Resilience: How to Respond to Climate Change?

NASA Astrophysics Data System (ADS)

Plag, H.; Earnest, D.; Jules-Plag, S.

2013-12-01

Our response to climate change is dominated by a deterministic approach that emphasizes the interaction between only the natural and the built environment. But in the non-ergodic world of unprecedented climate change, social factors drive recovery from unforeseen Black Swans much more than natural or built ones. Particularly the sea level rise discussion focuses on deterministic predictions, accounting for uncertainties in major driving processes with a set of forcing scenarios and public deliberations on which of the plausible trajectories is most likely. Science focuses on the prediction of future climate change, and policies focus on mitigation of both climate change itself and its impacts. The deterministic approach is based on two basic assumptions: 1) Climate change is an ergodic process; 2) The urban coast is a robust system. Evidence suggests that these assumptions may not hold. Anthropogenic changes are pushing key parameters of the climate system outside of the natural range of variability from the last 1 Million years, creating the potential for environmental Black Swans. A probabilistic approach allows for non-ergodic processes and focuses more on resilience, hence does not depend on the two assumptions. Recent experience with hurricanes revealed threshold limitations of the built environment of the urban coast, which, once exceeded, brought to the forefront the importance of the social fabric and social networking in evaluating resilience. Resilience strongly depends on social capital, and building social capital that can create resilience must be a key element in our response to climate change. Although social capital cannot mitigate hazards, social scientists have found that communities rich in strong norms of cooperation recover more quickly than communities without social capital. There is growing evidence that the built environment can affect the social capital of a community, for example public health and perceptions of public safety. This suggests an intriguing hypothesis: disaster risk reduction programs need to account for whether they also facilitate the public trust, cooperation, and communication needed to recover from a disaster. Our work in the Hampton Roads area, where the probability of hazardous flooding and inundation events exceeding the thresholds of the infrastructure is high, suggests that to facilitate the paradigm shift from the deterministic to a probabilistic approach, natural sciences have to focus on hazard probabilities, while engineering and social sciences have to work together to understand how interactions of the built and social environments impact robustness and resilience. The current science-policy relationship needs to be augmented by social structures that can learn from previous unexpected events. In this response to climate change, science does not have the primary goal to reduce uncertainties and prediction errors, but rather to develop processes that can utilize uncertainties and surprises to increase robustness, strengthen resilience, and reduce fragility of the social systems during times when infrastructure fails.

Analysis of filament statistics in fast camera data on MAST

NASA Astrophysics Data System (ADS)

Farley, Tom; Militello, Fulvio; Walkden, Nick; Harrison, James; Silburn, Scott; Bradley, James

2017-10-01

Coherent filamentary structures have been shown to play a dominant role in turbulent cross-field particle transport [D'Ippolito 2011]. An improved understanding of filaments is vital in order to control scrape off layer (SOL) density profiles and thus control first wall erosion, impurity flushing and coupling of radio frequency heating in future devices. The Elzar code [T. Farley, 2017 in prep.] is applied to MAST data. The code uses information about the magnetic equilibrium to calculate the intensity of light emission along field lines as seen in the camera images, as a function of the field lines' radial and toroidal locations at the mid-plane. In this way a `pseudo-inversion' of the intensity profiles in the camera images is achieved from which filaments can be identified and measured. In this work, a statistical analysis of the intensity fluctuations along field lines in the camera field of view is performed using techniques similar to those typically applied in standard Langmuir probe analyses. These filament statistics are interpreted in terms of the theoretical ergodic framework presented by F. Militello & J.T. Omotani, 2016, in order to better understand how time averaged filament dynamics produce the more familiar SOL density profiles. This work has received funding from the RCUK Energy programme (Grant Number EP/P012450/1), from Euratom (Grant Agreement No. 633053) and from the EUROfusion consortium.

Optimal spectral tracking--adapting to dynamic regime change.

PubMed

Brittain, John-Stuart; Halliday, David M

2011-01-30

Real world data do not always obey the statistical restraints imposed upon them by sophisticated analysis techniques. In spectral analysis for instance, an ergodic process--the interchangeability of temporal for spatial averaging--is assumed for a repeat-trial design. Many evolutionary scenarios, such as learning and motor consolidation, do not conform to such linear behaviour and should be approached from a more flexible perspective. To this end we previously introduced the method of optimal spectral tracking (OST) in the study of trial-varying parameters. In this extension to our work we modify the OST routines to provide an adaptive implementation capable of reacting to dynamic transitions in the underlying system state. In so doing, we generalise our approach to characterise both slow-varying and rapid fluctuations in time-series, simultaneously providing a metric of system stability. The approach is first applied to a surrogate dataset and compared to both our original non-adaptive solution and spectrogram approaches. The adaptive OST is seen to display fast convergence and desirable statistical properties. All three approaches are then applied to a neurophysiological recording obtained during a study on anaesthetic monitoring. Local field potentials acquired from the posterior hypothalamic region of a deep brain stimulation patient undergoing anaesthesia were analysed. The characterisation of features such as response delay, time-to-peak and modulation brevity are considered. Copyright © 2010 Elsevier B.V. All rights reserved.

Asymptotic Time Decay in Quantum Physics: a Selective Review and Some New Results

NASA Astrophysics Data System (ADS)

Marchetti, Domingos H. U.; Wreszinski, Walter F.

2013-05-01

Decay of various quantities (return or survival probability, correlation functions) in time are the basis of a multitude of important and interesting phenomena in quantum physics, ranging from spectral properties, resonances, return and approach to equilibrium, to dynamical stability properties and irreversibility and the "arrow of time" in [Asymptotic Time Decay in Quantum Physics (World Scientific, 2013)]. In this review, we study several types of decay — decay in the average, decay in the Lp-sense, and pointwise decay — of the Fourier-Stieltjes transform of a measure, usually identified with the spectral measure, which appear naturally in different mathematical and physical settings. In particular, decay in the Lp-sense is related both to pointwise decay and to decay in the average and, from a physical standpoint, relates to a rigorous form of the time-energy uncertainty relation. Both decay on the average and in the Lp-sense are related to spectral properties, in particular, absolute continuity of the spectral measure. The study of pointwise decay for singular continuous measures (Rajchman measures) provides a bridge between ergodic theory, number theory and analysis, including the method of stationary phase. The theory is illustrated by some new results in the theory of sparse models.

The Statistical Mechanics of Ideal MHD Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2003-01-01

Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.

Dynamical manifestations of quantum chaos: correlation hole and bulge

NASA Astrophysics Data System (ADS)

Torres-Herrera, E. J.; Santos, Lea F.

2017-10-01

A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Image Encryption Algorithm Based on Hyperchaotic Maps and Nucleotide Sequences Database

PubMed Central

2017-01-01

Image encryption technology is one of the main means to ensure the safety of image information. Using the characteristics of chaos, such as randomness, regularity, ergodicity, and initial value sensitiveness, combined with the unique space conformation of DNA molecules and their unique information storage and processing ability, an efficient method for image encryption based on the chaos theory and a DNA sequence database is proposed. In this paper, digital image encryption employs a process of transforming the image pixel gray value by using chaotic sequence scrambling image pixel location and establishing superchaotic mapping, which maps quaternary sequences and DNA sequences, and by combining with the logic of the transformation between DNA sequences. The bases are replaced under the displaced rules by using DNA coding in a certain number of iterations that are based on the enhanced quaternary hyperchaotic sequence; the sequence is generated by Chen chaos. The cipher feedback mode and chaos iteration are employed in the encryption process to enhance the confusion and diffusion properties of the algorithm. Theoretical analysis and experimental results show that the proposed scheme not only demonstrates excellent encryption but also effectively resists chosen-plaintext attack, statistical attack, and differential attack. PMID:28392799

Many-body localization of bosons in optical lattices

NASA Astrophysics Data System (ADS)

Sierant, Piotr; Zakrzewski, Jakub

2018-04-01

Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.

Uncertainty Analysis of Power Grid Investment Capacity Based on Monte Carlo

NASA Astrophysics Data System (ADS)

Qin, Junsong; Liu, Bingyi; Niu, Dongxiao

By analyzing the influence factors of the investment capacity of power grid, to depreciation cost, sales price and sales quantity, net profit, financing and GDP of the second industry as the dependent variable to build the investment capacity analysis model. After carrying out Kolmogorov-Smirnov test, get the probability distribution of each influence factor. Finally, obtained the grid investment capacity uncertainty of analysis results by Monte Carlo simulation.

Effect of heating on the suppression of tearing modes in tokamaks.

PubMed

Classen, I G J; Westerhof, E; Domier, C W; Donné, A J H; Jaspers, R J E; Luhmann, N C; Park, H K; van de Pol, M J; Spakman, G W; Jakubowski, M W

2007-01-19

The suppression of (neoclassical) tearing modes is of great importance for the success of future fusion reactors like ITER. Electron cyclotron waves can suppress islands, both by driving noninductive current in the island region and by heating the island, causing a perturbation to the Ohmic plasma current. This Letter reports on experiments on the TEXTOR tokamak, investigating the effect of heating, which is usually neglected. The unique set of tools available on TEXTOR, notably the dynamic ergodic divertor to create islands with a fully known driving term, and the electron cyclotron emission imaging diagnostic to provide detailed 2D electron temperature information, enables a detailed study of the suppression process and a comparison with theory.

Quantum phase slips: from condensed matter to ultracold quantum gases.

PubMed

D'Errico, C; Abbate, S Scaffidi; Modugno, G

2017-12-13

Quantum phase slips (QPS) are the primary excitations in one-dimensional superfluids and superconductors at low temperatures. They have been well characterized in most condensed-matter systems, and signatures of their existence have been recently observed in superfluids based on quantum gases too. In this review, we briefly summarize the main results obtained on the investigation of phase slips from superconductors to quantum gases. In particular, we focus our attention on recent experimental results of the dissipation in one-dimensional Bose superfluids flowing along a shallow periodic potential, which show signatures of QPS.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'. © 2017 The Author(s).

Steady States, Fluctuation-Dissipation Theorems and Homogenization for Reversible Diffusions in a Random Environment

NASA Astrophysics Data System (ADS)

Mathieu, P.; Piatnitski, A.

2018-04-01

Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle, we introduce the notions of steady state and weak steady state. We establish the continuity of weak steady states for an ergodic and uniformly elliptic environment. When the environment has finite range of dependence, we prove the existence of the steady state and weak steady state and compute its derivative at a vanishing force. Thus we obtain a complete `fluctuation-dissipation Theorem' in this context as well as the continuity of the effective variance.

Dimer motion on a periodic substrate: spontaneous symmetry breaking and absolute negative mobility.

PubMed

Speer, David; Eichhorn, Ralf; Evstigneev, Mykhaylo; Reimann, Peter

2012-06-01

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.

Unbiased Sampling of Globular Lattice Proteins in Three Dimensions

NASA Astrophysics Data System (ADS)

Jacobsen, Jesper Lykke

2008-03-01

We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular proteins, upon adding suitable local interactions. Our algorithm can easily be equipped with such interactions, but we study here mainly the flexible homopolymer case where each conformation is generated with uniform probability. We argue that the algorithm is ergodic and has dynamical exponent z=0. We then use it to study polymers of size up to 643=262144 monomers. Results are presented for the effective interaction between end points, and the interaction with the boundaries of the system.

Physical aspects of biophotons.

PubMed

Popp, F A; Li, K H; Mei, W P; Galle, M; Neurohr, R

1988-07-15

By comparing the theoretically expected results of photon emission from a chaotic (thermal) field and those of an ordered (fully coherent) field with the actual experimental data, one finds ample indications for the hypothesis that 'biophotons' originate from a coherent field occurring within living tissues. A direct proof may be seen in the hyperbolic relaxation dynamics of spectral delayed luminescence under ergodic conditions. A possible mechanism has to be founded on Einstein's balance equation and, under stationary conditions, on energy conservation including a photochemical potential. It is shown that the considered equations deliver, besides the thermal equilibrium, a conditionally stable region far away from equilibrium, which can help to describe both 'biophoton emission' and biological regulation.

Stochastic optimal control as non-equilibrium statistical mechanics: calculus of variations over density and current

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.

2014-01-01

In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.

A decision model for selecting sustainable drinking water supply and greywater reuse systems for developing communities with a case study in Cimahi, Indonesia.

PubMed

Henriques, Justin J; Louis, Garrick E

2011-01-01

Capacity Factor Analysis is a decision support system for selection of appropriate technologies for municipal sanitation services in developing communities. Developing communities are those that lack the capability to provide adequate access to one or more essential services, such as water and sanitation, to their residents. This research developed two elements of Capacity Factor Analysis: a capacity factor based classification for technologies using requirements analysis, and a matching policy for choosing technology options. First, requirements analysis is used to develop a ranking for drinking water supply and greywater reuse technologies. Second, using the Capacity Factor Analysis approach, a matching policy is developed to guide decision makers in selecting the appropriate drinking water supply or greywater reuse technology option for their community. Finally, a scenario-based informal hypothesis test is developed to assist in qualitative model validation through case study. Capacity Factor Analysis is then applied in Cimahi Indonesia as a form of validation. The completed Capacity Factor Analysis model will allow developing communities to select drinking water supply and greywater reuse systems that are safe, affordable, able to be built and managed by the community using local resources, and are amenable to expansion as the community's management capacity increases. Copyright © 2010 Elsevier Ltd. All rights reserved.

Time and Measurement Days

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

2017-01-01

Questions in data analysis involving the concepts of time and measurement are often pushed into the background or reserved for a philosophical discussion. Some examples are: a) Is causality a consequence of the laws of physics, or can the arrow of time be reversed? b) Can we determine the arrow of time of an event? c) Do we need the continuum hypothesis for the underlying function in any measurement process? d) Can we say anything about the analyticity of the underlying process of an event? e) Would it be valid to model a non-analytical process as function of time? f) What are the implications of all these questions for classical Fourier techniques? However, in the age of big data gathered either from space missions supplying ultra-precise long time series, or e.g. LIGO data from the ground, the moment to bring these questions to the foreground seems arrived. The limitations of our understanding of some fundamental processes is emphasized by the lack of solution for problems open for more than 2 decades, such as the non-detection of solar g-modes, or the modal identification of main sequence stellar pulsators like delta Scuti stars. Flicker noise or 1/f noise, for example, attributed in solar-like stars to granulation, is analyzed mostly only to apply noise reduction techniques, neither considering the classical problem of 1/f noise that was introduced a 100 years ago, nor taking into account ergodic or non-ergodic solutions that make inapplicable spectral analysis techniques in practice. This topic was discussed by Nicholas W. Watkins during the ITISE meeting held in Granada in 2016. There he presented preliminary results of his research on Mandelbrot's related work. We reproduce here his quotation of Mandelbrot (1999) "There is a sharp contrast between a highly anomalous ("non-white") noise that proceeds in ordinary clock time and a noise whose principal anomaly is that it is restricted to fractal time", suggesting a connection with the above proposed topics that could be phrased as the following additional questions:a) Is self-organized criticality (SOC) frequent in astrophysical phenomena? b) Could all fractals in nature be considered stochastic? c) Could we establish mathematical/physical relationships between chaotic and fractal behaviors in time series? d) Could the differences between fractals and chaos in terms of analyticity be used to understand the residuals of the fitting of stellar light curves? In this meeting we would like to approximate these problems from a holistic and multidisciplinary perspective, taking into account not only technical issues but also the deeper implications. In particular the concept of connectivity (introduced in Pascual-Granado et al. A&A, 2015) could be used to implement, within the framework of ARMA processes, an "arrow of time" (see attached document), and so studying the possible implications in the concept of time as envisaged by Watkins.

Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way

NASA Astrophysics Data System (ADS)

Liao, Yunxiang; Levchenko, Alex; Foster, Matthew S.

2017-11-01

We derive the finite temperature Keldysh response theory for interacting fermions in the presence of quenched short-ranged disorder, as applicable to any of the 10 Altland-Zirnbauer classes in an Anderson delocalized phase with at least a U(1) continuous symmetry. In this formulation of the interacting Finkel'stein nonlinear sigma model, the statistics of one-body wave functions are encoded by the constrained matrix field, while physical correlations follow from the hydrodynamic density or spin response field, which decouples the interactions. Integrating out the matrix field first, we obtain weak (anti) localization and Altshuler-Aronov quantum conductance corrections from the hydrodynamic response function. This procedure automatically incorporates the correct infrared cutoff physics, and in particular gives the Altshuler-Aronov-Khmelnitsky (AAK) equations for dephasing of weak (anti)localization due to electron-electron collisions. We explicate the method by deriving known quantumcorrections in two dimensions for the symplectic metal class AII, as well as the spin-SU(2) invariant superconductor classes C and CI. We show that quantum conductance corrections due to the special modes at zero energy in nonstandard classes are automatically cut off by temperature, as previously expected, while the Wigner-Dyson class Cooperon modes that persist to all energies are cut by dephasing. We also show that for short-ranged interactions, the standard self-consistent solution for the dephasing rate is equivalent to a particular summation of diagrams via the self-consistent Born approximation. This should be compared to the corresponding AAK solution for long-ranged Coulomb interactions, which exploits the Markovian noise correlations induced by thermal fluctuations of the electromagnetic field. We discuss prospects for exploring the many-body localization transition as a dephasing catastrophe in short-range interacting models, as encountered by approaching from the ergodic side.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

PubMed

Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

2014-11-01

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Comprehensive Analysis of Protein Modifications by Top-down Mass Spectrometry

PubMed Central

Zhang, Han; Ge, Ying

2012-01-01

Mass spectrometry (MS)-based proteomics is playing an increasingly important role in cardiovascular research. Proteomics includes not only identification and quantification of proteins, but also the characterization of protein modifications such as post-translational modifications and sequence variants. The conventional bottom-up approach, involving proteolytic digestion of proteins into small peptides prior to MS analysis, is routinely used for protein identification and quantification with high throughput and automation. Nevertheless, it has limitations in the analysis of protein modifications mainly due to the partial sequence coverage and loss of connections among modifications on disparate portions of a protein. An alternative approach, top-down MS, has emerged as a powerful tool for the analysis of protein modifications. The top-down approach analyzes whole proteins directly, providing a “bird’s eye” view of all existing modifications. Subsequently, each modified protein form can be isolated and fragmented in the mass spectrometer to locate the modification site. The incorporation of the non-ergodic dissociation methods such as electron capture dissociation (ECD) greatly enhances the top-down capabilities. ECD is especially useful for mapping labile post-translational modifications which are well-preserved during the ECD fragmentation process. Top-down MS with ECD has been successfully applied to cardiovascular research with the unique advantages in unraveling the molecular complexity, quantifying modified protein forms, complete mapping of modifications with full sequence coverage, discovering unexpected modifications, and identifying and quantifying positional isomers and determining the order of multiple modifications. Nevertheless, top-down MS still needs to overcome some technical challenges to realize its full potential. Herein, we reviewed the advantages and challenges of top-down methodology with a focus on its application in cardiovascular research. PMID:22187450

Theory of amorphous ices.

PubMed

Limmer, David T; Chandler, David

2014-07-01

We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer simulations. Along with nonequilibrium transitions between the ergodic liquid and two distinct amorphous solids, we establish coexistence between these two amorphous solids. The phase diagram we predict includes a nonequilibrium triple point where two amorphous phases and the liquid coexist. Whereas the amorphous solids are long-lived and slowly aging glasses, their melting can lead quickly to the formation of crystalline ice. Further, melting of the higher density amorphous solid at low pressures takes place in steps, transitioning to the lower-density glass before accessing a nonequilibrium liquid from which ice coarsens.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-01-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Hierarchical relaxation dynamics in a tilted two-band Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Cosme, Jayson G.

2018-04-01

We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the eigenstate thermalization hypothesis for relevant physical observables is demonstrated for certain parameter regimes. Using the truncated Wigner representation in the semiclassical limit of the system, dynamics of relevant observables reveal hierarchical relaxation and the appearance of prethermalized states is studied from the perspective of statistics of the underlying mean-field trajectories. The observed prethermalization scenario can be attributed to different stages of glassy dynamics in the mode-time configuration space due to dynamical phase transition between ergodic and nonergodic trajectories.

Microscopic pressure-cooker model for studying molecules in confinement

NASA Astrophysics Data System (ADS)

Santamaria, Ruben; Adamowicz, Ludwik; Rosas-Acevedo, Hortensia

2015-04-01

A model for a system of a finite number of molecules in confinement is presented and expressions for determining the temperature, pressure, and volume of the system are derived. The present model is a generalisation of the Zwanzig-Langevin model because it includes pressure effects in the system. It also has general validity, preserves the ergodic hypothesis, and provides a formal framework for previous studies of hydrogen clusters in confinement. The application of the model is illustrated by an investigation of a set of prebiotic compounds exposed to varying pressure and temperature. The simulations performed within the model involve the use of a combination of molecular dynamics and density functional theory methods implemented on a computer system with a mixed CPU-GPU architecture.

