Analytical approximations for spatial stochastic gene expression in single cells and tissues

PubMed Central

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2016-01-01

Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686

An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping.

PubMed

Koh, Wonryull; Blackwell, Kim T

2011-04-21

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies.

Conservative Diffusions: a Constructive Approach to Nelson's Stochastic Mechanics.

NASA Astrophysics Data System (ADS)

Carlen, Eric Anders

In Nelson's stochastic mechanics, quantum phenomena are described in terms of diffusions instead of wave functions; this thesis is a study of that description. We emphasize that we are concerned here with the possibility of describing, as opposed to explaining, quantum phenomena in terms of diffusions. In this direction, the following questions arise: "Do the diffusions of stochastic mechanics--which are formally given by stochastic differential equations with extremely singular coefficients--really exist?" Given that they exist, one can ask, "Do these diffusions have physically reasonable sample path behavior, and can we use information about sample paths to study the behavior of physical systems?" These are the questions we treat in this thesis. In Chapter I we review stochastic mechanics and diffusion theory, using the Guerra-Morato variational principle to establish the connection with the Schroedinger equation. This chapter is largely expository; however, there are some novel features and proofs. In Chapter II we settle the first of the questions raised above. Using PDE methods, we construct the diffusions of stochastic mechanics. Our result is sufficiently general to be of independent mathematical interest. In Chapter III we treat potential scattering in stochastic mechanics and discuss direct probabilistic methods of studying quantum scattering problems. Our results provide a solid "Yes" in answer to the second question raised above.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Constrained ripple optimization of Tokamak bundle divertors

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

Hively, L.M.; Rome, J.A.; Lynch, V.E.

1983-02-01

Magnetic field ripple from a tokamak bundle divertor is localized to a small toroidal sector and must be treated differently from the usual (distributed) toroidal field (TF) coil ripple. Generally, in a tokamak with an unoptimized divertor design, all of the banana-trapped fast ions are quickly lost due to banana drift diffusion or to trapping between the 1/R variation in absolute value vector B ..xi.. B and local field maxima due to the divertor. A computer code has been written to optimize automatically on-axis ripple subject to these constraints, while varying up to nine design parameters. Optimum configurations have lowmore » on-axis ripple (<0.2%) so that, now, most banana-trapped fast ions are confined. Only those ions with banana tips near the outside region (absolute value theta < or equal to 45/sup 0/) are lost. However, because finite-sized TF coils have not been used in this study, the flux bundle is not expanded.« less

The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation.

PubMed

Drawert, Brian; Lawson, Michael J; Petzold, Linda; Khammash, Mustafa

2010-02-21

We have developed a computational framework for accurate and efficient simulation of stochastic spatially inhomogeneous biochemical systems. The new computational method employs a fractional step hybrid strategy. A novel formulation of the finite state projection (FSP) method, called the diffusive FSP method, is introduced for the efficient and accurate simulation of diffusive transport. Reactions are handled by the stochastic simulation algorithm.

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

Effects of polycrystallinity in nano patterning by ion-beam sputtering

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

Yoon, Sun Mi; Kim, J.-S., E-mail: jskim@sm.ac.kr; Yoon, D.

Employing graphites with distinctly different mean grain sizes, we study the effects of polycrystallinity on the pattern formation by ion-beam sputtering. The grains influence the growth of the ripples in a highly anisotropic fashion; both the mean uninterrupted ripple length along the ridges and the surface width depend on the mean size of the grains, which is attributed to the large sputter yield at the grain boundary compared with that on the terrace. In contrast, the ripple wavelength does not depend on the mean size of the grains, indicating that the mass transport across the grain boundaries should efficiently proceedmore » by both thermal diffusion and ion-induced processes.« less

Minimum uncertainty and squeezing in diffusion processes and stochastic quantization

NASA Technical Reports Server (NTRS)

Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe

1994-01-01

We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.

Rapid Coarsening of Ion Beam Ripple Patterns by Defect Annihilation

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

Hansen, Henri; Messlinger, Sebastian; Stoian, Georgiana

Ripple patterns formed on Pt(111) through grazing incidence ion beam erosion coarsen rapidly. At and below 450 K coarsening of the patterns is athermal and kinetic, unrelated to diffusion and surface free energy. Similar to the situation for sand dunes, coarsening takes place through annihilation reactions of mobile defects in the pattern. The defect velocity derived on the basis of a simple model agrees quantitatively with the velocity of monatomic steps illuminated by the ion beam.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

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

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

PubMed

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

Hippocampal Sharp-Wave Ripples Influence Selective Activation of the Default Mode Network

PubMed Central

Kaplan, Raphael; Adhikari, Mohit H.; Hindriks, Rikkert; Mantini, Dante; Murayama, Yusuke; Logothetis, Nikos K.; Deco, Gustavo

2016-01-01

Summary The default mode network (DMN) is a commonly observed resting-state network (RSN) that includes medial temporal, parietal, and prefrontal regions involved in episodic memory [1, 2, 3]. The behavioral relevance of endogenous DMN activity remains elusive, despite an emerging literature correlating resting fMRI fluctuations with memory performance [4, 5]—particularly in DMN regions [6, 7, 8]. Mechanistic support for the DMN’s role in memory consolidation might come from investigation of large deflections (sharp-waves) in the hippocampal local field potential that co-occur with high-frequency (>80 Hz) oscillations called ripples—both during sleep [9, 10] and awake deliberative periods [11, 12, 13]. Ripples are ideally suited for memory consolidation [14, 15], since the reactivation of hippocampal place cell ensembles occurs during ripples [16, 17, 18, 19]. Moreover, the number of ripples after learning predicts subsequent memory performance in rodents [20, 21, 22] and humans [23], whereas electrical stimulation of the hippocampus after learning interferes with memory consolidation [24, 25, 26]. A recent study in macaques showed diffuse fMRI neocortical activation and subcortical deactivation specifically after ripples [27]. Yet it is unclear whether ripples and other hippocampal neural events influence endogenous fluctuations in specific RSNs—like the DMN—unitarily. Here, we examine fMRI datasets from anesthetized monkeys with simultaneous hippocampal electrophysiology recordings, where we observe a dramatic increase in the DMN fMRI signal following ripples, but not following other hippocampal electrophysiological events. Crucially, we find increases in ongoing DMN activity after ripples, but not in other RSNs. Our results relate endogenous DMN fluctuations to hippocampal ripples, thereby linking network-level resting fMRI fluctuations with behaviorally relevant circuit-level neural dynamics. PMID:26898464

Electron heat transport measured in a stochastic magnetic field.

PubMed

Biewer, T M; Forest, C B; Anderson, J K; Fiksel, G; Hudson, B; Prager, S C; Sarff, J S; Wright, J C; Brower, D L; Ding, W X; Terry, S D

2003-07-25

New profile measurements have allowed the electron thermal diffusivity profile to be estimated from power balance in the Madison Symmetric Torus where magnetic islands overlap and field lines are stochastic. The measurements show that (1) the electron energy transport is conductive not convective, (2) the measured thermal diffusivities are in good agreement with numerical simulations of stochastic transport, and (3) transport is greatly reduced near the reversal surface where magnetic diffusion is small.

Kinetic Monte Carlo simulations of ion-induced ripple formation: Dependence on flux, temperature, and defect concentration in the linear regime

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

Chason, E.; Chan, W. L.; Bharathi, M. S.

Low-energy ion bombardment produces spontaneous periodic structures (sputter ripples) on many surfaces. Continuum theories describe the pattern formation in terms of ion-surface interactions and surface relaxation kinetics, but many features of these models (such as defect concentration) are unknown or difficult to determine. In this work, we present results of kinetic Monte Carlo simulations that model surface evolution using discrete atomistic versions of the physical processes included in the continuum theories. From simulations over a range of parameters, we obtain the dependence of the ripple growth rate, wavelength, and velocity on the ion flux and temperature. The results are discussedmore » in terms of the thermally dependent concentration and diffusivity of ion-induced surface defects. We find that in the early stages of ripple formation the simulation results are surprisingly well described by the predictions of the continuum theory, in spite of simplifying approximations used in the continuum model.« less

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

NASA Astrophysics Data System (ADS)

Sposini, Vittoria; Chechkin, Aleksei V.; Seno, Flavio; Pagnini, Gianni; Metzler, Ralf

2018-04-01

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.

Stochastic mechanics of reciprocal diffusions

NASA Astrophysics Data System (ADS)

Levy, Bernard C.; Krener, Arthur J.

1996-02-01

The dynamics and kinematics of reciprocal diffusions were examined in a previous paper [J. Math. Phys. 34, 1846 (1993)], where it was shown that reciprocal diffusions admit a chain of conservation laws, which close after the first two laws for two disjoint subclasses of reciprocal diffusions, the Markov and quantum diffusions. For the case of quantum diffusions, the conservation laws are equivalent to Schrödinger's equation. The Markov diffusions were employed by Schrödinger [Sitzungsber. Preuss. Akad. Wiss. Phys. Math Kl. 144 (1931); Ann. Inst. H. Poincaré 2, 269 (1932)], Nelson [Dynamical Theories of Brownian Motion (Princeton University, Princeton, NJ, 1967); Quantum Fluctuations (Princeton University, Princeton, NJ, 1985)], and other researchers to develop stochastic formulations of quantum mechanics, called stochastic mechanics. We propose here an alternative version of stochastic mechanics based on quantum diffusions. A procedure is presented for constructing the quantum diffusion associated to a given wave function. It is shown that quantum diffusions satisfy the uncertainty principle, and have a locality property, whereby given two dynamically uncoupled but statistically correlated particles, the marginal statistics of each particle depend only on the local fields to which the particle is subjected. However, like Wigner's joint probability distribution for the position and momentum of a particle, the finite joint probability densities of quantum diffusions may take negative values.

The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems.

PubMed

Lampoudi, Sotiria; Gillespie, Dan T; Petzold, Linda R

2009-03-07

The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is a variant of the stochastic simulation algorithm in which the spatially inhomogeneous volume of the system is divided into homogeneous subvolumes, and the chemical reactions in those subvolumes are augmented by diffusive transfers of molecules between adjacent subvolumes. The ISSA can be prohibitively slow when the system is such that diffusive transfers occur much more frequently than chemical reactions. In this paper we present the Multinomial Simulation Algorithm (MSA), which is designed to, on the one hand, outperform the ISSA when diffusive transfer events outnumber reaction events, and on the other, to handle small reactant populations with greater accuracy than deterministic-stochastic hybrid algorithms. The MSA treats reactions in the usual ISSA fashion, but uses appropriately conditioned binomial random variables for representing the net numbers of molecules diffusing from any given subvolume to a neighbor within a prescribed distance. Simulation results illustrate the benefits of the algorithm.

Stochastic reaction-diffusion algorithms for macromolecular crowding

NASA Astrophysics Data System (ADS)

Sturrock, Marc

2016-06-01

Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

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

Zhou Tao, E-mail: tzhou@lsec.cc.ac.c; Tang Tao, E-mail: ttang@hkbu.edu.h

2010-11-01

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

Periodic bedforms generated by sublimation on terrestrial and martian ice sheets under the influence of the turbulent atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Bordiec, Maï; Carpy, Sabrina; Perret, Laurent; Bourgeois, Olivier; Massé, Marion

2017-04-01

The redistribution of surface ice induced the wind flow may lead to the development and migration of periodic bedforms, or "ice ripples", at the surface of ice sheets. In certain cold and dry environments, this redistribution need not involve solid particle transport but may be dominated by sublimation and condensation, inducing mass transfers between the ice surface and the overlying steady boundary layer turbulent flow. These mass transfers diffuse the water vapour sublimated from the ice into the atmosphere and become responsible for the amplification and propagation of ripples in a direction perpendicular to their crests. Such ice ripples, 24 cm in wavelength, have been described in the so-called Blue Ice Areas of Antarctica. In order to understand the mechanisms that generate and develop these periodic bedforms on terrestrial glaciers and to evaluate the plausibility that similar bedforms may develop on Mars, we performed a linear stability analysis applied to a turbulent boundary layer flow perturbed by a wavy ice surface. The model is developed as follow. We first solve the flow dynamics using numerical methods analogous to those used in sand wave models assuming that the airflow is similar in both problems. We then add the transport/diffusion equation of water vapour following the same scheme. We use the Reynolds-averaged description of the equation with a Prandtl-like closure. We insert a damping term in the exponential formula of the Van Driest mixing length, depending on the pressure gradient felt by the flow and related to the thickness of the viscous sublayer at the ice-atmosphere interface. This formulation is an efficient way to properly represent the transitional regime under which the ripples grow. Once the mass flux of water vapour is solved, the phase shift between the ripples crests and the maximum of the flux can be deduced for different environments. The temporal evolution of the ice surface can be expressed from these quantities to infer the growth rate, migration direction and velocity of the ripples. The present approach has been first used to model the atmospheric flow developing over wavy terrestrial ice bedforms in the Blue Ice Areas of Antarctica. Both the predicted preferential wavelength and propagation direction of the ice ripple have been found to be in agreement with the observations. The present model has subsequently been applied to the same flow configuration but on Mars. Ice ripples are indeed likely to exist there, given that temperature and pressure conditions in the martian atmosphere favors sublimation/condensation as the dominant mass-transport process. The model has proved able to predict not only the development of ice-ripple on Mars (i.e it showed that some most amplified wavelength also exist under Martian atmospheric conditions) but also both their wavelength and propagation direction. The preferential wavelength of ices-ripples on the Martian polar caps appears to be much larger than on the Earth. Finally, a good match between the most likely ice-ripple wavelength predicted by the model and those deduced from recent available observations of the surface of Martian polar caps is shown.

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.

On time-dependent diffusion coefficients arising from stochastic processes with memory

NASA Astrophysics Data System (ADS)

Carpio-Bernido, M. Victoria; Barredo, Wilson I.; Bernido, Christopher C.

2017-08-01

Time-dependent diffusion coefficients arise from anomalous diffusion encountered in many physical systems such as protein transport in cells. We compare these coefficients with those arising from analysis of stochastic processes with memory that go beyond fractional Brownian motion. Facilitated by the Hida white noise functional integral approach, diffusion propagators or probability density functions (pdf) are obtained and shown to be solutions of modified diffusion equations with time-dependent diffusion coefficients. This should be useful in the study of complex transport processes.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

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

Spill, Fabian, E-mail: fspill@bu.edu; Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139; Guerrero, Pilar

2015-10-15

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and smallmore » in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.« less

Impulsive synchronization of stochastic reaction-diffusion neural networks with mixed time delays.

PubMed

Sheng, Yin; Zeng, Zhigang

2018-07-01

This paper discusses impulsive synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and hybrid time delays. By virtue of inequality techniques, theories of stochastic analysis, linear matrix inequalities, and the contradiction method, sufficient criteria are proposed to ensure exponential synchronization of the addressed stochastic reaction-diffusion neural networks with mixed time delays via a designed impulsive controller. Compared with some recent studies, the neural network models herein are more general, some restrictions are relaxed, and the obtained conditions enhance and generalize some published ones. Finally, two numerical simulations are performed to substantiate the validity and merits of the developed theoretical analysis. Copyright © 2018 Elsevier Ltd. All rights reserved.

Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

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

Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong

2014-05-30

The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closedmore » solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.« less

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

NASA Astrophysics Data System (ADS)

Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar

2017-03-01

We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

DOE PAGES

Kim, Changho; Nonaka, Andy; Bell, John B.; ...

2017-03-24

Here, we develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules,more » to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. Furthermore, by comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.« less

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

Redi, M.H.; Mynick, H.E.; Suewattana, M.

Hamiltonian coordinate, guiding-center code calculations of the confinement of suprathermal ions in quasi-axisymmetric stellarator (QAS) designs have been carried out to evaluate the attractiveness of compact configurations which are optimized for ballooning stability. A new stellarator particle-following code is used to predict ion loss rates and particle confinement for thermal and neutral beam ions in a small experiment with R = 145 cm, B = 1-2 T and for alpha particles in a reactor-size device. In contrast to tokamaks, it is found that high edge poloidal flux has limited value in improving ion confinement in QAS, since collisional pitch-angle scatteringmore » drives ions into ripple wells and stochastic field regions, where they are quickly lost. The necessity for reduced stellarator ripple fields is emphasized. The high neutral beam ion loss predicted for these configurations suggests that more interesting physics could be explored with an experiment of less constrained size and magnetic field geometry.« less

Correlation Structure of Fractional Pearson Diffusions.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-09-01

The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative.

The Time Dependent Propensity Function for Acceleration of Spatial Stochastic Simulation of Reaction-Diffusion Systems

PubMed Central

Wu, Sheng; Li, Hong; Petzold, Linda R.

2015-01-01

The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy. PMID:26609185

Thickness-dependent blue shift in the excitonic peak of conformally grown ZnO:Al on ion-beam fabricated self-organized Si ripples

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

Basu, T.; Kumar, M.; Som, T., E-mail: tsom@iopb.res.in

2015-09-14

Al-doped ZnO (AZO) thin films of thicknesses 5,10, 15, 20, and 30 nm were deposited on 500 eV argon ion-beam fabricated nanoscale self-organized rippled-Si substrates at room temperature and are compared with similar films deposited on pristine-Si substrates (without ripples). It is observed that morphology of self-organized AZO films is driven by the underlying substrate morphology. For instance, for pristine-Si substrates, a granular morphology evolves for all AZO films. On the other hand, for rippled-Si substrates, morphologies having chain-like arrangement (anisotropic in nature) are observed up to a thickness of 20 nm, while a granular morphology evolves (isotropic in nature) for 30 nm-thick film.more » Photoluminescence studies reveal that excitonic peaks corresponding to 5–15 nm-thick AZO films, grown on rippled-Si templates, show a blue shift of 8 nm and 3 nm, respectively, whereas the peak shift is negligible for 20-nm thick film (with respect to their pristine counter parts). The observed blue shifts are substantiated by diffuse reflectance study and attributed to quantum confinement effect, associated with the size of the AZO grains and their spatial arrangements driven by the anisotropic morphology of underlying rippled-Si templates. The present findings will be useful for making tunable AZO-based light-emitting devices.« less

Disentangling the stochastic behavior of complex time series

NASA Astrophysics Data System (ADS)

Anvari, Mehrnaz; Tabar, M. Reza Rahimi; Peinke, Joachim; Lehnertz, Klaus

2016-10-01

Complex systems involving a large number of degrees of freedom, generally exhibit non-stationary dynamics, which can result in either continuous or discontinuous sample paths of the corresponding time series. The latter sample paths may be caused by discontinuous events - or jumps - with some distributed amplitudes, and disentangling effects caused by such jumps from effects caused by normal diffusion processes is a main problem for a detailed understanding of stochastic dynamics of complex systems. Here we introduce a non-parametric method to address this general problem. By means of a stochastic dynamical jump-diffusion modelling, we separate deterministic drift terms from different stochastic behaviors, namely diffusive and jumpy ones, and show that all of the unknown functions and coefficients of this modelling can be derived directly from measured time series. We demonstrate appli- cability of our method to empirical observations by a data-driven inference of the deterministic drift term and of the diffusive and jumpy behavior in brain dynamics from ten epilepsy patients. Particularly these different stochastic behaviors provide extra information that can be regarded valuable for diagnostic purposes.

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration

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

Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and themore » perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.« less

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration.

PubMed

Berezhkovskii, Alexander M; Shvartsman, Stanislav Y

2016-05-28

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.

Algorithm refinement for stochastic partial differential equations: II. Correlated systems

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

Alexander, Francis J.; Garcia, Alejandro L.; Tartakovsky, Daniel M.

2005-08-10

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia,more » D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.« less

Stochastic modeling of experimental chaotic time series.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2007-01-26

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions of the corresponding Fokker-Planck equation are in excellent agreement with experimental data.

Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

NASA Astrophysics Data System (ADS)

Zheng, Liheng; Chan, Anthony A.; Albert, Jay M.; Elkington, Scot R.; Koller, Josef; Horne, Richard B.; Glauert, Sarah A.; Meredith, Nigel P.

2014-09-01

A 3-D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of Itô stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3-D diffusion tensor, including the radial-local cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90° is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90°, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0-independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration.

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

NASA Astrophysics Data System (ADS)

Deng, M. L.; Zhu, W. Q.

2007-10-01

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged Itô stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

DOE PAGES

Cao, Boqiang; Zhang, Qimin; Ye, Ming

2016-11-29

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

Effects of plasma flows on particle diffusion in stochastic magnetic fields

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

Vlad, M.; Spineanu, F.; Misguich, J.H.

1996-07-01

The study of collisional test particle diffusion in stochastic magnetic fields is extended to include the effects of the macroscopic flows of the plasma (drifts). We show that a substantial amplification of the diffusion coefficient can be obtained. This effect is produced by the combined action of the parallel collisional velocity and of the average drifts. The perpendicular collisional velocity influences the effective diffusion only in the limit of small average drifts. {copyright} {ital 1996 The American Physical Society.}

Diffusive transport in the presence of stochastically gated absorption

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; Karamched, Bhargav R.; Lawley, Sean D.; Levien, Ethan

2017-08-01

We analyze a population of Brownian particles moving in a spatially uniform environment with stochastically gated absorption. The state of the environment at time t is represented by a discrete stochastic variable k (t )∈{0 ,1 } such that the rate of absorption is γ [1 -k (t )] , with γ a positive constant. The variable k (t ) evolves according to a two-state Markov chain. We focus on how stochastic gating affects the attenuation of particle absorption with distance from a localized source in a one-dimensional domain. In the static case (no gating), the steady-state attenuation is given by an exponential with length constant √{D /γ }, where D is the diffusivity. We show that gating leads to slower, nonexponential attenuation. We also explore statistical correlations between particles due to the fact that they all diffuse in the same switching environment. Such correlations can be determined in terms of moments of the solution to a corresponding stochastic Fokker-Planck equation.

An efficient hybrid method for stochastic reaction-diffusion biochemical systems with delay

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Ilie, Silvana

2017-12-01

Many chemical reactions, such as gene transcription and translation in living cells, need a certain time to finish once they are initiated. Simulating stochastic models of reaction-diffusion systems with delay can be computationally expensive. In the present paper, a novel hybrid algorithm is proposed to accelerate the stochastic simulation of delayed reaction-diffusion systems. The delayed reactions may be of consuming or non-consuming delay type. The algorithm is designed for moderately stiff systems in which the events can be partitioned into slow and fast subsets according to their propensities. The proposed algorithm is applied to three benchmark problems and the results are compared with those of the delayed Inhomogeneous Stochastic Simulation Algorithm. The numerical results show that the new hybrid algorithm achieves considerable speed-up in the run time and very good accuracy.

Stochastic lattice model of synaptic membrane protein domains.

PubMed

Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A

2017-05-01

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics.

PubMed

Strehl, Robert; Ilie, Silvana

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.

Fluctuations and correlations in modulation instability

NASA Astrophysics Data System (ADS)

Solli, D. R.; Herink, G.; Jalali, B.; Ropers, C.

2012-07-01

Stochastically driven nonlinear processes are responsible for spontaneous pattern formation and instabilities in numerous natural and artificial systems, including well-known examples such as sand ripples, cloud formations, water waves, animal pigmentation and heart rhythms. Technologically, a type of such self-amplification drives free-electron lasers and optical supercontinuum sources whose radiation qualities, however, suffer from the stochastic origins. Through time-resolved observations, we identify intrinsic properties of these fluctuations that are hidden in ensemble measurements. We acquire single-shot spectra of modulation instability produced by laser pulses in glass fibre at megahertz real-time capture rates. The temporally confined nature of the gain physically limits the number of amplified modes, which form an antibunched arrangement as identified from a statistical analysis of the data. These dynamics provide an example of pattern competition and interaction in confined nonlinear systems.

Robust stochastic Turing patterns in the development of a one-dimensional cyanobacterial organism.

PubMed

Di Patti, Francesca; Lavacchi, Laura; Arbel-Goren, Rinat; Schein-Lubomirsky, Leora; Fanelli, Duccio; Stavans, Joel

2018-05-01

Under nitrogen deprivation, the one-dimensional cyanobacterial organism Anabaena sp. PCC 7120 develops patterns of single, nitrogen-fixing cells separated by nearly regular intervals of photosynthetic vegetative cells. We study a minimal, stochastic model of developmental patterns in Anabaena that includes a nondiffusing activator, two diffusing inhibitor morphogens, demographic fluctuations in the number of morphogen molecules, and filament growth. By tracking developing filaments, we provide experimental evidence for different spatiotemporal roles of the two inhibitors during pattern maintenance and for small molecular copy numbers, justifying a stochastic approach. In the deterministic limit, the model yields Turing patterns within a region of parameter space that shrinks markedly as the inhibitor diffusivities become equal. Transient, noise-driven, stochastic Turing patterns are produced outside this region, which can then be fixed by downstream genetic commitment pathways, dramatically enhancing the robustness of pattern formation, also in the biologically relevant situation in which the inhibitors' diffusivities may be comparable.

Time-delayed feedback control of diffusion in random walkers.