Lipschitz regularity results for nonlinear strictly elliptic equations and applications

NASA Astrophysics Data System (ADS)

Ley, Olivier; Nguyen, Vinh Duc

2017-10-01

Most of Lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic growth power in gradient, one usually uses weak Bernstein-type arguments which require regularity and/or convex-type assumptions on the gradient nonlinearity. In this article, we obtain new Lipschitz regularity results for a large class of nonlinear strictly elliptic equations with possibly arbitrary growth power of the Hamiltonian with respect to the gradient variable using some ideas coming from Ishii-Lions' method. We use these bounds to solve an ergodic problem and to study the regularity and the large time behavior of the solution of the evolution equation.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-06-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Metastable Distributions of Markov Chains with Rare Transitions

NASA Astrophysics Data System (ADS)

Freidlin, M.; Koralov, L.

2017-06-01

In this paper we consider Markov chains X^\\varepsilon _t with transition rates that depend on a small parameter \\varepsilon . We are interested in the long time behavior of X^\\varepsilon _t at various \\varepsilon -dependent time scales t = t(\\varepsilon ). The asymptotic behavior depends on how the point (1/\\varepsilon , t(\\varepsilon )) approaches infinity. We introduce a general notion of complete asymptotic regularity (a certain asymptotic relation between the ratios of transition rates), which ensures the existence of the metastable distribution for each initial point and a given time scale t(\\varepsilon ). The technique of i-graphs allows one to describe the metastable distribution explicitly. The result may be viewed as a generalization of the ergodic theorem to the case of parameter-dependent Markov chains.

Self-consistent approach to many-body localization and subdiffusion

NASA Astrophysics Data System (ADS)

Prelovšek, P.; Herbrych, J.

2017-07-01

An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of many-body localization. Results show a qualitative agreement with the numerically obtained dynamical structure factor in the whole range of frequencies and wave vectors, as well as across the transition to nonergodic behavior. The theory reveals the singular nature of the one-dimensional problem, whereby on the ergodic side the dynamics is subdiffusive with dynamical conductivity σ (ω ) ∝|ω| α , i.e., with vanishing dc limit σ0=0 and α <1 varying with disorder, while we get α >1 in the localized phase.

Chaos-assisted tunneling in the presence of Anderson localization.

PubMed

Doggen, Elmer V H; Georgeot, Bertrand; Lemarié, Gabriel

2017-10-01

Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate. Here we study chaos-assisted tunneling in the presence of Anderson localization effects in the chaotic sea. Our results show that the standard tunneling rate distribution is strongly modified by localization, going from the Cauchy distribution in the ergodic regime to a log-normal distribution in the strongly localized case, for both a deterministic and a disordered model. We develop a single-parameter scaling description which accurately describes the numerical data. Several possible experimental implementations using cold atoms, photonic lattices, or microwave billiards are discussed.

Short-term cascaded hydroelectric system scheduling based on chaotic particle swarm optimization using improved logistic map

NASA Astrophysics Data System (ADS)

He, Yaoyao; Yang, Shanlin; Xu, Qifa

2013-07-01

In order to solve the model of short-term cascaded hydroelectric system scheduling, a novel chaotic particle swarm optimization (CPSO) algorithm using improved logistic map is introduced, which uses the water discharge as the decision variables combined with the death penalty function. According to the principle of maximum power generation, the proposed approach makes use of the ergodicity, symmetry and stochastic property of improved logistic chaotic map for enhancing the performance of particle swarm optimization (PSO) algorithm. The new hybrid method has been examined and tested on two test functions and a practical cascaded hydroelectric system. The experimental results show that the effectiveness and robustness of the proposed CPSO algorithm in comparison with other traditional algorithms.

Universal Algorithm for Identification of Fractional Brownian Motion. A Case of Telomere Subdiffusion

PubMed Central

Burnecki, Krzysztof; Kepten, Eldad; Janczura, Joanna; Bronshtein, Irena; Garini, Yuval; Weron, Aleksander

2012-01-01

We present a systematic statistical analysis of the recently measured individual trajectories of fluorescently labeled telomeres in the nucleus of living human cells. The experiments were performed in the U2OS cancer cell line. We propose an algorithm for identification of the telomere motion. By expanding the previously published data set, we are able to explore the dynamics in six time orders, a task not possible earlier. As a result, we establish a rigorous mathematical characterization of the stochastic process and identify the basic mathematical mechanisms behind the telomere motion. We find that the increments of the motion are stationary, Gaussian, ergodic, and even more chaotic—mixing. Moreover, the obtained memory parameter estimates, as well as the ensemble average mean square displacement reveal subdiffusive behavior at all time spans. All these findings statistically prove a fractional Brownian motion for the telomere trajectories, which is confirmed by a generalized p-variation test. Taking into account the biophysical nature of telomeres as monomers in the chromatin chain, we suggest polymer dynamics as a sufficient framework for their motion with no influence of other models. In addition, these results shed light on other studies of telomere motion and the alternative telomere lengthening mechanism. We hope that identification of these mechanisms will allow the development of a proper physical and biological model for telomere subdynamics. This array of tests can be easily implemented to other data sets to enable quick and accurate analysis of their statistical characteristics. PMID:23199912

Strategic Mobility 21: Rail Network Capacity Analysis

DTIC Science & Technology

2006-09-30

of commercial freight and passenger train movements per peak day on the rail main lines in the study area for Year 2000 (actual...levels in Year 2010 and beyond with transit times comparable to Year 2000, at least four main tracks on the south slope of Cajon Pass are required... study . Rail Network Capacity Analysis 1 1.0 INTRODUCTION This document contains the analysis of rail capacity

Assessment of current AASHTO LRFD methods for static pile capacity analysis in Rhode Island soils.

DOT National Transportation Integrated Search

2013-07-01

This report presents an assessment of current AASHTO LRFD methods for static pile capacity analysis in Rhode : Island soils. Current static capacity methods and associated resistance factors are based on pile load test data in sands : and clays. Some...

Enhancement of a network analysis tool to accommodate multiple construction work zone analysis (initial investigation).

DOT National Transportation Integrated Search

2010-08-30

A major issue in transportation projects is capacity reduction due to lane closures. Calculating capacity for a specific project can be done using information from the Highway Capacity Manual, but how often should a lane closure be expected is still ...

Discussion of the Method to Determine the Ultimate Bearing Capacity of Soil Foundation

NASA Astrophysics Data System (ADS)

Du, Peng; Liu, Xiaoling; Zhang, Yangfu

2017-12-01

Combining literature examples, this paper has carried out Contrastive analysis of the theoretical formula method and finite element method about the ultimate bearing capacity of foundation, To verify rationality and superiority of the incremental load method in finite element ABAQUS in solving the bearing capacity of foundation soil. The study can provide certain reference for practical engineering calculation and analysis of foundation bearing capacity.

Comparing capacity coefficient and dual task assessment of visual multitasking workload

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blaha, Leslie M.

Capacity coefficient analysis could offer a theoretically grounded alternative approach to subjective measures and dual task assessment of cognitive workload. Workload capacity or workload efficiency is a human information processing modeling construct defined as the amount of information that can be processed by the visual cognitive system given a specified of amount of time. In this paper, I explore the relationship between capacity coefficient analysis of workload efficiency and dual task response time measures. To capture multitasking performance, I examine how the relatively simple assumptions underlying the capacity construct generalize beyond the single visual decision making tasks. The fundamental toolsmore » for measuring workload efficiency are the integrated hazard and reverse hazard functions of response times, which are defined by log transforms of the response time distribution. These functions are used in the capacity coefficient analysis to provide a functional assessment of the amount of work completed by the cognitive system over the entire range of response times. For the study of visual multitasking, capacity coefficient analysis enables a comparison of visual information throughput as the number of tasks increases from one to two to any number of simultaneous tasks. I illustrate the use of capacity coefficients for visual multitasking on sample data from dynamic multitasking in the modified Multi-attribute Task Battery.« less

The Aviation System Analysis Capability Airport Capacity and Delay Models

NASA Technical Reports Server (NTRS)

Lee, David A.; Nelson, Caroline; Shapiro, Gerald

1998-01-01

The ASAC Airport Capacity Model and the ASAC Airport Delay Model support analyses of technologies addressing airport capacity. NASA's Aviation System Analysis Capability (ASAC) Airport Capacity Model estimates the capacity of an airport as a function of weather, Federal Aviation Administration (FAA) procedures, traffic characteristics, and the level of technology available. Airport capacity is presented as a Pareto frontier of arrivals per hour versus departures per hour. The ASAC Airport Delay Model allows the user to estimate the minutes of arrival delay for an airport, given its (weather dependent) capacity. Historical weather observations and demand patterns are provided by ASAC as inputs to the delay model. The ASAC economic models can translate a reduction in delay minutes into benefit dollars.

Repeatable source, site, and path effects on the standard deviation for empirical ground-motion prediction models

USGS Publications Warehouse

Lin, P.-S.; Chiou, B.; Abrahamson, N.; Walling, M.; Lee, C.-T.; Cheng, C.-T.

2011-01-01

In this study, we quantify the reduction in the standard deviation for empirical ground-motion prediction models by removing ergodic assumption.We partition the modeling error (residual) into five components, three of which represent the repeatable source-location-specific, site-specific, and path-specific deviations from the population mean. A variance estimation procedure of these error components is developed for use with a set of recordings from earthquakes not heavily clustered in space.With most source locations and propagation paths sampled only once, we opt to exploit the spatial correlation of residuals to estimate the variances associated with the path-specific and the source-location-specific deviations. The estimation procedure is applied to ground-motion amplitudes from 64 shallow earthquakes in Taiwan recorded at 285 sites with at least 10 recordings per site. The estimated variance components are used to quantify the reduction in aleatory variability that can be used in hazard analysis for a single site and for a single path. For peak ground acceleration and spectral accelerations at periods of 0.1, 0.3, 0.5, 1.0, and 3.0 s, we find that the singlesite standard deviations are 9%-14% smaller than the total standard deviation, whereas the single-path standard deviations are 39%-47% smaller.

Soliton Turbulence in Shallow Water Ocean Surface Waves

NASA Astrophysics Data System (ADS)

Costa, Andrea; Osborne, Alfred R.; Resio, Donald T.; Alessio, Silvia; Chrivı, Elisabetta; Saggese, Enrica; Bellomo, Katinka; Long, Chuck E.

2014-09-01

We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of soliton turbulence in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a dense soliton gas, described theoretically by the soliton limit of the Korteweg-deVries equation, a completely integrable soliton system: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodic-quasiperiodic boundary conditions the ergodic solutions of Korteweg-deVries are exactly solvable by finite gap theory (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as ˜ω-1. We use the linear Fourier transform to estimate this power law from the power spectrum and to filter densely packed soliton wave trains from the data. We apply FGT to determine the soliton spectrum and find that the low frequency ˜ω-1 region is soliton dominated. The solitons have random FGT phases, a soliton random phase approximation, which supports our interpretation of the data as soliton turbulence. From the probability density of the solitons we are able to demonstrate that the solitons are dense in time and highly non-Gaussian.

A Latent Variable Analysis of Working Memory Capacity, Short-Term Memory Capacity, Processing Speed, and General Fluid Intelligence.

ERIC Educational Resources Information Center

Conway, Andrew R. A.; Cowan, Nelsin; Bunting, Michael F.; Therriault, David J.; Minkoff, Scott R. B.

2002-01-01

Studied the interrelationships among general fluid intelligence, short-term memory capacity, working memory capacity, and processing speed in 120 young adults and used structural equation modeling to determine the best predictor of general fluid intelligence. Results suggest that working memory capacity, but not short-term memory capacity or…

Measuring laboratory-based influenza surveillance capacity: development of the 'International Influenza Laboratory Capacity Review' Tool.

PubMed

Muir-Paulik, S A; Johnson, L E A; Kennedy, P; Aden, T; Villanueva, J; Reisdorf, E; Humes, R; Moen, A C

2016-01-01

The 2005 International Health Regulations (IHR 2005) emphasized the importance of laboratory capacity to detect emerging diseases including novel influenza viruses. To support IHR 2005 requirements and the need to enhance influenza laboratory surveillance capacity, the Association of Public Health Laboratories (APHL) and the Centers for Disease Control and Prevention (CDC) Influenza Division developed the International Influenza Laboratory Capacity Review (Tool). Data from 37 assessments were reviewed and analyzed to verify that the quantitative analysis results accurately depicted a laboratory's capacity and capabilities. Subject matter experts in influenza and laboratory practice used an iterative approach to develop the Tool incorporating feedback and lessons learnt through piloting and implementation. To systematically analyze assessment data, a quantitative framework for analysis was added to the Tool. The review indicated that changes in scores consistently reflected enhanced or decreased capacity. The review process also validated the utility of adding a quantitative analysis component to the assessments and the benefit of establishing a baseline from which to compare future assessments in a standardized way. Use of the Tool has provided APHL, CDC and each assessed laboratory with a standardized analysis of the laboratory's capacity. The information generated is used to improve laboratory systems for laboratory testing and enhance influenza surveillance globally. We describe the development of the Tool and lessons learnt. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

A new methodology for assessing health policy and systems research and analysis capacity in African universities.

PubMed

Lê, Gillian; Mirzoev, Tolib; Orgill, Marsha; Erasmus, Ermin; Lehmann, Uta; Okeyo, Stephen; Goudge, Jane; Maluka, Stephen; Uzochukwu, Benjamin; Aikins, Moses; de Savigny, Don; Tomson, Goran; Gilson, Lucy

2014-10-08

The importance of health policy and systems research and analysis (HPSR+A) has been increasingly recognised, but it is still unclear how most effectively to strengthen the capacity of the different organisations involved in this field. Universities are particularly crucial but the expansive literature on capacity development has little to offer the unique needs of HPSR+A activity within universities, and often overlooks the pivotal contribution of capacity assessments to capacity strengthening. The Consortium for Health Policy and Systems Analysis in Africa 2011-2015 designed and implemented a new framework for capacity assessment for HPSR+A within universities. The methodology is reported in detail. Our reflections on developing and conducting the assessment generated four lessons for colleagues in the field. Notably, there are currently no published capacity assessment methodologies for HPSR+A that focus solely on universities - we report a first for the field to initiate the dialogue and exchange of experiences with others. Second, in HPSR+A, the unit of assessment can be a challenge, because HPSR+A groups within universities tend to overlap between academic departments and are embedded in different networks. Third, capacity assessment experience can itself be capacity strengthening, even when taking into account that doing such assessments require capacity. From our experience, we propose that future systematic assessments of HPSR+A capacity need to focus on both capacity assets and needs and assess capacity at individual, organisational, and systems levels, whilst taking into account the networked nature of HPSR+A activity. A genuine partnership process between evaluators and those participating in an assessment can improve the quality of assessment and uptake of results in capacity strengthening.

Demand and capacity planning in the emergency department: how to do it.

PubMed

Higginson, I; Whyatt, J; Silvester, K

2011-02-01

Unless emergency departments have adequate capacity to meet demand, they will fail to meet clinical and performance standards and will be operating in the 'coping zone'. This carries risks both for staff and patients. As part of a quality improvement programme, the authors undertook an in-depth analysis of demand and capacity for an emergency department in the UK. The paper describes this rigorous approach to capacity planning, which draws on techniques from other industries. Proper capacity planning is vital, but is often poorly done. Planning using aggregated data will lead to inadequate capacity. Understanding demand, and particularly the variation in that demand, is critical to success. Analysis of emergency department demand and capacity is the first step towards effective workforce planning and process redesign.

Assessment of capacity for Health Policy and Systems Research and Analysis in seven African universities: results from the CHEPSAA project.

PubMed

Mirzoev, Tolib; Lê, Gillian; Green, Andrew; Orgill, Marsha; Komba, Adalgot; Esena, Reuben K; Nyapada, Linet; Uzochukwu, Benjamin; Amde, Woldekidan K; Nxumalo, Nonhlanhla; Gilson, Lucy

2014-10-01

The importance of health policy and systems research and analysis (HPSR+A) is widely recognized. Universities are central to strengthening and sustaining the HPSR+A capacity as they teach the next generation of decision-makers and health professionals. However, little is known about the capacity of universities, specifically, to develop the field. In this article, we report results of capacity self- assessments by seven universities within five African countries, conducted through the Consortium for Health Policy and Systems Analysis in Africa (CHEPSAA). The capacity assessments focused on both capacity 'assets' and 'needs', and covered the wider context, as well as organizational and individual capacity levels. Six thematic areas of capacity were examined: leadership and governance, organizations' resources, scope of HPSR+A teaching and research, communication, networking and getting research into policy and practice (GRIPP), demand for HPRS+A and resource environment. The self-assessments by each university used combinations of document reviews, semi-structured interviews and staff surveys, followed by comparative analysis. A framework approach, guided by the six thematic areas, was used to analyse data. We found that HPSR+A is an international priority, and an existing activity in Africa, though still neglected field with challenges including its reliance on unpredictable international funding. All universities have capacity assets, such as ongoing HPSR+A teaching and research. There are, however, varying levels of assets (such as differences in staff numbers, group sizes and amount of HPSR+A teaching and research), which, combined with different capacity needs at all three levels (such as individual training, improvement in systems for quality assurance and fostering demand for HPSR+A work), can shape a future agenda for HPSR+A capacity strengthening. Capacity assets and needs at different levels appear related. Possible integrated strategies for strengthening universities' capacity include: refining HPSR+A vision, mainstreaming the subject into under- and post-graduate teaching, developing emerging leaders and aligning HPSR+A capacity strengthening within the wider organizational development. Published by Oxford University Press in association with The London School of Hygiene and Tropical Medicine © The Author 2013; all rights reserved.

Assessment of capacity for Health Policy and Systems Research and Analysis in seven African universities: results from the CHEPSAA project

PubMed Central

Mirzoev, Tolib; Lê, Gillian; Green, Andrew; Orgill, Marsha; Komba, Adalgot; Esena, Reuben K; Nyapada, Linet; Uzochukwu, Benjamin; Amde, Woldekidan K; Nxumalo, Nonhlanhla; Gilson, Lucy

2014-01-01

The importance of health policy and systems research and analysis (HPSR+A) is widely recognized. Universities are central to strengthening and sustaining the HPSR+A capacity as they teach the next generation of decision-makers and health professionals. However, little is known about the capacity of universities, specifically, to develop the field. In this article, we report results of capacity self- assessments by seven universities within five African countries, conducted through the Consortium for Health Policy and Systems Analysis in Africa (CHEPSAA). The capacity assessments focused on both capacity ‘assets’ and ‘needs’, and covered the wider context, as well as organizational and individual capacity levels. Six thematic areas of capacity were examined: leadership and governance, organizations’ resources, scope of HPSR+A teaching and research, communication, networking and getting research into policy and practice (GRIPP), demand for HPRS+A and resource environment. The self-assessments by each university used combinations of document reviews, semi-structured interviews and staff surveys, followed by comparative analysis. A framework approach, guided by the six thematic areas, was used to analyse data. We found that HPSR+A is an international priority, and an existing activity in Africa, though still neglected field with challenges including its reliance on unpredictable international funding. All universities have capacity assets, such as ongoing HPSR+A teaching and research. There are, however, varying levels of assets (such as differences in staff numbers, group sizes and amount of HPSR+A teaching and research), which, combined with different capacity needs at all three levels (such as individual training, improvement in systems for quality assurance and fostering demand for HPSR+A work), can shape a future agenda for HPSR+A capacity strengthening. Capacity assets and needs at different levels appear related. Possible integrated strategies for strengthening universities’ capacity include: refining HPSR+A vision, mainstreaming the subject into under- and post-graduate teaching, developing emerging leaders and aligning HPSR+A capacity strengthening within the wider organizational development. PMID:24038107

Converting HAZUS capacity curves to seismic hazard-compatible building fragility functions: effect of hysteretic models

USGS Publications Warehouse

Ryu, Hyeuk; Luco, Nicolas; Baker, Jack W.; Karaca, Erdem

2008-01-01

A methodology was recently proposed for the development of hazard-compatible building fragility models using parameters of capacity curves and damage state thresholds from HAZUS (Karaca and Luco, 2008). In the methodology, HAZUS curvilinear capacity curves were used to define nonlinear dynamic SDOF models that were subjected to the nonlinear time history analysis instead of the capacity spectrum method. In this study, we construct a multilinear capacity curve with negative stiffness after an ultimate (capping) point for the nonlinear time history analysis, as an alternative to the curvilinear model provided in HAZUS. As an illustration, here we propose parameter values of the multilinear capacity curve for a moderate-code low-rise steel moment resisting frame building (labeled S1L in HAZUS). To determine the final parameter values, we perform nonlinear time history analyses of SDOF systems with various parameter values and investigate their effects on resulting fragility functions through sensitivity analysis. The findings improve capacity curves and thereby fragility and/or vulnerability models for generic types of structures.

The role of postural control in the association between aerobic capacity and walking capacity in chronic stroke: a cross-sectional analysis.