PubMed

Ando, Hiroyasu; Takehara, Kohta; Kobayashi, Miki U

2017-07-01

Time delay in general leads to instability in some systems, while specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a stochastic process, i.e., a random walk, and observe its diffusion phenomenon with time-delayed feedback. As a result, the diffusion coefficient decreases with increasing delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying time-delayed feedback to a molecular dynamics model.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Plasma Equilibrium in a Magnetic Field with Stochastic Field-Line Trajectories

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2008-11-01

The nature of plasma equilibrium in a magnetic field with stochastic field lines is examined, expanding upon the ideas first described by Reiman et al. The magnetic partial differential equation (PDE) that determines the equilibrium Pfirsch-Schlüter currents is treated as a passive stochastic PDE for μj/B. Renormalization leads to a stochastic Langevin equation for μ in which the resonances at the rational surfaces are broadened by the stochastic diffusion of the field lines; even weak radial diffusion can significantly affect the equilibrium, which need not be flattened in the stochastic region. Particular attention is paid to satisfying the periodicity constraints in toroidal configurations with sheared magnetic fields. A numerical scheme that couples the renormalized Langevin equation to Ampere's law is described. A. Reiman et al, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes, Phys. Reports 360, 1--351.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

PubMed

Kalantzis, Georgios

2009-06-01

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics

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

Strehl, Robert; Ilie, Silvana, E-mail: silvana@ryerson.ca

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated onmore » three benchmarking systems, with special focus on approximation accuracy and efficiency.« less

Flow injection analysis simulations and diffusion coefficient determination by stochastic and deterministic optimization methods.

PubMed

Kucza, Witold

2013-07-25

Stochastic and deterministic simulations of dispersion in cylindrical channels on the Poiseuille flow have been presented. The random walk (stochastic) and the uniform dispersion (deterministic) models have been used for computations of flow injection analysis responses. These methods coupled with the genetic algorithm and the Levenberg-Marquardt optimization methods, respectively, have been applied for determination of diffusion coefficients. The diffusion coefficients of fluorescein sodium, potassium hexacyanoferrate and potassium dichromate have been determined by means of the presented methods and FIA responses that are available in literature. The best-fit results agree with each other and with experimental data thus validating both presented approaches. Copyright © 2013 The Author. Published by Elsevier B.V. All rights reserved.

Resolving High Amplitude Surface Motion with Diffusing Light

NASA Technical Reports Server (NTRS)

Wright, W.; Budakian, R.; Putterman, Seth J.

1996-01-01

A new technique has been developed for the purpose of imaging high amplitude surface motion. With this method one can quantitatively measure the transition to ripple wave turbulence. In addition, one can measure the phase of the turbulent state. These experiments reveal strong coherent structures in turbulent range of motion.

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

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

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

PubMed

Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

2017-03-14

Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

Stochastic Convection Parameterizations: The Eddy-Diffusivity/Mass-Flux (EDMF) Approach (Invited)

NASA Astrophysics Data System (ADS)

Teixeira, J.

2013-12-01

In this presentation it is argued that moist convection parameterizations need to be stochastic in order to be realistic - even in deterministic atmospheric prediction systems. A new unified convection and boundary layer parameterization (EDMF) that optimally combines the Eddy-Diffusivity (ED) approach for smaller-scale boundary layer mixing with the Mass-Flux (MF) approach for larger-scale plumes is discussed. It is argued that for realistic simulations stochastic methods have to be employed in this new unified EDMF. Positive results from the implementation of the EDMF approach in atmospheric models are presented.

FAIMS Operation for Realistic Gas Flow Profile and Asymmetric Waveforms Including Electronic Noise and Ripple

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

Shvartsburg, Alexandre A.; Tang, Keqi; Smith, Richard D.

The use of Field Asymmetric waveform Ion Mobility Spectrometry (FAIMS) has rapidly grown with the advent of commercial FAIMS systems coupled to mass spectrometry. However, many fundamental aspects of FAIMS remain obscure, hindering its technological improvement and expansion of analytical utility. Recently, we developed a comprehensive numerical simulation approach to FAIMS that can handle any device geometry and operational conditions. The formalism was originally set up in one dimension for a uniform gas flow and limited to ideal asymmetric voltage waveforms. Here we extend the model to account for a realistic gas flow velocity distribution in the analytical gap, axialmore » ion diffusion, and waveform imperfections (e.g. noise and ripple). The non-uniformity of gas flow velocity profile has only a minor effect, slightly improving resolution. However, waveform perturbations are significant even at very low levels, in some cases {approx} 0.01% of nominal voltage. These perturbations always improve resolution and decrease sensitivity. Variation of noise or ripple amplitude produces a trade-off between resolution and sensitivity. This trade-off is physically equivalent to that obtained via adjustment of the gap width and/or asymmetric waveform frequency, but the scaling of low-frequency ripple appears to be a more practical way to control FAIMS resolution.« less

Measurements of confined alphas and tritons in the MHD quiescent core of TFTR plasmas using the pellet charge exchange diagnostic

NASA Astrophysics Data System (ADS)

Medley, S. S.; Budny, R. V.; Mansfield, D. K.; Redi, M. H.; Roquemore, A. L.; Fisher, R. K.; Duong, H. H.; McChesney, J. M.; Parks, P. B.; Petrov, M. P.; Gorelenkov, N. N.

1996-10-01

The energy distributions and radial density profiles of the fast confined trapped alpha particles in DT experiments on TFTR are being measured in the energy range 0.5 - 3.5 MeV using the pellet charge exchange (PCX) diagnostic. A brief description of the measurement technique which involves active neutral particle analysis using the ablation cloud surrounding an injected impurity pellet as the neutralizer is presented. This paper focuses on alpha and triton measurements in the core of MHD quiescent TFTR discharges where the expected classical slowing-down and pitch angle scattering effects are not complicated by stochastic ripple diffusion and sawtooth activity. In particular, the first measurement of the alpha slowing-down distribution up to the birth energy, obtained using boron pellet injection, is presented. The measurements are compared with predictions using either the TRANSP Monte Carlo code and/or a Fokker - Planck Post-TRANSP processor code, which assumes that the alphas and tritons are well confined and slow down classically. Both the shape of the measured alpha and triton energy distributions and their density ratios are in good agreement with the code calculations. We can conclude that the PCX measurements are consistent with classical thermalization of the fusion-generated alphas and tritons.

Effective Stochastic Model for Reactive Transport

NASA Astrophysics Data System (ADS)

Tartakovsky, A. M.; Zheng, B.; Barajas-Solano, D. A.

2017-12-01

We propose an effective stochastic advection-diffusion-reaction (SADR) model. Unlike traditional advection-dispersion-reaction models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, the mechanical mixing is driven by random advective velocity with the variance given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a fickian diffusion with the effective diffusion coefficient. Both coefficients are given in terms of Peclet number (Pe) and the coefficient of molecular diffusion. We use the experimental results of to demonstrate that for transport and bimolecular reactions in porous media the SADR model is significantly more accurate than the traditional dispersion model, which overestimates the mass of the reaction product by as much as 25%.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

A stochastic maximum principle for backward control systems with random default time

NASA Astrophysics Data System (ADS)

Shen, Yang; Kuen Siu, Tak

2013-05-01

This paper establishes a necessary and sufficient stochastic maximum principle for backward systems, where the state processes are governed by jump-diffusion backward stochastic differential equations with random default time. An application of the sufficient stochastic maximum principle to an optimal investment and capital injection problem in the presence of default risk is discussed.

Slow-fast stochastic diffusion dynamics and quasi-stationarity for diploid populations with varying size.

PubMed

Coron, Camille

2016-01-01

We are interested in the long-time behavior of a diploid population with sexual reproduction and randomly varying population size, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with competition, weak cooperation and Mendelian reproduction. This stochastic process is indexed by a scaling parameter K that goes to infinity, following a large population assumption. When the individual birth and natural death rates are of order K, the sequence of stochastic processes indexed by K converges toward a new slow-fast dynamics with variable population size. We indeed prove the convergence toward 0 of a fast variable giving the deviation of the population from quasi Hardy-Weinberg equilibrium, while the sequence of slow variables giving the respective numbers of occurrences of each allele converges toward a 2-dimensional diffusion process that reaches (0,0) almost surely in finite time. The population size and the proportion of a given allele converge toward a Wright-Fisher diffusion with stochastically varying population size and diploid selection. We insist on differences between haploid and diploid populations due to population size stochastic variability. Using a non trivial change of variables, we study the absorption of this diffusion and its long time behavior conditioned on non-extinction. In particular we prove that this diffusion starting from any non-trivial state and conditioned on not hitting (0,0) admits a unique quasi-stationary distribution. We give numerical approximations of this quasi-stationary behavior in three biologically relevant cases: neutrality, overdominance, and separate niches.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

NASA Astrophysics Data System (ADS)

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-10-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

PubMed

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

2015-10-15

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

PubMed Central

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-01-01

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. PMID:26478601

A Stochastic Diffusion Process for the Dirichlet Distribution

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2013-03-01

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability ofNcoupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded sample space, a coupled nonlinear diffusion process is required: the Wiener processes in the equivalent system of stochastic differential equations are multiplicative with coefficients dependent on all the stochastic variables. Individual samples of a discrete ensemble, obtained from the stochastic process, satisfy a unit-sum constraint at all times. The process may be used to represent realizations of a fluctuating ensemble ofNvariables subject to a conservation principle.more » Similar to the multivariate Wright-Fisher process, whose invariant is also Dirichlet, the univariate case yields a process whose invariant is the beta distribution. As a test of the results, Monte Carlo simulations are used to evolve numerical ensembles toward the invariant Dirichlet distribution.« less

Self-diffusion in a stochastically heated two-dimensional dusty plasma

NASA Astrophysics Data System (ADS)

Sheridan, T. E.

2016-09-01

Diffusion in a two-dimensional dusty plasma liquid (i.e., a Yukawa liquid) is studied experimentally. The dusty plasma liquid is heated stochastically by a surrounding three-dimensional toroidal dusty plasma gas which acts as a thermal reservoir. The measured dust velocity distribution functions are isotropic Maxwellians, giving a well-defined kinetic temperature. The mean-square displacement for dust particles is found to increase linearly with time, indicating normal diffusion. The measured diffusion coefficients increase approximately linearly with temperature. The effective collision rate is dominated by collective dust-dust interactions rather than neutral gas drag, and is comparable to the dusty-plasma frequency.

Steepest Ascent Low/Non-Low-Frequency Ratio in Empirical Mode Decomposition to Separate Deterministic and Stochastic Velocities From a Single Lagrangian Drifter

NASA Astrophysics Data System (ADS)

Chu, Peter C.

2018-03-01

SOund Fixing And Ranging (RAFOS) floats deployed by the Naval Postgraduate School (NPS) in the California Current system from 1992 to 2001 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) are used to study 2-D turbulent characteristics. Each drifter trajectory is adaptively decomposed using the empirical mode decomposition (EMD) into a series of intrinsic mode functions (IMFs) with corresponding specific scale for each IMF. A new steepest ascent low/non-low-frequency ratio is proposed in this paper to separate a Lagrangian trajectory into low-frequency (nondiffusive, i.e., deterministic) and high-frequency (diffusive, i.e., stochastic) components. The 2-D turbulent (or called eddy) diffusion coefficients are calculated on the base of the classical turbulent diffusion with mixing length theory from stochastic component of a single drifter. Statistical characteristics of the calculated 2-D turbulence length scale, strength, and diffusion coefficients from the NPS RAFOS data are presented with the mean values (over the whole drifters) of the 2-D diffusion coefficients comparable to the commonly used diffusivity tensor method.

Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen-Loeve expansion.

PubMed

Barber, Jared; Tanase, Roxana; Yotov, Ivan

2016-06-01

Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.

Rippled area formed by surface plasmon polaritons upon femtosecond laser double-pulse irradiation of silicon.

PubMed

Derrien, Thibault J-Y; Krüger, Jörg; Itina, Tatiana E; Höhm, Sandra; Rosenfeld, Arkadi; Bonse, Jörn

2013-12-02

The formation of near-wavelength laser-induced periodic surface structures (LIPSS) on silicon upon irradiation with sequences of Ti:sapphire femtosecond laser pulse pairs (pulse duration 150 fs, central wavelength 800 nm) is studied theoretically. For this purpose, the nonlinear generation of conduction band electrons in silicon and their relaxation is numerically calculated using a two-temperature model approach including intrapulse changes of optical properties, transport, diffusion and recombination effects. Following the idea that surface plasmon polaritons (SPP) can be excited when the material turns from semiconducting to metallic state, the "SPP active area" is calculated as function of fluence and double-pulse delay up to several picoseconds and compared to the experimentally observed rippled surface areas. Evidence is presented that multi-photon absorption explains the large increase of the rippled area for temporally overlapping pulses. For longer double-pulse delays, relevant relaxation processes are identified. The results demonstrate that femtosecond LIPSS on silicon are caused by the excitation of SPP and can be controlled by temporal pulse shaping.

Stochastic modelling of intermittency.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2010-01-13

Recently, methods have been developed to model low-dimensional chaotic systems in terms of stochastic differential equations. We tested such methods in an electronic circuit experiment. We aimed to obtain reliable drift and diffusion coefficients even without a pronounced time-scale separation of the chaotic dynamics. By comparing the analytical solutions of the corresponding Fokker-Planck equation with experimental data, we show here that crisis-induced intermittency can be described in terms of a stochastic model which is dominated by state-space-dependent diffusion. Further on, we demonstrate and discuss some limits of these modelling approaches using numerical simulations. This enables us to state a criterion that can be used to decide whether a stochastic model will capture the essential features of a given time series. This journal is © 2010 The Royal Society

Electron-cyclotron resonance preionization and heating in the Proto-cleo torsatron

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

Goes, L.C.S.

1986-01-01

ECR-breakdown and heating in a bifurcated torsatron topology are investigated with extraordinary mode injection from the high-field side (7.2 GHz/2 KW/10 ms). The breakdown characteristics are explained by stochastic heating enhanced by helical ripple effects. In the quasi-stationary regime (0.01 n/sub cr/ < n < 0.6 n/sub cr/), two-dimensional plasma profiles indicated heating inhomogeneities associated with RF power absorption near the UHR layer. The production of a suprathermal electron population, at the outer plasma edge, was indicated by nonthermal microwave emission and target SXR emission.

Bedform Dimensions and Suspended Sediment Observations in a Mixed Sand-Mud Intertidal Environment

NASA Astrophysics Data System (ADS)

Lichtman, I. D.; Amoudry, L.; Peter, T.; Jaco, B.

2016-02-01

Small-scale bedforms, such as ripples, can profoundly modify near-bed hydrodynamics, near-bed sediment transport and resuspension, and benthic-pelagic fluxes. Knowledge of their dimensions is important for a number of applications. Fundamentally different processes can occur depending on the dimensions of ripples: for low and long ripples, the bed remains dynamically flat and diffusive processes dominate sediment entrainment; for steep ripples, flow separation occurs above the ripples creating vortices, which are far more efficient at entraining sediment into the water column. Recent laboratory experiments for mixtures of sand and mud have shown that bedform dimensions decrease with increasing sediment mud content. However, these same experiments also showed that mud is selectively taken into suspension when bedforms are created and migrate on the bed, leaving sandy bedforms. This entrainment process, selectively suspending fine sediment, is referred to as winnowing. To improve our understanding of bedform and entrainment dynamics of mixed sediments, in situ observations were made on intertidal flats in the Dee Estuary, United Kingdom. A suite of instruments were deployed collecting co-located measurements of the near-bed hydrodynamics, waves, small-scale bed morphology and suspended sediment. Three sites were occupied consecutively, over a Spring-Neap cycle, collecting data for different bed compositions, tide levels and wind conditions. Bed samples were taken when the flats became exposed at low water and a sediment trap collected suspended load when inundated. This study will combine these measurements to investigate the interactions between small-scale bed morphology, near-bed hydrodynamics and sediment entrainment. We will examine bedform development in the complex hydrodynamic and wave climate of tidal flats, in relation to standard ripple predictors. We will also relate the variability in small-scale bedforms to variation in hydrodynamic and wave conditions, and to suspension and entrainment processes for mixed sediments.

Mesoscopic description of random walks on combs

NASA Astrophysics Data System (ADS)

Méndez, Vicenç; Iomin, Alexander; Campos, Daniel; Horsthemke, Werner

2015-12-01

Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches, and compare our analytical results with stochastic simulations.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

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

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

Stochastic flux freezing and magnetic dynamo.

PubMed

Eyink, Gregory L

2011-05-01

Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr(m)) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr(m)=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered. © 2011 American Physical Society

Plasma Equilibria With Stochastic Magnetic Fields

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2009-05-01

Plasma equilibria that include regions of stochastic magnetic fields are of interest in a variety of applications, including tokamaks with ergodic limiters and high-pressure stellarators. Such equilibria are examined theoretically, and a numerical algorithm for their construction is described.^2,3 % The balance between stochastic diffusion of magnetic lines and small effects^2 omitted from the simplest MHD description can support pressure and current profiles that need not be flattened in stochastic regions. The diffusion can be described analytically by renormalizing stochastic Langevin equations for pressure and parallel current j, with particular attention being paid to the satisfaction of the periodicity constraints in toroidal configurations with sheared magnetic fields. The equilibrium field configuration can then be constructed by coupling the prediction for j to Amp'ere's law, which is solved numerically. A. Reiman et al., Pressure-induced breaking of equilibrium flux surfaces in the W7AS stellarator, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes and A. H. Reiman, Plasma equilibrium in a magnetic field with stochastic regions, submitted to Phys. Plasmas. J. A. Krommes, Fundamental statistical theories of plasma turbulence in magnetic fields, Phys. Reports 360, 1--351.

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

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

Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp; Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realisticmore » biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.« less

Diffusion of test particles in stochastic magnetic fields for small Kubo numbers.

PubMed

Neuer, Marcus; Spatschek, Karl H

2006-02-01

Motion of charged particles in a collisional plasma with stochastic magnetic field lines is investigated on the basis of the so-called A-Langevin equation. Compared to the previously used A-Langevin model, here finite Larmor radius effects are taken into account. The A-Langevin equation is solved under the assumption that the Lagrangian correlation function for the magnetic field fluctuations is related to the Eulerian correlation function (in Gaussian form) via the Corrsin approximation. The latter is justified for small Kubo numbers. The velocity correlation function, being averaged with respect to the stochastic variables including collisions, leads to an implicit differential equation for the mean square displacement. From the latter, different transport regimes, including the well-known Rechester-Rosenbluth diffusion coefficient, are derived. Finite Larmor radius contributions show a decrease of the diffusion coefficient compared to the guiding center limit. The case of small (or vanishing) mean fields is also discussed.

Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux

NASA Astrophysics Data System (ADS)

Endo, Noritaka

2016-12-01

A simple stochastic cellular automaton model is proposed for simulating bedload transport, especially for cases with a low transport rate and where available sediments are very sparse on substrates in a subaqueous system. Numerical simulations show that the bed type changes from sheet flow through sand patches to ripples as the amount of sand increases; this is consistent with observations in flume experiments and in the field. Without changes in external conditions, the sand flux calculated for a given amount of sand decreases over time as bedforms develop from a flat bed. This appears to be inconsistent with the general understanding that sand flux remains unchanged under the constant-fluid condition, but it is consistent with the previous experimental data. For areas of low sand abundance, the sand flux versus sand amount (flux-density relation) in the simulation shows a single peak with an abrupt decrease, followed by a long tail; this is very similar to the flux-density relation seen in automobile traffic flow. This pattern (the relation between segments of the curve and the corresponding bed states) suggests that sand sheets, sand patches, and sand ripples correspond respectively to the free-flow phase, congested phase, and jam phase of traffic flows. This implies that sand topographic features on starved beds are determined by the degree of interference between sand particles. Although the present study deals with simple cases only, this can provide a simplified but effective modeling of the more complicated sediment transport processes controlled by interference due to contact between grains, such as the pulsatory migration of grain-size bimodal mixtures with repetition of clustering and scattering.

Surface morphology evolution during plasma etching of silicon: roughening, smoothing and ripple formation

NASA Astrophysics Data System (ADS)

Ono, Kouichi; Nakazaki, Nobuya; Tsuda, Hirotaka; Takao, Yoshinori; Eriguchi, Koji

2017-10-01

Atomic- or nanometer-scale roughness on feature surfaces has become an important issue to be resolved in the fabrication of nanoscale devices in industry. Moreover, in some cases, smoothing of initially rough surfaces is required for planarization of film surfaces, and controlled surface roughening is required for maskless fabrication of organized nanostructures on surfaces. An understanding, under what conditions plasma etching results in surface roughening and/or smoothing and what are the mechanisms concerned, is of great technological as well as fundamental interest. In this article, we review recent developments in the experimental and numerical study of the formation and evolution of surface roughness (or surface morphology evolution such as roughening, smoothing, and ripple formation) during plasma etching of Si, with emphasis being placed on a deeper understanding of the mechanisms or plasma-surface interactions that are responsible for. Starting with an overview of the experimental and theoretical/numerical aspects concerned, selected relevant mechanisms are illustrated and discussed primarily on the basis of systematic/mechanistic studies of Si etching in Cl-based plasmas, including noise (or stochastic roughening), geometrical shadowing, surface reemission of etchants, micromasking by etch inhibitors, and ion scattering/chanelling. A comparison of experiments (etching and plasma diagnostics) and numerical simulations (Monte Carlo and classical molecular dynamics) indicates a crucial role of the ion scattering or reflection from microscopically roughened feature surfaces on incidence in the evolution of surface roughness (and ripples) during plasma etching; in effect, the smoothing/non-roughening condition is characterized by reduced effects of the ion reflection, and the roughening-smoothing transition results from reduced ion reflections caused by a change in the predominant ion flux due to that in plasma conditions. Smoothing of initially rough surfaces as well as non-roughening of initially planar surfaces during etching (normal ion incidence) and formation of surface ripples by plasma etching (off-normal ion incidence) are also presented and discussed in this context.

Reduced equations of motion for quantum systems driven by diffusive Markov processes.

PubMed

Sarovar, Mohan; Grace, Matthew D

2012-09-28

The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.

Random walk, diffusion and mixing in simulations of scalar transport in fluid flows

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2008-12-01

Physical similarity and mathematical equivalence of continuous diffusion and particle random walk form one of the cornerstones of modern physics and the theory of stochastic processes. In many applied models used in simulation of turbulent transport and turbulent combustion, mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. We show that the continuous scalar transport and diffusion can be accurately specified by means of mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. This gives an alternative formulation for the stochastic process which is selected to represent the continuous diffusion. This paper focuses on statistical errors and deals with relatively simple cases, where one-particle distributions are sufficient for a complete description of the problem.

Chaotic ion motion in magnetosonic plasma waves

NASA Technical Reports Server (NTRS)

Varvoglis, H.

1984-01-01

The motion of test ions in a magnetosonic plasma wave is considered, and the 'stochasticity threshold' of the wave's amplitude for the onset of chaotic motion is estimated. It is shown that for wave amplitudes above the stochasticity threshold, the evolution of an ion distribution can be described by a diffusion equation with a diffusion coefficient D approximately equal to 1/v. Possible applications of this process to ion acceleration in flares and ion beam thermalization are discussed.

Conceptual design of a Bitter-magnet toroidal-field system for the ZEPHYR Ignition Test Reactor

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

Williams, J.E.C.; Becker, H.D.; Bobrov, E.S.

1981-05-01

The following problems are described and discussed: (1) parametric studies - these studies examine among other things the interdependence of throat stresses, plasma parameters (margins of ignition) and stored energy. The latter is a measure of cost and is minimized in the present design; (2) magnet configuration - the shape of the plates are considered in detail including standard turns, turns located at beam ports, diagnostic and closure flanges; (3) ripple computation - this section describes the codes by which ripple is computed; (4) field diffusion and nuclear heating - the effect of magnetic field diffusion on heating is consideredmore » along with neutron heating. Current, field and temperature profiles are computed; (5) finite element analysis - the two and three dimensional finite element codes are described and the results discussed in detail; (6) structures engineering - this considers the calculation of critical stresses due to toroidal and overturning forces and discusses the method of constraint of these forces. The Materials Testing Program is also discussed; (7) fabrication - the methods available for the manufacture of the constituent parts of the Bitter plates, the method of assembly and remote maintenance are summarized.« less

A hybrid continuous-discrete method for stochastic reaction-diffusion processes.

PubMed

Lo, Wing-Cheong; Zheng, Likun; Nie, Qing

2016-09-01

Stochastic fluctuations in reaction-diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method.

Control Improvement for Jump-Diffusion Processes with Applications to Finance

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

Baeuerle, Nicole, E-mail: nicole.baeuerle@kit.edu; Rieder, Ulrich, E-mail: ulrich.rieder@uni-ulm.de

2012-02-15

We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control {pi}, a new control with a better value. If no improvement is possible, then {pi} is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard's policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in financial portfolio optimization.

Stochastic cellular automata model of cell migration, proliferation and differentiation: validation with in vitro cultures of muscle satellite cells.

PubMed

Garijo, N; Manzano, R; Osta, R; Perez, M A

2012-12-07

Cell migration and proliferation has been modelled in the literature as a process similar to diffusion. However, using diffusion models to simulate the proliferation and migration of cells tends to create a homogeneous distribution in the cell density that does not correlate to empirical observations. In fact, the mechanism of cell dispersal is not diffusion. Cells disperse by crawling or proliferation, or are transported in a moving fluid. The use of cellular automata, particle models or cell-based models can overcome this limitation. This paper presents a stochastic cellular automata model to simulate the proliferation, migration and differentiation of cells. These processes are considered as completely stochastic as well as discrete. The model developed was applied to predict the behaviour of in vitro cell cultures performed with adult muscle satellite cells. Moreover, non homogeneous distribution of cells has been observed inside the culture well and, using the above mentioned stochastic cellular automata model, we have been able to predict this heterogeneous cell distribution and compute accurate quantitative results. Differentiation was also incorporated into the computational simulation. The results predicted the myotube formation that typically occurs with adult muscle satellite cells. In conclusion, we have shown how a stochastic cellular automata model can be implemented and is capable of reproducing the in vitro behaviour of adult muscle satellite cells. Copyright © 2012 Elsevier Ltd. All rights reserved.

Stochastic collective dynamics of charged-particle beams in the stability regime

NASA Astrophysics Data System (ADS)

Petroni, Nicola Cufaro; de Martino, Salvatore; de Siena, Silvio; Illuminati, Fabrizio

2001-01-01

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time-reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by λcN, where N is the number of particles in the beam and λc the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schrödinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so-called ``quantum-like approaches'' to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

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

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

A Numerical Method for the Simulation of Skew Brownian Motion and its Application to Diffusive Shock Acceleration of Charged Particles

NASA Astrophysics Data System (ADS)

McEvoy, Erica L.

Stochastic differential equations are becoming a popular tool for modeling the transport and acceleration of cosmic rays in the heliosphere. In diffusive shock acceleration, cosmic rays diffuse across a region of discontinuity where the up- stream diffusion coefficient abruptly changes to the downstream value. Because the method of stochastic integration has not yet been developed to handle these types of discontinuities, I utilize methods and ideas from probability theory to develop a conceptual framework for the treatment of such discontinuities. Using this framework, I then produce some simple numerical algorithms that allow one to incorporate and simulate a variety of discontinuities (or boundary conditions) using stochastic integration. These algorithms were then modified to create a new algorithm which incorporates the discontinuous change in diffusion coefficient found in shock acceleration (known as Skew Brownian Motion). The originality of this algorithm lies in the fact that it is the first of its kind to be statistically exact, so that one obtains accuracy without the use of approximations (other than the machine precision error). I then apply this algorithm to model the problem of diffusive shock acceleration, modifying it to incorporate the additional effect of the discontinuous flow speed profile found at the shock. A steady-state solution is obtained that accurately simulates this phenomenon. This result represents a significant improvement over previous approximation algorithms, and will be useful for the simulation of discontinuous diffusion processes in other fields, such as biology and finance.

Stochastic Analysis and Applied Probability(3.3.1): Topics in the Theory and Applications of Stochastic Analysis

DTIC Science & Technology

2015-08-13

is due to Reiman [36] who considered the case where the arrivals and services are mutually independent renewal processes with square integrable summands...to a reflected diffusion process with drift and diffusion coefficients that depend on the state of the process. In models considered in works of Reiman ...the infinity Laplacian. Jour. AMS, to appear [36] M. I. Reiman . Open queueing networks in heavy traffic. Mathematics of Operations Research, 9(3): 441

Investigation Of Plasma Critical Surface Rippling By Harmonics Generation In Laser Plasmas

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

Racz, E.; Foeldes, I. B.; Szatmari, S.

2006-01-15

Experiments were carried out by a tightly focused, prepulse-free hybrid KrF excimer-dye laser system (700fs pulse duration, 248nm wavelength, 15mJ pulse energy). Intense 2{omega}, 3{omega} and near threshold 4{omega} were generated in laser plasmas on solid surfaces for p- and s-polarized 1.5{center_dot}1017 W/cm2 radiation intensity. Directionality and polarization properties were investigated depending on the laser intensity and polarization. The observations showed diffuse propagation of harmonics for intensities above 1016 W/cm2 and the polarization of harmonics was mixed for the highest intensities. The explanation of these results is surface rippling of the plasma critical surface because of the Rayleigh-Taylor instability, whichmore » is an intrinsic consequence of the unstable balance between light pressure and plasma expansion.« less

Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units

PubMed Central

Vigelius, Matthias; Meyer, Bernd

2012-01-01

For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for an implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway. PMID:22506001

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

NASA Astrophysics Data System (ADS)

Syed Ali, M.; Yogambigai, J.; Kwon, O. M.

2018-03-01

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov-Krasovskii's functional and utilisation of Jensen's inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

Multi-Algorithm Particle Simulations with Spatiocyte.

PubMed

Arjunan, Satya N V; Takahashi, Koichi

2017-01-01

As quantitative biologists get more measurements of spatially regulated systems such as cell division and polarization, simulation of reaction and diffusion of proteins using the data is becoming increasingly relevant to uncover the mechanisms underlying the systems. Spatiocyte is a lattice-based stochastic particle simulator for biochemical reaction and diffusion processes. Simulations can be performed at single molecule and compartment spatial scales simultaneously. Molecules can diffuse and react in 1D (filament), 2D (membrane), and 3D (cytosol) compartments. The implications of crowded regions in the cell can be investigated because each diffusing molecule has spatial dimensions. Spatiocyte adopts multi-algorithm and multi-timescale frameworks to simulate models that simultaneously employ deterministic, stochastic, and particle reaction-diffusion algorithms. Comparison of light microscopy images to simulation snapshots is supported by Spatiocyte microscopy visualization and molecule tagging features. Spatiocyte is open-source software and is freely available at http://spatiocyte.org .

Ion precipitation from the inner plasma sheet due to stochastic diffusion

NASA Technical Reports Server (NTRS)

Zelenyi, L.; Galeev, A.; Kennel, C. F.

1990-01-01

Plasma sheet ions do not conserve their first adiabatic invariant when the magnetic field is appreciably tail-like. They do conserve a different adiabatic invariant but only to linear, rather than exponential, accuracy in the appropriate small parameter. Thus significant stochastic diffusion can occur for particles crossing the separatrix dividing the segments of orbits on which the particles cross and do not cross the tail midplane. Such ions can escape the plasma sheet and precipitate into the atmosphere. Stochastic scattering is strongest from those field lines where the ion's Larmor period in the normal component of the neutral sheet magnetic field approximately equals its bounce period. By comparing the rates of stochastic ion loss and convection in the tail, it is possible to estimate the location and thickness of the inner edge of the ion plasma sheet created by stochastic ion loss. Ions of different masses precipitate into the atmosphere at slightly different locations. Since wave particle interactions are not needed, this precipitation will always occur and should be particularly evident during quiet geomagnetic conditions, when it is less likely to be masked by other precipitation mechanisms.

A diffusion-based approach to stochastic individual growth and energy budget, with consequences to life-history optimization and population dynamics.

PubMed

Filin, I

2009-06-01

Using diffusion processes, I model stochastic individual growth, given exogenous hazards and starvation risk. By maximizing survival to final size, optimal life histories (e.g. switching size for habitat/dietary shift) are determined by two ratios: mean growth rate over growth variance (diffusion coefficient) and mortality rate over mean growth rate; all are size dependent. For example, switching size decreases with either ratio, if both are positive. I provide examples and compare with previous work on risk-sensitive foraging and the energy-predation trade-off. I then decompose individual size into reversibly and irreversibly growing components, e.g. reserves and structure. I provide a general expression for optimal structural growth, when reserves grow stochastically. I conclude that increased growth variance of reserves delays structural growth (raises threshold size for its commencement) but may eventually lead to larger structures. The effect depends on whether the structural trait is related to foraging or defence. Implications for population dynamics are discussed.

Active motion assisted by correlated stochastic torques.

PubMed

Weber, Christian; Radtke, Paul K; Schimansky-Geier, Lutz; Hänggi, Peter

2011-07-01

The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular dynamics of the particle determining the orientation of motion. In addition to a constant torque, the particle is supplemented by random torques, which are modeled as an Ornstein-Uhlenbeck process with given correlation time τ(c). These nonvanishing correlations cause a persistence of the particles' trajectories and a change of the effective spatial diffusion coefficient. We discuss the mean square displacement as a function of the correlation time and the noise intensity and detect a nonmonotonic dependence of the effective diffusion coefficient with respect to both correlation time and noise strength. A maximal diffusion behavior is obtained if the correlated angular noise straightens the curved trajectories, interrupted by small pirouettes, whereby the correlated noise amplifies a straightening of the curved trajectories caused by the constant torque.

Estimation of Kubo number and correlation length of fluctuating magnetic fields and pressure in BOUT + + edge pedestal collapse simulation

NASA Astrophysics Data System (ADS)

Kim, Jaewook; Lee, W.-J.; Jhang, Hogun; Kaang, H. H.; Ghim, Y.-C.

2017-10-01

Stochastic magnetic fields are thought to be as one of the possible mechanisms for anomalous transport of density, momentum and heat across the magnetic field lines. Kubo number and Chirikov parameter are quantifications of the stochasticity, and previous studies show that perpendicular transport strongly depends on the magnetic Kubo number (MKN). If MKN is smaller than one, diffusion process will follow Rechester-Rosenbluth model; whereas if it is larger than one, percolation theory dominates the diffusion process. Thus, estimation of Kubo number plays an important role to understand diffusion process caused by stochastic magnetic fields. However, spatially localized experimental measurement of fluctuating magnetic fields in a tokamak is difficult, and we attempt to estimate MKNs using BOUT + + simulation data with pedestal collapse. In addition, we calculate correlation length of fluctuating pressures and Chirikov parameters to investigate variation correlation lengths in the simulation. We, then, discuss how one may experimentally estimate MKNs.

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

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

Padgett, Jill M. A.; Ilie, Silvana, E-mail: silvana@ryerson.ca

2016-03-15

Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating themore » solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.« less

Lognormal-like statistics of a stochastic squeeze process

NASA Astrophysics Data System (ADS)

Shapira, Dekel; Cohen, Doron

2017-10-01

We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate w and the angular diffusion coefficient D . We carry out an exact analysis to determine the drift and the diffusion coefficient of log(r ) , where r is the radial coordinate. The results go beyond the heuristic lognormal description that is implied by the central limit theorem. Contrary to the common "quantum Zeno" approximation, the radial diffusion is not simply Dr=(1 /8 ) w2/D but has a nonmonotonic dependence on w /D . Furthermore, the calculation of the radial moments is dominated by the far non-Gaussian tails of the log(r ) distribution.

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

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

D'Elia, M.; Edwards, H. C.; Hu, J.

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

DOE PAGES

D'Elia, M.; Edwards, H. C.; Hu, J.; ...

2018-01-18

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

The Influence of Turbulent Coherent Structure on Suspended Sediment Transport

NASA Astrophysics Data System (ADS)

Huang, S. H.; Tsai, C.

2017-12-01

The anomalous diffusion of turbulent sedimentation has received more and more attention in recent years. With the advent of new instruments and technologies, researchers have found that sediment behavior may deviate from Fickian assumptions when particles are heavier. In particle-laden flow, bursting phenomena affects instantaneous local concentrations, and seems to carry suspended particles for a longer distance. Instead of the pure diffusion process in an analogy to Brownian motion, Levy flight which allows particles to move in response to bursting phenomena is suspected to be more suitable for describing particle movement in turbulence. And the fractional differential equation is a potential candidate to improve the concentration profile. However, stochastic modeling (the Differential Chapmen-Kolmogorov Equation) also provides an alternative mathematical framework to describe system transits between different states through diffusion/the jump processes. Within this framework, the stochastic particle tracking model linked with advection diffusion equation is a powerful tool to simulate particle locations in the flow field. By including the jump process to this model, a more comprehensive description for suspended sediment transport can be provided with a better physical insight. This study also shows the adaptability and expandability of the stochastic particle tracking model for suspended sediment transport modeling.

A hybrid continuous-discrete method for stochastic reaction–diffusion processes

PubMed Central

Zheng, Likun; Nie, Qing

2016-01-01

Stochastic fluctuations in reaction–diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method. PMID:27703710

Towards a minimal stochastic model for a large class of diffusion-reactions on biological membranes.

PubMed

Chevalier, Michael W; El-Samad, Hana

2012-08-28

Diffusion of biological molecules on 2D biological membranes can play an important role in the behavior of stochastic biochemical reaction systems. Yet, we still lack a fundamental understanding of circumstances where explicit accounting of the diffusion and spatial coordinates of molecules is necessary. In this work, we illustrate how time-dependent, non-exponential reaction probabilities naturally arise when explicitly accounting for the diffusion of molecules. We use the analytical expression of these probabilities to derive a novel algorithm which, while ignoring the exact position of the molecules, can still accurately capture diffusion effects. We investigate the regions of validity of the algorithm and show that for most parameter regimes, it constitutes an accurate framework for studying these systems. We also document scenarios where large spatial fluctuation effects mandate explicit consideration of all the molecules and their positions. Taken together, our results derive a fundamental understanding of the role of diffusion and spatial fluctuations in these systems. Simultaneously, they provide a general computational methodology for analyzing a broad class of biological networks whose behavior is influenced by diffusion on membranes.

Diffusion of multiple species with excluded-volume effects.

PubMed

Bruna, Maria; Chapman, S Jonathan

2012-11-28

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results.

Bifurcation physics of magnetic islands and stochasticity explored by heat pulse propagation studies in toroidal plasmas

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

Ida, K.; Kobayashi, T.; Yoshinuma, M.

Bifurcation physics of the magnetic island was investigated using the heat pulse propagation technique produced by the modulation of electron cyclotron heating. There are two types of bifurcation phenomena observed in LHD and DIII-D. One is a bifurcation of the magnetic topology between nested and stochastic fields. The nested state is characterized by the bi-directional (inward and outward) propagation of the heat pulse with slow propagation speed. The stochastic state is characterized by the fast propagation of the heat pulse with electron temperature flattening. The other bifurcation is between magnetic island with larger thermal diffusivity and that with smaller thermalmore » diffusivity. The damping of toroidal flow is observed at the O-point of the magnetic island both in helical plasmas and in tokamak plasmas during a mode locking phase with strong flow shears at the boundary of the magnetic island. Associated with the stochastization of the magnetic field, the abrupt damping of toroidal flow is observed in LHD. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. Lastly, this observation suggests that this flow damping is due to the change in the non-diffusive term of momentum transport.« less

Bifurcation physics of magnetic islands and stochasticity explored by heat pulse propagation studies in toroidal plasmas

DOE PAGES

Ida, K.; Kobayashi, T.; Yoshinuma, M.; ...

2016-07-29

Bifurcation physics of the magnetic island was investigated using the heat pulse propagation technique produced by the modulation of electron cyclotron heating. There are two types of bifurcation phenomena observed in LHD and DIII-D. One is a bifurcation of the magnetic topology between nested and stochastic fields. The nested state is characterized by the bi-directional (inward and outward) propagation of the heat pulse with slow propagation speed. The stochastic state is characterized by the fast propagation of the heat pulse with electron temperature flattening. The other bifurcation is between magnetic island with larger thermal diffusivity and that with smaller thermalmore » diffusivity. The damping of toroidal flow is observed at the O-point of the magnetic island both in helical plasmas and in tokamak plasmas during a mode locking phase with strong flow shears at the boundary of the magnetic island. Associated with the stochastization of the magnetic field, the abrupt damping of toroidal flow is observed in LHD. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. Lastly, this observation suggests that this flow damping is due to the change in the non-diffusive term of momentum transport.« less

Confinement and diffusion modulate bistability and stochastic switching in a reaction network with positive feedback

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

Mlynarczyk, Paul J.; Pullen, Robert H.; Abel, Steven M., E-mail: abel@utk.edu

2016-01-07

Positive feedback is a common feature in signal transduction networks and can lead to phenomena such as bistability and signal propagation by domain growth. Physical features of the cellular environment, such as spatial confinement and the mobility of proteins, play important but inadequately understood roles in shaping the behavior of signaling networks. Here, we use stochastic, spatially resolved kinetic Monte Carlo simulations to explore a positive feedback network as a function of system size, system shape, and mobility of molecules. We show that these physical properties can markedly alter characteristics of bistability and stochastic switching when compared with well-mixed simulations.more » Notably, systems of equal volume but different shapes can exhibit qualitatively different behaviors under otherwise identical conditions. We show that stochastic switching to a state maintained by positive feedback occurs by cluster formation and growth. Additionally, the frequency at which switching occurs depends nontrivially on the diffusion coefficient, which can promote or suppress switching relative to the well-mixed limit. Taken together, the results provide a framework for understanding how confinement and protein mobility influence emergent features of the positive feedback network by modulating molecular concentrations, diffusion-influenced rate parameters, and spatiotemporal correlations between molecules.« less

Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

PubMed

Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W

2017-09-26

The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.

A stochastic multi-scale method for turbulent premixed combustion

NASA Astrophysics Data System (ADS)

Cha, Chong M.

2002-11-01

The stochastic chemistry algorithm of Bunker et al. and Gillespie is used to perform the chemical reactions in a transported probability density function (PDF) modeling approach of turbulent combustion. Recently, Kraft & Wagner have demonstrated a 100-fold gain in computational speed (for a 100 species mechanism) using the stochastic approach over the conventional, direct integration method of solving for the chemistry. Here, the stochastic chemistry algorithm is applied to develop a new transported PDF model of turbulent premixed combustion. The methodology relies on representing the relevant spatially dependent physical processes as queuing events. The canonical problem of a one-dimensional premixed flame is used for validation. For the laminar case, molecular diffusion is described by a random walk. For the turbulent case, one of two different material transport submodels can provide the necessary closure: Taylor dispersion or Kerstein's one-dimensional turbulence approach. The former exploits ``eddy diffusivity'' and hence would be much more computationally tractable for practical applications. Various validation studies are performed. Results from the Monte Carlo simulations compare well to asymptotic solutions of laminar premixed flames, both with and without high activation temperatures. The correct scaling of the turbulent burning velocity is predicted in both Damköhler's small- and large-scale turbulence limits. The effect of applying the eddy diffusivity concept in the various regimes is discussed.

Dependence of Perpendicular Viscosity on Magnetic Fluctuations in a Stochastic Topology

NASA Astrophysics Data System (ADS)

Fridström, R.; Chapman, B. E.; Almagri, A. F.; Frassinetti, L.; Brunsell, P. R.; Nishizawa, T.; Sarff, J. S.

2018-06-01

In a magnetically confined plasma with a stochastic magnetic field, the dependence of the perpendicular viscosity on the magnetic fluctuation amplitude is measured for the first time. With a controlled, ˜ tenfold variation in the fluctuation amplitude, the viscosity increases ˜100 -fold, exhibiting the same fluctuation-amplitude-squared dependence as the predicted rate of stochastic field line diffusion. The absolute value of the viscosity is well predicted by a model based on momentum transport in a stochastic field, the first in-depth test of this model.

Characterization of submillisecond response optical addressing phase modulator based on low light scattering polymer network liquid crystal

NASA Astrophysics Data System (ADS)

Xiangjie, Zhao; Cangli, Liu; Jiazhu, Duan; Dayong, Zhang; Yongquan, Luo

2015-01-01

Optically addressed conventional nematic liquid crystal spatial light modulator has attracted wide research interests. But the slow response speed limited its further application. In this paper, polymer network liquid crystal (PNLC) was proposed to replace the conventional nematic liquid crystal to enhance the response time to the order of submillisecond. The maximum light scattering of the employed PNLC was suppressed to be less than 2% at 1.064 μm by optimizing polymerization conditions and selecting large viscosity liquid crystal as solvent. The occurrence of phase ripple phenomenon due to electron diffusion and drift in photoconductor was found to deteriorate the phase modulation effect of the optical addressed PNLC phase modulator. The wavelength effect and AC voltage frequency effect on the on state dynamic response of phase change was investigated by experimental methods. These effects were interpreted by electron diffusion and drift theory based on the assumption that free electron was inhomogeneously distributed in accordance with the writing beam intensity distribution along the incident direction. The experimental results indicated that the phase ripple could be suppressed by optimizing the wavelength of the writing beam and the driving AC voltage frequency when varying the writing beam intensity to generate phase change in 2π range. The modulation transfer function was also measured.

Computing diffusivities from particle models out of equilibrium

NASA Astrophysics Data System (ADS)

Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia

2018-04-01

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.

Fluctuation correlation models for receptor immobilization

NASA Astrophysics Data System (ADS)

Fourcade, B.

2017-12-01

Nanoscale dynamics with cycles of receptor diffusion and immobilization by cell-external-or-internal factors is a key process in living cell adhesion phenomena at the origin of a plethora of signal transduction pathways. Motivated by modern correlation microscopy approaches, the receptor correlation functions in physical models based on diffusion-influenced reaction is studied. Using analytical and stochastic modeling, this paper focuses on the hybrid regime where diffusion and reaction are not truly separable. The time receptor autocorrelation functions are shown to be indexed by different time scales and their asymptotic expansions are given. Stochastic simulations show that this analysis can be extended to situations with a small number of molecules. It is also demonstrated that this analysis applies when receptor immobilization is coupled to environmental noise.

Monte-Carlo simulation of a stochastic differential equation

NASA Astrophysics Data System (ADS)

Arif, ULLAH; Majid, KHAN; M, KAMRAN; R, KHAN; Zhengmao, SHENG

2017-12-01

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient, Monte Carlo (MC) techniques are considered to be more effective than other algorithms, such as finite element method or finite difference method. The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques. For better convergence, methods with higher orders have been kept forward to allow MC codes with large step size. The main focus of this work is to look for operators that can produce converging results for large step sizes. As a first step, our comparative analysis has been applied to a general stochastic problem. Subsequently, our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.

Density behavior of spatial birth-and-death stochastic evolution of mutating genotypes under selection rates

NASA Astrophysics Data System (ADS)

Finkelshtein, D.; Kondratiev, Yu.; Kutoviy, O.; Molchanov, S.; Zhizhina, E.

2014-10-01

We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate, which provides a stochastic changing of lengths by a free diffusion law. The birth and death rates are length dependent, which corresponds to a selection effect. We study an asymptotic behavior of a density for an infinite collection of genotypes. The cases of space homogeneous and space heterogeneous densities are considered.

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

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

Granita, E-mail: granitafc@gmail.com; Bahar, A.

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Diffusion in biased turbulence

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

Vlad, M.; Spineanu, F.; Misguich, J. H.

2001-06-01

Particle transport in two-dimensional divergence-free stochastic velocity fields with constant average is studied. Analytical expressions for the Lagrangian velocity correlation and for the time-dependent diffusion coefficients are obtained. They apply to stationary and homogeneous Gaussian velocity fields.

Jump rates for surface diffusion of large molecules from first principles

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

Shea, Patrick, E-mail: patrick.shea@dal.ca; Kreuzer, Hans Jürgen

2015-04-21

We apply a recently developed stochastic model for the surface diffusion of large molecules to calculate jump rates for 9,10-dithioanthracene on a Cu(111) surface. The necessary input parameters for the stochastic model are calculated from first principles using density functional theory (DFT). We find that the inclusion of van der Waals corrections to the DFT energies is critical to obtain good agreement with experimental results for the adsorption geometry and energy barrier for diffusion. The predictions for jump rates in our model are in excellent agreement with measured values and show a marked improvement over transition state theory (TST). Wemore » find that the jump rate prefactor is reduced by an order of magnitude from the TST estimate due to frictional damping resulting from energy exchange with surface phonons, as well as a rotational mode of the diffusing molecule.« less

Simulation of stochastic diffusion via first exit times

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

Lötstedt, Per, E-mail: perl@it.uu.se; Meinecke, Lina, E-mail: lina.meinecke@it.uu.se

2015-11-01

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a methodmore » based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions.« less

Simulation of stochastic diffusion via first exit times

PubMed Central

Lötstedt, Per; Meinecke, Lina

2015-01-01

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a method based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions. PMID:26600600

From quantum stochastic differential equations to Gisin-Percival state diffusion

NASA Astrophysics Data System (ADS)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.

2007-01-01

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.

PubMed

Harrison, Jonathan U; Yates, Christian A

2016-09-01

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. © 2016 The Authors.

A hybrid algorithm for coupling partial differential equation and compartment-based dynamics

PubMed Central

Yates, Christian A.

2016-01-01

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction–diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. PMID:27628171

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers

PubMed Central

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation. PMID:28239346

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers.

PubMed

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation.

Sparse learning of stochastic dynamical equations

NASA Astrophysics Data System (ADS)

Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia

2018-06-01

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.

DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

DOE PAGES

Chen, Zheng; Liu, Liu; Mu, Lin

2017-05-03

In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof ofmore » the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.« less

A stochastic diffusion process for Lochner's generalized Dirichlet distribution

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2013-10-01

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner’s generalized Dirichlet distribution as its asymptotic solution. Individual samples of a discrete ensemble, obtained from the system of stochastic differential equations, equivalent to the Fokker-Planck equation developed here, satisfy a unit-sum constraint at all times and ensure a bounded sample space, similarly to the process developed in for the Dirichlet distribution. Consequently, the generalized Dirichlet diffusion process may be used to represent realizations of a fluctuating ensemble of N variables subject to a conservation principle.more » Compared to the Dirichlet distribution and process, the additional parameters of the generalized Dirichlet distribution allow a more general class of physical processes to be modeled with a more general covariance matrix.« less

Stochastic Stabilityfor Contracting Lorenz Maps and Flows

NASA Astrophysics Data System (ADS)

Metzger, R. J.