PubMed

Outermans, Jacqueline C; van de Port, Ingrid; Kwakkel, Gert; Visser-Meily, Johanna M; Wittink, Harriet

2018-03-12

Reports on the association between aerobic capacity and walking capacity in people after stroke show disparate results. To determine (1) if the predictive validity of peak oxygen uptake (VO2peak) for walking capacity post stroke is different from that of maximal oxygen uptake (VO2max) and (2) if postural control, hemiplegic lower extremity muscle strength, age and gender distort the association between aerobic capacity and walking capacity. Cross-sectional study. General community in Utrecht, the Netherlands. Community-dwelling people more than three months after stroke. Measurement of aerobic capacity were performed with cardiopulmonary exercise testing (CPET) and differentiated between the achievement of VO2peak or VO2max. Measurement of walking capacity with the Six Minute Walk Test (6MWT), postural control with the Performance Oriented Mobility Assessment (POMA) and hemiplegic lower extremity muscle strength with the Motricity Index (MI-LE). Fifty-one out of 62 eligible participants, aged 64.7 (±12.5) years were included. Analysis of covariance (ANCOVA) showed a nonsignificant difference between the predictive validities of VO2max (N = 22, β = 0.56; 95%CI 0.12 - 0.97) and VO2peak (N = 29, β = 0.72; 95%CI 0.38 - 0.92). Multiple regression analysis of the pooled sample showed a significant decrease in the β value of VO2peak (21.6%) for the 6MWT when adding the POMA as a covariate in the association model. VO2peak remained significantly related to 6MWT after correcting for the POMA (β = 0.56 (95%CI 0.39 - 0.75)) CONCLUSIONS: The results suggest similar predictive validity of aerobic capacity for walking capacity in participants achieving VO2max compared to those only achieving VO2peak. Postural control confounds the association between aerobic capacity and walking capacity. Aerobic capacity remains a valid predictor of walking capacity. Aerobic capacity is an important factor associated with walking capacity after stroke. However, to understand this relationship, postural control needs to be measured. Both aerobic capacity and postural control may need to be addressed during interventions aiming to improve walking capacity after stroke.

FAST TRACK COMMUNICATION: Field dependence of temperature induced irreversible transformations of magnetic phases in Pr0.5Ca0.5Mn0.975Al0.025O3 crystalline oxide

NASA Astrophysics Data System (ADS)

Lakhani, Archana; Kushwaha, Pallavi; Rawat, R.; Kumar, Kranti; Banerjee, A.; Chaddah, P.

2010-01-01

Glass-like arrest has recently been reported in various magnetic materials. As in structural glasses, the kinetics of a first order transformation is arrested while retaining the higher entropy phase as a non-ergodic state. We show visual mesoscopic evidence of the irreversible transformation of the arrested antiferromagnetic-insulating phase in Pr0.5Ca0.5Mn0.975Al0.025O3 to its equilibrium ferromagnetic-metallic phase with an isothermal increase of magnetic field, similar to its iso-field transformation on warming. The magnetic field dependence of the non-equilibrium to equilibrium transformation temperature is shown to be governed by Le Chatelier's principle.

The modified turning bands (MTB) model for space-time rainfall. I. Model definition and properties

NASA Astrophysics Data System (ADS)

Mellor, Dale

1996-02-01

A new stochastic model of space-time rainfall, the Modified Turning Bands (MTB) model, is proposed which reproduces, in particular, the movements and developments of rainbands, cluster potential regions and raincells, as well as their respective interactions. The ensemble correlation structure is unsuitable for practical estimation of the model parameters because the model is not ergodic in this statistic, and hence it cannot easily be measured from a single real storm. Thus, some general theory on the internal covariance structure of a class of stochastic models is presented, of which the MTB model is an example. It is noted that, for the MTB model, the internal covariance structure may be measured from a single storm, and can thus be used for model identification.

The generalization ability of online SVM classification based on Markov sampling.

PubMed

Xu, Jie; Yan Tang, Yuan; Zou, Bin; Xu, Zongben; Li, Luoqing; Lu, Yang

2015-03-01

In this paper, we consider online support vector machine (SVM) classification learning algorithms with uniformly ergodic Markov chain (u.e.M.c.) samples. We establish the bound on the misclassification error of an online SVM classification algorithm with u.e.M.c. samples based on reproducing kernel Hilbert spaces and obtain a satisfactory convergence rate. We also introduce a novel online SVM classification algorithm based on Markov sampling, and present the numerical studies on the learning ability of online SVM classification based on Markov sampling for benchmark repository. The numerical studies show that the learning performance of the online SVM classification algorithm based on Markov sampling is better than that of classical online SVM classification based on random sampling as the size of training samples is larger.

Theory of amorphous ices

PubMed Central

Limmer, David T.; Chandler, David

2014-01-01

We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer simulations. Along with nonequilibrium transitions between the ergodic liquid and two distinct amorphous solids, we establish coexistence between these two amorphous solids. The phase diagram we predict includes a nonequilibrium triple point where two amorphous phases and the liquid coexist. Whereas the amorphous solids are long-lived and slowly aging glasses, their melting can lead quickly to the formation of crystalline ice. Further, melting of the higher density amorphous solid at low pressures takes place in steps, transitioning to the lower-density glass before accessing a nonequilibrium liquid from which ice coarsens. PMID:24858957

On Another Edge of Defocusing: Hyperbolicity of Asymmetric Lemon Billiards

NASA Astrophysics Data System (ADS)

Bunimovich, Leonid; Zhang, Hong-Kun; Zhang, Pengfei

2016-02-01

Defocusing mechanism provides a way to construct chaotic (hyperbolic) billiards with focusing components by separating all regular components of the boundary of a billiard table sufficiently far away from each focusing component. If all focusing components of the boundary of the billiard table are circular arcs, then the above separation requirement reduces to that all circles obtained by completion of focusing components are contained in the billiard table. In the present paper we demonstrate that a class of convex tables— asymmetric lemons, whose boundary consists of two circular arcs, generate hyperbolic billiards. This result is quite surprising because the focusing components of the asymmetric lemon table are extremely close to each other, and because these tables are perturbations of the first convex ergodic billiard constructed more than 40 years ago.

Daydreaming, Thought Blocking and Strudels in the Taskless, Resting Human Brain's Magnetic Fields

NASA Astrophysics Data System (ADS)

Mandell, Arnold J.; Selz, Karen A.; Aven, John; Holroyd, Tom; Coppola, Richard

2011-04-01

The incidence, i(S), and duration, l(S), of transient, intermittent, hierarchical vorticities, strudels, S, in magnetic flux fluctuations, were computed from MEG records. from 91 task-free resting subjects. The MEG's i(S) and l(S) manifested characteristic times and entropic sensitivity resembling those reported in psychological studies of daydreaming and task-unrelated thoughts, TUTs. Transient reduction or absences of strudels can be found in patients with syndromes characterized by thought blocking. Positive ergodic single orbit measures of expansiveness and mixing predict i(S) and l(S). An analogy with the relationship between intermittent pontine-geniculate-occipital waves and dreaming is made to strudels with daydreaming. Both can be interpreted as neurophysiological correlates of the spontaneous intrusions into consciousness of the never idle unconscious mind.

On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

NASA Astrophysics Data System (ADS)

Hu, Zixi; Yao, Zhewei; Li, Jinglai

2017-03-01

Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

Floquet Supersymmetry

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Hsieh, Timothy H.

2018-05-01

We show that time-reflection symmetry in periodically driven (Floquet) quantum systems enables an inherently nonequilibrium phenomenon structurally similar to quantum-mechanical supersymmetry. In particular, we find Floquet analogs of the Witten index that place lower bounds on the degeneracies of states with quasienergies 0 and π . Moreover, we show that in some cases time-reflection symmetry can also interchange fermions and bosons, leading to fermion-boson pairs with opposite quasienergy. We provide a simple class of disordered, interacting, and ergodic Floquet models with an exponentially large number of states at quasienergies 0 and π , which are robust as long as the time-reflection symmetry is preserved. Floquet supersymmetry manifests itself in the evolution of certain local observables as a period-doubling effect with dramatic finite-size scaling, providing a clear signature for experiments.

Intermittent many-body dynamics at equilibrium

NASA Astrophysics Data System (ADS)

Danieli, C.; Campbell, D. K.; Flach, S.

2017-06-01

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q -breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.

Dynamical manifestations of quantum chaos

NASA Astrophysics Data System (ADS)

Torres Herrera, Eduardo Jonathan; Santos, Lea

2017-04-01

A main feature of a chaotic quantum system is a rigid spectrum, where the levels do not cross. Dynamical quantities, such as the von Neumann entanglement entropy, Shannon information entropy, and out-of-time correlators can differentiate the ergodic from the nonergodic phase in disordered interacting systems, but not level repulsion from level crossing in the delocalized phase of disordered and clean models. This is in contrast with the long-time evolution of the survival probability of the initial state. The onset of correlated energy levels is manifested by a drop, referred to as correlation hole, below the asymptotic value of the survival probability. The correlation hole is an unambiguous indicator of the presence of level repulsion. EJTH is grateful to VIEP, BUAP for financial support through the VIEP projects program.

Delaunay-based derivative-free optimization for efficient minimization of time-averaged statistics of turbulent flows

NASA Astrophysics Data System (ADS)

Beyhaghi, Pooriya

2016-11-01

This work considers the problem of the efficient minimization of the infinite time average of a stationary ergodic process in the space of a handful of independent parameters which affect it. Problems of this class, derived from physical or numerical experiments which are sometimes expensive to perform, are ubiquitous in turbulence research. In such problems, any given function evaluation, determined with finite sampling, is associated with a quantifiable amount of uncertainty, which may be reduced via additional sampling. This work proposes the first algorithm of this type. Our algorithm remarkably reduces the overall cost of the optimization process for problems of this class. Further, under certain well-defined conditions, rigorous proof of convergence is established to the global minimum of the problem considered.

Quantum Anosov flows: A new family of examples

NASA Astrophysics Data System (ADS)

Peter, Ingo J.; Emch, Gérard G.

1998-09-01

A quantum version is presented for the Anosov system defined by the time evolution implemented by the geodesic coflow on the cotangent bundle of any compact quotient manifold obtained from the Poincaré half-plane. While the canonical Weyl algebra does not close under time evolution, the symplectic structure of these classical systems can be exploited to produce objects akin to the CCR algebras encountered in quantum field theory. This construction allows one to lift both the geodesic and the horocyclic flows to a Weyl algebra describing the quantum dynamics corresponding to the systems under consideration. The Anosov relations as proposed in Ref. Reference 1 are found to be valid for these models. A quantum version of the classical ergodicity of these systems is discussed in the last section.

Stochastic arbitrage return and its implication for option pricing

NASA Astrophysics Data System (ADS)

Fedotov, Sergei; Panayides, Stephanos

2005-01-01

The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary ergodic random process rapidly varying in time. We exploit the fact that option price and random arbitrage returns change on different time scales which allows us to develop an asymptotic pricing theory involving the central limit theorem for random processes. We restrict ourselves to finding pricing bands for options rather than exact prices. The resulting pricing bands are shown to be independent of the detailed statistical characteristics of the arbitrage return. We find that the volatility “smile” can also be explained in terms of random arbitrage opportunities.

[The development of evaluation capacity in primary healthcare management: a case study in Santa Catarina State, Brazil, 2008-2011].

PubMed

Nickel, Daniela Alba; Calvo, Maria Cristina Marino; Natal, Sonia; Freitas, Sérgio Fernando Torres de; Hartz, Zulmira Maria de Araújo

2014-04-01

This article analyzes evaluation capacity-building based on the case study of a State Health Secretariat participating in the Project to Strengthen the Technical Capacity of State Health Secretariats in Monitoring and Evaluating Primary Healthcare. The case study adopted a mixed design with information from documents, semi-structured interviews, and evaluation of primary care by the State Health Secretariat in 2008-2011. Process analysis was used to identify the logical events that contributed to evaluation capacity-building, with two categories: evaluation capacity-building events and events for building organizational structure. The logical chain of events was formed by negotiation and agreement on the decision-making levels for the continuity of evaluation, data collection and analysis by the State Health Secretariat, a change in key indicators, restructuring of the evaluation matrix, and communication of the results to the municipalities. The three-way analysis showed that the aim of developing evaluation capacity was achieved.

Review and evaluation of methods for analyzing capacity at signalized intersections.

DOT National Transportation Integrated Search

1996-01-01

VDOT's current policy is to use and accept from others the 1994 Highway Capacity Manual (HCM) as the basis for capacity analysis on Virginia's streets and highways. VDOT uses the latest version of the Highway Capacity Software (HCS). Software program...

Development status of a high cooling capacity single stage pulse tube cryocooler

NASA Astrophysics Data System (ADS)

Hirayama, T.; Li, R.; Y Xu, M.; Zhu, S. W.

2017-12-01

High temperature superconducting (HTS) applications require high-capacity and high-reliability cooling solutions to keep HTS materials at temperatures of approximately 80 K. In order to meet such requirements, Sumitomo Heavy Industries, Ltd.(SHI) has been developing high cooling capacity GM-type active-buffer pulse tube cryocooler. An experimental unit was designed, built and tested. A cooling capacity of 390.5 W at 80 K, COP 0.042 was achieved with an input power of approximately 9 kW. The cold stage usually reaches a stable temperature of about 25 K within one hour starting at room temperature. Also, a simplified analysis was carried out to better understand the experimental unit. In the analysis, the regenerator, thermal conduction, heat exchanger and radiation losses were calculated. The net cooling capacity was about 80% of the PV work. The experimental results, the analysis method and results are reported in this paper.

Personalized Rapid Transit Systems : a First Analysis

DOT National Transportation Integrated Search

1971-07-01

A preliminary systems analysis of the presonalized rapid transit system concept is given. It includes presentatin of the significant advantages and disadvantages. Question of system capacity, station capacity, urban grid design, and headway requireme...

Universal algorithm for identification of fractional Brownian motion. A case of telomere subdiffusion.

PubMed

Burnecki, Krzysztof; Kepten, Eldad; Janczura, Joanna; Bronshtein, Irena; Garini, Yuval; Weron, Aleksander

2012-11-07

We present a systematic statistical analysis of the recently measured individual trajectories of fluorescently labeled telomeres in the nucleus of living human cells. The experiments were performed in the U2OS cancer cell line. We propose an algorithm for identification of the telomere motion. By expanding the previously published data set, we are able to explore the dynamics in six time orders, a task not possible earlier. As a result, we establish a rigorous mathematical characterization of the stochastic process and identify the basic mathematical mechanisms behind the telomere motion. We find that the increments of the motion are stationary, Gaussian, ergodic, and even more chaotic--mixing. Moreover, the obtained memory parameter estimates, as well as the ensemble average mean square displacement reveal subdiffusive behavior at all time spans. All these findings statistically prove a fractional Brownian motion for the telomere trajectories, which is confirmed by a generalized p-variation test. Taking into account the biophysical nature of telomeres as monomers in the chromatin chain, we suggest polymer dynamics as a sufficient framework for their motion with no influence of other models. In addition, these results shed light on other studies of telomere motion and the alternative telomere lengthening mechanism. We hope that identification of these mechanisms will allow the development of a proper physical and biological model for telomere subdynamics. This array of tests can be easily implemented to other data sets to enable quick and accurate analysis of their statistical characteristics. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

BOOK REVIEW:

NASA Astrophysics Data System (ADS)

Berkolaiko, G.

2003-12-01

The book represents the collected lectures given at the Summer School on Mathematical Aspects of Quantum Maps held at Bologna University in September 2001. Quantum maps gained their prominence as a testing ground for mathematical understanding of various concepts in quantum chaos, such as the spectral statistics, quantum ergodicity, scarring of the eigenfunctions and the connection to algebraic number theory. The book is nicely structured. It begins by reviewing the relevant concepts and results from dynamical systems (a contribution by A Knauf) and number theory (by Z Rudnick). A contribution by the editors, M Degli Esposti and S Graffi, explains the quantization procedure for the quantum maps and proceeds to discuss some properties of the quantized maps, such as ergodicity and scarring, and the number theoretical techniques involved in proving these properties. The contribution by A Bäacker discusses the numerical methods used to study quantum chaotic systems. It contains both the mathematical background and a detailed explanation of the numerical techniques, possible pitfalls at the implementation stage and how to avoid them. It even contains a computer program in Python used by the author to compute the eigenvalues of a perturbed cat map. The last contribution, by R Artuso, while very interesting in itself, feels somewhat disconnected from the rest of the book. It deals with deterministic transport in hyperbolic and weakly chaotic systems, where one can observe normal and anomalous diffusion respectively. Although being a collection of contributions from various authors, the book feels very much like a well-coordinated team effort, with frequent cross-contributional references underlying the connections between different facets of the discussed subjects. I consider it an invaluable reference for researchers in the field of quantum chaos and would recommend it as a first read for people just entering the field. It contains both the necessary background information and tasters of the main results and concepts of quantum chaos. The only slight drawback of the book is the misprints in some of the contributions, which can make an understanding more difficult than it should be.

Protein electron transfer: is biology (thermo)dynamic?

NASA Astrophysics Data System (ADS)

Matyushov, Dmitry V.

2015-12-01

Simple physical mechanisms are behind the flow of energy in all forms of life. Energy comes to living systems through electrons occupying high-energy states, either from food (respiratory chains) or from light (photosynthesis). This energy is transformed into the cross-membrane proton-motive force that eventually drives all biochemistry of the cell. Life’s ability to transfer electrons over large distances with nearly zero loss of free energy is puzzling and has not been accomplished in synthetic systems. The focus of this review is on how this energetic efficiency is realized. General physical mechanisms and interactions that allow proteins to fold into compact water-soluble structures are also responsible for a rugged landscape of energy states and a broad distribution of relaxation times. Specific to a protein as a fluctuating thermal bath is the protein-water interface, which is heterogeneous both dynamically and structurally. The spectrum of interfacial fluctuations is a consequence of protein’s elastic flexibility combined with a high density of surface charges polarizing water dipoles into surface nanodomains. Electrostatics is critical to the protein function and the relevant questions are: (i) What is the spectrum of interfacial electrostatic fluctuations? (ii) Does the interfacial biological water produce electrostatic signatures specific to proteins? (iii) How is protein-mediated chemistry affected by electrostatics? These questions connect the fluctuation spectrum to the dynamical control of chemical reactivity, i.e. the dependence of the activation free energy of the reaction on the dynamics of the bath. Ergodicity is often broken in protein-driven reactions and thermodynamic free energies become irrelevant. Continuous ergodicity breaking in a dense spectrum of relaxation times requires using dynamically restricted ensembles to calculate statistical averages. When applied to the calculation of the rates, this formalism leads to the nonergodic activated kinetics, which extends the transition-state theory to dynamically dispersive media. Releasing the grip of thermodynamics in kinetic calculations through nonergodicity provides the mechanism for an efficient optimization between reaction rates and the spectrum of relaxation times of the protein-water thermal bath. Bath dynamics, it appears, play as important role as the free energy in optimizing biology’s performance.

Physics-Based Hazard Assessment for Critical Structures Near Large Earthquake Sources

NASA Astrophysics Data System (ADS)

Hutchings, L.; Mert, A.; Fahjan, Y.; Novikova, T.; Golara, A.; Miah, M.; Fergany, E.; Foxall, W.

2017-09-01

We argue that for critical structures near large earthquake sources: (1) the ergodic assumption, recent history, and simplified descriptions of the hazard are not appropriate to rely on for earthquake ground motion prediction and can lead to a mis-estimation of the hazard and risk to structures; (2) a physics-based approach can address these issues; (3) a physics-based source model must be provided to generate realistic phasing effects from finite rupture and model near-source ground motion correctly; (4) wave propagations and site response should be site specific; (5) a much wider search of possible sources of ground motion can be achieved computationally with a physics-based approach; (6) unless one utilizes a physics-based approach, the hazard and risk to structures has unknown uncertainties; (7) uncertainties can be reduced with a physics-based approach, but not with an ergodic approach; (8) computational power and computer codes have advanced to the point that risk to structures can be calculated directly from source and site-specific ground motions. Spanning the variability of potential ground motion in a predictive situation is especially difficult for near-source areas, but that is the distance at which the hazard is the greatest. The basis of a "physical-based" approach is ground-motion syntheses derived from physics and an understanding of the earthquake process. This is an overview paper and results from previous studies are used to make the case for these conclusions. Our premise is that 50 years of strong motion records is insufficient to capture all possible ranges of site and propagation path conditions, rupture processes, and spatial geometric relationships between source and site. Predicting future earthquake scenarios is necessary; models that have little or no physical basis but have been tested and adjusted to fit available observations can only "predict" what happened in the past, which should be considered description as opposed to prediction. We have developed a methodology for synthesizing physics-based broadband ground motion that incorporates the effects of realistic earthquake rupture along specific faults and the actual geology between the source and site.

Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory

NASA Astrophysics Data System (ADS)

Kos, Pavel; Ljubotina, Marko; Prosen, Tomaž

2018-04-01

A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985), 10.1098/rspa.1985.0078] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K (t ) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004), 10.1103/PhysRevLett.93.014103]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the "many-body localized phase" and "ergodic phase." In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K (t ) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1 /2 models in a periodically kicking transverse field. In particular, we relate K (t ) to partition functions of a class of twisted classical Ising models on a ring of size t ; hence, the leading-order RMT behavior K (t )≃2 t is a consequence of translation and reflection symmetry of the Ising partition function.