In a previous work [M], we proved the existence of absolutely continuous invariant measures for contracting Lorenz-like maps, and constructed Sinai-Ruelle-Bowen measures f or the flows that generate them. Here, we prove stochastic stability for such one-dimensional maps and use this result to prove that the corresponding flows generating these maps are stochastically stable under small diffusion-type perturbations, even though, as shown by Rovella [Ro], they are persistent only in a measure theoretical sense in a parameter space. For the one-dimensional maps we also prove strong stochastic stability in the sense of Baladi and Viana[BV].

Stochastic inflation in phase space: is slow roll a stochastic attractor?

NASA Astrophysics Data System (ADS)

Grain, Julien; Vennin, Vincent

2017-05-01

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ``slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

PubMed

Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M

2016-12-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Nonlinear dynamics of Aeolian sand ripples.

PubMed

Prigozhin, L

1999-07-01

We study the initial instability of flat sand surface and further nonlinear dynamics of wind ripples. The proposed continuous model of ripple formation allowed us to simulate the development of a typical asymmetric ripple shape and the evolution of a sand ripple pattern. We suggest that this evolution occurs via ripple merger preceded by several soliton-like interaction of ripples.

Simulation of quantum dynamics based on the quantum stochastic differential equation.

PubMed

Li, Ming

2013-01-01

The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

Stochastic fire-diffuse-fire model with realistic cluster dynamics.

PubMed

Calabrese, Ana; Fraiman, Daniel; Zysman, Daniel; Ponce Dawson, Silvina

2010-09-01

Living organisms use waves that propagate through excitable media to transport information. Ca2+ waves are a paradigmatic example of this type of processes. A large hierarchy of Ca2+ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, Ca2+ release occurs trough inositol 1,4,5-trisphosphate receptors (IP3Rs) which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of IP3R 's that replicates the experimental observations reported in [D. Fraiman, Biophys. J. 90, 3897 (2006)]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the IP3 concentration is increased.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

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

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Diffusion with stochastic resetting at power-law times.

PubMed

Nagar, Apoorva; Gupta, Shamik

2016-06-01

What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ∼τ^{-(1+α)};α>0? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for α<1, to one that is time independent for α>1. The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal α that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.

Rippled disc electrostatic generator/motor configurations utilizing magnetic insulation

DOEpatents

Post, Richard F

2017-04-04

Electrostatic generators/motors designs are provided that generally may include a first rippled stator centered about a longitudinal axis; a second rippled stator centered about the axis, a first rippled rotor centered about the axis and located between the first rippled stator and the second rippled stator. A magnetic field having field lines about parallel with the average plane of at least one of the first rippled stator or the second rippled stator is provided with either a Halbach array configuration or a conductor array configuration.

Origin of the Two Scales of Wind Ripples on Mars

NASA Technical Reports Server (NTRS)

Lapotre, Mathieu G. A.; Ewing, Ryan C.; Lamb, Michael P.; Fischer, Woodward W.; Grotzinger, John P.; Rubin, David M.; Lewis, Kevin W.; Day, Mackenzie; Gupta, Sanjeev; Banham, Steeve G.;

Origin of the two scales of wind ripples on Mars

NASA Astrophysics Data System (ADS)

Lapotre, M. G. A.; Ewing, R. C.; Lamb, M. P.; Fischer, W. W.; Grotzinger, J. P.; Rubin, D. M.; Lewis, K. W.; Ballard, M.; Day, M. D.; Gupta, S.; Banham, S.; Bridges, N.; Des Marais, D. J.; Fraeman, A. A.; Grant, J. A., III; Ming, D. W.; Mischna, M.; Rice, M. S.; Sumner, D. Y.; Vasavada, A. R.; Yingst, R. A.

2016-12-01

Earth's sandy deserts host two main types of bedforms - decimeter-scale ripples and larger dunes. Years of orbital observations on Mars also confirmed the existence of two modes of active eolian bedforms - meter-scale ripples, and dunes. By analogy to terrestrial ripples, which are thought to form from a grain mechanism, it was hypothesized that large martian ripples also formed from grain impacts, but spaced further apart due to elongated saltation trajectories from the lower martian gravity and different atmospheric properties. However, the Curiosity rover recently documented the coexistence of three scales of bedforms in Gale crater. Because a grain impact mechanism cannot readily explain two distinct and coeval ripple modes in similar sand sizes, a new mechanism seems to be required to explain one of the scales of ripples. Small ripples are most similar to Earth's impact ripples, with straight crests and subdued profiles. In contrast, large martian ripples are sinuous and asymmetric, with lee slopes dominated by grain flows and grainfall deposits. Thus, large martian ripples resemble current ripples formed underwater on Earth, suggesting that they may form from a fluid-drag mechanism. To test this hypothesis, we develop a scaling relation to predict the spacing of fluid-drag ripples from an extensive flume data compilation. The size of large martian ripples is predicted by our scaling relation when adjusted for martian atmospheric properties. Specifically, we propose that the wavelength of martian wind-drag ripples arises from the high kinematic viscosity of the low-density atmosphere. Because fluid density controls drag-ripple size, our scaling relation can help constrain paleoatmospheric density from wind-drag ripple stratification.

The Variability of Transverse Aeolian Ripples in Troughs on Mars

NASA Technical Reports Server (NTRS)

Bourke, M. C.; Wilson, S.A.; Zimbelman, J. R.

2003-01-01

A precursory glance at MGS images of the surface of Mars show an abundance of aeolian transverse ridges. These ridges are located in a variety of geological terrains. Zimbelman and Wilson have separated the small-scale aeolian features of Syrtis Major into six categories: ripples associated with obstacles, ripple bands, ripple fields, ripple patches, isolated ripple patches and ripples associated with dunes. This paper focuses on one of these categories, that of ripple bands which tend to accumulate within linear troughs. As the origin of these features is still being studied (i.e. ripples versus dunes), we refer to them simply as transverse aeolian ridges.

Characterization of submillisecond response optical addressing phase modulator based on low light scattering polymer network liquid crystal

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

Xiangjie, Zhao, E-mail: zxjdouble@163.com, E-mail: zxjdouble@gmail.com; Cangli, Liu; Jiazhu, Duan

Optically addressed conventional nematic liquid crystal spatial light modulator has attracted wide research interests. But the slow response speed limited its further application. In this paper, polymer network liquid crystal (PNLC) was proposed to replace the conventional nematic liquid crystal to enhance the response time to the order of submillisecond. The maximum light scattering of the employed PNLC was suppressed to be less than 2% at 1.064 μm by optimizing polymerization conditions and selecting large viscosity liquid crystal as solvent. The occurrence of phase ripple phenomenon due to electron diffusion and drift in photoconductor was found to deteriorate the phase modulationmore » effect of the optical addressed PNLC phase modulator. The wavelength effect and AC voltage frequency effect on the on state dynamic response of phase change was investigated by experimental methods. These effects were interpreted by electron diffusion and drift theory based on the assumption that free electron was inhomogeneously distributed in accordance with the writing beam intensity distribution along the incident direction. The experimental results indicated that the phase ripple could be suppressed by optimizing the wavelength of the writing beam and the driving AC voltage frequency when varying the writing beam intensity to generate phase change in 2π range. The modulation transfer function was also measured.« less

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

PubMed

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries

NASA Astrophysics Data System (ADS)

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

Tidal-cycle changes in oscillation ripples on the inner part of an estuarine sand flat

USGS Publications Warehouse

Dingler, J.R.; Clifton, H.E.

1984-01-01

Oscillation ripples form on subaqueous sand beds when wave-generated, near-bottom water motions are strong enough to move sand grains. The threshold of grain motion is the lower bound of the regime of oscillation ripples and the onset of sheet flow is the upper bound. Based on the relation between ripple spacing and orbital diameter, three types of symmetrical ripples occur within the ripple regime. In the lower part of the ripple regime (orbital ripples), spacing is proportional to orbital diameter; in the upper part (anorbital ripples) spacing is independent of orbital diameter. Between these regions occurs a transitional region (suborbital ripples). Oscillation ripples develop on a sandy tidal flat in Willapa Bay, Washington, as a result of waves traversing the area when it is submerged. Because wave energy is usually low within the bay, the ripples are primarily orbital in type. This means that their spacing should respond in a systematic way to changes in wave conditions. During the high-water parts of some tidal cycles, ripples near the beach decrease in spacing during the latter stage of the ebb tide while ripples farther offshore do not change. Observations made over several tidal cycles show that the zone of active ripples shifts on- or offshore in response to different wave conditions. Detailed bed profiles and current measurements taken during the high-water part of spring tides show the manner in which the oscillation ripples change with changes in orbital diameter. Changes in ripple spacing at the study site could be correlated with changes in orbital diameter in the manner suggested by the criterion for orbital ripples. However, there appeared to be a lag time between a decrease in orbital diameter and the corresponding decrease in ripple spacing. Absence of change during a tidal cycle could be attributed to orbital velocities below the threshold for grain motion that negated the effects of changes in orbital diameter. Because changes in sand-flat ripples depend both upon changes in orbital diameter and upon the magnitude of the orbital velocity, exposed ripples were not necessarily produced during the preceding high tide. In fact, some ripples may have been just produced, while others, farther offshore, may have been produced an unknown number of tides earlier. Therefore, when interpreting past wave conditions over tidal flats from low-tide ripples, one must remember that wave periods have to be short enough to produce velocities greater than the threshold velocity for the orbital diameters calculated from the observed ripple spacings. ?? 1984.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

PubMed Central

Gao, Fei; Li, Ye; Novak, Igor L.; Slepchenko, Boris M.

2016-01-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium ‘sparks’ as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell. PMID:27959915

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

PubMed

Cotter, C J; Gottwald, G A; Holm, D D

2017-09-01

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice

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

Ellery, Adam J.; Simpson, Matthew J.; Baker, Ruth E.

2016-05-07

The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motionmore » of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.« less

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions.

PubMed

Bauler, Patricia; Huber, Gary A; McCammon, J Andrew

2012-04-28

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Scaling behavior studies of Ar{sup +} ion irradiated ripple structured mica surfaces

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

Metya, Amaresh, E-mail: amaresh.metya@saha.ac.in; Ghose, Debabrata, E-mail: amaresh.metya@saha.ac.in

We have studied scaling behavior of ripple structured mica surfaces. Clean mica (001) surface is sputtered by 500 eV Ar{sup +} ion beam at 40° incidence angle for different time ranging from 28 minutes to 245 minutes to form ripples on it. The scaling of roughness of sputtered surface characterized by AFM is observed into two regime here; one is super roughening which is for above the crossover bombardment time (i.e, t{sub x} ≥ 105 min) with the scaling exponents α = α{sub s} = 1.45 ± 0.03, α{sub local} = 0.87 ± 0.03, β = 1.81 ± 0.01, β{submore » local} = 1.67 ± 0.07 and another is a new type of scaling dynamics for t{sub x} ≤ 105 min with the scaling exponents α = 0.95 (calculated), α{sub s} = 1.45 ± 0.03, α{sub local} = 0.87 ± 0.03, β = 1.81 ± 0.01, β{sub local} = 1.67 ± 0.07. In the super roughening scaling dynamics, two types of power law dependency is observed on spatial frequency of morphology (k): for higher k values PSD ∼ k{sup −4} describing diffusion controlled smoothening and for lower k values PSD ∼ k{sup −2} reflecting kinetic roughening.« less

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth.

PubMed

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

NASA Astrophysics Data System (ADS)

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Saturation Length of Erodible Sediment Beds Subject to Shear Flow

NASA Astrophysics Data System (ADS)

Casler, D. M.; Kahn, B. P.; Furbish, D. J.; Schmeeckle, M. W.

2016-12-01

We examine the initial growth and wavelength selection of sand ripples based on probabilistic formulations of the flux and the Exner equation. Current formulations of this problem as a linear stability analysis appeal to the idea of a saturation length-the lag between the bed stress and the flux-as a key stabilizing influence leading to selection of a finite wavelength. We present two contrasting formulations. The first is based on the Fokker-Planck approximation of the divergence form of the Exner equation, and thus involves particle diffusion associated with variations in particle activity, in addition to the conventionally assumed advective term. The role of a saturation length associated with the particle activity is similar to previous analyses. However, particle diffusion provides an attenuating influence on the growth of small wavelengths, independent of a saturation length, and is thus a sufficient, if not necessary, condition contributing to selection of a finite wavelength. The second formulation is based on the entrainment form of the Exner equation. As a precise, probabilistic formulation of conservation, this form of the Exner equation does not distinguish between advection and diffusion, and, because it directly accounts for all particle motions via a convolution of the distribution of particle hop distances, it pays no attention to the idea of a saturation length. The formulation and resulting description of initial ripple growth and wavelength selection thus inherently subsume the effects embodied in the ideas of advection, diffusion, and a saturation length as used in other formulations. Moreover, the formulation does not distinguish between bed load and suspended load, and is thus broader in application. The analysis reveals that the length scales defined by the distribution of hop distances are more fundamental than the saturation length in determining the initial growth or decay of bedforms. Formulations involving the saturation length coincide with the special case of an exponential distribution of hop distance, where the saturation length is equal to the mean hop distance.

Spatial Stochastic Intracellular Kinetics: A Review of Modelling Approaches.

PubMed

Smith, Stephen; Grima, Ramon

2018-05-21

Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing models is vast, but two stand out by virtue of their popularity: the reaction-diffusion master equation and Brownian dynamics. In this review, we critically address a number of open questions surrounding these models: How can they be justified physically? How do they relate to each other? How do they fit into the wider landscape of chemical models, ranging from the rate equations to molecular dynamics? This review assumes no prior knowledge of modelling chemical kinetics and should be accessible to a wide range of readers.

Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

NASA Astrophysics Data System (ADS)

Rana, Navdeep; Ghosh, Pushpita; Perlekar, Prasad

2017-11-01

We study spreading of a nonmotile bacteria colony on a hard agar plate by using agent-based and continuum models. We show that the spreading dynamics depends on the initial nutrient concentration, the motility, and the inherent demographic noise. Population fluctuations are inherent in an agent-based model, whereas for the continuum model we model them by using a stochastic Langevin equation. We show that the intrinsic population fluctuations coupled with nonlinear diffusivity lead to a transition from a diffusion limited aggregation type of morphology to an Eden-like morphology on decreasing the initial nutrient concentration.

Intermediate scattering function of an anisotropic active Brownian particle

PubMed Central

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-01-01

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations. PMID:27830719

Intermediate scattering function of an anisotropic active Brownian particle.

PubMed

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-10-10

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

Fixation, transient landscape, and diffusion dilemma in stochastic evolutionary game dynamics

NASA Astrophysics Data System (ADS)

Zhou, Da; Qian, Hong

2011-09-01

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical “device” that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.

Intermediate scattering function of an anisotropic active Brownian particle

NASA Astrophysics Data System (ADS)

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-10-01

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

Nonlinear Image Denoising Methodologies

DTIC Science & Technology

2002-05-01

53 5.3 A Multiscale Approach to Scale-Space Analysis . . . . . . . . . . . . . . . . 53 5.4...etc. In this thesis, Our approach to denoising is first based on a controlled nonlinear stochastic random walk to achieve a scale space analysis ( as in... stochastic treatment or interpretation of the diffusion. In addition, unless a specific stopping time is known to be adequate, the resulting evolution

Transport in sheared stochastic magnetic fields

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

Vanden Eijnden, E.; Balescu, R.

1997-02-01

The transport of test particles in a stochastic magnetic field with a sheared component is studied. Two stages in the particle dynamics are distinguished depending on whether the collisional effects perpendicular to the main field are negligible or not. Whenever the perpendicular collisions are unimportant, the particles show a subdiffusive behavior which is slower in the presence of shear. The particle dynamics is then inhomogeneous and non-Markovian and no diffusion coefficient may be properly defined. When the perpendicular collision frequency is small, this subdiffusive stage may be very long. In the truly asymptotic stage, however, the perpendicular collisions must bemore » accounted for and the particle motion eventually becomes diffusive. Here again, however, the shear is shown to reduce the anomalous diffusion coefficient of the system. {copyright} {ital 1997 American Institute of Physics.}« less

Neutral evolution in a biological population as diffusion in phenotype space: reproduction with local mutation but without selection.

PubMed

Lawson, Daniel John; Jensen, Henrik Jeldtoft

2007-03-02

The process of "evolutionary diffusion," i.e., reproduction with local mutation but without selection in a biological population, resembles standard diffusion in many ways. However, evolutionary diffusion allows the formation of localized peaks that undergo drift, even in the infinite population limit. We relate a microscopic evolution model to a stochastic model which we solve fully. This allows us to understand the large population limit, relates evolution to diffusion, and shows that independent local mutations act as a diffusion of interacting particles taking larger steps.

On the Radio-emitting Particles of the Crab Nebula: Stochastic Acceleration Model

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

Tanaka, Shuta J.; Asano, Katsuaki, E-mail: sjtanaka@center.konan-u.ac.jp

The broadband emission of pulsar wind nebulae (PWNe) is well described by non-thermal emissions from accelerated electrons and positrons. However, the standard shock acceleration model of PWNe does not account for the hard spectrum in radio wavelengths. The origin of the radio-emitting particles is also important to determine the pair production efficiency in the pulsar magnetosphere. Here, we propose a possible resolution for the particle energy distribution in PWNe; the radio-emitting particles are not accelerated at the pulsar wind termination shock but are stochastically accelerated by turbulence inside PWNe. We upgrade our past one-zone spectral evolution model to include themore » energy diffusion, i.e., the stochastic acceleration, and apply the model to the Crab Nebula. A fairly simple form of the energy diffusion coefficient is assumed for this demonstrative study. For a particle injection to the stochastic acceleration process, we consider the continuous injection from the supernova ejecta or the impulsive injection associated with supernova explosion. The observed broadband spectrum and the decay of the radio flux are reproduced by tuning the amount of the particle injected to the stochastic acceleration process. The acceleration timescale and the duration of the acceleration are required to be a few decades and a few hundred years, respectively. Our results imply that some unveiled mechanisms, such as back reaction to the turbulence, are required to make the energies of stochastically and shock-accelerated particles comparable.« less

Stochastic inflation in phase space: is slow roll a stochastic attractor?

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

Grain, Julien; Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue.more » The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.« less

Network Mechanisms Generating Abnormal and Normal Hippocampal High-Frequency Oscillations: A Computational Analysis1,2,3

PubMed Central

Catoni, Nicholas

2015-01-01

Abstract High-frequency oscillations (HFOs) are an intriguing potential biomarker for epilepsy, typically categorized according to peak frequency as either ripples (100–250 Hz) or fast ripples (>250 Hz). In the hippocampus, fast ripples were originally thought to be more specific to epileptic tissue, but it is still very difficult to distinguish which HFOs are caused by normal versus pathological brain activity. In this study, we use a computational model of hippocampus to investigate possible network mechanisms underpinning normal ripples, pathological ripples, and fast ripples. Our results unify several prior findings regarding HFO mechanisms, and also make several new predictions regarding abnormal HFOs. We show that HFOs are generic, emergent phenomena whose characteristics reflect a wide range of connectivity and network input. Although produced by different mechanisms, both normal and abnormal HFOs generate similar ripple frequencies, underscoring that peak frequency is unable to distinguish the two. Abnormal ripples are generic phenomena that arise when input to pyramidal cells overcomes network inhibition, resulting in high-frequency, uncoordinated firing. In addition, fast ripples transiently and sporadically arise from the precise conditions that produce abnormal ripples. Lastly, we show that such abnormal conditions do not require any specific network structure to produce coherent HFOs, as even completely asynchronous activity is capable of producing abnormal ripples and fast ripples in this manner. These results provide a generic, network-based explanation for the link between pathological ripples and fast ripples, and a unifying description for the entire spectrum from normal ripples to pathological fast ripples. PMID:26146658

Experimental Observation of Thin-shell Instability in a Collisionless Plasma

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

Ahmed, H.; Doria, D.; Sarri, G.

We report on the experimental observation of the instability of a plasma shell, which formed during the expansion of a laser-ablated plasma into a rarefied ambient medium. By means of a proton radiography technique, the evolution of the instability is temporally and spatially resolved on a timescale much shorter than the hydrodynamic one. The density of the thin shell exceeds that of the surrounding plasma, which lets electrons diffuse outward. An ambipolar electric field grows on both sides of the thin shell that is antiparallel to the density gradient. Ripples in the thin shell result in a spatially varying balancemore » between the thermal pressure force mediated by this field and the ram pressure force that is exerted on it by the inflowing plasma. This mismatch amplifies the ripples by the same mechanism that drives the hydrodynamic nonlinear thin-shell instability (NTSI). Our results thus constitute the first experimental verification that the NTSI can develop in colliding flows.« less

Experimental Observation of Thin-shell Instability in a Collisionless Plasma

NASA Astrophysics Data System (ADS)

Ahmed, H.; Doria, D.; Dieckmann, M. E.; Sarri, G.; Romagnani, L.; Bret, A.; Cerchez, M.; Giesecke, A. L.; Ianni, E.; Kar, S.; Notley, M.; Prasad, R.; Quinn, K.; Willi, O.; Borghesi, M.

2017-01-01

We report on the experimental observation of the instability of a plasma shell, which formed during the expansion of a laser-ablated plasma into a rarefied ambient medium. By means of a proton radiography technique, the evolution of the instability is temporally and spatially resolved on a timescale much shorter than the hydrodynamic one. The density of the thin shell exceeds that of the surrounding plasma, which lets electrons diffuse outward. An ambipolar electric field grows on both sides of the thin shell that is antiparallel to the density gradient. Ripples in the thin shell result in a spatially varying balance between the thermal pressure force mediated by this field and the ram pressure force that is exerted on it by the inflowing plasma. This mismatch amplifies the ripples by the same mechanism that drives the hydrodynamic nonlinear thin-shell instability (NTSI). Our results thus constitute the first experimental verification that the NTSI can develop in colliding flows.

Surface structuring in polypropylene using Ar+ beam sputtering: Pattern transition from ripples to dot nanostructures

NASA Astrophysics Data System (ADS)

Goyal, Meetika; Aggarwal, Sanjeev; Sharma, Annu; Ojha, Sunil

2018-05-01

Temporal variations in nano-scale surface morphology generated on Polypropylene (PP) substrates utilizing 40 keV oblique argon ion beam have been presented. Due to controlled variation of crucial beam parameters i.e. ion incidence angle and erosion time, formation of ripple patterns and further its transition into dot nanostructures have been realized. Experimental investigations have been supported by evaluation of Bradley and Harper (B-H) coefficients estimated using SRIM (The Stopping and Range of Ions in Matter) simulations. Roughness of pristine target surfaces has been accredited to be a crucial factor behind the early time evolution of nano-scale patterns over the polymeric surface. Study of Power spectral density (PSD) spectra reveals that smoothing mechanism switch from ballistic drift to ion enhanced surface diffusion (ESD) which can be the most probable cause for such morphological transition under given experimental conditions. Compositional analysis and depth profiling of argon ion irradiated specimens using Rutherford Backscattering Spectroscopy (RBS) has also been correlated with the AFM findings.

Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes

USGS Publications Warehouse

Zhang, Yong; Green, Christopher T.; Tick, Geoffrey R.

2015-01-01

This study evaluates the role of the Peclet number as affected by molecular diffusion in transient anomalous transport, which is one of the major knowledge gaps in anomalous transport, by combining Monte Carlo simulations and stochastic model analysis. Two alluvial settings containing either short- or long-connected hydrofacies are generated and used as media for flow and transport modeling. Numerical experiments show that 1) the Peclet number affects both the duration of the power-law segment of tracer breakthrough curves (BTCs) and the transition rate from anomalous to Fickian transport by determining the solute residence time for a given low-permeability layer, 2) mechanical dispersion has a limited contribution to the anomalous characteristics of late-time transport as compared to molecular diffusion due to an almost negligible velocity in floodplain deposits, and 3) the initial source dimensions only enhance the power-law tail of the BTCs at short travel distances. A tempered stable stochastic (TSS) model is then applied to analyze the modeled transport. Applications show that the time-nonlocal parameters in the TSS model relate to the Peclet number, Pe. In particular, the truncation parameter in the TSS model increases nonlinearly with a decrease in Pe due to the decrease of the mean residence time, and the capacity coefficient increases with an increase in molecular diffusion which is probably due to the increase in the number of immobile particles. The above numerical experiments and stochastic analysis therefore reveal that the Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer–aquitard complexes.

Validation of a clinical assessment of spectral-ripple resolution for cochlear implant users.