Role of point defects in bipolar fatigue behavior of Bi(Mg{sub 1/2}Ti{sub 1/2})O{sub 3} modified (Bi{sub 1/2}K{sub 1/2})TiO{sub 3}-(Bi{sub 1/2}Na{sub 1/2})TiO{sub 3} relaxor ceramics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Nitish, E-mail: nitishkumar.iitk@gmail.com; Ansell, Troy Y.; Cann, David P.

Lead-free Bi(Mg{sub 1/2}Ti{sub 1/2})O{sub 3}-(Bi{sub 1/2}K{sub 1/2})TiO{sub 3}-(Bi{sub 1/2}Na{sub 1/2})TiO{sub 3} (BMT-BKT-BNT) ceramics have been shown to exhibit large electromechanical strains under high electric fields along with negligible fatigue under strong electric fields. To investigate the role of point defects on the fatigue characteristics, the composition 5BMT-40BKT-55BNT was doped to incorporate acceptor and donor defects on the A and B sites by adjusting the Bi/Na and Ti/Mg stoichiometries. All samples had pseudo-cubic symmetries based on x-ray diffraction, typical of relaxors. Dielectric measurements showed that the high and low temperature phase transitions were largely unaffected by doping. Acceptor doping resulted inmore » the observation of a typical ferroelectric-like polarization with a remnant polarization and strain hysteresis loops with significant negative strain. Donor-doped compositions exhibited characteristics that were indicative of an ergodic relaxor phase. Fatigue measurements were carried out on all of the compositions. While the A-site acceptor-doped composition showed a small degradation in maximum strain after 10{sup 6} cycles, the other compositions were essentially fatigue free. Impedance measurements were used to identify the important conduction mechanisms in these compositions. As expected, the presence of defects did not strongly influence the fatigue behavior in donor-doped compositions owing to the nature of their reversible field-induced phase transformation. Even for the acceptor-doped compositions, which had stable domains in the absence of an electric field at room temperature, there was negligible degradation in the maximum strain due to fatigue. This suggests that either the defects introduced through stoichiometric variations do not play a prominent role in fatigue in these systems or it is compensated by factors like decrease in coercive field, an increase in ergodicity, symmetry change, or other factors.« less

Non-equilibrium phase transitions in a liquid crystal

NASA Astrophysics Data System (ADS)

Dan, K.; Roy, M.; Datta, A.

2015-09-01

The present manuscript describes kinetic behaviour of the glass transition and non-equilibrium features of the "Nematic-Isotropic" (N-I) phase transition of a well known liquid crystalline material N-(4-methoxybenzylidene)-4-butylaniline from the effects of heating rate and initial temperature on the transitions, through differential scanning calorimetry (DSC), Fourier transform infrared and fluorescence spectroscopy. Around the vicinity of the glass transition temperature (Tg), while only a change in the baseline of the ΔCp vs T curve is observed for heating rate (β) > 5 K min-1, consistent with a glass transition, a clear peak for β ≤ 5 K min-1 and the rapid reduction in the ΔCp value from the former to the latter rate correspond to an order-disorder transition and a transition from ergodic to non-ergodic behaviour. The ln β vs 1000/T curve for the glass transition shows convex Arrhenius behaviour that can be explained very well by a purely entropic activation barrier [Dan et al., Eur. Phys. Lett. 108, 36007 (2014)]. Fourier transform infrared spectroscopy indicates sudden freezing of the out-of-plane distortion vibrations of the benzene rings around the glass transition temperature and a considerable red shift indicating enhanced coplanarity of the benzene rings and, consequently, enhancement in the molecular ordering compared to room temperature. We further provide a direct experimental evidence of the non-equilibrium nature of the N-I transition through the dependence of this transition temperature (TNI) and associated enthalpy change (ΔH) on the initial temperature (at fixed β-values) for the DSC scans. A plausible qualitative explanation based on Mesquita's extension of Landau-deGennes theory [O. N. de Mesquita, Braz. J. Phys. 28, 257 (1998)] has been put forward. The change in the molecular ordering from nematic to isotropic phase has been investigated through fluorescence anisotropy measurements where the order parameter, quantified by the anisotropy, goes to zero from nematic to isotropic phase. To a point below the transition temperature, the order parameter is constant but decreases linearly with increase in temperature below that indicating the dependence of nematic ordering on the initial temperature during heating consistent with the non-equilibrium nature of nematic-isotropic phase transition.

The canonical quantization of chaotic maps on the torus

NASA Astrophysics Data System (ADS)

Rubin, Ron Shai

In this thesis, a quantization method for classical maps on the torus is presented. The quantum algebra of observables is defined as the quantization of measurable functions on the torus with generators exp (2/pi ix) and exp (2/pi ip). The Hilbert space we use remains the infinite-dimensional L2/ (/IR, dx). The dynamics is given by a unitary quantum propagator such that as /hbar /to 0, the classical dynamics is returned. We construct such a quantization for the Kronecker map, the cat map, the baker's map, the kick map, and the Harper map. For the cat map, we find the same for the propagator on the plane the same integral kernel conjectured in (HB) using semiclassical methods. We also define a quantum 'integral over phase space' as a trace over the quantum algebra. Using this definition, we proceed to define quantum ergodicity and mixing for maps on the torus. We prove that the quantum cat map and Kronecker map are both ergodic, but only the cat map is mixing, true to its classical origins. For Planck's constant satisfying the integrality condition h = 1/N, with N/in doubz+, we construct an explicit isomorphism between L2/ (/IR, dx) and the Hilbert space of sections of an N-dimensional vector bundle over a θ-torus T2 of boundary conditions. The basis functions are distributions in L2/ (/IR, dx), given by an infinite comb of Dirac δ-functions. In Bargmann space these distributions take on the form of Jacobi ϑ-functions. Transformations from position to momentum representation can be implemented via a finite N-dimensional discrete Fourier transform. With the θ-torus, we provide a connection between the finite-dimensional quantum maps given in the physics literature and the canonical quantization presented here and found in the language of pseudo-differential operators elsewhere in mathematics circles. Specifically, at a fixed point of the dynamics on the θ-torus, we return a finite-dimensional matrix propagator. We present this connection explicitly for several examples.

Effects of Voice Coding and Speech Rate on a Synthetic Speech Display in a Telephone Information System

DTIC Science & Technology

1988-05-01

Seeciv Limited- System for varying Senses term filter capacity output until some Figure 2. Original limited-capacity channel model (Frim Broadbent, 1958) S...2 Figure 2. Original limited-capacity channel model (From Broadbent, 1958) .... 10 Figure 3. Experimental...unlimited variety of human voices for digital recording sources. Synthesis by Analysis Analysis-synthesis methods electronically model the human voice

A study of the feasibility of statistical analysis of airport performance simulation

NASA Technical Reports Server (NTRS)

Myers, R. H.

1982-01-01

The feasibility of conducting a statistical analysis of simulation experiments to study airport capacity is investigated. First, the form of the distribution of airport capacity is studied. Since the distribution is non-Gaussian, it is important to determine the effect of this distribution on standard analysis of variance techniques and power calculations. Next, power computations are made in order to determine how economic simulation experiments would be if they are designed to detect capacity changes from condition to condition. Many of the conclusions drawn are results of Monte-Carlo techniques.

Estimating the supply and demand for deep geologic CO2 storage capacity over the course of the 21st Century: A meta-analysis of the literature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dooley, James J.

2013-08-05

Whether there is sufficient geologic CO2 storage capacity to allow CCS to play a significant role in mitigating climate change has been the subject of debate since the 1990s. This paper presents a meta- analysis of a large body of recently published literature to derive updated estimates of the global deep geologic storage resource as well as the potential demand for this geologic CO2 storage resource over the course of this century. This analysis reveals that, for greenhouse gas emissions mitigation scenarios that have end-of-century atmospheric CO2 concentrations of between 350 ppmv and 725 ppmv, the average demand for deepmore » geologic CO2 storage over the course of this century is between 410 GtCO2 and 1,670 GtCO2. The literature summarized here suggests that -- depending on the stringency of criteria applied to calculate storage capacity – global geologic CO2 storage capacity could be: 35,300 GtCO2 of “theoretical” capacity; 13,500 GtCO2 of “effective” capacity; 3,900 GtCO2, of “practical” capacity; and 290 GtCO2 of “matched” capacity for the few regions where this narrow definition of capacity has been calculated. The cumulative demand for geologic CO2 storage is likely quite small compared to global estimates of the deep geologic CO2 storage capacity, and therefore, a “lack” of deep geologic CO2 storage capacity is unlikely to be an impediment for the commercial adoption of CCS technologies in this century.« less

Teaching and Learning Resilience: Building Adaptive Capacity for Rural Practice. A Report and Subsequent Analysis of a Workshop Conducted at the Rural Medical Educators Conference, Savannah, Georgia, May 18, 2010

ERIC Educational Resources Information Center

Longenecker, Randall; Zink, Therese; Florence, Joseph

2012-01-01

Purpose: Resilience, the capacity to endure and overcome hardship, has been suggested as a basic competency for rural medical practice. Unfortunately for physician educators, the medical education literature offers only limited guidance for nurturing this adaptive capacity. We describe the process and subsequent analysis of a daylong curriculum…

Cycling capacity recovery effect: A coulombic efficiency and post-mortem study

NASA Astrophysics Data System (ADS)

Wilhelm, Jörn; Seidlmayer, Stefan; Keil, Peter; Schuster, Jörg; Kriele, Armin; Gilles, Ralph; Jossen, Andreas

2017-10-01

The analysis of lithium-ion battery aging relies on correct differentiation between irreversible and reversible capacity changes. Anode overhang regions have been observed to influence Coulombic Efficiency (CE) measurements through lithium diffusion into and out of these areas, complicating precise capacity determination. This work presents an analysis of the extent of graphite anode overhang lithiation after calendar storage by means of local X-ray diffraction (XRD), CE measurements, and color change analysis. We found LiC12 lithiation of the anode overhang area after 20 month storage at 40 °C at high state of charge (SoC) and partial lithiation (LiC18) at medium SoC storage at 40 °C and 25 °C. Graphite color changes in the overhang areas are observed and consistent with the state of lithiation measured by XRD. Coulombic efficiencies greater than unity and increasing capacity during 1200 h of cycling are detected for high SoC storage cells. The capacity difference between high and low storage SoC batteries decreases by up to 40 mAh (3.6% of nominal capacity) after cycling compared to tests directly after storage. Consequently, the size of the anode overhang areas as well as the battery storage temperature and duration need to be considered in CE analysis and state of health assessment.

Assessment of the transportation route of oversize and excessive loads in relation to the load-bearing capacity of existing bridges

NASA Astrophysics Data System (ADS)

Doležel, Jiří; Novák, Drahomír; Petrů, Jan

2017-09-01

Transportation routes of oversize and excessive loads are currently planned in relation to ensure the transit of a vehicle through critical points on the road. Critical points are level-intersection of roads, bridges etc. This article presents a comprehensive procedure to determine a reliability and a load-bearing capacity level of the existing bridges on highways and roads using the advanced methods of reliability analysis based on simulation techniques of Monte Carlo type in combination with nonlinear finite element method analysis. The safety index is considered as a main criterion of the reliability level of the existing construction structures and the index is described in current structural design standards, e.g. ISO and Eurocode. An example of a single-span slab bridge made of precast prestressed concrete girders of the 60 year current time and its load bearing capacity is set for the ultimate limit state and serviceability limit state. The structure’s design load capacity was estimated by the full probability nonlinear MKP analysis using a simulation technique Latin Hypercube Sampling (LHS). Load-bearing capacity values based on a fully probabilistic analysis are compared with the load-bearing capacity levels which were estimated by deterministic methods of a critical section of the most loaded girders.

Integrated network capacity analysis for freight railroads.

DOT National Transportation Integrated Search

2016-02-23

Rail network capacity analysis should consider all network infrastructures in an integrated way, with the challenges of the nonlinear relationships at each network element, a link or a node, and complexity of the interaction between various network e...

A Novel Capacity Analysis for Wireless Backhaul Mesh Networks

NASA Astrophysics Data System (ADS)

Chung, Tein-Yaw; Lee, Kuan-Chun; Lee, Hsiao-Chih

This paper derived a closed-form expression for inter-flow capacity of a backhaul wireless mesh network (WMN) with centralized scheduling by employing a ring-based approach. Through the definition of an interference area, we are able to accurately describe a bottleneck collision area for a WMN and calculate the upper bound of inter-flow capacity. The closed-form expression shows that the upper bound is a function of the ratio between transmission range and network radius. Simulations and numerical analysis show that our analytic solution can better estimate the inter-flow capacity of WMNs than that of previous approach.

Design and cost analysis of rapid aquifer restoration systems using flow simulation and quadratic programming.

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1986-01-01

Detailed two-dimensional flow simulation of a complex ground-water system is combined with quadratic and linear programming to evaluate design alternatives for rapid aquifer restoration. Results show how treatment and pumping costs depend dynamically on the type of treatment process, and capacity of pumping and injection wells, and the number of wells. The design for an inexpensive treatment process minimizes pumping costs, while an expensive process results in the minimization of treatment costs. Substantial reductions in pumping costs occur with increases in injection capacity or in the number of wells. Treatment costs are reduced by expansions in pumping capacity or injecion capacity. The analysis identifies maximum pumping and injection capacities.-from Authors

The Wigner distribution and 2D classical maps

NASA Astrophysics Data System (ADS)

Sakhr, Jamal

2017-07-01

The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a novel connection between the Wigner distribution and 2D classical mechanics is introduced. Based on a well-known correspondence between the Wigner distribution and the 2D Poisson point process, the hypothesis that typical pseudo-trajectories of a 2D ergodic map have a Wignerian nearest-neighbor spacing distribution (NNSD) is put forward and numerically tested. The standard Euclidean metric is used to compute the interpoint spacings. In all test cases, the hypothesis is upheld, and the range of validity of the hypothesis appears to be robust in the sense that it is not affected by the presence or absence of: (i) mixing; (ii) time-reversal symmetry; and/or (iii) dissipation.

Dynamics and asymptotics of correlations in a many-body localized system

NASA Astrophysics Data System (ADS)

Campbell, Steve; Power, Matthew J. M.; De Chiara, Gabriele

2017-08-01

We examine the dynamics of nearest-neighbor bipartite concurrence and total correlations in the spin-1/2 XXZ model with random fields. We show, starting from factorized random initial states, that the concurrence can suffer entanglement sudden death in the long time limit and therefore may not be a useful indicator of the properties of the system. In contrast, we show that the total correlations capture the dynamics more succinctly, and further reveal a fundamental difference in the dynamics governed by the ergodic versus many-body localized phases, with the latter exhibiting dynamical oscillations. Finally, we consider an initial state composed of several singlet pairs and show that by fixing the correlation properties, while the dynamics do not reveal noticeable differences between the phases, the long-time values of the correlation measures appear to indicate the critical region.

Thermodynamics of quantum information scrambling

NASA Astrophysics Data System (ADS)

Campisi, Michele; Goold, John

2017-06-01

Scrambling of quantum information can conveniently be quantified by so-called out-of-time-order correlators (OTOCs), i.e., correlators of the type <[Wτ,V ] †[Wτ,V ] > , whose measurements present a formidable experimental challenge. Here we report on a method for the measurement of OTOCs based on the so-called two-point measurement scheme developed in the field of nonequilibrium quantum thermodynamics. The scheme is of broader applicability than methods employed in current experiments and provides a clear-cut interpretation of quantum information scrambling in terms of nonequilibrium fluctuations of thermodynamic quantities, such as work and heat. Furthermore, we provide a numerical example on a spin chain which highlights the utility of our thermodynamic approach when understanding the differences between integrable and ergodic behaviors. We also discuss how the method can be used to extend the reach of current experiments.

Daydreaming, Thought Blocking and Strudels in the Taskless, Resting Human Brain's Magnetic Fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mandell, Arnold J.; Cielo Institute, 486 Sunset Dr., Asheville, NC 28804-3727; Selz, Karen A.

The incidence, i(S), and duration, l(S), of transient, intermittent, hierarchical vorticities, strudels, S, in magnetic flux fluctuations, were computed from MEG records. from 91 task-free resting subjects. The MEG's i(S) and l(S) manifested characteristic times and entropic sensitivity resembling those reported in psychological studies of daydreaming and task-unrelated thoughts, TUTs. Transient reduction or absences of strudels can be found in patients with syndromes characterized by thought blocking. Positive ergodic single orbit measures of expansiveness and mixing predict i(S) and l(S). An analogy with the relationship between intermittent pontine-geniculate-occipital waves and dreaming is made to strudels with daydreaming. Both can bemore » interpreted as neurophysiological correlates of the spontaneous intrusions into consciousness of the never idle unconscious mind.« less

Topological order and memory time in marginally-self-correcting quantum memory

NASA Astrophysics Data System (ADS)

Siva, Karthik; Yoshida, Beni

2017-03-01

We examine two proposals for marginally-self-correcting quantum memory: the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We then show that memory time in the welded code is doubly exponential in inverse temperature via the Peierls argument. These results introduce further connections between thermal topological order and self-correction from the viewpoint of free energy and quantum circuit depth.

Connected components of irreducible maps and 1D quantum phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Szehr, Oleg, E-mail: oleg.szehr@posteo.de; Wolf, Michael M., E-mail: wolf@ma.tum.de

We investigate elementary topological properties of sets of completely positive (CP) maps that arise in quantum Perron-Frobenius theory. We prove that the set of primitive CP maps of fixed Kraus rank is path-connected and we provide a complete classification of the connected components of irreducible CP maps at given Kraus rank and fixed peripheral spectrum in terms of a multiplicity index. These findings are then applied to analyse 1D quantum phases by studying equivalence classes of translational invariant matrix product states that correspond to the connected components of the respective CP maps. Our results extend the previously obtained picture inmore » that they do not require blocking of physical sites, they lead to analytic paths, and they allow us to decompose into ergodic components and to study the breaking of translational symmetry.« less

Turbulent fluid motion IV-averages, Reynolds decomposition, and the closure problem

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1992-01-01

Ensemble, time, and space averages as applied to turbulent quantities are discussed, and pertinent properties of the averages are obtained. Those properties, together with Reynolds decomposition, are used to derive the averaged equations of motion and the one- and two-point moment or correlation equations. The terms in the various equations are interpreted. The closure problem of the averaged equations is discussed, and possible closure schemes are considered. Those schemes usually require an input of supplemental information unless the averaged equations are closed by calculating their terms by a numerical solution of the original unaveraged equations. The law of the wall for velocities and temperatures, the velocity- and temperature-defect laws, and the logarithmic laws for velocities and temperatures are derived. Various notions of randomness and their relation to turbulence are considered in light of ergodic theory.

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

Neural Network and Nearest Neighbor Algorithms for Enhancing Sampling of Molecular Dynamics.

PubMed

Galvelis, Raimondas; Sugita, Yuji

2017-06-13

The free energy calculations of complex chemical and biological systems with molecular dynamics (MD) are inefficient due to multiple local minima separated by high-energy barriers. The minima can be escaped using an enhanced sampling method such as metadynamics, which apply bias (i.e., importance sampling) along a set of collective variables (CV), but the maximum number of CVs (or dimensions) is severely limited. We propose a high-dimensional bias potential method (NN2B) based on two machine learning algorithms: the nearest neighbor density estimator (NNDE) and the artificial neural network (ANN) for the bias potential approximation. The bias potential is constructed iteratively from short biased MD simulations accounting for correlation among CVs. Our method is capable of achieving ergodic sampling and calculating free energy of polypeptides with up to 8-dimensional bias potential.

Emergent kinetic constraints, ergodicity breaking, and cooperative dynamics in noisy quantum systems

NASA Astrophysics Data System (ADS)

Everest, B.; Marcuzzi, M.; Garrahan, J. P.; Lesanovsky, I.

2016-11-01

Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.

Tunneling with a hydrodynamic pilot-wave model

NASA Astrophysics Data System (ADS)

Nachbin, André; Milewski, Paul A.; Bush, John W. M.

2017-03-01

Eddi et al. [Phys. Rev Lett. 102, 240401 (2009), 10.1103/PhysRevLett.102.240401] presented experimental results demonstrating the unpredictable tunneling of a classical wave-particle association as may arise when a droplet walking across the surface of a vibrating fluid bath approaches a submerged barrier. We here present a theoretical model that captures the influence of bottom topography on this wave-particle association and so enables us to investigate its interaction with barriers. The coupled wave-droplet dynamics results in unpredictable tunneling events. As reported in the experiments by Eddi et al. and as is the case in quantum tunneling [Gamow, Nature (London) 122, 805 (1928), 10.1038/122805b0], the predicted tunneling probability decreases exponentially with increasing barrier width. In the parameter regimes examined, tunneling between two cavities suggests an underlying stationary ergodic process for the droplet's position.