PubMed

Drennan, Ward R; Anderson, Elizabeth S; Won, Jong Ho; Rubinstein, Jay T

2014-01-01

Nonspeech psychophysical tests of spectral resolution, such as the spectral-ripple discrimination task, have been shown to correlate with speech-recognition performance in cochlear implant (CI) users. However, these tests are best suited for use in the research laboratory setting and are impractical for clinical use. A test of spectral resolution that is quicker and could more easily be implemented in the clinical setting has been developed. The objectives of this study were (1) To determine whether this new clinical ripple test would yield individual results equivalent to the longer, adaptive version of the ripple-discrimination test; (2) To evaluate test-retest reliability for the clinical ripple measure; and (3) To examine the relationship between clinical ripple performance and monosyllabic word recognition in quiet for a group of CI listeners. Twenty-eight CI recipients participated in the study. Each subject was tested on both the adaptive and the clinical versions of spectral ripple discrimination, as well as consonant-nucleus-consonant word recognition in quiet. The adaptive version of spectral ripple used a two-up, one-down procedure for determining spectral ripple discrimination threshold. The clinical ripple test used a method of constant stimuli, with trials for each of 12 fixed ripple densities occurring six times in random order. Results from the clinical ripple test (proportion correct) were then compared with ripple-discrimination thresholds (in ripples per octave) from the adaptive test. The clinical ripple test showed strong concurrent validity, evidenced by a good correlation between clinical ripple and adaptive ripple results (r = 0.79), as well as a correlation with word recognition (r = 0.7). Excellent test-retest reliability was also demonstrated with a high test-retest correlation (r = 0.9). The clinical ripple test is a reliable nonlinguistic measure of spectral resolution, optimized for use with CI users in a clinical setting. The test might be useful as a diagnostic tool or as a possible surrogate outcome measure for evaluating treatment effects in hearing.

Grain Size Measurements of Eolian Ripples in Gale Crater, Mars

NASA Astrophysics Data System (ADS)

Weitz, C. M.; Sullivan, R. J., Jr.; Lapotre, M. G. A.; Rowland, S. K.; Edgett, K. S.; Grant, J. A., III; Yingst, R. A.

2017-12-01

The Curiosity rover team has explored several different eolian sand targets in Gale crater, including dunes and ripples. Using Curiosity's Mars Hand Lens Imager (MAHLI), we measured the size of grains on or near ripple crests within dunes, ripple fields, and in isolated ripples. The Barby target (Sol 1184) is on the crest of a ripple on the lower stoss slope of the barchan High dune. Flume Ridge (Sol 1604) and Avery Peak (Sol 1651) are smaller ripples on the Nathan Bridges and Mount Desert Island linear dunes. Schoolhouse Ledge (Sol 1688) is an isolated megaripple not associated with either a dune or ripple field. Enchanted Island (Sol 1751) is a ripple contained within a larger ripple field near the Vera Rubin Ridge. Our results show the grains of the Avery Peak and Flume Ridge targets are mostly 75-150 µm in size and grain motion was observed during each MAHLI imaging sequence. Barby is dominated by 250-450 µm grains assumed to be active based upon the lack of a dust coating, though grain motion was not observed. The Enchanted Island target has slightly larger grains than Barby, with most between 300-500 µm. The grains have some dust aggregates on their surfaces, suggesting they have been less active in recent months or years relative to the ripples examined within the Bagnold dune field. Finally, grains along the crest of Schoolhouse Ledge are the largest, 400-600 µm, and all of the grain surfaces have a thin dust coating, indicating the ripple is not currently active. Some of the ripple crests have similar grain sizes on both the stoss and lee sides (Schoolhouse Ledge, Barby) whereas other ripples showed larger grains concentrated on the stoss side (Enchanted Island, Avery Peak, Flume Ridge). Scuffing by the rover's front wheel revealed both Schoolhouse Ledge and Enchanted Island had coarser grains dominating the ripple surface with finer grains within the ripple interior. In general, the surfaces of active sand ripples have smaller grains compared to the inactive ripples which exhibit an armor of larger grains. Our results indicate grain sizes vary widely depending upon such factors as ripple activity, location along the ripple, ripple size, dune type, and orientation relative to the wind direction.

Membrane Potential Dynamics of CA1 Pyramidal Neurons During Hippocampal Ripples in Awake Mice

PubMed Central

Hulse, Brad K.; Moreaux, Laurent C.; Lubenov, Evgueniy V.; Siapas, Athanassios G.

2016-01-01

Ripples are high-frequency oscillations associated with population bursts in area CA1 of the hippocampus that play a prominent role in theories of memory consolidation. While spiking during ripples has been extensively studied, our understanding of the subthreshold behavior of hippocampal neurons during these events remains incomplete. Here, we combine in vivo whole-cell and multisite extracellular recordings to characterize the membrane potential dynamics of identified CA1 pyramidal neurons during ripples. We find that the subthreshold depolarization during ripples is uncorrelated with the net excitatory input to CA1, while the post-ripple hyperpolarization varies proportionately. This clarifies the circuit mechanism keeping most neurons silent during ripples. On a finer time scale, the phase delay between intracellular and extracellular ripple oscillations varies systematically with membrane potential. Such smoothly varying delays are inconsistent with models of intracellular ripple generation involving perisomatic inhibition alone. Instead, they suggest that ripple-frequency excitation leading inhibition shapes intracellular ripple oscillations. PMID:26889811

Beamforming applied to surface EEG improves ripple visibility.

PubMed

van Klink, Nicole; Mol, Arjen; Ferrier, Cyrille; Hillebrand, Arjan; Huiskamp, Geertjan; Zijlmans, Maeike

2018-01-01

Surface EEG can show epileptiform ripples in people with focal epilepsy, but identification is impeded by the low signal-to-noise ratio of the electrode recordings. We used beamformer-based virtual electrodes to improve ripple identification. We analyzed ten minutes of interictal EEG of nine patients with refractory focal epilepsy. EEGs with more than 60 channels and 20 spikes were included. We computed ∼79 virtual electrodes using a scalar beamformer and marked ripples (80-250 Hz) co-occurring with spikes in physical and virtual electrodes. Ripple numbers in physical and virtual electrodes were compared, and sensitivity and specificity of ripples for the region of interest (ROI; based on clinical information) were determined. Five patients had ripples in the physical electrodes and eight in the virtual electrodes, with more ripples in virtual than in physical electrodes (101 vs. 57, p = .007). Ripples in virtual electrodes predicted the ROI better than physical electrodes (AUC 0.65 vs. 0.56, p = .03). Beamforming increased ripple visibility in surface EEG. Virtual ripples predicted the ROI better than physical ripples, although sensitivity was still poor. Beamforming can facilitate ripple identification in EEG. Ripple localization needs to be improved to enable its use for presurgical evaluation in people with epilepsy. Copyright © 2017 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved.

Ripple-Triggered Stimulation of the Locus Coeruleus during Post-Learning Sleep Disrupts Ripple/Spindle Coupling and Impairs Memory Consolidation

ERIC Educational Resources Information Center

Novitskaya, Yulia; Sara, Susan J.; Logothetis, Nikos K.; Eschenko, Oxana

2016-01-01

Experience-induced replay of neuronal ensembles occurs during hippocampal high-frequency oscillations, or ripples. Post-learning increase in ripple rate is predictive of memory recall, while ripple disruption impairs learning. Ripples may thus present a fundamental component of a neurophysiological mechanism of memory consolidation. In addition to…

Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case

NASA Astrophysics Data System (ADS)

Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.

2010-06-01

Continuous-time random walks, or compound renewal processes, are pure-jump stochastic processes with several applications in insurance, finance, economics and physics. Based on heuristic considerations, a definition is given for stochastic integrals driven by continuous-time random walks, which includes the Itô and Stratonovich cases. It is then shown how the definition can be used to compute these two stochastic integrals by means of Monte Carlo simulations. Our example is based on the normal compound Poisson process, which in the diffusive limit converges to the Wiener process.

Random-order fractional bistable system and its stochastic resonance

NASA Astrophysics Data System (ADS)

Gao, Shilong; Zhang, Li; Liu, Hui; Kan, Bixia

2017-01-01

In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.

Feynman-Kac formula for stochastic hybrid systems.

PubMed

Bressloff, Paul C

2017-01-01

We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

PubMed Central

Cotter, C. J.

2017-01-01

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316

STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies.

PubMed

Hepburn, Iain; Chen, Weiliang; Wils, Stefan; De Schutter, Erik

2012-05-10

Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins), conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. We describe STEPS, a stochastic reaction-diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction-diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. STEPS simulates models of cellular reaction-diffusion systems with complex boundaries with high accuracy and high performance in C/C++, controlled by a powerful and user-friendly Python interface. STEPS is free for use and is available at http://steps.sourceforge.net/

STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies

PubMed Central

2012-01-01

Background Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins), conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. Results We describe STEPS, a stochastic reaction–diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction–diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. Conclusion STEPS simulates models of cellular reaction–diffusion systems with complex boundaries with high accuracy and high performance in C/C++, controlled by a powerful and user-friendly Python interface. STEPS is free for use and is available at http://steps.sourceforge.net/ PMID:22574658

Theoretical Studies of Defects in Tetrahedral Semiconductors.

DTIC Science & Technology

1980-08-01

pulse. The exact time of the maximal sur- has been measured by Shvarev et al. [I I at 1.0, face temperature depends on pulse duration, thermal 0.7 and...0.4 lAn from 57.50 off normal incidence. diffusivity (which is generally T dependent ), pulse Auston et al. (81 reported the time resolved reflec- shape...surface occur 30 to 40 ns after the peak of their 25 ns HWHM or ripples on the surface or a temperature depend - gaussian pulse rather than within

Ripples on spikes show increased phase-amplitude coupling in mesial temporal lobe epilepsy seizure onset zones

PubMed Central

Weiss, Shennan A; Orosz, Iren; Salamon, Noriko; Moy, Stephanie; Wei, Linqing; Van ’t Klooster, Maryse A; Knight, Robert T; Harper, Ronald M; Bragin, Anatol; Fried, Itzhak; Engel, Jerome; Staba, Richard J

2016-01-01

Objective Ripples (80–150 Hz) recorded from clinical macroelectrodes have been shown to be an accurate biomarker of epileptogenic brain tissue. We investigated coupling between epileptiform spike phase and ripple amplitude to better understand the mechanisms that generate this type of pathological ripple (pRipple) event. Methods We quantified phase amplitude coupling (PAC) between epileptiform EEG spike phase and ripple amplitude recorded from intracranial depth macroelectrodes during episodes of sleep in 12 patients with mesial temporal lobe epilepsy. PAC was determined by 1) a phasor transform that corresponds to the strength and rate of ripples coupled with spikes, and a 2) ripple-triggered average to measure the strength, morphology, and spectral frequency of the modulating and modulated signals. Coupling strength was evaluated in relation to recording sites within and outside the seizure onset zone (SOZ). Results Both the phasor transform and ripple-triggered averaging methods showed ripple amplitude was often robustly coupled with epileptiform EEG spike phase. Coupling was more regularly found inside than outside the SOZ, and coupling strength correlated with the likelihood a macroelectrode’s location was within the SOZ (p<0.01). The ratio of the rate of ripples coupled with EEG spikes inside the SOZ to rates of coupled ripples in non-SOZ was greater than the ratio of rates of ripples on spikes detected irrespective of coupling (p<0.05). Coupling strength correlated with an increase in mean normalized ripple amplitude (p<0.01), and a decrease in mean ripple spectral frequency (p<0.05). Significance Generation of low-frequency (80–150 Hz) pRipples in the SOZ involves coupling between epileptiform spike phase and ripple amplitude. The changes in excitability reflected as epileptiform spikes may also cause clusters of pathologically interconnected bursting neurons to grow and synchronize into aberrantly large neuronal assemblies. PMID:27723936

Perturbation expansions of stochastic wavefunctions for open quantum systems

NASA Astrophysics Data System (ADS)

Ke, Yaling; Zhao, Yi

2017-11-01

Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.

Conserving the linear momentum in stochastic dynamics: Dissipative particle dynamics as a general strategy to achieve local thermostatization in molecular dynamics simulations.

PubMed

Passler, Peter P; Hofer, Thomas S

2017-02-15

Stochastic dynamics is a widely employed strategy to achieve local thermostatization in molecular dynamics simulation studies; however, it suffers from an inherent violation of momentum conservation. Although this short-coming has little impact on structural and short-time dynamic properties, it can be shown that dynamics in the long-time limit such as diffusion is strongly dependent on the respective thermostat setting. Application of the methodically similar dissipative particle dynamics (DPD) provides a simple, effective strategy to ensure the advantages of local, stochastic thermostatization while at the same time the linear momentum of the system remains conserved. In this work, the key parameters to employ the DPD thermostats in the framework of periodic boundary conditions are investigated, in particular the dependence of the system properties on the size of the DPD-region as well as the treatment of forces near the cutoff. Structural and dynamical data for light and heavy water as well as a Lennard-Jones fluid have been compared to simulations executed via stochastic dynamics as well as via use of the widely employed Nose-Hoover chain and Berendsen thermostats. It is demonstrated that a small size of the DPD region is sufficient to achieve local thermalization, while at the same time artifacts in the self-diffusion characteristic for stochastic dynamics are eliminated. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems.

PubMed

Woolley, Thomas E; Baker, Ruth E; Gaffney, Eamonn A; Maini, Philip K; Seirin-Lee, Sungrim

2012-05-01

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases.

VALIDATION OF A CLINICAL ASSESSMENT OF SPECTRAL RIPPLE RESOLUTION FOR COCHLEAR-IMPLANT USERS

PubMed Central

Drennan, Ward. R.; Anderson, Elizabeth S.; Won, Jong Ho; Rubinstein, Jay T.

2013-01-01

Objectives Non-speech psychophysical tests of spectral resolution, such as the spectral-ripple discrimination task, have been shown to correlate with speech recognition performance in cochlear implant (CI) users (Henry et al., 2005; Won et al. 2007, 2011; Drennan et al. 2008; Anderson et al. 2011). However, these tests are best suited for use in the research laboratory setting and are impractical for clinical use. A test of spectral resolution that is quicker and could more easily be implemented in the clinical setting has been developed. The objectives of this study were 1) To determine if this new clinical ripple test would yield individual results equivalent to the longer, adaptive version of the ripple discrimination test; 2) To evaluate test-retest reliability for the clinical ripple measure; and 3) To examine the relationship between clinical ripple performance and monosyllabic word recognition in quiet for a group of CI listeners. Design Twenty-eight CI recipients participated in the study. Each subject was tested on both the adaptive and the clinical versions of spectral ripple discrimination, as well as CNC word recognition in quiet. The adaptive version of spectral ripple employed a 2-up, 1-down procedure for determining spectral ripple discrimination threshold. The clinical ripple test used a method of constant stimuli, with trials for each of 12 fixed ripple densities occurring six times in random order. Results from the clinical ripple test (proportion correct) were then compared to ripple discrimination thresholds (in ripples per octave) from the adaptive test. Results The clinical ripple test showed strong concurrent validity, evidenced by a good correlation between clinical ripple and adaptive ripple results (r=0.79), as well as a correlation with word recognition (r = 0.7). Excellent test-retest reliability was also demonstrated with a high test-retest correlation (r = 0.9). Conclusions The clinical ripple test is a reliable non-linguistic measure of spectral resolution, optimized for use with cochlear implant users in a clinical setting. The test might be useful as a diagnostic tool or as a possible surrogate outcome measure for evaluating treatment effects in hearing. PMID:24552679

Reconstruction of stochastic temporal networks through diffusive arrival times

NASA Astrophysics Data System (ADS)

Li, Xun; Li, Xiang

2017-06-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications.

Reconstruction of stochastic temporal networks through diffusive arrival times

PubMed Central

Li, Xun; Li, Xiang

2017-01-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications. PMID:28604687

Nuclear quadrupole resonance lineshape analysis for different motional models: Stochastic Liouville approach

NASA Astrophysics Data System (ADS)

Kruk, D.; Earle, K. A.; Mielczarek, A.; Kubica, A.; Milewska, A.; Moscicki, J.

2011-12-01

A general theory of lineshapes in nuclear quadrupole resonance (NQR), based on the stochastic Liouville equation, is presented. The description is valid for arbitrary motional conditions (particularly beyond the valid range of perturbation approaches) and interaction strengths. It can be applied to the computation of NQR spectra for any spin quantum number and for any applied magnetic field. The treatment presented here is an adaptation of the "Swedish slow motion theory," [T. Nilsson and J. Kowalewski, J. Magn. Reson. 146, 345 (2000), 10.1006/jmre.2000.2125] originally formulated for paramagnetic systems, to NQR spectral analysis. The description is formulated for simple (Brownian) diffusion, free diffusion, and jump diffusion models. The two latter models account for molecular cooperativity effects in dense systems (such as liquids of high viscosity or molecular glasses). The sensitivity of NQR slow motion spectra to the mechanism of the motional processes modulating the nuclear quadrupole interaction is discussed.

Existence and uniqueness, attraction for stochastic age-structured population systems with diffusion and Poisson jump

NASA Astrophysics Data System (ADS)

Chen, Huabin

2013-08-01

In this paper, the problems about the existence and uniqueness, attraction for strong solution of stochastic age-structured population systems with diffusion and Poisson jump are considered. Under the non-Lipschitz condition with the Lipschitz condition being considered as a special case, the existence and uniqueness for such systems is firstly proved by using the Burkholder-Davis-Gundy inequality (B-D-G inequality) and Itô's formula. And then by using a novel inequality technique, some sufficient conditions ensuring the existence for the domain of attraction are established. As another by-product, the exponential stability in mean square moment of strong solution for such systems can be also discussed.

Reduced spike-timing reliability correlates with the emergence of fast ripples in the rat epileptic hippocampus.

PubMed

Foffani, Guglielmo; Uzcategui, Yoryani G; Gal, Beatriz; Menendez de la Prida, Liset

2007-09-20

Ripples are sharp-wave-associated field oscillations (100-300 Hz) recorded in the hippocampus during behavioral immobility and slow-wave sleep. In epileptic rats and humans, a different and faster oscillation (200-600 Hz), termed fast ripples, has been described. However, the basic mechanisms are unknown. Here, we propose that fast ripples emerge from a disorganized ripple pattern caused by unreliable firing in the epileptic hippocampus. Enhanced synaptic activity is responsible for the irregular bursting of CA3 pyramidal cells due to large membrane potential fluctuations. Lower field interactions and a reduced spike-timing reliability concur with decreased spatial synchronization and the emergence of fast ripples. Reducing synaptically driven membrane potential fluctuations improves both spike-timing reliability and spatial synchronization and restores ripples in the epileptic hippocampus. Conversely, a lower spike-timing reliability, with reduced potassium currents, is associated with ripple shuffling in normal hippocampus. Therefore, fast ripples may reflect a pathological desynchronization of the normal ripple pattern.

Neutral Evolution in a Biological Population as Diffusion in Phenotype Space: Reproduction with Local Mutation but without Selection

NASA Astrophysics Data System (ADS)

Lawson, Daniel John; Jensen, Henrik Jeldtoft

2007-03-01

The process of “evolutionary diffusion,” i.e., reproduction with local mutation but without selection in a biological population, resembles standard diffusion in many ways. However, evolutionary diffusion allows the formation of localized peaks that undergo drift, even in the infinite population limit. We relate a microscopic evolution model to a stochastic model which we solve fully. This allows us to understand the large population limit, relates evolution to diffusion, and shows that independent local mutations act as a diffusion of interacting particles taking larger steps.

A Probabilistic, Dynamic, and Attribute-wise Model of Intertemporal Choice

PubMed Central

Dai, Junyi; Busemeyer, Jerome R.

2014-01-01

Most theoretical and empirical research on intertemporal choice assumes a deterministic and static perspective, leading to the widely adopted delay discounting models. As a form of preferential choice, however, intertemporal choice may be generated by a stochastic process that requires some deliberation time to reach a decision. We conducted three experiments to investigate how choice and decision time varied as a function of manipulations designed to examine the delay duration effect, the common difference effect, and the magnitude effect in intertemporal choice. The results, especially those associated with the delay duration effect, challenged the traditional deterministic and static view and called for alternative approaches. Consequently, various static or dynamic stochastic choice models were explored and fit to the choice data, including alternative-wise models derived from the traditional exponential or hyperbolic discount function and attribute-wise models built upon comparisons of direct or relative differences in money and delay. Furthermore, for the first time, dynamic diffusion models, such as those based on decision field theory, were also fit to the choice and response time data simultaneously. The results revealed that the attribute-wise diffusion model with direct differences, power transformations of objective value and time, and varied diffusion parameter performed the best and could account for all three intertemporal effects. In addition, the empirical relationship between choice proportions and response times was consistent with the prediction of diffusion models and thus favored a stochastic choice process for intertemporal choice that requires some deliberation time to make a decision. PMID:24635188

Clustering and optimal arrangement of enzymes in reaction-diffusion systems.

PubMed

Buchner, Alexander; Tostevin, Filipe; Gerland, Ulrich

2013-05-17

Enzymes within biochemical pathways are often colocalized, yet the consequences of specific spatial enzyme arrangements remain poorly understood. We study the impact of enzyme arrangement on reaction efficiency within a reaction-diffusion model. The optimal arrangement transitions from a cluster to a distributed profile as a single parameter, which controls the probability of reaction versus diffusive loss of pathway intermediates, is varied. We introduce the concept of enzyme exposure to explain how this transition arises from the stochastic nature of molecular reactions and diffusion.

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

NASA Astrophysics Data System (ADS)

Romanczuk, P.; Bär, M.; Ebeling, W.; Lindner, B.; Schimansky-Geier, L.

2012-03-01

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.

The nature and role of advection in advection-diffusion equations used for modelling bed load transport

NASA Astrophysics Data System (ADS)

Ancey, Christophe; Bohorquez, Patricio; Heyman, Joris

2016-04-01

The advection-diffusion equation arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Stochastic models can also be used to derive this equation, with the significant advantage that they provide information on the statistical properties of particle activity. Stochastic models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. We develop an approach based on birth-death Markov processes, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received little attention. We show that particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Local Generation and Propagation of Ripples along the Septotemporal Axis of the Hippocampus

PubMed Central

Patel, Jagdish; Schomburg, Erik W.; Berényi, Antal; Fujisawa, Shigeyoshi

2013-01-01

A topographical relationship exists between the septotemporal segments of the hippocampus and their entorhinal–neocortical targets, but the physiological organization of activity along the septotemporal axis is poorly understood. We recorded sharp-wave ripple patterns in rats during sleep from the entire septotemporal axis of the CA1 pyramidal layer. Qualitatively similar ripples emerged at all levels. From the local seed, ripples traveled septally or temporally at a speed of ∼0.35 m/s, and the spatial spread depended on ripple magnitude. Ripples propagated smoothly across the septal and intermediate segments of the hippocampus, but ripples in the temporal segment often remained isolated. These findings show that ripples can combine information from the septal and intermediate hippocampus and transfer integrated signals downstream. In contrast, ripples that emerged in the temporal pole broadcast largely independent information to their cortical and subcortical targets. PMID:24155307

Assessing the role of spectral and intensity cues in spectral ripple detection and discrimination in cochlear-implant users.

PubMed

Anderson, Elizabeth S; Oxenham, Andrew J; Nelson, Peggy B; Nelson, David A

2012-12-01

Measures of spectral ripple resolution have become widely used psychophysical tools for assessing spectral resolution in cochlear-implant (CI) listeners. The objective of this study was to compare spectral ripple discrimination and detection in the same group of CI listeners. Ripple detection thresholds were measured over a range of ripple frequencies and were compared to spectral ripple discrimination thresholds previously obtained from the same CI listeners. The data showed that performance on the two measures was correlated, but that individual subjects' thresholds (at a constant spectral modulation depth) for the two tasks were not equivalent. In addition, spectral ripple detection was often found to be possible at higher rates than expected based on the available spectral cues, making it likely that temporal-envelope cues played a role at higher ripple rates. Finally, spectral ripple detection thresholds were compared to previously obtained speech-perception measures. Results confirmed earlier reports of a robust relationship between detection of widely spaced ripples and measures of speech recognition. In contrast, intensity difference limens for broadband noise did not correlate with spectral ripple detection measures, suggesting a dissociation between the ability to detect small changes in intensity across frequency and across time.

Age Is Associated with Reduced Sharp-Wave Ripple Frequency and Altered Patterns of Neuronal Variability

PubMed Central

Wiegand, Jean-Paul L.; Gray, Daniel T.; Schimanski, Lesley A.; Lipa, Peter; Barnes, C. A.