Glass/Jamming Transition in Colloidal Aggregation

NASA Technical Reports Server (NTRS)

Segre, Philip N.; Prasad, Vikram; Weitz, David A.; Rose, M. Franklin (Technical Monitor)

2000-01-01

We have studied colloidal aggregation in a model colloid plus polymer system with short-range attractive interactions. By varying the colloid concentration and the strength of the attraction, we explored regions where the equilibrium phase is expected to consist of colloidal crystallites in coexistance with colloidal gas (i.e. monomers). This occurs for moderate values of the potential depth, U approximately equal to 2-5 kT. Crystallization was not always observed. Rather, over an extended sub-region two new metastable phases appear, one fluid-like and one solid-like. These were examined in detail with light scattering and microscopy techniques. Both phases consist of a near uniform distribution of small irregular shaped clusters of colloidal particles. The dynamical and structural characteristics of the ergodic-nonergodic transition between the two phases share much in common with the colloidal hard sphere glass transition.

Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains

NASA Astrophysics Data System (ADS)

Formentin, M.; Külske, C.; Reichenbachs, A.

2012-01-01

We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.

Dynamic Nuclear Polarization and the Paradox of Quantum Thermalization.

PubMed

De Luca, Andrea; Rosso, Alberto

2015-08-21

Dynamic nuclear polarization (DNP) is to date the most effective technique to increase the nuclear polarization opening disruptive perspectives for medical applications. In a DNP setting, the interacting spin system is quasi-isolated and brought out of equilibrium by microwave irradiation. Here we show that the resulting stationary state strongly depends on the ergodicity properties of the spin many-body eigenstates. In particular, the dipolar interactions compete with the disorder induced by local magnetic fields resulting in two distinct dynamical phases: while for weak interaction, only a small enhancement of polarization is observed, for strong interactions the spins collectively equilibrate to an extremely low effective temperature that boosts DNP efficiency. We argue that these two phases are intimately related to the problem of thermalization in closed quantum systems where a many-body localization transition can occur varying the strength of the interactions.

LRFD software for design and actual ultimate capacity of confined rectangular columns.

DOT National Transportation Integrated Search

2013-04-01

The analysis of concrete columns using unconfined concrete models is a well established practice. On the : other hand, prediction of the actual ultimate capacity of confined concrete columns requires specialized nonlinear : analysis. Modern codes and...

Window and Overlap Processing Effects on Power Estimates from Spectra

NASA Astrophysics Data System (ADS)

Trethewey, M. W.

2000-03-01

Fast Fourier transform (FFT) spectral processing is based on the assumption of stationary ergodic data. In engineering practice, the assumption is often violated and non-stationary data processed. Data windows are commonly used to reduce leakage by decreasing the signal amplitudes near the boundaries of the discrete samples. With certain combinations of non-stationary signals and windows, the temporal weighting may attenuate important signal characteristics to adversely affect any subsequent processing. In other words, the window artificially reduces a significant section of the time signal. Consequently, spectra and overall power estimated from the affected samples are unreliable. FFT processing can be particularly problematic when the signal consists of randomly occurring transients superimposed on a more continuous signal. Overlap processing is commonly used in this situation to improve the estimates. However, the results again depend on the temporal character of the signal in relation to the window weighting. A worst-case scenario, a short-duration half sine pulse, is used to illustrate the relationship between overlap percentage and resulting power estimates. The power estimates are shown to depend on the temporal behaviour of the square of overlapped window segments. An analysis shows that power estimates may be obtained to within 0.27 dB for the following windows and overlap combinations: rectangular (0% overlap), Hanning (62.5% overlap), Hamming (60.35% overlap) and flat-top (82.25% overlap).

Increasing community capacity to prevent childhood obesity: challenges, lessons learned and results from the Romp & Chomp intervention.

PubMed

de Groot, Florentine P; Robertson, Narelle M; Swinburn, Boyd A; de Silva-Sanigorski, Andrea M

2010-08-31

Obesity is a major public health issue; however, only limited evidence is available about effective ways to prevent obesity, particularly in early childhood. Romp & Chomp was a community-wide obesity prevention intervention conducted in Geelong Australia with a target group of 12,000 children aged 0-5 years. The intervention had an environmental and capacity building focus and we have recently demonstrated that the prevalence of overweight/obesity was lower in intervention children, post-intervention. Capacity building is defined as the development of knowledge, skills, commitment, structures, systems and leadership to enable effective health promotion and the aim of this study was to determine if the capacity of the Geelong community, represented by key stakeholder organisations, to support healthy eating and physical activity for young children was increased after Romp & Chomp. A mixed methods evaluation with three data sources was utilised. 1) Document analysis comprised assessment of the documented formative and intervention activities against a capacity building framework (five domains: Partnerships, Leadership, Resource Allocation, Workforce Development, and Organisational Development); 2) Thematic analysis of key informant interviews (n = 16); and 3) the quantitative Community Capacity Index Survey. Document analysis showed that the majority of the capacity building activities addressed the Partnerships, Resource Allocation and Organisational Development domains of capacity building, with a lack of activity in the Leadership and Workforce Development domains. The thematic analysis revealed the establishment of sustainable partnerships, use of specialist advice, and integration of activities into ongoing formal training for early childhood workers. Complex issues also emerged from the key informant interviews regarding the challenges of limited funding, high staff turnover, changing governance structures, lack of high level leadership and unclear communication strategies. The Community Capacity Index provided further evidence that the project implementation network achieved a moderate level of capacity. Romp & Chomp increased the capacity of organisations, settings and services in the Geelong community to support healthy eating and physical activity for young children. Despite this success there are important learnings from this mixed methods evaluation that should inform current and future community-based public health and health promotion initiatives. ANZCTRN12607000374460.

Capacity analysis of a bypass of roundabouts

NASA Astrophysics Data System (ADS)

Sedlačik, Ivan; Slabý, Petr

2017-09-01

The capacity of the roads network mainly depends on the capacity of its nodal points - intersections. A connecting branch or a bypass is a lane or lanes inserted between two adjacent branches of a roundabout, providing redirection of vehicles, that would otherwise burden a circular lane. A bypass effect to the capacity of roundabouts, but also other types of level intersections, is undeniable. A connecting branch increases the total capacity of an intersection that takes a part of vehicles performing a manoeuver of the first right turn completely out of an intersection area. Redirecting vehicles reduces delay times at intersections and reduces queues at the entrance to an intersection. Bypasses improve the quality of transport. Limiting for the capacity of bypasses is the point of disconnection from the entrance into the roundabout and the connection point into the exit from the roundabout. Central parts of the bypasses have minimal effects on the capacity. The length of a bypass has to match with the maximum length of a queue of waiting vehicles at a given intensity level. The article deals with analysis of the bypass capacity at the roundabouts.

Building surgical capacity in low-resource countries: a qualitative analysis of task shifting from surgeon volunteers' perspectives.

PubMed

Aliu, Oluseyi; Corlew, Scott D; Heisler, Michele E; Pannucci, Christopher J; Chung, Kevin C

2014-01-01

Surgical volunteer organizations (SVOs) focus considerable resources on addressing the backlog of cases in low-resource countries. This model of service may perpetuate dependency. Efforts should focus on models that establish independence in providing surgical care. Independence could be achieved through surgical capacity building. However, there has been scant discussion in literature on SVO involvement in surgical capacity building. Using qualitative methods, we evaluated the perspectives of surgeons with extensive volunteer experience in low-resource countries. We collected data through in-depth interviews that centered on SVOs using task shifting as a tool for surgical capacity building. Some of the key themes from our analysis include the ethical ramifications of task shifting, the challenges of addressing technical and clinical education in capacity building for low-resource settings, and the allocation of limited volunteer resources toward surgical capacity building. These themes will be the foundation of subsequent studies that will focus on other stakeholders in surgical capacity building including host communities and SVO administrators.

Predictors of exercise capacity following exercise-based rehabilitation in patients with coronary heart disease and heart failure: A meta-regression analysis.

PubMed

Uddin, Jamal; Zwisler, Ann-Dorthe; Lewinter, Christian; Moniruzzaman, Mohammad; Lund, Ken; Tang, Lars H; Taylor, Rod S

2016-05-01

The aim of this study was to undertake a comprehensive assessment of the patient, intervention and trial-level factors that may predict exercise capacity following exercise-based rehabilitation in patients with coronary heart disease and heart failure. Meta-analysis and meta-regression analysis. Randomized controlled trials of exercise-based rehabilitation were identified from three published systematic reviews. Exercise capacity was pooled across trials using random effects meta-analysis, and meta-regression used to examine the association between exercise capacity and a range of patient (e.g. age), intervention (e.g. exercise frequency) and trial (e.g. risk of bias) factors. 55 trials (61 exercise-control comparisons, 7553 patients) were included. Following exercise-based rehabilitation compared to control, overall exercise capacity was on average 0.95 (95% CI: 0.76-1.41) standard deviation units higher, and in trials reporting maximum oxygen uptake (VO2max) was 3.3 ml/kg.min(-1) (95% CI: 2.6-4.0) higher. There was evidence of a high level of statistical heterogeneity across trials (I(2) statistic > 50%). In multivariable meta-regression analysis, only exercise intervention intensity was found to be significantly associated with VO2max (P = 0.04); those trials with the highest average exercise intensity had the largest mean post-rehabilitation VO2max compared to control. We found considerable heterogeneity across randomized controlled trials in the magnitude of improvement in exercise capacity following exercise-based rehabilitation compared to control among patients with coronary heart disease or heart failure. Whilst higher exercise intensities were associated with a greater level of post-rehabilitation exercise capacity, there was no strong evidence to support other intervention, patient or trial factors to be predictive. © The European Society of Cardiology 2015.

Estimation of railroad capacity using parametric methods.

DOT National Transportation Integrated Search

2013-12-01

This paper reviews different methodologies used for railroad capacity estimation and presents a user-friendly method to measure capacity. The objective of this paper is to use multivariate regression analysis to develop a continuous relation of the d...

Influence of Synaptic Depression on Memory Storage Capacity

NASA Astrophysics Data System (ADS)

Otsubo, Yosuke; Nagata, Kenji; Oizumi, Masafumi; Okada, Masato

2011-08-01

Synaptic efficacy between neurons is known to change within a short time scale dynamically. Neurophysiological experiments show that high-frequency presynaptic inputs decrease synaptic efficacy between neurons. This phenomenon is called synaptic depression, a short term synaptic plasticity. Many researchers have investigated how the synaptic depression affects the memory storage capacity. However, the noise has not been taken into consideration in their analysis. By introducing ``temperature'', which controls the level of the noise, into an update rule of neurons, we investigate the effects of synaptic depression on the memory storage capacity in the presence of the noise. We analytically compute the storage capacity by using a statistical mechanics technique called Self Consistent Signal to Noise Analysis (SCSNA). We find that the synaptic depression decreases the storage capacity in the case of finite temperature in contrast to the case of the low temperature limit, where the storage capacity does not change.

Capacity Model and Constraints Analysis for Integrated Remote Wireless Sensor and Satellite Network in Emergency Scenarios

PubMed Central

Zhang, Wei; Zhang, Gengxin; Dong, Feihong; Xie, Zhidong; Bian, Dongming

2015-01-01

This article investigates the capacity problem of an integrated remote wireless sensor and satellite network (IWSSN) in emergency scenarios. We formulate a general model to evaluate the remote sensor and satellite network capacity. Compared to most existing works for ground networks, the proposed model is time varying and space oriented. To capture the characteristics of a practical network, we sift through major capacity-impacting constraints and analyze the influence of these constraints. Specifically, we combine the geometric satellite orbit model and satellite tool kit (STK) engineering software to quantify the trends of the capacity constraints. Our objective in analyzing these trends is to provide insights and design guidelines for optimizing the integrated remote wireless sensor and satellite network schedules. Simulation results validate the theoretical analysis of capacity trends and show the optimization opportunities of the IWSSN. PMID:26593919

Capacity Model and Constraints Analysis for Integrated Remote Wireless Sensor and Satellite Network in Emergency Scenarios.

PubMed

Zhang, Wei; Zhang, Gengxin; Dong, Feihong; Xie, Zhidong; Bian, Dongming

2015-11-17

This article investigates the capacity problem of an integrated remote wireless sensor and satellite network (IWSSN) in emergency scenarios. We formulate a general model to evaluate the remote sensor and satellite network capacity. Compared to most existing works for ground networks, the proposed model is time varying and space oriented. To capture the characteristics of a practical network, we sift through major capacity-impacting constraints and analyze the influence of these constraints. Specifically, we combine the geometric satellite orbit model and satellite tool kit (STK) engineering software to quantify the trends of the capacity constraints. Our objective in analyzing these trends is to provide insights and design guidelines for optimizing the integrated remote wireless sensor and satellite network schedules. Simulation results validate the theoretical analysis of capacity trends and show the optimization opportunities of the IWSSN.

Investigation on phase transitions of 1-decylammonium hydrochloride as the potential thermal energy storage material

NASA Astrophysics Data System (ADS)

Dan, Wen-Yan; Di, You-Ying; He, Dong-Hua; Liu, Yu-Pu

2011-02-01

1-Decylammonium hydrochloride was synthesized by the method of liquid phase synthesis. Chemical analysis, elemental analysis, and X-ray single crystal diffraction techniques were applied to characterize its composition and structure. Low-temperature heat capacities of the compounds were measured with a precision automated adiabatic calorimeter over the temperature range from 78 to 380 K. Three solid-solid phase transitions have been observed at the peak temperatures of 307.52 ± 0.13, 325.02 ± 0.19, and 327.26 ± 0.07 K. The molar enthalpies and entropies of three phase transitions were determined based on the analysis of heat capacity curves. Experimental molar heat capacities were fitted to two polynomial equations of the heat capacities as a function of temperature by least square method. Smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15 K were calculated and tabulated at intervals of 5 K based on the fitted polynomials.

Geothermal Project Database Supporting Barriers and Viability Analysis for Development by 2020 Timeline

DOE Data Explorer

Anna Wall

2014-10-21

This data provides the underlying project-level analysis and data sources complied in response to the DOE request to determine the amount of geothermal capacity that could be available to meet the President's request to double renewable energy capacity by 2020. The enclosed data contains compiled data on individual project names and locations (by geothermal area and region), ownership, estimated nameplate capacity, and project status, and also contains inferred data on the barriers and viability of the project to meet a 2020 development timeline. The analysis of this data is discussed in the attached NREL report.

Efficacy of N-Acetylcysteine in Idiopathic Pulmonary Fibrosis: A Systematic Review and Meta-Analysis.

PubMed

Sun, Tong; Liu, Jing; Zhao, De Wei

2016-05-01

There are a number of conflicting reports describing the clinical outcomes of using N-acetylcysteine for the treatment of idiopathic pulmonary fibrosis. We have, therefore, performed a meta-analysis to evaluate the efficacy of N-acetylcysteine, compared with control, for the treatment of idiopathic pulmonary fibrosis.Original controlled clinical trials evaluating the efficacy of N-acetylcysteine for the treatment of idiopathic pulmonary fibrosis were included in the analysis. Searches for relevant articles were carried out in July 2014 by 2 independent researchers using PubMed, Embase, Cochrane Central, and Google Scholar. Change in forced vital capacity, change in percentage of predicted vital capacity, change in percentage of predicted carbon monoxide diffusing capacity, changes in 6 minutes walking test distance, rate of adverse events, and rate of death were expressed as outcomes using RevMan 5.0.1.Five trials, with a total of 564 patients, were included in this meta-analysis. The meta-analysis showed that the control group had significant decreases in percentage of predicted vital capacity (standardized mean difference [SMD] = 0.37; 95% confidence interval [CI]: 0.13 to -0.62; P = 0.003) and 6 minutes walking test distance (SMD = 0.25; 95% CI: 0.02-0.48; P = 0.04). There were no statistically significant differences in forced vital capacity (SMD = 0.07; 95% CI: -0.13-0.27; P = 0.52), percentage of predicted carbon monoxide diffusing capacity (SMD = 0.12; 95% CI: -0.06-0.30; P = 0.18), rates of adverse events (odd ratio = 4.50; 95% CI: 0.19-106.41; P = 0.35), or death rates (odd ratio = 1.79; 95% CI: 0.3-5.12; P = 0.28) between the N-acetylcysteine group and the control group.N-Acetylcysteine was found to have a significant effect only on decreases in percentage of predicted vital capacity and 6 minutes walking test distance. N-acetylcysteine showed no beneficial effect on changes in forced vital capacity, changes in predicted carbon monoxide diffusing capacity, rates of adverse events, or death rates.

Image watermarking capacity analysis based on Hopfield neural network

NASA Astrophysics Data System (ADS)

Zhang, Fan; Zhang, Hongbin

2004-11-01

In watermarking schemes, watermarking can be viewed as a form of communication problems. Almost all of previous works on image watermarking capacity are based on information theory, using Shannon formula to calculate the capacity of watermarking. In this paper, we present a blind watermarking algorithm using Hopfield neural network, and analyze watermarking capacity based on neural network. In our watermarking algorithm, watermarking capacity is decided by attraction basin of associative memory.

Estimating design flood and HEC-RAS modelling approach for flood analysis in Bojonegoro city

NASA Astrophysics Data System (ADS)

Prastica, R. M. S.; Maitri, C.; Hermawan, A.; Nugroho, P. C.; Sutjiningsih, D.; Anggraheni, E.

2018-03-01

Bojonegoro faces flood every year with less advanced prevention development. Bojonegoro city development could not peak because the flood results material losses. It affects every sectors in Bojonegoro: education, politics, economy, social, and infrastructure development. This research aims to analyse and to ensure that river capacity has high probability to be the main factor of flood in Bojonegoro. Flood discharge analysis uses Nakayasu synthetic unit hydrograph for period of 5 years, 10 years, 25 years, 50 years, and 100 years. They would be compared to the water maximum capacity that could be loaded by downstream part of Bengawan Solo River in Bojonegoro. According to analysis result, Bengawan Solo River in Bojonegoro could not able to load flood discharges. Another method used is HEC-RAS analysis. The conclusion that shown by HEC-RAS analysis has the same view. It could be observed that flood water loading is more than full bank capacity elevation in the river. To conclude, the main factor that should be noticed by government to solve flood problem is river capacity.

Rotation Capacity of Bolted Flush End-Plate Stiffened Beam-to-Column Connection

NASA Astrophysics Data System (ADS)

Ostrowski, Krzysztof; Kozłowski, Aleksander

2017-06-01

One of the flexibility parameters of semi-rigid joints is rotation capacity. Plastic rotation capacity is especially important in plastic design of framed structures. Current design codes, including Eurocode 3, do not posses procedures enabling designers to obtain value of rotation capacity. In the paper the calculation procedure of the rotation capacity for stiffened bolted flush end-plate beam-to-column connections has been proposed. Theory of experiment design was applied with the use of Hartley's PS/DS-P:Ha3 plan. The analysis was performed with the use of finite element method (ANSYS), based on the numerical experiment plan. The determination of maximal rotation angle was carried out with the use of regression analysis. The main variables analyzed in parametric study were: pitch of the bolt "w" (120-180 mm), the distance between the bolt axis and the beam upper edge cg1 (50-90 mm) and the thickness of the end-plate tp (10-20 mm). Power function was proposed to describe available rotation capacity of the joint. Influence of the particular components on the rotation capacity was also investigated. In the paper a general procedure for determination of rotation capacity was proposed.

Golden Ratio Genetic Algorithm Based Approach for Modelling and Analysis of the Capacity Expansion of Urban Road Traffic Network

PubMed Central

Zhang, Lun; Zhang, Meng; Yang, Wenchen; Dong, Decun

2015-01-01

This paper presents the modelling and analysis of the capacity expansion of urban road traffic network (ICURTN). Thebilevel programming model is first employed to model the ICURTN, in which the utility of the entire network is maximized with the optimal utility of travelers' route choice. Then, an improved hybrid genetic algorithm integrated with golden ratio (HGAGR) is developed to enhance the local search of simple genetic algorithms, and the proposed capacity expansion model is solved by the combination of the HGAGR and the Frank-Wolfe algorithm. Taking the traditional one-way network and bidirectional network as the study case, three numerical calculations are conducted to validate the presented model and algorithm, and the primary influencing factors on extended capacity model are analyzed. The calculation results indicate that capacity expansion of road network is an effective measure to enlarge the capacity of urban road network, especially on the condition of limited construction budget; the average computation time of the HGAGR is 122 seconds, which meets the real-time demand in the evaluation of the road network capacity. PMID:25802512

Urban development control based on transportation carrying capacity

NASA Astrophysics Data System (ADS)

Miharja, M.; Sjafruddin, A. H.

2017-06-01

Severe transportation problems in Indonesian urban areas are stimulated by one fundamental factor, namely lack of awareness on transportation carrying capacity in these areas development control. Urban land use development towards more physical coverage is typically not related with the capability of transportation system to accommodate additional trips volume. Lack of clear connection between development permit with its implication on the transportation side has led to a phenomenon of exceeding transport demand over supply capacity. This paper discusses the concept of urban land use development control which will be related with transport carrying capacity. The discussion would cover both supply and demand sides of transportation. From supply side, the analysis regarding the capacity of transport system would take both existing as well as potential road network capacity could be developed. From demand side, the analysis would be through the control of a maximum floor area and public transport provision. Allowed maximum floor area for development would be at the level of generating traffic at reasonable volume. Ultimately, the objective of this paper is to introduce model to incorporate transport carrying capacity in Indonesian urban land use development control.

Regional frequency analysis to asses wind resource spatial and temporal variations in Washington State

NASA Astrophysics Data System (ADS)

Mortuza, M.; Demissie, D.

2013-12-01

According to the U.S. Department of Energy's annual wind technologies market report, the wind power capacity in the country grew from 2.5 gigawatts in early 2000 to 60 gigawatts in 2012, making it one of the largest new sources of electric capacity additions in the U.S. in recent years. With over 2.8 gigawatts of current capacity (eighth largest in the nation), Washington State plays a significant role in this rapidly increasing energy resource. To further expand and/or optimize these capacities, assessment of wind resource and its spatial and temporal variations are important. However, since at-site frequency analysis using meteorological data is not adequate for extending wind frequency to locations with no data, longer return period, and heterogeneous topography and surface, a regional frequency analysis based on L-moment method is adopted in this study to estimate regional wind speed patterns and return periods in Washington State using hourly mean wind speed data from 1979 - 2010. The analysis applies the k-means, hierarchical and self-organizing map clustering techniques to explore potential clusters or regions; statistical tests are then applied to identify homogeneous regions and appropriate probability distribution models. The result from the analysis is expected to provide essential knowledge about the areas with potential capacity of constructing wind power plants, which can also be readily extended to assist decisions on their daily operations.

Time-varying bispectral analysis of visually evoked multi-channel EEG

NASA Astrophysics Data System (ADS)

Chandran, Vinod

2012-12-01

Theoretical foundations of higher order spectral analysis are revisited to examine the use of time-varying bicoherence on non-stationary signals using a classical short-time Fourier approach. A methodology is developed to apply this to evoked EEG responses where a stimulus-locked time reference is available. Short-time windowed ensembles of the response at the same offset from the reference are considered as ergodic cyclostationary processes within a non-stationary random process. Bicoherence can be estimated reliably with known levels at which it is significantly different from zero and can be tracked as a function of offset from the stimulus. When this methodology is applied to multi-channel EEG, it is possible to obtain information about phase synchronization at different regions of the brain as the neural response develops. The methodology is applied to analyze evoked EEG response to flash visual stimulii to the left and right eye separately. The EEG electrode array is segmented based on bicoherence evolution with time using the mean absolute difference as a measure of dissimilarity. Segment maps confirm the importance of the occipital region in visual processing and demonstrate a link between the frontal and occipital regions during the response. Maps are constructed using bicoherence at bifrequencies that include the alpha band frequency of 8Hz as well as 4 and 20Hz. Differences are observed between responses from the left eye and the right eye, and also between subjects. The methodology shows potential as a neurological functional imaging technique that can be further developed for diagnosis and monitoring using scalp EEG which is less invasive and less expensive than magnetic resonance imaging.

Parallel computing in enterprise modeling.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldsby, Michael E.; Armstrong, Robert C.; Shneider, Max S.

2008-08-01

This report presents the results of our efforts to apply high-performance computing to entity-based simulations with a multi-use plugin for parallel computing. We use the term 'Entity-based simulation' to describe a class of simulation which includes both discrete event simulation and agent based simulation. What simulations of this class share, and what differs from more traditional models, is that the result sought is emergent from a large number of contributing entities. Logistic, economic and social simulations are members of this class where things or people are organized or self-organize to produce a solution. Entity-based problems never have an a priorimore » ergodic principle that will greatly simplify calculations. Because the results of entity-based simulations can only be realized at scale, scalable computing is de rigueur for large problems. Having said that, the absence of a spatial organizing principal makes the decomposition of the problem onto processors problematic. In addition, practitioners in this domain commonly use the Java programming language which presents its own problems in a high-performance setting. The plugin we have developed, called the Parallel Particle Data Model, overcomes both of these obstacles and is now being used by two Sandia frameworks: the Decision Analysis Center, and the Seldon social simulation facility. While the ability to engage U.S.-sized problems is now available to the Decision Analysis Center, this plugin is central to the success of Seldon. Because Seldon relies on computationally intensive cognitive sub-models, this work is necessary to achieve the scale necessary for realistic results. With the recent upheavals in the financial markets, and the inscrutability of terrorist activity, this simulation domain will likely need a capability with ever greater fidelity. High-performance computing will play an important part in enabling that greater fidelity.« less

Use of pile driving analysis for assessment of axial load capacity of piles.

DOT National Transportation Integrated Search

2012-05-01

Driven piles are commonly used in foundation engineering. Pile driving formulae, which directly relate the pile set per blow : to the capacity of the pile, are commonly used to decide whether an installed pile will have the designed capacity. However...

Use of Pile Driving Analysis for Assessment of Axial Load Capacity of Piles

DOT National Transportation Integrated Search

2012-05-01

Driven piles are commonly used in foundation engineering. Pile driving formulae, which directly relate the pile set per blow : to the capacity of the pile, are commonly used to decide whether an installed pile will have the designed capacity. However...

Non-Contact Analysis of the Adsorptive Ink Capacity of Nano Silica Pigments on a Printing Coating Base

PubMed Central

Jiang, Bo; Huang, Yu Dong

2014-01-01

Near infrared spectra combined with partial least squares were proposed as a means of non-contact analysis of the adsorptive ink capacity of recording coating materials in ink jet printing. First, the recording coating materials were prepared based on nano silica pigments. 80 samples of the recording coating materials were selected to develop the calibration of adsorptive ink capacity against ink adsorption (g/m2). The model developed predicted samples in the validation set with r2  = 0.80 and SEP  = 1.108, analytical results showed that near infrared spectra had significant potential for the adsorption of ink capacity on the recording coating. The influence of factors such as recording coating thickness, mass ratio silica: binder-polyvinyl alcohol and the solution concentration on the adsorptive ink capacity were studied. With the help of the near infrared spectra, the adsorptive ink capacity of a recording coating material can be rapidly controlled. PMID:25329464

Non-contact analysis of the adsorptive ink capacity of nano silica pigments on a printing coating base.

PubMed

Jiang, Bo; Huang, Yu Dong

2014-01-01

Near infrared spectra combined with partial least squares were proposed as a means of non-contact analysis of the adsorptive ink capacity of recording coating materials in ink jet printing. First, the recording coating materials were prepared based on nano silica pigments. 80 samples of the recording coating materials were selected to develop the calibration of adsorptive ink capacity against ink adsorption (g/m2). The model developed predicted samples in the validation set with r2  = 0.80 and SEP = 1.108, analytical results showed that near infrared spectra had significant potential for the adsorption of ink capacity on the recording coating. The influence of factors such as recording coating thickness, mass ratio silica: binder-polyvinyl alcohol and the solution concentration on the adsorptive ink capacity were studied. With the help of the near infrared spectra, the adsorptive ink capacity of a recording coating material can be rapidly controlled.

Short-term memory capacity in networks via the restricted isometry property.

PubMed

Charles, Adam S; Yap, Han Lun; Rozell, Christopher J

2014-06-01

Cortical networks are hypothesized to rely on transient network activity to support short-term memory (STM). In this letter, we study the capacity of randomly connected recurrent linear networks for performing STM when the input signals are approximately sparse in some basis. We leverage results from compressed sensing to provide rigorous nonasymptotic recovery guarantees, quantifying the impact of the input sparsity level, the input sparsity basis, and the network characteristics on the system capacity. Our analysis demonstrates that network memory capacities can scale superlinearly with the number of nodes and in some situations can achieve STM capacities that are much larger than the network size. We provide perfect recovery guarantees for finite sequences and recovery bounds for infinite sequences. The latter analysis predicts that network STM systems may have an optimal recovery length that balances errors due to omission and recall mistakes. Furthermore, we show that the conditions yielding optimal STM capacity can be embodied in several network topologies, including networks with sparse or dense connectivities.

Weakly Nonergodic Dynamics in the Gross-Pitaevskii Lattice

NASA Astrophysics Data System (ADS)

Mithun, Thudiyangal; Kati, Yagmur; Danieli, Carlo; Flach, Sergej

2018-05-01

The microcanonical Gross-Pitaevskii (also known as the semiclassical Bose-Hubbard) lattice model dynamics is characterized by a pair of energy and norm densities. The grand canonical Gibbs distribution fails to describe a part of the density space, due to the boundedness of its kinetic energy spectrum. We define Poincaré equilibrium manifolds and compute the statistics of microcanonical excursion times off them. The tails of the distribution functions quantify the proximity of the many-body dynamics to a weakly nonergodic phase, which occurs when the average excursion time is infinite. We find that a crossover to weakly nonergodic dynamics takes place inside the non-Gibbs phase, being unnoticed by the largest Lyapunov exponent. In the ergodic part of the non-Gibbs phase, the Gibbs distribution should be replaced by an unknown modified one. We relate our findings to the corresponding integrable limit, close to which the actions are interacting through a short range coupling network.

A Perron-Frobenius Type of Theorem for Quantum Operations

NASA Astrophysics Data System (ADS)

Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

2017-10-01

We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.

Asymptotic proportionality (weak ergodicity) and conditional asymptotic equality of solutions to time-heterogeneous sublinear difference and differential equations

NASA Astrophysics Data System (ADS)

Thieme, Horst R.

The concept of asymptotic proportionality and conditional asymptotic equality which is presented here aims at making global asymptotic stability statements for time-heterogeneous difference and differential equations. For such non-autonomous problems (apart from special cases) no prominent special solutions (equilibra, periodic solutions) exist which are natural candidates for the asymptotic behaviour of arbitrary solutions. One way out of this dilemma consists in looking for conditions under which any two solutions to the problem (with different initial conditions) behave in a similar or even the same way as time tends to infinity. We study a general sublinear difference equation in an ordered Banach space and, for illustration, time-heterogeneous versions of several well-known differential equations modelling the spread of gonorrhea in a heterogeneous population, the spread of a vector-borne infectious disease, and the dynamics of a logistically growing spatially diffusing population.

Boosting association rule mining in large datasets via Gibbs sampling.

PubMed

Qian, Guoqi; Rao, Calyampudi Radhakrishna; Sun, Xiaoying; Wu, Yuehua

2016-05-03

Current algorithms for association rule mining from transaction data are mostly deterministic and enumerative. They can be computationally intractable even for mining a dataset containing just a few hundred transaction items, if no action is taken to constrain the search space. In this paper, we develop a Gibbs-sampling-induced stochastic search procedure to randomly sample association rules from the itemset space, and perform rule mining from the reduced transaction dataset generated by the sample. Also a general rule importance measure is proposed to direct the stochastic search so that, as a result of the randomly generated association rules constituting an ergodic Markov chain, the overall most important rules in the itemset space can be uncovered from the reduced dataset with probability 1 in the limit. In the simulation study and a real genomic data example, we show how to boost association rule mining by an integrated use of the stochastic search and the Apriori algorithm.

A model of non-Gaussian diffusion in heterogeneous media

NASA Astrophysics Data System (ADS)

Lanoiselée, Yann; Grebenkov, Denis S.

2018-04-01

Recent progress in single-particle tracking has shown evidence of the non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. Similar behavior has also been observed in granular materials, turbulent flows, gels and colloidal suspensions, suggesting that this is a general feature of diffusion in complex media. A possible interpretation of this phenomenon is that a tracer explores a medium with spatio-temporal fluctuations which result in local changes of diffusivity. We propose and investigate an ergodic, easily interpretable model, which implements the concept of diffusing diffusivity. Depending on the parameters, the distribution of displacements can be either flat or peaked at small displacements with an exponential tail at large displacements. We show that the distribution converges slowly to a Gaussian one. We calculate statistical properties, derive the asymptotic behavior and discuss some implications and extensions.

Quantitative recurrence for free semigroup actions

NASA Astrophysics Data System (ADS)

Carvalho, Maria; Rodrigues, Fagner B.; Varandas, Paulo

2018-03-01

We consider finitely generated free semigroup actions on a compact metric space and obtain quantitative information on Poincaré recurrence, average first return time and hitting frequency for the random orbits induced by the semigroup action. Besides, we relate the recurrence to balls with the rates of expansion of the semigroup generators and the topological entropy of the semigroup action. Finally, we establish a partial variational principle and prove an ergodic optimization for this kind of dynamical action. MC has been financially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER) under the partnership agreement PT2020. FR and PV were partially supported by BREUDS. PV has also benefited from a fellowship awarded by CNPq-Brazil and is grateful to the Faculty of Sciences of the University of Porto for the excellent research conditions.

Zero entropy continuous interval maps and MMLS-MMA property

NASA Astrophysics Data System (ADS)

Jiang, Yunping

2018-06-01

We prove that the flow generated by any continuous interval map with zero topological entropy is minimally mean-attractable and minimally mean-L-stable. One of the consequences is that any oscillating sequence is linearly disjoint from all flows generated by all continuous interval maps with zero topological entropy. In particular, the Möbius function is linearly disjoint from all flows generated by all continuous interval maps with zero topological entropy (Sarnak’s conjecture for continuous interval maps). Another consequence is a non-trivial example of a flow having discrete spectrum. We also define a log-uniform oscillating sequence and show a result in ergodic theory for comparison. This material is based upon work supported by the National Science Foundation. It is also partially supported by a collaboration grant from the Simons Foundation (grant number 523341) and PSC-CUNY awards and a grant from NSFC (grant number 11571122).

Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion

NASA Astrophysics Data System (ADS)

Chen, Yao; Wang, Xudong; Deng, Weihua

2017-10-01

This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.

Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior

NASA Astrophysics Data System (ADS)

Barles, Guy; Ley, Olivier; Topp, Erwin

2017-02-01

In this paper, we provide suitable adaptations of the ‘weak version of Bernstein method’ introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and parabolic equations set in the whole space. Our interest is to obtain such Lipschitz results to possibly degenerate equations, or to equations which are indeed ‘uniformly elliptic’ (maybe in the nonlocal sense) but which do not satisfy the usual ‘growth condition’ on the gradient term allowing to use (for example) the Ishii-Lions’ method. We treat the case of a model equation with a superlinear coercivity on the gradient term which has a leading role in the equation. This regularity result together with comparison principle provided for the problem allow to obtain the ergodic large time behavior of the evolution problem in the periodic setting.

Topology-driven phase transitions in the classical monomer-dimer-loop model.

PubMed

Li, Sazi; Li, Wei; Chen, Ziyu

2015-06-01

In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product state technique to contract the partition function TN, and determine the thermodynamic properties with high accuracy. In this monomer-dimer-loop model, we find a second-order phase transition between a trivial monomer-condensation and a loop-condensation (LC) phase, which cannot be distinguished by any local order parameter, while nevertheless the two phases have distinct topological properties. In the LC phase, we find two degenerate dominating eigenvalues in the transfer-matrix spectrum, as well as a nonvanishing (nonlocal) string order parameter, both of which identify the topological ergodicity breaking in the LC phase and can serve as the order parameter for detecting the phase transitions.

Control and Data Acquisition for the Spherical Tokamak MEDUSA-CR

NASA Astrophysics Data System (ADS)

Soto, Christian; Gonzalez, Jeferson; Carvajal, Johan; Ribeiro, Celso

2013-10-01

The former spherical tokamak (ST) MEDUSA (Madison EDUcation Small Aspect.ratio tokamak, R < 0.14 m, a < 0.10 m, BT < 0.5 T, Ip < 40 kA, 3 ms pulse) is being recommissioned in Costa Rica Institute of Technology. The main objectives of the MEDUSA-CR project are training and to clarify several issues in relevant physics for conventional and mainly STs, including beta studies in bean-shaped ST plasmas, transport, heating and current drive via Alfvén wave, and natural divertor STs with ergodic magnetic limiter. We present here the control and data acquisition systems for MEDUSA-CR device which are based on National Instruments (NI) software (LabView) and hardware on loan to our laboratory via NI-Costa Rica. The interface with the energy, gas fueling, and security systems are also presented. VIE-ITCR, IAEA-CRP contract 17592, National Instruments of Costa Rica.

Energy, Vacuum, Gas Fueling, and Security Systems for the Spherical Tokamak MEDUSA-CR

NASA Astrophysics Data System (ADS)

Gonzalez, Jeferson; Soto, Christian; Carvajal, Johan; Ribeiro, Celso

2013-10-01

The former spherical tokamak (ST) MEDUSA (Madison EDUcation Small Aspect.ratio tokamak, R < 0.14 m, a < 0.10 m, BT < 0.5 T, Ip < 40 kA, 3 ms pulse) is being recommissioned in Costa Rica Institute of Technology. The main objectives of the MEDUSA-CR project are training and to clarify several issues in relevant physics for conventional and mainly STs, including beta studies in bean-shaped ST plasmas, transport, heating and current drive via Alfvén wave, and natural divertor STs with ergodic magnetic limiter. We present here the energy, vacuum, gas fueling, and security systems for MEDUSA-CR device. The interface with the control and data acquisition systems based on National Instruments (NI) software (LabView) and hardware (on loan to our laboratory via NI-Costa Rica) are also presented. VIE-ITCR, IAEA-CRP contract 17592, National Instruments of Costa Rica.

Acoustic dynamics of supercooled indomethacin probed by Brillouin light scattering.

PubMed

De Panfilis, S; Pogna, E A A; Virga, A; Scopigno, T

2014-07-21

Acoustics dynamics of the molecular glass-former indomethacin (IMC) have been investigated by Brillouin light scattering (BLS) at GHz frequencies. Elastic response of the system has been tracked from the melting temperature down to the glass transition through the supercooled liquid. Both the structural arrest and the vibrational dynamics are described by modeling the experimentally determined dynamic structure factor within the framework of the Langevin equation, through a simplified choice of memory function which allows one to determine sound velocity and the acoustic attenuation coefficient as a function of temperature. The density fluctuation spectra in the glassy phase, as probed by BLS, are compared with time-domain results from photoacoustics experiments. The arising scenario is discussed in the context of current literature reporting inelastic X-ray scattering and BLS in platelet geometry. The link between the probed elastic properties and the non-ergodicity factor of the glass phase is finally scrutinized.

Entropy and long-range memory in random symbolic additive Markov chains

NASA Astrophysics Data System (ADS)

Melnik, S. S.; Usatenko, O. V.

2016-06-01

The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory.

Dynamics of Granular Materials

NASA Technical Reports Server (NTRS)

Behringer, Robert P.

1996-01-01

Granular materials exhibit a rich variety of dynamical behavior, much of which is poorly understood. Fractal-like stress chains, convection, a variety of wave dynamics, including waves which resemble capillary waves, l/f noise, and fractional Brownian motion provide examples. Work beginning at Duke will focus on gravity driven convection, mixing and gravitational collapse. Although granular materials consist of collections of interacting particles, there are important differences between the dynamics of a collections of grains and the dynamics of a collections of molecules. In particular, the ergodic hypothesis is generally invalid for granular materials, so that ordinary statistical physics does not apply. In the absence of a steady energy input, granular materials undergo a rapid collapse which is strongly influenced by the presence of gravity. Fluctuations on laboratory scales in such quantities as the stress can be very large-as much as an order of magnitude greater than the mean.

Entropy and long-range memory in random symbolic additive Markov chains.

PubMed

Melnik, S S; Usatenko, O V

2016-06-01

The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory.

Decomposition of conditional probability for high-order symbolic Markov chains.

PubMed

Melnik, S S; Usatenko, O V

2017-07-01

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Decomposition of conditional probability for high-order symbolic Markov chains

NASA Astrophysics Data System (ADS)

Melnik, S. S.; Usatenko, O. V.

2017-07-01

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

NASA Astrophysics Data System (ADS)

Hu, Xiaohu; Hong, Liang; Dean Smith, Micholas; Neusius, Thomas; Cheng, Xiaolin; Smith, Jeremy C.

2016-02-01

Internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behaviour with effective relaxation times existing over many decades in time, from ps up to ~102 s (refs ,,,). Here, using molecular dynamics simulations, we show that, on timescales from 10-12 to 10-5 s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of the energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behaviour persists up to timescales approaching the in vivo lifespan of individual protein molecules.

Fluorescence correlation spectroscopy: the case of subdiffusion.

PubMed

Lubelski, Ariel; Klafter, Joseph

2009-03-18

The theory of fluorescence correlation spectroscopy is revisited here for the case of subdiffusing molecules. Subdiffusion is assumed to stem from a continuous-time random walk process with a fat-tailed distribution of waiting times and can therefore be formulated in terms of a fractional diffusion equation (FDE). The FDE plays the central role in developing the fluorescence correlation spectroscopy expressions, analogous to the role played by the simple diffusion equation for regular systems. Due to the nonstationary nature of the continuous-time random walk/FDE, some interesting properties emerge that are amenable to experimental verification and may help in discriminating among subdiffusion mechanisms. In particular, the current approach predicts 1), a strong dependence of correlation functions on the initial time (aging); 2), sensitivity of correlation functions to the averaging procedure, ensemble versus time averaging (ergodicity breaking); and 3), that the basic mean-squared displacement observable depends on how the mean is taken.