2016-01-01

Spatial and episodic memory performance declines with age, and the neural basis for this decline is not well understood. Sharp-wave ripples are brief (∼70 ms) high-frequency oscillatory events generated in the hippocampus and are associated with the consolidation of spatial memories. Given the connection between ripple oscillations and memory consolidation, we investigated whether the structure of ripple oscillations and ripple-triggered patterns of single-unit activity are altered in aged rats. Local field and single-unit activity surrounding sharp-wave ripple events were examined in the CA1 region of the hippocampus of old (n = 5) and young (n = 6) F344 rats during periods of rest preceding and following performance on a place-dependent eyeblink-conditioning task. Neural responses in aged rats differed from responses in young rats in several ways. First, compared with young rats, the rate of ripple occurrence (ripple density) is reduced in aged rats during postbehavior rest. Second, mean ripple frequency during prebehavior and postbehavior rest is lower in aged animals (aged: 132 Hz; young: 146 Hz). Third, single neurons in aged animals responded more consistently from ripple to ripple. Fourth, variability in interspike intervals was greater in aged rats. Finally, neurons were tuned to a narrower range of phases of the ripple oscillation relative to young animals. Together, these results suggest that the CA1 network in aged animals has a reduced “vocabulary” of available representational states. SIGNIFICANCE STATEMENT The hippocampus is a structure that is critical for the formation of episodic memories. Sharp-wave ripple events generated in the hippocampus have been implicated in memory consolidation processes critical to memory stabilization. We examine here whether these ripple oscillations are altered over the course of the life span, which could contribute to hippocampus-dependent memory deficits that occur during aging. This experiment used young and aged memory-impaired rats to examine age-related changes in ripple architecture, ripple-triggered spike variance, and spike-phase coherence. We found that there are, indeed, significant changes in characteristics of ripples in older animals that could impact consolidation processes and memory stabilization in the aged brain. PMID:27194342

Multithreaded Stochastic PDES for Reactions and Diffusions in Neurons.

PubMed

Lin, Zhongwei; Tropper, Carl; Mcdougal, Robert A; Patoary, Mohammand Nazrul Ishlam; Lytton, William W; Yao, Yiping; Hines, Michael L

2017-07-01

Cells exhibit stochastic behavior when the number of molecules is small. Hence a stochastic reaction-diffusion simulator capable of working at scale can provide a more accurate view of molecular dynamics within the cell. This paper describes a parallel discrete event simulator, Neuron Time Warp-Multi Thread (NTW-MT), developed for the simulation of reaction diffusion models of neurons. To the best of our knowledge, this is the first parallel discrete event simulator oriented towards stochastic simulation of chemical reactions in a neuron. The simulator was developed as part of the NEURON project. NTW-MT is optimistic and thread-based, which attempts to capitalize on multi-core architectures used in high performance machines. It makes use of a multi-level queue for the pending event set and a single roll-back message in place of individual anti-messages to disperse contention and decrease the overhead of processing rollbacks. Global Virtual Time is computed asynchronously both within and among processes to get rid of the overhead for synchronizing threads. Memory usage is managed in order to avoid locking and unlocking when allocating and de-allocating memory and to maximize cache locality. We verified our simulator on a calcium buffer model. We examined its performance on a calcium wave model, comparing it to the performance of a process based optimistic simulator and a threaded simulator which uses a single priority queue for each thread. Our multi-threaded simulator is shown to achieve superior performance to these simulators. Finally, we demonstrated the scalability of our simulator on a larger CICR model and a more detailed CICR model.

Diffusive processes in a stochastic magnetic field

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

Wang, H.; Vlad, M.; Vanden Eijnden, E.

1995-05-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing,more » in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.« less

Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes.

PubMed

Zhang, Yong; Green, Christopher T; Tick, Geoffrey R

2015-01-01

This study evaluates the role of the Peclet number as affected by molecular diffusion in transient anomalous transport, which is one of the major knowledge gaps in anomalous transport, by combining Monte Carlo simulations and stochastic model analysis. Two alluvial settings containing either short- or long-connected hydrofacies are generated and used as media for flow and transport modeling. Numerical experiments show that 1) the Peclet number affects both the duration of the power-law segment of tracer breakthrough curves (BTCs) and the transition rate from anomalous to Fickian transport by determining the solute residence time for a given low-permeability layer, 2) mechanical dispersion has a limited contribution to the anomalous characteristics of late-time transport as compared to molecular diffusion due to an almost negligible velocity in floodplain deposits, and 3) the initial source dimensions only enhance the power-law tail of the BTCs at short travel distances. A tempered stable stochastic (TSS) model is then applied to analyze the modeled transport. Applications show that the time-nonlocal parameters in the TSS model relate to the Peclet number, Pe. In particular, the truncation parameter in the TSS model increases nonlinearly with a decrease in Pe due to the decrease of the mean residence time, and the capacity coefficient increases with an increase in molecular diffusion which is probably due to the increase in the number of immobile particles. The above numerical experiments and stochastic analysis therefore reveal that the Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes. Copyright © 2015 Elsevier B.V. All rights reserved.

Excitation and inhibition compete to control spiking during hippocampal ripples: intracellular study in behaving mice.

PubMed

English, Daniel F; Peyrache, Adrien; Stark, Eran; Roux, Lisa; Vallentin, Daniela; Long, Michael A; Buzsáki, György

2014-12-03

High-frequency ripple oscillations, observed most prominently in the hippocampal CA1 pyramidal layer, are associated with memory consolidation. The cellular and network mechanisms underlying the generation of the rhythm and the recruitment of spikes from pyramidal neurons are still poorly understood. Using intracellular, sharp electrode recordings in freely moving, drug-free mice, we observed consistent large depolarizations in CA1 pyramidal cells during sharp wave ripples, which are associated with ripple frequency fluctuation of the membrane potential ("intracellular ripple"). Despite consistent depolarization, often exceeding pre-ripple spike threshold values, current pulse-induced spikes were strongly suppressed, indicating that spiking was under the control of concurrent shunting inhibition. Ripple events were followed by a prominent afterhyperpolarization and spike suppression. Action potentials during and outside ripples were orthodromic, arguing against ectopic spike generation, which has been postulated by computational models of ripple generation. These findings indicate that dendritic excitation of pyramidal neurons during ripples is countered by shunting of the membrane and postripple silence is mediated by hyperpolarizing inhibition. Copyright © 2014 the authors 0270-6474/14/3316509-09$15.00/0.

Diffraction analysis of sidelobe characteristics of optical elements with ripple error

NASA Astrophysics Data System (ADS)

Zhao, Lei; Luo, Yupeng; Bai, Jian; Zhou, Xiangdong; Du, Juan; Liu, Qun; Luo, Yujie

2018-03-01

The ripple errors of the lens lead to optical damage in high energy laser system. The analysis of sidelobe on the focal plane, caused by ripple error, provides a reference to evaluate the error and the imaging quality. In this paper, we analyze the diffraction characteristics of sidelobe of optical elements with ripple errors. First, we analyze the characteristics of ripple error and build relationship between ripple error and sidelobe. The sidelobe results from the diffraction of ripple errors. The ripple error tends to be periodic due to fabrication method on the optical surface. The simulated experiments are carried out based on angular spectrum method by characterizing ripple error as rotationally symmetric periodic structures. The influence of two major parameter of ripple including spatial frequency and peak-to-valley value to sidelobe is discussed. The results indicate that spatial frequency and peak-to-valley value both impact sidelobe at the image plane. The peak-tovalley value is the major factor to affect the energy proportion of the sidelobe. The spatial frequency is the major factor to affect the distribution of the sidelobe at the image plane.

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.

PubMed

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2017-12-21

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green's function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as "black-box" simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.

Development of a restricted state space stochastic differential equation model for bacterial growth in rich media.

PubMed

Møller, Jan Kloppenborg; Bergmann, Kirsten Riber; Christiansen, Lasse Engbo; Madsen, Henrik

2012-07-21

In the present study, bacterial growth in a rich media is analysed in a Stochastic Differential Equation (SDE) framework. It is demonstrated that the SDE formulation and smoothened state estimates provide a systematic framework for data driven model improvements, using random walk hidden states. Bacterial growth is limited by the available substrate and the inclusion of diffusion must obey this natural restriction. By inclusion of a modified logistic diffusion term it is possible to introduce a diffusion term flexible enough to capture both the growth phase and the stationary phase, while concentration is restricted to the natural state space (substrate and bacteria non-negative). The case considered is the growth of Salmonella and Enterococcus in a rich media. It is found that a hidden state is necessary to capture the lag phase of growth, and that a flexible logistic diffusion term is needed to capture the random behaviour of the growth model. Further, it is concluded that the Monod effect is not needed to capture the dynamics of bacterial growth in the data presented. Copyright © 2012 Elsevier Ltd. All rights reserved.

Estimation and prediction under local volatility jump-diffusion model

NASA Astrophysics Data System (ADS)

Kim, Namhyoung; Lee, Younhee

2018-02-01

Volatility is an important factor in operating a company and managing risk. In the portfolio optimization and risk hedging using the option, the value of the option is evaluated using the volatility model. Various attempts have been made to predict option value. Recent studies have shown that stochastic volatility models and jump-diffusion models reflect stock price movements accurately. However, these models have practical limitations. Combining them with the local volatility model, which is widely used among practitioners, may lead to better performance. In this study, we propose a more effective and efficient method of estimating option prices by combining the local volatility model with the jump-diffusion model and apply it using both artificial and actual market data to evaluate its performance. The calibration process for estimating the jump parameters and local volatility surfaces is divided into three stages. We apply the local volatility model, stochastic volatility model, and local volatility jump-diffusion model estimated by the proposed method to KOSPI 200 index option pricing. The proposed method displays good estimation and prediction performance.

Metastable ripple phase of fully hydrated dipalmitoylphosphatidylcholine as studied by small angle x-ray scattering

PubMed Central

Yao, Haruhiko; Matuoka, Sinzi; Tenchov, Boris; Hatta, Ichiro

1991-01-01

Fully hydrated dipalmitoylphosphatidylcholine (DPPC) undergoes liquid crystalline to metastable Pβ, phase transition in cooling. A small angle x-ray scattering study has been performed for obtaining further evidence about the structure of this phase. From a high-resolution observation of x-ray diffraction profiles, a distinct multipeak pattern has become obvious. Among them the (01) reflection in the secondary ripple structure is identified clearly. There are peaks assigned straightforwardly to (10) and (20) reflections in the primary ripple structure and peaks assigned to (10) and (20) reflections in the secondary ripple structure. Therefore the multipeak pattern is due to superposition of the reflections cause by the primary and secondary ripple structures. The lattice parameters are estimated as follows: for the primary ripple structure a = 7.09 nm, b = 13.64 nm, and γ = 95°, and for the secondary ripple structure a = 8.2 nm, b = 26.6 nm, and γ = 90°. The lattice parameters thus obtained for the secondary ripple structure are not conclusive, however. The hydrocarbon chains in the primary ripple structure have been reported as being tilted against the bilayer plane and, on the other hand, the hydrocarbon chains in the secondary ripple structure are likely to be perpendicular to the bilayer plane. This fact seems to be related to a sequential mechanism of phase transitions. On heating from the Lβ, phase where the hydrocarbon chains are tilted the primary ripple structure having tilted hydrocarbon chains takes place and on cooling from the Lα phase where the hydrocarbon chains are not tilted the secondary ripple structure with untilted chains tends to be stabilized. It appears that the truly metastable ripple phase is expressed by the second ripple structure although in the course of the actual cooling transition both the secondary and primary ripple structures form and coexist. PMID:19431787

Fluctuation theorem: A critical review

NASA Astrophysics Data System (ADS)

Malek Mansour, M.; Baras, F.

2017-10-01

Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.

Automatic detection and visualisation of MEG ripple oscillations in epilepsy.

PubMed

van Klink, Nicole; van Rosmalen, Frank; Nenonen, Jukka; Burnos, Sergey; Helle, Liisa; Taulu, Samu; Furlong, Paul Lawrence; Zijlmans, Maeike; Hillebrand, Arjan

2017-01-01

High frequency oscillations (HFOs, 80-500 Hz) in invasive EEG are a biomarker for the epileptic focus. Ripples (80-250 Hz) have also been identified in non-invasive MEG, yet detection is impeded by noise, their low occurrence rates, and the workload of visual analysis. We propose a method that identifies ripples in MEG through noise reduction, beamforming and automatic detection with minimal user effort. We analysed 15 min of presurgical resting-state interictal MEG data of 25 patients with epilepsy. The MEG signal-to-noise was improved by using a cross-validation signal space separation method, and by calculating ~ 2400 beamformer-based virtual sensors in the grey matter. Ripples in these sensors were automatically detected by an algorithm optimized for MEG. A small subset of the identified ripples was visually checked. Ripple locations were compared with MEG spike dipole locations and the resection area if available. Running the automatic detection algorithm resulted in on average 905 ripples per patient, of which on average 148 ripples were visually reviewed. Reviewing took approximately 5 min per patient, and identified ripples in 16 out of 25 patients. In 14 patients the ripple locations showed good or moderate concordance with the MEG spikes. For six out of eight patients who had surgery, the ripple locations showed concordance with the resection area: 4/5 with good outcome and 2/3 with poor outcome. Automatic ripple detection in beamformer-based virtual sensors is a feasible non-invasive tool for the identification of ripples in MEG. Our method requires minimal user effort and is easily applicable in a clinical setting.

Global behavior analysis for stochastic system of 1,3-PD continuous fermentation

NASA Astrophysics Data System (ADS)

Zhu, Xi; Kliemann, Wolfgang; Li, Chunfa; Feng, Enmin; Xiu, Zhilong

2017-12-01

Global behavior for stochastic system of continuous fermentation in glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae is analyzed in this paper. This bioprocess cannot avoid the stochastic perturbation caused by internal and external disturbance which reflect on the growth rate. These negative factors can limit and degrade the achievable performance of controlled systems. Based on multiplicity phenomena, the equilibriums and bifurcations of the deterministic system are analyzed. Then, a stochastic model is presented by a bounded Markov diffusion process. In order to analyze the global behavior, we compute the control sets for the associated control system. The probability distributions of relative supports are also computed. The simulation results indicate that how the disturbed biosystem tend to stationary behavior globally.

Assessing the role of spectral and intensity cues in spectral ripple detection and discrimination in cochlear-implant users

PubMed Central

Anderson, Elizabeth S.; Oxenham, Andrew J.; Nelson, Peggy B.; Nelson, David A.

2012-01-01

Measures of spectral ripple resolution have become widely used psychophysical tools for assessing spectral resolution in cochlear-implant (CI) listeners. The objective of this study was to compare spectral ripple discrimination and detection in the same group of CI listeners. Ripple detection thresholds were measured over a range of ripple frequencies and were compared to spectral ripple discrimination thresholds previously obtained from the same CI listeners. The data showed that performance on the two measures was correlated, but that individual subjects’ thresholds (at a constant spectral modulation depth) for the two tasks were not equivalent. In addition, spectral ripple detection was often found to be possible at higher rates than expected based on the available spectral cues, making it likely that temporal-envelope cues played a role at higher ripple rates. Finally, spectral ripple detection thresholds were compared to previously obtained speech-perception measures. Results confirmed earlier reports of a robust relationship between detection of widely spaced ripples and measures of speech recognition. In contrast, intensity difference limens for broadband noise did not correlate with spectral ripple detection measures, suggesting a dissociation between the ability to detect small changes in intensity across frequency and across time. PMID:23231122

Evidence of across-channel processing for spectral-ripple discrimination in cochlear implant listeners.

PubMed

Won, Jong Ho; Jones, Gary L; Drennan, Ward R; Jameyson, Elyse M; Rubinstein, Jay T

2011-10-01

Spectral-ripple discrimination has been used widely for psychoacoustical studies in normal-hearing, hearing-impaired, and cochlear implant listeners. The present study investigated the perceptual mechanism for spectral-ripple discrimination in cochlear implant listeners. The main goal of this study was to determine whether cochlear implant listeners use a local intensity cue or global spectral shape for spectral-ripple discrimination. The effect of electrode separation on spectral-ripple discrimination was also evaluated. Results showed that it is highly unlikely that cochlear implant listeners depend on a local intensity cue for spectral-ripple discrimination. A phenomenological model of spectral-ripple discrimination, as an "ideal observer," showed that a perceptual mechanism based on discrimination of a single intensity difference cannot account for performance of cochlear implant listeners. Spectral modulation depth and electrode separation were found to significantly affect spectral-ripple discrimination. The evidence supports the hypothesis that spectral-ripple discrimination involves integrating information from multiple channels. © 2011 Acoustical Society of America

Evidence of across-channel processing for spectral-ripple discrimination in cochlear implant listeners a

PubMed Central

Ho Won, Jong; Jones, Gary L.; Drennan, Ward R.; Jameyson, Elyse M.; Rubinstein, Jay T.

2011-01-01

Spectral-ripple discrimination has been used widely for psychoacoustical studies in normal-hearing, hearing-impaired, and cochlear implant listeners. The present study investigated the perceptual mechanism for spectral-ripple discrimination in cochlear implant listeners. The main goal of this study was to determine whether cochlear implant listeners use a local intensity cue or global spectral shape for spectral-ripple discrimination. The effect of electrode separation on spectral-ripple discrimination was also evaluated. Results showed that it is highly unlikely that cochlear implant listeners depend on a local intensity cue for spectral-ripple discrimination. A phenomenological model of spectral-ripple discrimination, as an “ideal observer,” showed that a perceptual mechanism based on discrimination of a single intensity difference cannot account for performance of cochlear implant listeners. Spectral modulation depth and electrode separation were found to significantly affect spectral-ripple discrimination. The evidence supports the hypothesis that spectral-ripple discrimination involves integrating information from multiple channels. PMID:21973363

A Broad Continuum of Aeolian Impact Ripple Sizes on Mars is Allowed by Low Dynamic Wind Pressures

NASA Astrophysics Data System (ADS)

Sullivan, R. J., Jr.; Kok, J. F.; Yizhaq, H.

2017-12-01

Aeolian impact ripples are generated by impacts of wind-blown sand grains, and are common in environments with loose sand on Earth and Mars. Previous work has shown that, within a fully developed saltation cloud, impact ripple height grows upward into the boundary layer until limited by the effects of increasing wind dynamic pressure at the crest (e.g., lengthening of splash trajectories, or direct entrainment of grains by the wind). On Earth, this process limits ripples of well-sorted 250 µm dune sands to heights of millimeters, and strong winds can impose sufficient lateral dynamic pressure to flatten and erase these ripples. Rover observations show much larger ripple-like bedforms on Mars, raising questions about their formative mechanism. Here, we hypothesize that two factors allow impact ripples to grow much higher on Mars than on Earth: (1) previous work predicts a much larger difference between impact threshold and fluid threshold wind speeds on Mars than on Earth; and (2) recent analysis has revealed how low saltation flux can be initiated and sustained well below fluid threshold on Mars, allowing impact ripples to migrate entirely under prevailing conditions of relatively low wind speeds in the thin martian atmosphere. Under these circumstances, martian ripples would need to grow much larger than on Earth before reaching their maximum height limited by wind dynamic pressure effects. Because the initial size of impact ripples is similar on Mars and Earth, this should generate a much broader continuum of impact ripple sizes on Mars. Compared with Earth, far more time should be needed on Mars for impact ripples to achieve their maximum possible size. Consequently, in cases where wind azimuths are mixed but one azimuth is more dominant than others, martian impact ripples of all sizes can exist together in the same setting, with the largest examples reflecting the most common/formative wind azimuths. In cases where wind azimuth is not dominated by a single azimuth over others, ripple height should vary with orientation and the maximum possible height might never have the chance to be achieved. Our hypothesis could explain the wide range of observed ripple sizes on Mars having wavelengths from cm to several m, and suggests that the largest martian ripples are in fact large impact ripples.

Age Is Associated with Reduced Sharp-Wave Ripple Frequency and Altered Patterns of Neuronal Variability.

PubMed

Wiegand, Jean-Paul L; Gray, Daniel T; Schimanski, Lesley A; Lipa, Peter; Barnes, C A; Cowen, Stephen L

2016-05-18

Spatial and episodic memory performance declines with age, and the neural basis for this decline is not well understood. Sharp-wave ripples are brief (∼70 ms) high-frequency oscillatory events generated in the hippocampus and are associated with the consolidation of spatial memories. Given the connection between ripple oscillations and memory consolidation, we investigated whether the structure of ripple oscillations and ripple-triggered patterns of single-unit activity are altered in aged rats. Local field and single-unit activity surrounding sharp-wave ripple events were examined in the CA1 region of the hippocampus of old (n = 5) and young (n = 6) F344 rats during periods of rest preceding and following performance on a place-dependent eyeblink-conditioning task. Neural responses in aged rats differed from responses in young rats in several ways. First, compared with young rats, the rate of ripple occurrence (ripple density) is reduced in aged rats during postbehavior rest. Second, mean ripple frequency during prebehavior and postbehavior rest is lower in aged animals (aged: 132 Hz; young: 146 Hz). Third, single neurons in aged animals responded more consistently from ripple to ripple. Fourth, variability in interspike intervals was greater in aged rats. Finally, neurons were tuned to a narrower range of phases of the ripple oscillation relative to young animals. Together, these results suggest that the CA1 network in aged animals has a reduced "vocabulary" of available representational states. The hippocampus is a structure that is critical for the formation of episodic memories. Sharp-wave ripple events generated in the hippocampus have been implicated in memory consolidation processes critical to memory stabilization. We examine here whether these ripple oscillations are altered over the course of the life span, which could contribute to hippocampus-dependent memory deficits that occur during aging. This experiment used young and aged memory-impaired rats to examine age-related changes in ripple architecture, ripple-triggered spike variance, and spike-phase coherence. We found that there are, indeed, significant changes in characteristics of ripples in older animals that could impact consolidation processes and memory stabilization in the aged brain. Copyright © 2016 the authors 0270-6474/16/365650-11$15.00/0.

Mesopontine median raphe regulates hippocampal ripple oscillation and memory consolidation.

PubMed

Wang, Dong V; Yau, Hau-Jie; Broker, Carl J; Tsou, Jen-Hui; Bonci, Antonello; Ikemoto, Satoshi

2015-05-01

Sharp wave-associated field oscillations (∼200 Hz) of the hippocampus, referred to as ripples, are believed to be important for consolidation of explicit memory. Little is known about how ripples are regulated by other brain regions. We found that the median raphe region (MnR) is important for regulating hippocampal ripple activity and memory consolidation. We performed in vivo simultaneous recording in the MnR and hippocampus of mice and found that, when a group of MnR neurons was active, ripples were absent. Consistently, optogenetic stimulation of MnR neurons suppressed ripple activity and inhibition of these neurons increased ripple activity. Notably, using a fear conditioning procedure, we found that photostimulation of MnR neurons interfered with memory consolidation. Our results demonstrate a critical role of the MnR in regulating ripples and memory consolidation.

Direct measurements of mean Reynolds stress and ripple roughness in the presence of energetic forcing by surface waves

USGS Publications Warehouse

Scully, Malcolm; Trowbridge, John; Sherwood, Christopher R.; Jones, Katie R.; Traykovski, Peter A.

2018-01-01

Direct covariance observations of the mean flow Reynolds stress and sonar images of the seafloor collected on a wave‐exposed inner continental shelf demonstrate that the drag exerted by the seabed on the overlying flow is consistent with boundary layer models for wave‐current interaction, provided that the orientation and anisotropy of the bed roughness are appropriately quantified. Large spatial and temporal variations in drag result from nonequilibrium ripple dynamics, ripple anisotropy, and the orientation of the ripples relative to the current. At a location in coarse sand characterized by large two‐dimensional orbital ripples, the observed drag shows a strong dependence on the relative orientation of the mean current to the ripple crests. At a contrasting location in fine sand, where more isotropic sub‐orbital ripples are observed, the sensitivity of the current to the orientation of the ripples is reduced. Further, at the coarse site under conditions when the currents are parallel to the ripple crests and the wave orbital diameter is smaller than the wavelength of the relic orbital ripples, the flow becomes hydraulically smooth. This transition is not observed at the fine site, where the observed wave orbital diameter is always greater than the wavelength of the observed sub‐orbital ripples. Paradoxically, the dominant along‐shelf flows often experience lower drag at the coarse site than at the fine site, despite the larger ripples, highlighting the complex dynamics controlling drag in wave‐exposed environments with heterogeneous roughness.

Observations of plan-view sand ripple behavior and spectral wave climate on the inner shelf of San Pedro Bay, California

USGS Publications Warehouse

Xu, J. P.

2005-01-01

Concurrent video images of sand ripples and current meter measurements of directional wave spectra are analyzed to study the relations between waves and wave-generated sand ripples. The data were collected on the inner shelf off Huntington Beach, California, at 15 m water depth, where the sea floor is comprised of well-sorted very fine sands (D50=92 ??m), during the winter of 2002. The wave climate, which was controlled by southerly swells (12-18 s period) and westerly wind waves (5-10 s period), included three wave types: (A) uni-modal, swells only; (B) bi-modal, swells dominant; and (C) bi-modal, wind-wave dominant. Each wave type has distinct relations with the plan-view shapes of ripples that are classified into five types: (1) sharp-crested, two-dimensional (2-D) ripples; (2) sharp-crested, brick-pattern, 3-D ripples; (3) bifurcated, 3-D ripples; (4) round-crested, shallow, 3-D ripples; and (5) flat bed. The ripple spacing is very small and varies between 4.5 and 7.5 cm. These ripples are anorbital as ripples in many field studies. Ripple orientation is only correlated with wave directions during strong storms (wave type C). In a poly-modal, multi-directional spectral wave environment, the use of the peak parameters (frequency, direction), a common practice when spectral wave measurements are unavailable, may lead to significant errors in boundary layer and sediment transport calculations. ?? 2004 Elsevier Ltd. All rights reserved.