Invariant measures in brain dynamics

NASA Astrophysics Data System (ADS)

Boyarsky, Abraham; Góra, Paweł

2006-10-01

This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a “folding” property on the space of ensembles.

Entropy of finite random binary sequences with weak long-range correlations.

PubMed

Melnik, S S; Usatenko, O V

2014-11-01

We study the N-step binary stationary ergodic Markov chain and analyze its differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and represent the entropy as a functional of the pair correlator. Since the model uses the two-point correlators instead of the block probability, it makes it possible to calculate the entropy of strings at much longer distances than using standard methods. A fluctuation contribution to the entropy due to finiteness of random chains is examined. This contribution can be of the same order as its regular part even at the relatively short lengths of subsequences. A self-similar structure of entropy with respect to the decimation transformations is revealed for some specific forms of the pair correlation function. Application of the theory to the DNA sequence of the R3 chromosome of Drosophila melanogaster is presented.

Intermittent Fermi-Pasta-Ulam Dynamics at Equilibrium

NASA Astrophysics Data System (ADS)

Campbell, David; Danieli, Carlo; Flach, Sergej

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body syste. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. We show that previously obtained scaling laws for equipartition times are modified at low energy density due to an unexpected slowing down of the relaxation. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. The long excursions arise from sticky dynamics close to regular orbits in the phase space. Our method is generalizable to large classes of many-body systems. The authors acknowledge financial support from IBS (Project Code IBS-R024-D1).

BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices

NASA Astrophysics Data System (ADS)

Janse van Rensburg, E. J.; Rechnitzer, A.

2011-04-01

In this paper, the elementary moves of the BFACF-algorithm (Aragão de Carvalho and Caracciolo 1983 Phys. Rev. B 27 1635-45, Aragão de Carvalho and Caracciolo 1983 Nucl. Phys. B 215 209-48, Berg and Foester 1981 Phys. Lett. B 106 323-6) for lattice polygons are generalized to elementary moves of BFACF-style algorithms for lattice polygons in the body-centered (BCC) and face-centered (FCC) cubic lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC lattices and so expand a similar result for the cubic lattice (see Janse van Rensburg and Whittington (1991 J. Phys. A: Math. Gen. 24 5553-67)). Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC lattices.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Jie; Krems, Roman V.; Li, Zhiying

We use classical trajectory calculations to study the effects of the interaction strength and the geometry of rigid polyatomic molecules on the formation of long-lived collision complexes at low collision energies. We first compare the results of the calculations for collisions of benzene molecules with rare gas atoms He, Ne, Ar, Kr, and Xe. The comparison illustrates that the mean lifetimes of the collision complexes increase monotonically with the strength of the atom–molecule interaction. We then compare the results of the atom–benzene calculations with those for benzene–benzene collisions. The comparison illustrates that the mean lifetimes of the benzene–benzene collision complexesmore » are significantly reduced due to non-ergodic effects prohibiting the molecules from sampling the entire configuration space. We find that the thermally averaged lifetimes of the benzene–benzene collisions are much shorter than those for Xe with benzene and similar to those for Ne with benzene.« less

Tunable resistivity due to kinetic arrest of antiferro-ferromagnetic transition in FeRh0.46Pd0.54

NASA Astrophysics Data System (ADS)

Saha, Pampi; Rawat, R.

2018-05-01

We show a large negative magnetoresistance (MR) of ≈10% near room temperature in FeRh0.46Pd0.54, which increases to more than 60% at low temperatures. The magnitude of resistivity and, hence, MR depend on the history of the sample in HT (magnetic field-temperature) space, e.g., resistivity at 5 K changes by more than 70% with thermal cycling. These results are explained due to slow kinetics of the transformation from austenite antiferromagnetic (AF) to martensite ferromagnetic (FM) state with the decrease in temperature. As a result, AF to FM transformation remains incomplete on experimental time scales and non-ergodic AF phase co-exists with a low temperature equilibrium FM phase. In the present system, the kinetics of the transition is shown to dominate up to 150 K, which is significantly high in comparison to other kinetically arrested systems.

Entropy of finite random binary sequences with weak long-range correlations

NASA Astrophysics Data System (ADS)

Melnik, S. S.; Usatenko, O. V.

2014-11-01

We study the N -step binary stationary ergodic Markov chain and analyze its differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and represent the entropy as a functional of the pair correlator. Since the model uses the two-point correlators instead of the block probability, it makes it possible to calculate the entropy of strings at much longer distances than using standard methods. A fluctuation contribution to the entropy due to finiteness of random chains is examined. This contribution can be of the same order as its regular part even at the relatively short lengths of subsequences. A self-similar structure of entropy with respect to the decimation transformations is revealed for some specific forms of the pair correlation function. Application of the theory to the DNA sequence of the R3 chromosome of Drosophila melanogaster is presented.

Dynamics of symmetry breaking during quantum real-time evolution in a minimal model system.

PubMed

Heyl, Markus; Vojta, Matthias

2014-10-31

One necessary criterion for the thermalization of a nonequilibrium quantum many-particle system is ergodicity. It is, however, not sufficient in cases where the asymptotic long-time state lies in a symmetry-broken phase but the initial state of nonequilibrium time evolution is fully symmetric with respect to this symmetry. In equilibrium, one particular symmetry-broken state is chosen as a result of an infinitesimal symmetry-breaking perturbation. From a dynamical point of view the question is: Can such an infinitesimal perturbation be sufficient for the system to establish a nonvanishing order during quantum real-time evolution? We study this question analytically for a minimal model system that can be associated with symmetry breaking, the ferromagnetic Kondo model. We show that after a quantum quench from a completely symmetric state the system is able to break its symmetry dynamically and discuss how these features can be observed experimentally.

Limiting Energy Dissipation Induces Glassy Kinetics in Single-Cell High-Precision Responses

PubMed Central

Das, Jayajit

2016-01-01

Single cells often generate precise responses by involving dissipative out-of-thermodynamic-equilibrium processes in signaling networks. The available free energy to fuel these processes could become limited depending on the metabolic state of an individual cell. How does limiting dissipation affect the kinetics of high-precision responses in single cells? I address this question in the context of a kinetic proofreading scheme used in a simple model of early-time T cell signaling. Using exact analytical calculations and numerical simulations, I show that limiting dissipation qualitatively changes the kinetics in single cells marked by emergence of slow kinetics, large cell-to-cell variations of copy numbers, temporally correlated stochastic events (dynamic facilitation), and ergodicity breaking. Thus, constraints in energy dissipation, in addition to negatively affecting ligand discrimination in T cells, can create a fundamental difficulty in determining single-cell kinetics from cell-population results. PMID:26958894

Magnetohydrodynamic Turbulence and the Geodynamo

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2014-01-01

The ARES Directorate at JSC has researched the physical processes that create planetary magnetic fields through dynamo action since 2007. The "dynamo problem" has existed since 1600, when William Gilbert, physician to Queen Elizabeth I, recognized that the Earth was a giant magnet. In 1919, Joseph Larmor proposed that solar (and by implication, planetary) magnetism was due to magnetohydrodynamics (MHD), but full acceptance did not occur until Glatzmaier and Roberts solved the MHD equations numerically and simulated a geomagnetic reversal in 1995. JSC research produced a unique theoretical model in 2012 that provided a novel explanation of these physical observations and computational results as an essential manifestation of broken ergodicity in MHD turbulence. Research is ongoing, and future work is aimed at understanding quantitative details of magnetic dipole alignment in the Earth as well as in Mercury, Jupiter and its moon Ganymede, Saturn, Uranus, Neptune, and the Sun and other stars.

An investigation of chaotic Kolmogorov flows

NASA Technical Reports Server (NTRS)

Platt, N.; Sirovich, L.; Fitzmaurice, N.

1990-01-01

A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.

Young Adult Capacity Initiative Cross-Site Analysis

ERIC Educational Resources Information Center

Academy for Educational Development, 2012

2012-01-01

This cross-site analysis presents findings about the implementation, impact, and outcomes of the Young Adult Capacity Initiative (YACI), at 13 community-based organizations in New York City. These agencies received technical assistance and small incentive grants from the Fund for the City of New York Youth Development Institute (YDI) to build…

Closing the Chasm: Preparing and Building Post-Conflict Civil Capacity

DTIC Science & Technology

2010-03-18

vii Background and Analysis ...CLOSING THE CHASM: PREPARING AND BUILDING POST-CONFLICT CIVIL CAPACITY Background and Analysis Introduction Plans fail for lack of counsel... rhythmic comfort zone. The lack of Human Resource depth in the military and other Federal agencies‘ directly impact their priorities of ongoing

The person's conception of the structures of developing intellect: early adolescence to middle age.

PubMed

Demetriou, A; Efklides, A

1989-08-01

According to experiential structuralism, thought abilities have six capacity spheres: experimental, propositional, quantitative, imaginal, qualitative, and metacognitive. The first five are applied to the environment. The metacognitive capacity is applied to the others, serving as the interface between reality and the cognitive system or between any of the other capacities. To test this postulate, 648 subjects aged 12 to 40 years, solved eight tasks that were addressed, in pairs, to the first four capacity spheres. One of the tasks in each pair tapped the first and the other the third formal level of the sphere. Having solved the tasks, the subjects were required to rate each pair of tasks in terms of similarity of operations, difficulty, and success of solution. Factor analysis of difficulty and success evaluation scores revealed the same capacity-specific factors as the analysis of performance scores. Factor analysis of similarity scores differentiated between same- and different-sphere pairs. Analysis of variance showed that difficulty and success evaluation scores preserved performance differences between the first and the third formal tasks. Cognitive level, age, socioeconomic status, and sex were related to the metacognitive measures in ways similar to their relations to performance measures. These findings were integrated into a model aimed at capturing real-time metacognitive functioning.

Optimizing one-shot learning with binary synapses.

PubMed

Romani, Sandro; Amit, Daniel J; Amit, Yali

2008-08-01

A network of excitatory synapses trained with a conservative version of Hebbian learning is used as a model for recognizing the familiarity of thousands of once-seen stimuli from those never seen before. Such networks were initially proposed for modeling memory retrieval (selective delay activity). We show that the same framework allows the incorporation of both familiarity recognition and memory retrieval, and estimate the network's capacity. In the case of binary neurons, we extend the analysis of Amit and Fusi (1994) to obtain capacity limits based on computations of signal-to-noise ratio of the field difference between selective and non-selective neurons of learned signals. We show that with fast learning (potentiation probability approximately 1), the most recently learned patterns can be retrieved in working memory (selective delay activity). A much higher number of once-seen learned patterns elicit a realistic familiarity signal in the presence of an external field. With potentiation probability much less than 1 (slow learning), memory retrieval disappears, whereas familiarity recognition capacity is maintained at a similarly high level. This analysis is corroborated in simulations. For analog neurons, where such analysis is more difficult, we simplify the capacity analysis by studying the excess number of potentiated synapses above the steady-state distribution. In this framework, we derive the optimal constraint between potentiation and depression probabilities that maximizes the capacity.

Pathways to Program Success: A Qualitative Comparative Analysis (QCA) of Communities Putting Prevention to Work Case Study Programs

PubMed Central

Kane, Heather; Hinnant, Laurie; Day, Kristine; Council, Mary; Tzeng, Janice; Soler, Robin; Chambard, Megan; Roussel, Amy; Heirendt, Wendy

2016-01-01

Objective To examine the elements of capacity, a measure of organizational resources supporting program implementation that result in successful completion of public health program objectives in a public health initiative serving 50 communities. Design We used crisp set Qualitative Comparative Analysis (QCA) to analyze case study and quantitative data collected during the evaluation of the Communities Putting Prevention to Work (CPPW) program. Setting CPPW awardee program staff and partners implemented evidence-based public health improvements in counties, cities, and organizations (eg, worksites, schools). Participants Data came from case studies of 22 CPPW awardee programs that implemented evidence-based, community-and organizational-level public health improvements. Intervention Program staff implemented a range of evidence-based public health improvements related to tobacco control and obesity prevention. Main Outcome Measure The outcome measure was completion of approximately 60% of work plan objectives. Results Analysis of the capacity conditions revealed 2 combinations for completing most work plan objectives: (1) having experience implementing public health improvements in combination with having a history of collaboration with partners; and (2) not having experience implementing public health improvements in combination with having leadership support. Conclusion Awardees have varying levels of capacity. The combinations identified in this analysis provide important insights into how awardees with different combinations of elements of capacity achieved most of their work plan objectives. Even when awardees lack some elements of capacity, they can build it through strategies such as hiring staff and engaging new partners with expertise. In some instances, lacking 1 or more elements of capacity did not prevent an awardee from successfully completing objectives. Implications for Policy & Practice These findings can help funders and practitioners recognize and assemble different aspects of capacity to achieve more successful programs; awardees can draw on extant organizational strengths to compensate when other aspects of capacity are absent. PMID:27598714

A Geometric Capacity-Demand Analysis of Maternal Levator Muscle Stretch Required for Vaginal Delivery.

PubMed

Tracy, Paige V; DeLancey, John O; Ashton-Miller, James A

2016-02-01

Because levator ani (LA) muscle injuries occur in approximately 13% of all vaginal births, insights are needed to better prevent them. In Part I of this paper, we conducted an analysis of the bony and soft tissue factors contributing to the geometric "capacity" of the maternal pelvis and pelvic floor to deliver a fetal head without incurring stretch injury of the maternal soft tissue. In Part II, we quantified the range in demand, represented by the variation in fetal head size and shape, placed on the maternal pelvic floor. In Part III, we analyzed the capacity-to-demand geometric ratio, g, in order to determine whether a mother can deliver a head of given size without stretch injury. The results of a Part I sensitivity analysis showed that initial soft tissue loop length (SL) had the greatest effect on maternal capacity, followed by the length of the soft tissue loop above the inferior pubic rami at ultimate crowning, then subpubic arch angle (SPAA) and head size, and finally the levator origin separation distance. We found the more caudal origin of the puborectal portion of the levator muscle helps to protect it from the stretch injuries commonly observed in the pubovisceral portion. Part II fetal head molding index (MI) and fetal head size revealed fetal head circumference values ranging from 253 to 351 mm, which would increase up to 11 mm upon face presentation. The Part III capacity-demand analysis of g revealed that, based on geometry alone, the 10th percentile maternal capacity predicted injury for all head sizes, the 25th percentile maternal capacity could deliver half of all head sizes, while the 50th percentile maternal capacity could deliver a head of any size without injury. If ultrasound imaging could be operationalized to make measurements of ratio g, it might be used to usefully inform women on their level of risk for levator injury during vaginal birth.

Organizational capacity needs of consumer-run organizations.

PubMed

Wituk, Scott; Vu, Chi C; Brown, Louis D; Meissen, Greg

2008-05-01

Consumer-run organizations (CROs) are self-help oriented organizations that are run entirely by consumers (people who use or have used mental health services). The current study utilizes an organizational capacity framework to explore the needs of operating CROs. This framework includes four core capacity areas: (1) technical, (2) management, (3) leadership, and (4) adaptive capacity. An analysis reveals that the greatest organizational needs are related to technical and management capacities. Implications are discussed in terms of strategies and activities that CRO leaders and mental health professionals and administrators can use to strengthen the organizational capacity of CROs in their community.

Managing risk and expected financial return from selective expansion of operating room capacity: mean-variance analysis of a hospital's portfolio of surgeons.

PubMed

Dexter, Franklin; Ledolter, Johannes

2003-07-01

Surgeons using the same amount of operating room (OR) time differ in their achieved hospital contribution margins (revenue minus variable costs) by >1000%. Thus, to improve the financial return from perioperative facilities, OR strategic decisions should selectively focus additional OR capacity and capital purchasing on a few surgeons or subspecialties. These decisions use estimates of each surgeon's and/or subspecialty's contribution margin per OR hour. The estimates are subject to uncertainty (e.g., from outliers). We account for the uncertainties by using mean-variance portfolio analysis (i.e., quadratic programming). This method characterizes the problem of selectively expanding OR capacity based on the expected financial return and risk of different portfolios of surgeons. The assessment reveals whether the choices, of which surgeons have their OR capacity expanded, are sensitive to the uncertainties in the surgeons' contribution margins per OR hour. Thus, mean-variance analysis reduces the chance of making strategic decisions based on spurious information. We also assess the financial benefit of using mean-variance portfolio analysis when the planned expansion of OR capacity is well diversified over at least several surgeons or subspecialties. Our results show that, in such circumstances, there may be little benefit from further changing the portfolio to reduce its financial risk. Surgeon and subspecialty specific hospital financial data are uncertain, a fact that should be taken into account when making decisions about expanding operating room capacity. We show that mean-variance portfolio analysis can incorporate this uncertainty, thereby guiding operating room management decision-making and reducing the chance of a strategic decision being made based on spurious information.

Cooling-capacity characteristics of Helium-4 JT cryocoolers

NASA Astrophysics Data System (ADS)

Wang, Y. L.; Liu, D. L.; Gan, Z. H.; Guo, Y. X.; Shen, Y. W.; Chen, S. F.

2017-12-01

Cooling capacity of a Helium-4 JT cryocooler may be achieved at a temperature higher than liquid helium temperature. The latent cooling capacity, which should be obtained at liquid helium temperature, is defined as a special part of cooling capacity. With the thermodynamic analysis on steady working conditions of a Helium-4 JT cryocooler, its cooling capacity and temperature characteristics are presented systematically. The effects of precooling temperature and high pressure on the cooling capacity and latent cooling capacity are illustrated. Furthermore, the JT cryocoolers using hydrogen and neon as the working fluids are also discussed. It is shown that helium JT cryocooler has a special cooling capacity characteristic which does not exist in JT cryocoolers using other pure working fluids.

Chemical evaluation, antioxidant capacity, and consumer acceptance of several oak infusions.

PubMed

Rocha-Guzmán, Nuria Elizabeth; Medina-Medrano, Jose Roberto; Gallegos-Infante, José Alberto; Gonzalez-Laredo, Rubén Francisco; Ramos-Gómez, Minerva; Reynoso-Camacho, Rosalía; Guzmán-Maldonado, Horacio; González-Herrera, Silvia Marina

2012-02-01

As part of an ongoing screening on natural products, 4 oak leaves were analyzed as potential nutraceutical beverages. The phenolic composition, antioxidant capacity, and sensory preferences of leaves infusions from Quercus resinosa, Q. sideroxyla, Q. eduadii, and Q. durifolia in comparison with 2 commercial green teas were investigated. Herbal infusions from oak leaves and Green teas (1%, 80 °C, 10 min) were evaluated for total polyphenol content (TPC), total flavonoid content (TFC), HPLC analysis, trolox equivalent antioxidant capacity (TEAC), oxygen radical absorbance capacity (ORAC), soluble solids, pH, color, and consumer preference analysis. Q. resinosa leaves infusions have shown the highest TPC, TEAC, and ORAC values but they have attained the lowest preference score. Quercus leaves infusions with higher content of gallic acid and catechins showed best antioxidant capacity but lower consumer preference. © 2012 Institute of Food Technologists®

Game-theoretic equilibrium analysis applications to deregulated electricity markets

NASA Astrophysics Data System (ADS)

Joung, Manho

This dissertation examines game-theoretic equilibrium analysis applications to deregulated electricity markets. In particular, three specific applications are discussed: analyzing the competitive effects of ownership of financial transmission rights, developing a dynamic game model considering the ramp rate constraints of generators, and analyzing strategic behavior in electricity capacity markets. In the financial transmission right application, an investigation is made of how generators' ownership of financial transmission rights may influence the effects of the transmission lines on competition. In the second application, the ramp rate constraints of generators are explicitly modeled using a dynamic game framework, and the equilibrium is characterized as the Markov perfect equilibrium. Finally, the strategic behavior of market participants in electricity capacity markets is analyzed and it is shown that the market participants may exaggerate their available capacity in a Nash equilibrium. It is also shown that the more conservative the independent system operator's capacity procurement, the higher the risk of exaggerated capacity offers.

Water stress induces changes in polyphenol profile and antioxidant capacity in poplar plants (Populus spp.).

PubMed

Popović, B M; Štajner, D; Ždero-Pavlović, R; Tumbas-Šaponjac, V; Čanadanović-Brunet, J; Orlović, S

2016-08-01

This paper is aimed to characterize young poplar plants under the influence of water stress provoked by polyethileneglycol 6000 (PEG 6000). Three polar genotypes (M1, B229, and PE19/66) were grown in hydroponics and subjected to 100 and 200 mOsm PEG 6000 during six days. Polyphenol characterization, two enzymatic markers and antioxidant capacity in leaves and roots were investigated in stressed plants. Total phenol content, ferric reducing antioxidant capacity (FRAP) and DPPH antiradical power (DPPH ARP) were determined for estimating total antioxidant capacity. Polyphenol oxidase (PPO) and phenylalanine ammonia lyase (PAL) were determined as enzymatic markers. Polyphenol characterization of poplar samples was performed by HPLC-PDA analysis. All results were subjected to correlation analysis and principal component analysis (PCA). Inspite of the decrease of total phenol content in investigated genotypes, as well as total antioxidant capacity, some of polyphenols were affected by stress like flavonoids chrysin, myricetine, kaempferol and isoferulic acid in roots of B229 genotype (Populus deltoides). Genotype B229 also showed the increase of antioxidant capacity and PAL activity in root and leaves under stress what could be the indicator of the adaptability of poplar plants to water stress. Significant positive correlations were obtained between PAL, antioxidant capacity as well as phenolic acids among themselves. Chemometric evaluation showed close interdependence between flavonoids, FRAP, DPPH antiradical power and both investigated enzymes of polyphenol metabolism, PAL and PPO. Copyright © 2016 Elsevier Masson SAS. All rights reserved.