Direct Measurements of Mean Reynolds Stress and Ripple Roughness in the Presence of Energetic Forcing by Surface Waves

NASA Astrophysics Data System (ADS)

Scully, Malcolm E.; Trowbridge, John H.; Sherwood, Christopher R.; Jones, Katie R.; Traykovski, Peter

2018-04-01

Direct covariance observations of the mean flow Reynolds stress and sonar images of the seafloor collected on a wave-exposed inner continental shelf demonstrate that the drag exerted by the seabed on the overlying flow is consistent with boundary layer models for wave-current interaction, provided that the orientation and anisotropy of the bed roughness are appropriately quantified. Large spatial and temporal variations in drag result from nonequilibrium ripple dynamics, ripple anisotropy, and the orientation of the ripples relative to the current. At a location in coarse sand characterized by large two-dimensional orbital ripples, the observed drag shows a strong dependence on the relative orientation of the mean current to the ripple crests. At a contrasting location in fine sand, where more isotropic sub-orbital ripples are observed, the sensitivity of the current to the orientation of the ripples is reduced. Further, at the coarse site under conditions when the currents are parallel to the ripple crests and the wave orbital diameter is smaller than the wavelength of the relic orbital ripples, the flow becomes hydraulically smooth. This transition is not observed at the fine site, where the observed wave orbital diameter is always greater than the wavelength of the observed sub-orbital ripples. Paradoxically, the dominant along-shelf flows often experience lower drag at the coarse site than at the fine site, despite the larger ripples, highlighting the complex dynamics controlling drag in wave-exposed environments with heterogeneous roughness.

Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited.

PubMed

Vellela, Melissa; Qian, Hong

2009-10-06

Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.

Stochastic tools hidden behind the empirical dielectric relaxation laws

NASA Astrophysics Data System (ADS)

Stanislavsky, Aleksander; Weron, Karina

2017-03-01

The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of ‘structures with variations’ (Goldenfield and Kadanoff 1999 Science 284 87-9) require application of such mathematical tools—by means of which their random nature can be analyzed and, independently of the details distinguishing various systems (dipolar materials, glasses, semiconductors, liquid crystals, polymers, etc), the empirical universal kinetic patterns can be derived. We begin with a brief survey of the historical background of the dielectric relaxation study. After a short outline of the theoretical ideas providing the random tools applicable to modeling of relaxation phenomena, we present probabilistic implications for the study of the relaxation-rate distribution models. In the framework of the probability distribution of relaxation rates we consider description of complex systems, in which relaxing entities form random clusters interacting with each other and single entities. Then we focus on stochastic mechanisms of the relaxation phenomenon. We discuss the diffusion approach and its usefulness for understanding of anomalous dynamics of relaxing systems. We also discuss extensions of the diffusive approach to systems under tempered random processes. Useful relationships among different stochastic approaches to the anomalous dynamics of complex systems allow us to get a fresh look at this subject. The paper closes with a final discussion on achievements of stochastic tools describing the anomalous time evolution of complex systems.

Regularity of random attractors for fractional stochastic reaction-diffusion equations on Rn

NASA Astrophysics Data System (ADS)

Gu, Anhui; Li, Dingshi; Wang, Bixiang; Yang, Han

2018-06-01

We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction-diffusion equations in Hs (Rn) with s ∈ (0 , 1). We prove the existence and uniqueness of the tempered random attractor that is compact in Hs (Rn) and attracts all tempered random subsets of L2 (Rn) with respect to the norm of Hs (Rn). The main difficulty is to show the pullback asymptotic compactness of solutions in Hs (Rn) due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.

Effect of current ripple on cathode erosion in 30 kWe class arcjets

NASA Technical Reports Server (NTRS)

Harris, William J.; O'Hair, Edgar A.; Hatfield, Lynn L.; Kristiansen, M.; Grimes, Montgomery D.

1991-01-01

An investigation was conducted to study the effect of current ripple on cathode erosion in 30 kWe class arcjets to determine the change in the cathode erosion rate for high (11 percent) and low (4 percent) current ripple. The measurements were conducted using a copper-tungsten cathode material to accelerate the cathode erosion process. It is shown that the high ripple erosion rate was initially higher than the low ripple erosion rate, but decreased asymptotically with time to a level less than half that of the low ripple value. Results suggest that high ripple extends the cathode lifetime for long duration operation, and improves arc stability by increasing the cathode attachment area.

Analytical Assessment for Transient Stability Under Stochastic Continuous Disturbances

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

Ju, Ping; Li, Hongyu; Gan, Chun

Here, with the growing integration of renewable power generation, plug-in electric vehicles, and other sources of uncertainty, increasing stochastic continuous disturbances are brought to power systems. The impact of stochastic continuous disturbances on power system transient stability attracts significant attention. To address this problem, this paper proposes an analytical assessment method for transient stability of multi-machine power systems under stochastic continuous disturbances. In the proposed method, a probability measure of transient stability is presented and analytically solved by stochastic averaging. Compared with the conventional method (Monte Carlo simulation), the proposed method is many orders of magnitude faster, which makes itmore » very attractive in practice when many plans for transient stability must be compared or when transient stability must be analyzed quickly. Also, it is found that the evolution of system energy over time is almost a simple diffusion process by the proposed method, which explains the impact mechanism of stochastic continuous disturbances on transient stability in theory.« less

Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems

NASA Astrophysics Data System (ADS)

Link, Valentin; Strunz, Walter T.

2017-11-01

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments. The Schrödinger equation in the coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operators. In this picture the reduced state of the system can be obtained as a stochastic average over pure state trajectories, for any temperature of the bath. The corresponding non-Markovian stochastic Schrödinger equations include a memory integral over the past states. In the case of harmonic environments and linear coupling the approach gives a new form of the established non-Markovian quantum state diffusion stochastic Schrödinger equation without functional derivatives. Utilizing spin coherent states, the evolution equation for spin environments resembles the bosonic case with, however, a non-Gaussian average for the reduced density operator.

Propagation of Galactic cosmic rays: the influence of anisotropic diffusion

NASA Astrophysics Data System (ADS)

AL-Zetoun, A.; Achterberg, A.

2018-06-01

We consider the anisotropic diffusion of cosmic rays in the large-scale Galactic magnetic field, where diffusion along the field and diffusion across the field proceeds at different rates. To calculate this diffusion, we use stochastic differential equations to describe the cosmic ray propagation, solving these numerically. The Galactic magnetic field is described using the Jansson-Farrar model for the Galactic magnetic field. In this paper, we study the influence of perpendicular diffusion on the residence time of cosmic rays in the Galaxy. This provides an estimate for the influence of anisotropic diffusion on the residence time and the amount of matter (grammage) that a typical cosmic ray traverses during its residence in the Galaxy.

Transient ensemble dynamics in time-independent galactic potentials

NASA Astrophysics Data System (ADS)

Mahon, M. Elaine; Abernathy, Robert A.; Bradley, Brendan O.; Kandrup, Henry E.

1995-07-01

This paper summarizes a numerical investigation of the short-time, possibly transient, behaviour of ensembles of stochastic orbits evolving in fixed non-integrable potentials, with the aim of deriving insights into the structure and evolution of galaxies. The simulations involved three different two-dimensional potentials, quite different in appearance. However, despite these differences, ensembles in all three potentials exhibit similar behaviour. This suggests that the conclusions inferred from the simulations are robust, relying only on basic topological properties, e.g., the existence of KAM tori and cantori. Generic ensembles of initial conditions, corresponding to stochastic orbits, exhibit a rapid coarse-grained approach towards a near-invariant distribution on a time-scale <>t_H, although various irregularities associated with external and/or internal irregularities can drastically accelerate this process. A principal tool in the analysis is the notion of a local Liapounov exponent, which provides a statistical characterization of the overall instability of stochastic orbits over finite time intervals. In particular, there is a precise sense in which confined stochastic orbits are less unstable, with smaller local Liapounov exponents, than are unconfined stochastic orbits.

Practical application of noise diffusion in U-70 synchrotron

NASA Astrophysics Data System (ADS)

Ivanov, S. V.; Lebedev, O. P.

2016-12-01

This paper briefly outlines the physical substantiation and the engineering implementation of technological systems in the U-70 synchrotron based on controllable noise diffusion of the beam. They include two systems of stochastic slow beam extraction (for high and intermediate energy) and the system of longitudinal noise RF gymnastics designated for flattening the bunch distribution over the azimuth.

Ripple pattern formation on silicon surfaces by low-energy ion-beam erosion: Experiment and theory

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

Ziberi, B.; Frost, F.; Rauschenbach, B.

The topography evolution of Si surfaces during low-energy noble-gas ion-beam erosion (ion energy {<=}2000 eV) at room temperature has been studied. Depending on the ion-beam parameters, self-organized ripple patterns evolve on the surface with a wavelength {lambda}<100 nm. Ripple patterns were found to occur at near-normal ion incidence angles (5 deg. -30 deg.) with the wave vector oriented parallel to the ion-beam direction. The ordering and homogeneity of these patterns increase with ion fluence, leading to very-well-ordered ripples. The ripple wavelength remains constant with ion fluence. Also, the influence of ion energy on the ripple wavelength is investigated. Additionally itmore » is shown that the mass of the bombarding ion plays a decisive role in the ripple formation process. Ripple patterns evolve for Ar{sup +},Kr{sup +}, and Xe{sup +} ions, while no ripples are observed using Ne{sup +} ions. These results are discussed in the context of continuum theories and by using Monte Carlo simulations.« less

High-Fidelity Thermal Radiation Models and Measurements for High-Pressure Reacting Laminar and Turbulent Flows

DTIC Science & Technology

2013-06-26

flow code used ( OpenFOAM ) to include differential diffusion and cell-based stochastic RTE solvers. The models were validated by simulation of laminar...wavenumber selection is improved about by a factor of 10. (5) OpenFOAM Improvements for Laminar Flames A laminar-diffusion combustion solver, taking into...account the effects of differential diffusion, was developed within the open source CFD package OpenFOAM [18]. In addition, OpenFOAM was augmented to take

Spectrum pattern resolution after noise exposure in a beluga whale, Delphinapterus leucas: Evoked potential study.

PubMed

Popov, Vladimir V; Nechaev, Dmitry I; Sysueva, Evgenia V; Rozhnov, Viatcheslav V; Supin, Alexander Ya

2015-07-01

Temporary threshold shift (TTS) and the discrimination of spectrum patterns after fatiguing noise exposure (170 dB re 1 μPa, 10 min duration) was investigated in a beluga whale, Delphinapterus leucas, using the evoked potential technique. Thresholds were measured using rhythmic (1000/s) pip trains of varying levels and recording the rhythmic evoked responses. Discrimination of spectrum patterns was investigated using rippled-spectrum test stimuli of various levels and ripple densities, recording the rhythmic evoked responses to ripple phase reversals. Before noise exposure, the greatest responses to rippled-spectrum probes were evoked by stimuli with a low ripple density with a decrease in the response magnitude occurring with an increasing ripple density. After noise exposure, both a TTS and a reduction of the responses to rippled-spectrum probes appeared and recovered in parallel. The reduction of the responses to rippled-spectrum probes was maximal for high-magnitude responses at low ripple densities and was negligible for low-magnitude responses at high ripple densities. It is hypothesized that the impacts of fatiguing sounds are not limited by increased thresholds and decreased sensitivity results in reduced ability to discriminate fine spectral content with the greatest impact on the discrimination of spectrum content that may carry the most obvious information about stimulus properties.

Stochastic field-line wandering in magnetic turbulence with shear. II. Decorrelation trajectory method

NASA Astrophysics Data System (ADS)

Negrea, M.; Petrisor, I.; Shalchi, A.

2017-11-01

We study the diffusion of magnetic field lines in turbulence with magnetic shear. In the first part of the series, we developed a quasi-linear theory for this type of scenario. In this article, we employ the so-called DeCorrelation Trajectory method in order to compute the diffusion coefficients of stochastic magnetic field lines. The magnetic field configuration used here contains fluctuating terms which are described by the dimensionless functions bi(X, Y, Z), i = (x, y) and they are assumed to be Gaussian processes and are perpendicular with respect to the main magnetic field B0. Furthermore, there is also a z-component of the magnetic field depending on radial coordinate x (representing the gradient of the magnetic field) and a poloidal average component. We calculate the diffusion coefficients for magnetic field lines for different values of the magnetic Kubo number K, the dimensionless inhomogeneous magnetic parallel and perpendicular Kubo numbers KB∥, KB⊥ , as well as Ka v=bya vKB∥/KB⊥ .

Stochastic theory of photon flow in homogeneous and heterogeneous anisotropic biological and artificial material

NASA Astrophysics Data System (ADS)

Miller, Steven D.

1995-05-01

Standard Monte Carlo methods used in photon diffusion score absorbed photons or statistical weight deposited within voxels comprising a mesh. An alternative approach to a stochastic description is considered for rapid surface flux calculations and finite medias. Matrix elements are assigned to a spatial lattice whose function is to score vector intersections of scattered photons making transitions into either the forward or back solid angle half spaces. These complete matrix elements can be related to the directional fluxes within the lattice space. This model differentiates between ballistic, quasi-ballistic, and highly diffuse photon contributions, and effectively models the subsurface generation of a scattered light flux from a ballistic source. The connection between a path integral and diffusion is illustrated. Flux perturbations can be effectively illustrated for tissue-tumor-tissue and for 3 layer systems with strong absorption in one or more layers. For conditions where the diffusion theory has difficulties such as strong absorption, highly collimated sources, small finite volumes, and subsurface regions, the computation time of the algorithm is rapid with good accuracy and compliments other description of photon diffusion. The model has the potential to do computations relevant to photodynamic therapy (PDT) and analysis of laser beam interaction with tissues.

Continuum models of cohesive stochastic swarms: The effect of motility on aggregation patterns

NASA Astrophysics Data System (ADS)

Hughes, Barry D.; Fellner, Klemens

2013-10-01

Mathematical models of swarms of moving agents with non-local interactions have many applications and have been the subject of considerable recent interest. For modest numbers of agents, cellular automata or related algorithms can be used to study such systems, but in the present work, instead of considering discrete agents, we discuss a class of one-dimensional continuum models, in which the agents possess a density ρ(x,t) at location x at time t. The agents are subject to a stochastic motility mechanism and to a global cohesive inter-agent force. The motility mechanisms covered include classical diffusion, nonlinear diffusion (which may be used to model, in a phenomenological way, volume exclusion or other short-range local interactions), and a family of linear redistribution operators related to fractional diffusion equations. A variety of exact analytic results are discussed, including equilibrium solutions and criteria for unimodality of equilibrium distributions, full time-dependent solutions, and transitions between asymptotic collapse and asymptotic escape. We address the behaviour of the system for diffusive motility in the low-diffusivity limit for both smooth and singular interaction potentials and show how this elucidates puzzling behaviour in fully deterministic non-local particle interaction models. We conclude with speculative remarks about extensions and applications of the models.

A proposal for the experimental detection of CSL induced random walk

PubMed Central

Bera, Sayantani; Motwani, Bhawna; Singh, Tejinder P.; Ulbricht, Hendrik

2015-01-01

Continuous Spontaneous Localization (CSL) is one possible explanation for dynamically induced collapse of the wave-function during a quantum measurement. The collapse is mediated by a stochastic non-linear modification of the Schrödinger equation. A consequence of the CSL mechanism is an extremely tiny violation of energy-momentum conservation, which can, in principle, be detected in the laboratory via the random diffusion of a particle induced by the stochastic collapse mechanism. In a paper in 2003, Collett and Pearle investigated the translational CSL diffusion of a sphere, and the rotational CSL diffusion of a disc, and showed that this effect dominates over the ambient environmental noise at low temperatures and extremely low pressures (about ten-thousandth of a pico-Torr). In the present paper, we revisit their analysis and argue that this stringent condition on pressure can be relaxed, and that the CSL effect can be seen at the pressure of about a pico-Torr. A similar analysis is provided for diffusion produced by gravity-induced decoherence, where the effect is typically much weaker than CSL. We also discuss the CSL induced random displacement of a quantum oscillator. Lastly, we propose possible experimental set-ups justifying that CSL diffusion is indeed measurable with the current technology. PMID:25563619

Kinematic dynamo, supersymmetry breaking, and chaos

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Enßlin, Torsten A.

2016-04-01

The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry, and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as the stochastic generalization of the concept of dynamical chaos. As this supersymmetry breaking happens in both the diffusive and the nondiffusive cases, the necessity of the underlying SDE being chaotic is given in either case. The observed exponentially growing and oscillating KD modes prove physically that dynamical spectra of the STS evolution operator that break the topological supersymmetry exist with both real and complex ground state eigenvalues. Finally, we comment on the nonexistence of dynamos for scalar quantities.

Effect of toroidal field ripple on plasma rotation in JET

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

De Vries, P.; Salmi, A.; Parail, V.

Dedicated experiments on TF ripple effects on the performance of tokamak plasmas have been carried out at JET. The TF ripple was found to have a profound effect on the plasma rotation. The central Mach number, M, defined as the ratio of the rotation velocity and the thermal velocity, was found to drop as a function of TF ripple amplitude ( ) from an average value of M = 0.40 0.55 for operations at the standard JET ripple of = 0.08% to M = 0.25 0.40 for = 0.5% and M = 0.1 0.3 for = 1%. TF ripple effectsmore » should be considered when estimating the plasma rotation in ITER. With standard co-current injection of neutral beam injection (NBI), plasmas were found to rotate in the co-current direction. However, for higher TF ripple amplitudes ( ~ 1%) an area of counter rotation developed at the edge of the plasma, while the core kept its co-rotation. The edge counter rotation was found to depend, besides on the TF ripple amplitude, on the edge temperature. The observed reduction of toroidal plasma rotation with increasing TF ripple could partly be explained by TF ripple induced losses of energetic ions, injected by NBI. However, the calculated torque due to these losses was insufficient to explain the observed counter rotation and its scaling with edge parameters. It is suggested that additional TF ripple induced losses of thermal ions contribute to this effect.« less

Stochastic differential equations and turbulent dispersion

NASA Technical Reports Server (NTRS)

Durbin, P. A.

1983-01-01

Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.

Ripple Communication.

ERIC Educational Resources Information Center

Wilcox, R. Stimson

1980-01-01

Discusses how surface-dwelling animals use the water surface as a mode of communication by making ripple signals while they swim about. Provides information about surfaces and surface waves, ripple communication in water striders, ripple signal characteristics, sensing and orienting, other modes of communication, and evolution of ripple…

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled. PMID:25481130

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.

Microtearing turbulence: Magnetic braiding and disruption limit

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

Firpo, Marie-Christine

2015-12-15

A realistic reduced model involving a large poloidal spectrum of microtearing modes is used to probe the existence of some stochasticity of magnetic field lines. Stochasticity is shown to occur even for the low values of the magnetic perturbation δB/B devoted to magnetic turbulence that have been experimentally measured. Because the diffusion coefficient may strongly depend on the radial (or magnetic-flux) coordinate, being very low near some resonant surfaces, and because its evaluation implicitly makes a normal diffusion hypothesis, one turns to another indicator appropriate to diagnose the confinement: the mean residence time of magnetic field lines. Their computation inmore » the microturbulence frame points to the existence of a disruption limit, namely of a critical order of magnitude of δB/B above which stochasticity is no longer benign yet, leads to a macroscopic loss of confinement in some tens to hundred of electron toroidal excursions. Since the level of magnetic turbulence δB/B has been measured to grow with the plasma electron density, this would also be a density limit.« less

A new topology of fuel cell hybrid power source for efficient operation and high reliability

NASA Astrophysics Data System (ADS)

Bizon, Nicu

2011-03-01

This paper analyzes a new fuel cell Hybrid Power Source (HPS) topology having the feature to mitigate the current ripple of the fuel cell inverter system. In the operation of the inverter system that is grid connected or supplies AC motors in vehicle application, the current ripple normally appears at the DC port of the fuel cell HPS. Consequently, if mitigation measures are not applied, this ripple is back propagated to the fuel cell stack. Other features of the proposed fuel cell HPS are the Maximum Power Point (MPP) tracking, high reliability in operation under sharp power pulses and improved energy efficiency in high power applications. This topology uses an inverter system directly powered from the appropriate fuel cell stack and a controlled buck current source as low power source used for ripple mitigation. The low frequency ripple mitigation is based on active control. The anti-ripple current is injected in HPS output node and this has the LF power spectrum almost the same with the inverter ripple. Consequently, the fuel cell current ripple is mitigated by the designed active control. The ripple mitigation performances are evaluated by indicators that are defined to measure the mitigation ratio of the low frequency harmonics. In this paper it is shown that good performances are obtained by using the hysteretic current control, but better if a dedicated nonlinear controller is used. Two ways to design the nonlinear control law are proposed. First is based on simulation trials that help to draw the characteristic of ripple mitigation ratio vs. fuel cell current ripple. The second is based on Fuzzy Logic Controller (FLC). The ripple factor is up to 1% in both cases.

Simulations of eddy kinetic energy transport in barotropic turbulence

NASA Astrophysics Data System (ADS)

Grooms, Ian

2017-11-01

Eddy energy transport in rotating two-dimensional turbulence is investigated using numerical simulation. Stochastic forcing is used to generate an inhomogeneous field of turbulence and the time-mean energy profile is diagnosed. An advective-diffusive model for the transport is fit to the simulation data by requiring the model to accurately predict the observed time-mean energy distribution. Isotropic harmonic diffusion of energy is found to be an accurate model in the case of uniform, solid-body background rotation (the f plane), with a diffusivity that scales reasonably well with a mixing-length law κ ∝V ℓ , where V and ℓ are characteristic eddy velocity and length scales. Passive tracer dynamics are added and it is found that the energy diffusivity is 75 % of the tracer diffusivity. The addition of a differential background rotation with constant vorticity gradient β leads to significant changes to the energy transport. The eddies generate and interact with a mean flow that advects the eddy energy. Mean advection plus anisotropic diffusion (with reduced diffusivity in the direction of the background vorticity gradient) is moderately accurate for flows with scale separation between the eddies and mean flow, but anisotropic diffusion becomes a much less accurate model of the transport when scale separation breaks down. Finally, it is observed that the time-mean eddy energy does not look like the actual eddy energy distribution at any instant of time. In the future, stochastic models of the eddy energy transport may prove more useful than models of the mean transport for predicting realistic eddy energy distributions.

Effect of ripple taper on band-gap overlap in a coaxial Bragg structure operating at terahertz frequency

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

Ding Xueyong; Li Hongfan; Lv Zhensu

Based on the mode-coupling method, numerical analysis is presented to demonstrate the influence of ripple taper on band-gap overlap in a coaxial Bragg structure operating at terahertz frequency. Results show that the interval between the band-gaps of the competing mode and the desired working mode is narrowed by use of positive-taper ripples, but is expanded if negative-taper ripples are employed, and the influence of the negative-taper ripples is obviously more advantageous than the positive-taper ripples; the band-gap overlap of modes can be efficiently separated by use of negative-taper ripples. The residual side-lobes of the frequency response in a coaxial Braggmore » structure with ripple taper also can be effectively suppressed by employing the windowing-function technique. These peculiarities provide potential advantage in constructing a coaxial Bragg cavity with high quality factor for single higher-order-mode operation of a high-power free-electron maser in the terahertz frequency range.« less

Utilization of independent component analysis for accurate pathological ripple detection in intracranial EEG recordings recorded extra- and intra-operatively

PubMed Central

Shimamoto, Shoichi; Waldman, Zachary J.; Orosz, Iren; Song, Inkyung; Bragin, Anatol; Fried, Itzhak; Engel, Jerome; Staba, Richard; Sharan, Ashwini; Wu, Chengyuan; Sperling, Michael R.; Weiss, Shennan A.

2018-01-01

Objective To develop and validate a detector that identifies ripple (80–200 Hz) events in intracranial EEG (iEEG) recordings in a referential montage and utilizes independent component analysis (ICA) to eliminate or reduce high-frequency artifact contamination. Also, investigate the correspondence of detected ripples and the seizure onset zone (SOZ). Methods iEEG recordings from 16 patients were first band-pass filtered (80–600 Hz) and Infomax ICA was next applied to derive the first independent component (IC1). IC1 was subsequently pruned, and an artifact index was derived to reduce the identification of high-frequency events introduced by the reference electrode signal. A Hilbert detector identified ripple events in the processed iEEG recordings using amplitude and duration criteria. The identified ripple events were further classified and characterized as true or false ripple on spikes, or ripples on oscillations by utilizing a topographical analysis to their time-frequency plot, and confirmed by visual inspection. Results The signal to noise ratio was improved by pruning IC1. The precision of the detector for ripple events was 91.27 ± 4.3%, and the sensitivity of the detector was 79.4 ± 3.0% (N = 16 patients, 5842 ripple events). The sensitivity and precision of the detector was equivalent in iEEG recordings obtained during sleep or intra-operatively. Across all the patients, true ripple on spike rates and also the rates of false ripple on spikes, that were generated due to filter ringing, classified the seizure onset zone (SOZ) with an area under the receiver operating curve (AUROC) of >76%. The magnitude and spectral content of true ripple on spikes generated in the SOZ was distinct as compared with the ripples generated in the NSOZ (p < .001). Conclusions Utilizing ICA to analyze iEEG recordings in referential montage provides many benefits to the study of high-frequency oscillations. The ripple rates and properties defined using this approach may accurately delineate the seizure onset zone. Significance Strategies to improve the spatial resolution of intracranial EEG and reduce artifact can help improve the clinical utility of HFO biomarkers. PMID:29113719

Effects of Resonant Helical Field on Toroidal Field Ripple in IR-T1 Tokamak

NASA Astrophysics Data System (ADS)

Mahdavipour, B.; Salar Elahi, A.; Ghoranneviss, M.