Efficacy of N-Acetylcysteine in Idiopathic Pulmonary Fibrosis

PubMed Central

Sun, Tong; Liu, Jing; Zhao, De Wei

2016-01-01

Abstract There are a number of conflicting reports describing the clinical outcomes of using N-acetylcysteine for the treatment of idiopathic pulmonary fibrosis. We have, therefore, performed a meta-analysis to evaluate the efficacy of N-acetylcysteine, compared with control, for the treatment of idiopathic pulmonary fibrosis. Original controlled clinical trials evaluating the efficacy of N-acetylcysteine for the treatment of idiopathic pulmonary fibrosis were included in the analysis. Searches for relevant articles were carried out in July 2014 by 2 independent researchers using PubMed, Embase, Cochrane Central, and Google Scholar. Change in forced vital capacity, change in percentage of predicted vital capacity, change in percentage of predicted carbon monoxide diffusing capacity, changes in 6 minutes walking test distance, rate of adverse events, and rate of death were expressed as outcomes using RevMan 5.0.1. Five trials, with a total of 564 patients, were included in this meta-analysis. The meta-analysis showed that the control group had significant decreases in percentage of predicted vital capacity (standardized mean difference [SMD] = 0.37; 95% confidence interval [CI]: 0.13 to −0.62; P = 0.003) and 6 minutes walking test distance (SMD = 0.25; 95% CI: 0.02–0.48; P = 0.04). There were no statistically significant differences in forced vital capacity (SMD = 0.07; 95% CI: −0.13–0.27; P = 0.52), percentage of predicted carbon monoxide diffusing capacity (SMD = 0.12; 95% CI: −0.06–0.30; P = 0.18), rates of adverse events (odd ratio = 4.50; 95% CI: 0.19–106.41; P = 0.35), or death rates (odd ratio = 1.79; 95% CI: 0.3–5.12; P = 0.28) between the N-acetylcysteine group and the control group. N-Acetylcysteine was found to have a significant effect only on decreases in percentage of predicted vital capacity and 6 minutes walking test distance. N-acetylcysteine showed no beneficial effect on changes in forced vital capacity, changes in predicted carbon monoxide diffusing capacity, rates of adverse events, or death rates. PMID:27175674

Correlation analysis of the heat capacity and thermal expansion of solid mercury

NASA Astrophysics Data System (ADS)

Bodryakov, V. Yu.; Babintsev, Yu. N.

2015-06-01

A detailed analysis of the correlation between the volumetric thermal expansion coefficient o( T) and heat capacity C( T) of solid mercury has been performed. It has been shown that there is a clear correlation dependence o( C) not only in the low-temperature range, where it is linear and known as the Grüneisen law, but also up to the melting point of mercury. The dependence o( C) substantially deviates from the low-temperature linear behavior when the heat capacity reaches the classical Dulong-Petit limit of 3 R.

Working Towards Net Zero Energy at Fort Irwin, CA

DTIC Science & Technology

2010-09-01

capacity factor for the solar photovoltaic analysis was based on simu- lations conducted by National Renewable Energy Laboratory (NREL) for Las Vegas, NV...kWhAC/kWhDC) x 8760 hrs = 5240 kWhAC/yr Savings for annual electricity savings are: 5240 kWh x 8.3 cents/kWh = $435/yr The capacity factor for the...43,668 kWh/yr Annual electricity savings are: 43,668 kWh x 8.3 cents/kWh = $3624/yr The capacity factor for the solar photovoltaic analysis was

Saint Lawrence Seaway Navigation-Aid System Study : Volume II - Appendix B - User's Manual and Documentation of Seaway Capacity and Capacity Analysis Programs

DOT National Transportation Integrated Search

1978-09-01

The requirements for a navigation guidance system which will effect an increase in the ship processing capacity of the Saint Lawrence Seaway (Lake Ontario to Montreal, Quebec) are developed. The requirements include a specification of system position...

Capacity Estimation Model for Signalized Intersections under the Impact of Access Point

PubMed Central

Zhao, Jing; Li, Peng; Zhou, Xizhao

2016-01-01

Highway Capacity Manual 2010 provides various factors to adjust the base saturation flow rate for the capacity analysis of signalized intersections. No factors, however, is considered for the potential change of signalized intersections capacity caused by the access point closeing to the signalized intersection. This paper presented a theoretical model to estimate the lane group capacity at signalized intersections with the consideration of the effects of access points. Two scenarios of access point locations, upstream or downstream of the signalized intersection, and impacts of six types of access traffic flow are taken into account. The proposed capacity model was validated based on VISSIM simulation. Results of extensive numerical analysis reveal the substantial impact of access point on the capacity, which has an inverse correlation with both the number of major street lanes and the distance between the intersection and access point. Moreover, among the six types of access traffic flows, the access traffic flow 1 (right-turning traffic from major street), flow 4 (left-turning traffic from access point), and flow 5 (left-turning traffic from major street) cause a more significant effect on lane group capacity than others. Some guidance on the mitigation of the negative effect is provided for practitioners. PMID:26726998

[Environment capacity of eco-tourism resort].

PubMed

Sun, Y; Wang, R

2000-08-01

The results of quantitative analysis on the amount of tourist, service-environment capacity, eco-environment capacity, and their relations in Five-finger Mountain eco-tourism resort indicate that the amount of tourist in common situation and in its extreme was 1918 and 2301 visitor-hour per day, and the service-environment capacity and eco-environment capacity were 6000 and 2400 visitor-hour per day, respectively. The eco-environment capacity was smaller than its service-environment capacity, and would become the first limiting factor to the increase of tourist amount, which was mainly due to the ecological fragility of resort, the lower resistance of biological communities to the disturbance, and the slower speed of ecosystem restoration after its being destroyed.

The Ultimate Pile Bearing Capacity from Conventional and Spectral Analysis of Surface Wave (SASW) Measurements

NASA Astrophysics Data System (ADS)

Faizah Bawadi, Nor; Anuar, Shamilah; Rahim, Mustaqqim A.; Mansor, A. Faizal

2018-03-01

A conventional and seismic method for determining the ultimate pile bearing capacity was proposed and compared. The Spectral Analysis of Surface Wave (SASW) method is one of the non-destructive seismic techniques that do not require drilling and sampling of soils, was used in the determination of shear wave velocity (Vs) and damping (D) profile of soil. The soil strength was found to be directly proportional to the Vs and its value has been successfully applied to obtain shallow bearing capacity empirically. A method is proposed in this study to determine the pile bearing capacity using Vs and D measurements for the design of pile and also as an alternative method to verify the bearing capacity from the other conventional methods of evaluation. The objectives of this study are to determine Vs and D profile through frequency response data from SASW measurements and to compare pile bearing capacities obtained from the method carried out and conventional methods. All SASW test arrays were conducted near the borehole and location of conventional pile load tests. In obtaining skin and end bearing pile resistance, the Hardin and Drnevich equation has been used with reference strains obtained from the method proposed by Abbiss. Back analysis results of pile bearing capacities from SASW were found to be 18981 kN and 4947 kN compared to 18014 kN and 4633 kN of IPLT with differences of 5% and 6% for Damansara and Kuala Lumpur test sites, respectively. The results of this study indicate that the seismic method proposed in this study has the potential to be used in estimating the pile bearing capacity.

A Fast and Scalable Algorithm for Calculating the Achievable Capacity of a Wireless Mesh Network

DTIC Science & Technology

2016-04-10

to interference from a given transmission . We then use our algorithm to perform a network capacity analysis comparing different wireless technologies...A Fast and Scalable Algorithm for Calculating the Achievable Capacity of a Wireless Mesh Network Greg Kuperman, Jun Sun, and Aradhana Narula-Tam MIT...the maximum achievable capacity of a multi-hop wireless mesh network subject to interference constraints. Being able to quickly determine the maximum

Winning the Future: An Investigation into the Creativity Capacity across the Levels of Education in Ireland

ERIC Educational Resources Information Center

Leahy, Keelin

2016-01-01

This research investigated the creativity capacity across the levels of education in Ireland, involving 702 participants. Creative capacity was investigated through a comparative analysis of creativity quotient (CQ). A divergent thinking task comprising the "how many uses" activity was assessed using the criteria for determining CQ;…

UNDERSTANDING REGIONAL OXIDATION CAPACITY BY COMPREHENSIVE OBSERVATIONS TO CONSTRAIN HYDROXYL RADICAL SOURCES AND SINKS DURING THE SOUTHERN OXIDANT AEROSOL STUDY (SOAS)

EPA Science Inventory

The proposed field measurements and data analysis will provide an important constraint to understand oxidation capacity in the Southeastern U.S. that determines SOA and photochemical ozone formation. Unexpectedly high levels of OH determining oxidation capacity have been co...

Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model

NASA Astrophysics Data System (ADS)

Hovhannisyan, V. V.; Ananikian, N. S.; Campa, A.; Ruffo, S.

2017-12-01

We study inequivalence of canonical and microcanonical ensembles in the mean-field Blume-Emery-Griffiths model. This generalizes previous results obtained for the Blume-Capel model. The phase diagram strongly depends on the value of the biquadratic exchange interaction K , the additional feature present in the Blume-Emery-Griffiths model. At small values of K , as for the Blume-Capel model, lines of first- and second-order phase transitions between a ferromagnetic and a paramagnetic phase are present, separated by a tricritical point whose location is different in the two ensembles. At higher values of K the phase diagram changes substantially, with the appearance of a triple point in the canonical ensemble, which does not find any correspondence in the microcanonical ensemble. Moreover, one of the first-order lines that starts from the triple point ends in a critical point, whose position in the phase diagram is different in the two ensembles. This line separates two paramagnetic phases characterized by a different value of the quadrupole moment. These features were not previously studied for other models and substantially enrich the landscape of ensemble inequivalence, identifying new aspects that had been discussed in a classification of phase transitions based on singularity theory. Finally, we discuss ergodicity breaking, which is highlighted by the presence of gaps in the accessible values of magnetization at low energies: it also displays new interesting patterns that are not present in the Blume-Capel model.

Simple wealth distribution model causing inequality-induced crisis without external shocks

NASA Astrophysics Data System (ADS)

Benisty, Henri

2017-05-01

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative processes, basically geometric Brownian motions. In contrast with the usual approach of injecting into such stochastic agent models either specific, idiosyncratic internal nonlinear interaction patterns or macroscopic disruptive features, we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency, the explicit coupling between the richest and the rest being a mere normalization mechanism, hence with minimal extrinsic assumptions. The model thus harnesses the recognized lack of ergodicity of geometric Brownian motions. It also provides a statistical intuition to the consequences of Thomas Piketty's recent "r >g " (return rate > growth rate) paradigmatic analysis of very-long-term wealth trends. We suggest that the "water-divide" of wealth flow may define effective classes, making an objective entry point to calibrate the model. Consistently, we check that a tax mechanism associated to a few percent relative bias on elementary daily transactions is able to slow or stop the build-up of large wealth. When extreme fluctuations are tamed down to a stationary regime with sizable but steadier inequalities, it should still offer opportunities to study the dynamics of crisis and the inner effective classes induced through external or internal factors.

Data challenges in estimating the capacity value of solar photovoltaics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gami, Dhruv; Sioshansi, Ramteen; Denholm, Paul

We examine the robustness of solar capacity-value estimates to three important data issues. The first is the sensitivity to using hourly averaged as opposed to subhourly solar-insolation data. The second is the sensitivity to errors in recording and interpreting load data. The third is the sensitivity to using modeled as opposed to measured solar-insolation data. We demonstrate that capacity-value estimates of solar are sensitive to all three of these factors, with potentially large errors in the capacity-value estimate in a particular year. If multiple years of data are available, the biases introduced by using hourly averaged solar-insolation can be smoothedmore » out. Multiple years of data will not necessarily address the other data-related issues that we examine. Our analysis calls into question the accuracy of a number of solar capacity-value estimates relying exclusively on modeled solar-insolation data that are reported in the literature (including our own previous works). Lastly, our analysis also suggests that multiple years’ historical data should be used for remunerating solar generators for their capacity value in organized wholesale electricity markets.« less

Data Challenges in Estimating the Capacity Value of Solar Photovoltaics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gami, Dhruv; Sioshansi, Ramteen; Denholm, Paul

We examine the robustness of solar capacity-value estimates to three important data issues. The first is the sensitivity to using hourly averaged as opposed to subhourly solar-insolation data. The second is the sensitivity to errors in recording and interpreting load data. The third is the sensitivity to using modeled as opposed to measured solar-insolation data. We demonstrate that capacity-value estimates of solar are sensitive to all three of these factors, with potentially large errors in the capacity-value estimate in a particular year. If multiple years of data are available, the biases introduced by using hourly averaged solar-insolation can be smoothedmore » out. Multiple years of data will not necessarily address the other data-related issues that we examine. Our analysis calls into question the accuracy of a number of solar capacity-value estimates relying exclusively on modeled solar-insolation data that are reported in the literature (including our own previous works). Our analysis also suggests that multiple years' historical data should be used for remunerating solar generators for their capacity value in organized wholesale electricity markets.« less

Data challenges in estimating the capacity value of solar photovoltaics

DOE PAGES

Gami, Dhruv; Sioshansi, Ramteen; Denholm, Paul

2017-04-30

We examine the robustness of solar capacity-value estimates to three important data issues. The first is the sensitivity to using hourly averaged as opposed to subhourly solar-insolation data. The second is the sensitivity to errors in recording and interpreting load data. The third is the sensitivity to using modeled as opposed to measured solar-insolation data. We demonstrate that capacity-value estimates of solar are sensitive to all three of these factors, with potentially large errors in the capacity-value estimate in a particular year. If multiple years of data are available, the biases introduced by using hourly averaged solar-insolation can be smoothedmore » out. Multiple years of data will not necessarily address the other data-related issues that we examine. Our analysis calls into question the accuracy of a number of solar capacity-value estimates relying exclusively on modeled solar-insolation data that are reported in the literature (including our own previous works). Lastly, our analysis also suggests that multiple years’ historical data should be used for remunerating solar generators for their capacity value in organized wholesale electricity markets.« less

Pivot method for global optimization: A study of structures and phase changes in water clusters

NASA Astrophysics Data System (ADS)

Nigra, Pablo Fernando

In this thesis, we have carried out a study of water clusters. The research work has been developed in two stages. In the first stage, we have investigated the properties of water clusters at zero temperature by means of global optimization. The clusters were modeled by using two well known pairwise potentials having distinct characteristics. One is the Matsuoka-Clementi-Yoshimine potential (MCY) that is an ab initio fitted function based on a rigid-molecule model, the other is the Sillinger-Rahman potential (SR) which is an empirical function based on a flexible-molecule model. The algorithm used for the global optimization of the clusters was the pivot method, which was developed in our group. The results have shown that, under certain conditions, the pivot method may yield optimized structures which are related to one another in such a way that they seem to form structural families. The structures in a family can be thought of as formed from the aggregation of single units. The particular types of structures we have found are quasi-one dimensional tubes built from stacking cyclic units such as tetramers, pentamers, and hexamers. The binding energies of these tubes form sequences that span smooth curves with clear asymptotic behavior; therefore, we have also studied the sequences applying the Bulirsch-Stoer (BST) algorithm to accelerate convergence. In the second stage of the research work, we have studied the thermodynamic properties of a typical water cluster at finite temperatures. The selected cluster was the water octamer which exhibits a definite solid-liquid phase change. The water octamer also has several low lying energy cubic structures with large energetic barriers that cause ergodicity breaking in regular Monte Carlo simulations. For that reason we have simulated the octamer using paralell tempering Monte Carlo combined with the multihistogram method. This has permited us to calculate the heat capacity from very low temperatures up to T = 230 K. We have found the melting temperature to be 178.5 K. In addition, we have been able to estimate at 12 K the onset temperature of a solid-solid phase change between the two lowest energy lying isomers.

Evaluation of predictive capacities of biomarkers based on research synthesis.

PubMed

Hattori, Satoshi; Zhou, Xiao-Hua

2016-11-10

The objective of diagnostic studies or prognostic studies is to evaluate and compare predictive capacities of biomarkers. Suppose we are interested in evaluation and comparison of predictive capacities of continuous biomarkers for a binary outcome based on research synthesis. In analysis of each study, subjects are often classified into two groups of the high-expression and low-expression groups according to a cut-off value, and statistical analysis is based on a 2 × 2 table defined by the response and the high expression or low expression of the biomarker. Because the cut-off is study specific, it is difficult to interpret a combined summary measure such as an odds ratio based on the standard meta-analysis techniques. The summary receiver operating characteristic curve is a useful method for meta-analysis of diagnostic studies in the presence of heterogeneity of cut-off values to examine discriminative capacities of biomarkers. We develop a method to estimate positive or negative predictive curves, which are alternative to the receiver operating characteristic curve based on information reported in published papers of each study. These predictive curves provide a useful graphical presentation of pairs of positive and negative predictive values and allow us to compare predictive capacities of biomarkers of different scales in the presence of heterogeneity in cut-off values among studies. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Questioning Masculinities: Interrogating Boys' Capacities for Self-Problematization in Schools

ERIC Educational Resources Information Center

Kehler, Michael; Martino, Wayne

2007-01-01

In drawing on selected interviews with adolescent boys from both Australia and North America, we present an analysis of boys' own capacities for interrogating gender normalisation in their school lives. We set this analysis against a critique of the public media debates about boys' education, which continue to be fuelled by a moral panic about the…

Capacity of scour-damaged bridges, part 2 : Integrated Analysis Program (IAP) - a program for the analysis of lateral performance of pile-supported structures under scour conditions.

DOT National Transportation Integrated Search

2013-11-01

Scour is the removal of soils in the vicinity of bridge foundations, resulting in a reduced capacity of the foundations, which can increase the risk of bridge : failure. To minimize bridge failure, the Federal Highway Administration (FHWA) has establ...

Renewable Energy Deployment in Colorado and the West: A Modeling Sensitivity and GIS Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barrows, Clayton; Mai, Trieu; Haase, Scott

2016-03-01

The Resource Planning Model is a capacity expansion model designed for a regional power system, such as a utility service territory, state, or balancing authority. We apply a geospatial analysis to Resource Planning Model renewable energy capacity expansion results to understand the likelihood of renewable development on various lands within Colorado.

Capacity of scour-damaged bridges, part 2 : Integrated Analysis Program (IAP) - a program for the analysis of lateral performance of pile-supported structures under scour conditions, [technical summary].

DOT National Transportation Integrated Search

2013-11-01

Scour is the removal of soils in the vicinity of bridge foundations, resulting in a reduced capacity of the foundations, which can increase the risk of bridge failure. To minimize bridge failure, the Federal Highway Administration (FHWA) has establis...

ICT Capacity Building: A Critical Discourse Analysis of Rwandan Policies from Higher Education Perspective

ERIC Educational Resources Information Center

Byungura, Jean Claude; Hansson, Henrik; Masengesho, Kamuzinzi; Karunaratne, Thashmee

2016-01-01

With the development of technology in the 21st Century, education systems attempt to integrate technology-based tools to improve experiences in pedagogy and administration. It is becoming increasingly prominent to build human and ICT infrastructure capacities at universities from policy to implementation level. Using a critical discourse analysis,…

Meta-Analysis of the Reasoned Action Approach (RAA) to Understanding Health Behaviors.

PubMed

McEachan, Rosemary; Taylor, Natalie; Harrison, Reema; Lawton, Rebecca; Gardner, Peter; Conner, Mark

2016-08-01

Reasoned action approach (RAA) includes subcomponents of attitude (experiential/instrumental), perceived norm (injunctive/descriptive), and perceived behavioral control (capacity/autonomy) to predict intention and behavior. To provide a meta-analysis of the RAA for health behaviors focusing on comparing the pairs of RAA subcomponents and differences between health protection and health-risk behaviors. The present research reports a meta-analysis of correlational tests of RAA subcomponents, examination of moderators, and combined effects of subcomponents on intention and behavior. Regressions were used to predict intention and behavior based on data from studies measuring all variables. Capacity and experiential attitude had large, and other constructs had small-medium-sized correlations with intention; all constructs except autonomy were significant independent predictors of intention in regressions. Intention, capacity, and experiential attitude had medium-large, and other constructs had small-medium-sized correlations with behavior; intention, capacity, experiential attitude, and descriptive norm were significant independent predictors of behavior in regressions. The RAA subcomponents have utility in predicting and understanding health behaviors.