2018-02-01

The toroidal magnetic field which is created by toroidal coils has the ripple in torus space. This magnetic field ripple has an importance in plasma equilibrium and stability studies in tokamak. In this paper, we present the investigation of the interaction between the toroidal magnetic field ripple and resonant helical field (RHF). We have estimated the amplitude of toroidal field ripples without and with RHF (with different q = m/n) ( m = 2, m = 3, m = 4, m = 5, m = 2 & 3, n = 1) using “Comsol Multiphysics” software. The simulations show that RHF has effects on the toroidal ripples.

Formation and evolution of ripples on ion-irradiated semiconductor surfaces

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

Kang, M.; Wu, J. H.; Ye, W.

We have examined the formation and evolution of ripples on focused-ion-beam (FIB) irradiated compound semiconductor surfaces. Using initially normal-incidence Ga{sup +} FIB irradiation of InSb, we tuned the local beam incidence angle (θ{sub eff}) by varying the pitch and/or dwell time. For single-pass FIB irradiation, increasing θ{sub eff} induces morphological evolution from pits and islands to ripples to featureless surfaces. Multiple-pass FIB irradiation of the rippled surfaces at a fixed θ{sub eff} leads to island formation on the ripple crests, followed by nanorod (NR) growth. This ripple-NR transition provides an alternative approach for achieving dense arrays of NRs.

Non-Markovian Quantum State Diffusion for temperature-dependent linear spectra of light harvesting aggregates

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

Ritschel, Gerhard; Möbius, Sebastian; Eisfeld, Alexander, E-mail: eisfeld@mpipks-dresden.mpg.de

2015-01-21

Non-Markovian Quantum State Diffusion (NMQSD) has turned out to be an efficient method to calculate excitonic properties of aggregates composed of organic chromophores, taking into account the coupling of electronic transitions to vibrational modes of the chromophores. NMQSD is an open quantum system approach that incorporates environmental degrees of freedom (the vibrations in our case) in a stochastic way. We show in this paper that for linear optical spectra (absorption, circular dichroism), no stochastics is needed, even for finite temperatures. Thus, the spectra can be obtained by propagating a single trajectory. To this end, we map a finite temperature environmentmore » to the zero temperature case using the so-called thermofield method. The resulting equations can then be solved efficiently by standard integrators.« less

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Cosmic Ray Propagation through the Magnetic Fields of the Galaxy with Extended Halo

NASA Technical Reports Server (NTRS)

Zhang, Ming

2005-01-01

In this project we perform theoretical studies of 3-dimensional cosmic ray propagation in magnetic field configurations of the Galaxy with an extended halo. We employ our newly developed Markov stochastic process methods to solve the diffusive cosmic ray transport equation. We seek to understand observations of cosmic ray spectra, composition under the constraints of the observations of diffuse gamma ray and radio emission from the Galaxy. The model parameters are directly are related to properties of our Galaxy, such as the size of the Galactic halo, particle transport in Galactic magnetic fields, distribution of interstellar gas, primary cosmic ray source distribution and their confinement in the Galaxy. The core of this investigation is the development of software for cosmic ray propagation models with the Markov stochastic process approach. Values of important model parameters for the halo diffusion model are examined in comparison with observations of cosmic ray spectra, composition and the diffuse gamma-ray background. This report summarizes our achievement in the grant period at the Florida Institute of Technology. Work at the co-investigator's institution, the University of New Hampshire, under a companion grant, will be covered in detail by a separate report.

Quantum diffusion during inflation and primordial black holes

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

Pattison, Chris; Assadullahi, Hooshyar; Wands, David

We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-δ N formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. Inmore » the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than ∼ 1 e -fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.« less

Quantum diffusion during inflation and primordial black holes

NASA Astrophysics Data System (ADS)

Pattison, Chris; Vennin, Vincent; Assadullahi, Hooshyar; Wands, David

2017-10-01

We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-δ N formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. In the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than ~ 1 e-fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.

Nanoscale diffusive memristor crossbars as physical unclonable functions.

PubMed

Zhang, R; Jiang, H; Wang, Z R; Lin, P; Zhuo, Y; Holcomb, D; Zhang, D H; Yang, J J; Xia, Q

2018-02-08

Physical unclonable functions have emerged as promising hardware security primitives for device authentication and key generation in the era of the Internet of Things. Herein, we report novel physical unclonable functions built upon the crossbars of nanoscale diffusive memristors that translate the stochastic distribution of Ag clusters in a SiO 2 matrix into a random binary bitmap that serves as a device fingerprint. The random dispersion of Ag led to an uneven number of clusters at each cross-point, which in turn resulted in a stochastic ability to switch in the Ag:SiO 2 diffusive memristors in an array. The randomness of the dispersion was a barrier to fingerprint cloning and the unique fingerprints of each device were persistent after fabrication. Using an optimized fabrication procedure, we maximized the randomness and achieved an inter-class Hamming distance of 50.68%. We also discovered that the bits were not flipping after over 10 4 s at 400 K, suggesting superior reliability of our physical unclonable functions. In addition, our diffusive memristor-based physical unclonable functions were easy to fabricate and did not require complicated post-processing for digitization and thus, provide new opportunities in hardware security applications.

A field study of large-scale oscillation ripples in a very coarse-grained, high-energy marine environment

USGS Publications Warehouse

Hirschaut, D.W.; Dingler, J.R.

1982-01-01

Monastery Beach, Carmel, California is a pocket beach that sits within 200 m of the head of Carmel Submarine Canyon. Coarse to very coarse sand covers both the beach and adjacent shelf; in the latter area incoming waves have shaped the sand into large oscillation ripples. The accessibility of this area and a variable wave climate produce a unique opportunity to study large-scale coarse-grained ripples in a high-energy environment. These ripples, which only occur in very coarse sand, form under the intense, wave-generated currents that exist during storm conditions. Once formed, these ripples do not significantly change under lower energy waves. On three separate occasions scuba divers measured ripples and collected sand samples from ripple crests near fixed reference stakes along three transects. Ripple wavelength and grain size decreased with an increase in water depth. Sediment sorting was best closest to the surf zone and poorest at the rim of Carmel Canyon. Cobbles and gravel observed in ripple troughs represent lag deposits. Carmel Canyon refracts waves approaching Monastery Beach such that wave energy is focused towards the northern and southern portions of the beach, leaving the central part of the beach lower in energy. This energy distribution causes spatial variations in the ripples and grain sizes with the shortest wavelengths and smallest grain sizes being in the central part of the shelf.

Ripple-triggered stimulation of the locus coeruleus during post-learning sleep disrupts ripple/spindle coupling and impairs memory consolidation

PubMed Central

Novitskaya, Yulia; Sara, Susan J.; Logothetis, Nikos K.

2016-01-01

Experience-induced replay of neuronal ensembles occurs during hippocampal high-frequency oscillations, or ripples. Post-learning increase in ripple rate is predictive of memory recall, while ripple disruption impairs learning. Ripples may thus present a fundamental component of a neurophysiological mechanism of memory consolidation. In addition to system-level local and cross-regional interactions, a consolidation mechanism involves stabilization of memory representations at the synaptic level. Synaptic plasticity within experience-activated neuronal networks is facilitated by noradrenaline release from the axon terminals of the locus coeruleus (LC). Here, to better understand interactions between the system and synaptic mechanisms underlying “off-line” consolidation, we examined the effects of ripple-associated LC activation on hippocampal and cortical activity and on spatial memory. Rats were trained on a radial maze; after each daily learning session neural activity was monitored for 1 h via implanted electrode arrays. Immediately following “on-line” detection of ripple, a brief train of electrical pulses (0.05 mA) was applied to LC. Low-frequency (20 Hz) stimulation had no effect on spatial learning, while higher-frequency (100 Hz) trains transiently blocked generation of ripple-associated cortical spindles and caused a reference memory deficit. Suppression of synchronous ripple/spindle events appears to interfere with hippocampal-cortical communication, thereby reducing the efficiency of “off-line” memory consolidation. PMID:27084931

Differentiation of specific ripple patterns helps to identify epileptogenic areas for surgical procedures.

PubMed

Kerber, Karolin; Dümpelmann, Matthias; Schelter, Björn; Le Van, Pierre; Korinthenberg, Rudolf; Schulze-Bonhage, Andreas; Jacobs, Julia

2014-07-01

High frequency oscillations (HFOs) at 80-500 Hz are promising markers of epileptic areas. Several retrospective studies reported that surgical removal of areas generating HFOs was associated with a good seizure outcome. Recent reports suggested that ripple (80-200 Hz) HFO patterns co-existed with different background EEG activities. We hypothesized that the coexisting background EEG pattern may distinguish physiological from epileptic ripples. Rates of HFOs were analyzed in intracranial EEG recordings of 22 patients. Additionally, ripple patterns were classified for each channel depending either as coexisting with a flat or oscillatory background activity. A multi-variate analysis was performed to determine whether removal of areas showing the above EEG markers correlated with seizure outcome. Removal of areas generating high rates of 'fast ripples (>200 Hz)' and 'ripples on a flat background activity' showed a significant correlation with a seizure-free outcome. In contrast, removal of high rates of 'ripples' or 'ripple patterns in a continuously oscillating background' was not significantly associated with seizure outcome. Ripples occurring in an oscillatory background activity may be suggestive of physiological activity, while those on a flat background reflect epileptic activity. Consideration of coexisting background patterns may improve the delineation of the epileptogenic areas using ripple oscillations. Copyright © 2013 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Multinucleon transfer in central collisions of 238U+238U

NASA Astrophysics Data System (ADS)

Ayik, S.; Yilmaz, B.; Yilmaz, O.; Umar, A. S.; Turan, G.

2017-08-01

Quantal diffusion mechanism of nucleon exchange is studied in the central collisions of 238U+238U in the framework of the stochastic mean-field (SMF) approach. For bombarding energies considered in this work, the dinuclear structure is maintained during the collision. Hence, it is possible to describe nucleon exchange as a diffusion process for mass and charge asymmetry. Quantal neutron and proton diffusion coefficients, including memory effects, are extracted from the SMF approach and the primary fragment distributions are calculated.

Mesopontine median raphe regulates hippocampal ripple oscillation and memory consolidation

PubMed Central

Wang, Dong V.; Yau, Hau-Jie; Broker, Carl J.; Tsou, Jen-Hui; Bonci, Antonello; Ikemoto, Satoshi

2015-01-01

Sharp-wave associated field-oscillations (~200 Hz) of the hippocampus, referred to as “ripples”, are believed to be important for consolidation of explicit memory. Little is known about how ripples are regulated by other brain regions. Here we show that the median raphe region (MnR) plays a key role in regulating hippocampal ripple activity and memory consolidation. We performed in vivo simultaneous recording in the MnR and hippocampus, and found that when a group of MnR neurons were active, ripples were absent. Consistently, optogenetic stimulation of MnR neurons suppressed ripple activity, while inhibition of these neurons increased ripple activity. Importantly, using a fear conditioning procedure, we provided evidence that photostimulation of MnR neurons interfered with memory consolidation. Our results demonstrate a critical role of the MnR in regulating ripples and memory consolidation. PMID:25867120

Combined inverse-forward artificial neural networks for fast and accurate estimation of the diffusion coefficients of cartilage based on multi-physics models.

PubMed

Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A

2016-09-06

Analytical and numerical methods have been used to extract essential engineering parameters such as elastic modulus, Poisson׳s ratio, permeability and diffusion coefficient from experimental data in various types of biological tissues. The major limitation associated with analytical techniques is that they are often only applicable to problems with simplified assumptions. Numerical multi-physics methods, on the other hand, enable minimizing the simplified assumptions but require substantial computational expertise, which is not always available. In this paper, we propose a novel approach that combines inverse and forward artificial neural networks (ANNs) which enables fast and accurate estimation of the diffusion coefficient of cartilage without any need for computational modeling. In this approach, an inverse ANN is trained using our multi-zone biphasic-solute finite-bath computational model of diffusion in cartilage to estimate the diffusion coefficient of the various zones of cartilage given the concentration-time curves. Robust estimation of the diffusion coefficients, however, requires introducing certain levels of stochastic variations during the training process. Determining the required level of stochastic variation is performed by coupling the inverse ANN with a forward ANN that receives the diffusion coefficient as input and returns the concentration-time curve as output. Combined together, forward-inverse ANNs enable computationally inexperienced users to obtain accurate and fast estimation of the diffusion coefficients of cartilage zones. The diffusion coefficients estimated using the proposed approach are compared with those determined using direct scanning of the parameter space as the optimization approach. It has been shown that both approaches yield comparable results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stochastic particle acceleration at shocks in the presence of braided magnetic fields.

NASA Astrophysics Data System (ADS)

Kirk, J. G.; Duffy, P.; Gallant, Y. A.

1996-10-01

The theory of diffusive acceleration of energetic particles at shock fronts assumes charged particles undergo spatial diffusion in a uniform magnetic field. If, however, the magnetic field is not uniform, but has a stochastic or braided structure, the transport of charged particles across the average direction of the field is more complicated. Assuming quasi-linear behaviour of the field lines, the particles undergo sub-diffusion on short time scales. We derive the propagator for such motion, which differs from the Gaussian form relevant for diffusion, and apply it to a configuration with a plane shock front whose normal is perpendicular to the average field direction. Expressions are given for the acceleration time as a function of the diffusion coefficient of the wandering magnetic field lines and the spatial diffusion coefficient of the charged particles parallel to the local field. In addition we calculate the spatial dependence of the particle density in both the upstream and downstream plasmas. In contrast to the diffusive case, the density of particles at the shock front is lower than it is far downstream. This is a consequence of the partial trapping of particles by structures in the magnetic field. As a result, the spectrum of accelerated particles is a power-law in momentum which is steeper than in the diffusive case. For a phase-space density f{prop.to}p^-s^, we find s=s_diff_[1+1/(2ρ_c_)], where ρ_c_ is the compression ratio of the shock front and s_diff_ is the standard result of diffusive acceleration: s_diff_=3ρ_c_/(ρ_c_-1). A strong shock in a monatomic ideal gas yields a spectrum of s=4.5. In the case of electrons, this corresponds to a radio synchrotron spectral index of α=0.75.

Characteristics of ripple structures revealed in OH airglow images

NASA Astrophysics Data System (ADS)

Li, Jing; Li, Tao; Dou, Xiankang; Fang, Xin; Cao, Bing; She, Chiao-Yao; Nakamura, Takuji; Manson, Alan; Meek, Chris; Thorsen, Denise

2017-03-01

Small-scale ripple structures observed in OH airglow images are most likely induced by either dynamic instability due to large wind shear or convective instability due to superadiabatic lapse rate. Using the data set taken in the mesopause region with an OH all-sky imager at Yucca Ridge Field Station, Colorado (40.7°N, 104.9°W), from September 2003 to December 2005, we study the characteristics and seasonal variations of ripple structures. By analyzing the simultaneous background wind and temperature observed by the nearby sodium temperature/wind lidar at Fort Collins, Colorado (40.6°N, 105°W), and a nearby medium-frequency radar at Platteville, Colorado (40.2°N, 105.8°W), we are able to statistically study the possible relation between ripples and the background atmosphere conditions. Characteristics and seasonal variations of ripples are presented in detail in this study. The occurrence frequency of ripples exhibits clear seasonal variability, with peak in autumn. The occurrence of ripples shows a local time dependence, which is most likely associated with the solar tides. The lifetime and spatial scale of these ripples are typically 5-20 min and 5-10 km, respectively, and most of the ripples move preferentially either southward or northward. However, more than half of the observed ripples do not advect with background flow; they have higher Richardson numbers than those ripples that advect with background flow. It is possible that they are not instability features but wave structures that are hard to be distinguished from the real instability features.

Design of Feedforward Controller to Reduce Force Ripple for Linear Motor using Halbach Magnet Array with T Shape Magnet

NASA Astrophysics Data System (ADS)

Kim, Moojong; Kim, Jinyoung; Lee, Moon G.

Recently, in micro/nano fabrication equipments, linear motors are widely used as an actuator to position workpiece, machining tool and measurement head. To control them faster and more precise, the motor should have high actuating force and small force ripple. High actuating force enable us to more workpiece with high acceleration. Eventually, it may provide higher throughput. Force ripple gives detrimental effect on the precision and tracking performance of the equipments. In order to accomplish more precise motion, it is important to make lower the force ripple. Force ripple is categorized into cogging and mutual ripple. First is dependent on the shape of magnets and/or core. The second is not dependent on them but dependent on current commutation. In this work, coreless mover i.e. coil winding is applied to the linear motor to avoid the cogging ripple. Therefore, the mutual ripple is only considered to be minimized. Ideal Halbach magnet array has continuously varying magnetization. The THMA (Halbach magnet array with T shape magnets) is proposed to approximate the ideal one. The THMA can not produce ideal sinusoidal flux, therefore, the linear motor with THMA and sinusoidal commutation of current generates the mutual force ripple. In this paper, in order to compensate mutual force ripple by feedforward(FF) controller, we calculate the optimized commutation of input current. The ripple is lower than 1.17% of actuating force if the commutation current agree with the magnetic flux from THMA. The performance of feedforward(FF) controller is verified by experiment.

Convective and diffusive ULF wave driven radiation belt electron transport

NASA Astrophysics Data System (ADS)

Degeling, A. W.; Rankin, R.; Elkington, S. R.

2011-12-01

The process of magnetospheric radiation belt electron transport driven by ULF waves is studied using a 2-D ideal MHD model for ULF waves in the equatorial plane including day/night asymmetry and a magnetopause boundary, and a test kinetic model for equatorially mirroring electrons. We find that ULF wave disturbances originating along the magnetopause flanks in the afternoon sector can act to periodically inject phase space density from these regions into the magnetosphere. Closely spaced drift-resonant surfaces for electrons with a given magnetic moment in the presence of the ULF waves create a layer of stochastic dynamics for L-shells above 6.5-7 in the cases examined, extending to the magnetopause. The phase decorrelation time scale for the stochastic region is estimated by the relaxation time for the diffusion coefficient to reach a steady value. This is found to be of the order of 10-15 wave periods, which is commensurate with the typical duration of observed ULF wave packets in the magnetosphere. For L-shells earthward of the stochastic layer, transport is limited to isolated drift-resonant islands in the case of narrowband ULF waves. We examine the effect of increasing the bandwidth of the ULF wave driver by summing together wave components produced by a set of independent runs of the ULF wave model. The wave source spectrum is given a flat-top amplitude of variable width (adjusted for constant power) and random phase. We find that increasing bandwidth can significantly enhance convective transport earthward of the stochastic layer and extend the stochastic layer to lower L-shells.

Proton imaging of stochastic magnetic fields

NASA Astrophysics Data System (ADS)

Bott, A. F. A.; Graziani, C.; Tzeferacos, P.; White, T. G.; Lamb, D. Q.; Gregori, G.; Schekochihin, A. A.

2017-12-01

Recent laser-plasma experiments (Fox et al., Phys. Rev. Lett., vol. 111, 2013, 225002; Huntington et al., Nat. Phys., vol. 11(2), 2015, 173-176 Tzeferacos et al., Phys. Plasmas, vol. 24(4), 2017a, 041404; Tzeferacos et al., 2017b, arXiv:1702.03016 [physics.plasm-ph]) report the existence of dynamically significant magnetic fields, whose statistical characterisation is essential for a complete understanding of the physical processes these experiments are attempting to investigate. In this paper, we show how a proton-imaging diagnostic can be used to determine a range of relevant magnetic-field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. This `Kugland image-flux relation' was previously derived (Kugland et al., Rev. Sci. Instrum. vol. 83(10), 2012, 101301) under simplifying assumptions typically valid in actual proton-imaging set-ups. We conclude that, as with regular electromagnetic fields, features of the beam's final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter - the contrast parameter s/{\\mathcal{M}}lB$ - which quantifies the relative size of the correlation length B$ of the stochastic field, proton displacements s$ due to magnetic deflections and the image magnification . For stochastic magnetic fields, we establish the existence of four contrast regimes, under which proton-flux images relate to their parent fields in a qualitatively distinct manner. These are linear, nonlinear injective, caustic and diffusive. The diffusive regime is newly identified and characterised. The nonlinear injective regime is distinguished from the caustic regime in manifesting nonlinear behaviour, but as in the linear regime, the path-integrated magnetic field experienced by the beam can be extracted uniquely. Thus, in the linear and nonlinear injective regimes we show that the magnetic-energy spectrum can be obtained under a further statistical assumption of isotropy. This is not the case in the caustic or diffusive regimes. We discuss complications to the contrast-regime characterisation arising for inhomogeneous, multi-scale stochastic fields, which can encompass many contrast regimes, as well as limitations currently placed by experimental capabilities on one's ability to extract magnetic-field statistics. The results presented in this paper are of consequence in providing a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of proton-flux images.

Reducing Ripple In A Switching Voltage Regulator

NASA Technical Reports Server (NTRS)

Paulkovich, John; Rodriguez, G. Ernest

1994-01-01

Ripple voltage in output of switching voltage regulator reduced substantially by simple additional circuitry adding little to overall weight and size of regulator. Heretofore, additional filtering circuitry needed to obtain comparable reductions in ripple typically as large and heavy as original regulator. Current opposing ripple current injected into filter capacitor.

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

NASA Astrophysics Data System (ADS)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

The concerted calculation of the BN-600 reactor for the deterministic and stochastic codes

NASA Astrophysics Data System (ADS)

Bogdanova, E. V.; Kuznetsov, A. N.

2017-01-01

The solution of the problem of increasing the safety of nuclear power plants implies the existence of complete and reliable information about the processes occurring in the core of a working reactor. Nowadays the Monte-Carlo method is the most general-purpose method used to calculate the neutron-physical characteristic of the reactor. But it is characterized by large time of calculation. Therefore, it may be useful to carry out coupled calculations with stochastic and deterministic codes. This article presents the results of research for possibility of combining stochastic and deterministic algorithms in calculation the reactor BN-600. This is only one part of the work, which was carried out in the framework of the graduation project at the NRC “Kurchatov Institute” in cooperation with S. S. Gorodkov and M. A. Kalugin. It is considering the 2-D layer of the BN-600 reactor core from the international benchmark test, published in the report IAEA-TECDOC-1623. Calculations of the reactor were performed with MCU code and then with a standard operative diffusion algorithm with constants taken from the Monte - Carlo computation. Macro cross-section, diffusion coefficients, the effective multiplication factor and the distribution of neutron flux and power were obtained in 15 energy groups. The reasonable agreement between stochastic and deterministic calculations of the BN-600 is observed.

Anomalous sea surface structures as an object of statistical topography

NASA Astrophysics Data System (ADS)

Klyatskin, V. I.; Koshel, K. V.

2015-06-01

By exploiting ideas of statistical topography, we analyze the stochastic boundary problem of emergence of anomalous high structures on the sea surface. The kinematic boundary condition on the sea surface is assumed to be a closed stochastic quasilinear equation. Applying the stochastic Liouville equation, and presuming the stochastic nature of a given hydrodynamic velocity field within the diffusion approximation, we derive an equation for a spatially single-point, simultaneous joint probability density of the surface elevation field and its gradient. An important feature of the model is that it accounts for stochastic bottom irregularities as one, but not a single, perturbation. Hence, we address the assumption of the infinitely deep ocean to obtain statistic features of the surface elevation field and the squared elevation gradient field. According to the calculations, we show that clustering in the absolute surface elevation gradient field happens with the unit probability. It results in the emergence of rare events such as anomalous high structures and deep gaps on the sea surface almost in every realization of a stochastic velocity field.

Wind ripples in low density atmospheres

NASA Technical Reports Server (NTRS)

Miller, J. S.; Marshall, J. R.; Greeley, R.

1987-01-01

The effect of varying fluid density (rho) on particle transport was examined by conducting tests at atmospheric pressures between 1 and 0.004 bar in the Martian Surface Wind Tunnel (MARSWIT). This study specifically concerns the effect of varying rho on the character of wind ripples, and elicits information concerning generalized ripple models as well as specific geological circumstances for ripple formation such as those prevailing on Mars. Tests were conducted primarily with 95 micron quartz sand, and for each atmospheric pressure chosen, tests were conducted at two freestream wind speeds: 1.1 U*(t) and 1.5 U*(t), where U*(t) is saltation threshold. Preliminary analysis of the data suggests: (1) ballistic ripple wavelength is not at variance with model predictions; (2) an atmospheric pressure of approximately 0.2 bar could represent a discontinuity in ripple behavior; and (4) ripple formation on Mars may not be readily predicted by extrapolation of terrestrial observations.

Comparing the force ripple during asynchronous and conventional stimulation.

PubMed

Downey, Ryan J; Tate, Mark; Kawai, Hiroyuki; Dixon, Warren E

2014-10-01

Asynchronous stimulation has been shown to reduce fatigue during electrical stimulation; however, it may also exhibit a force ripple. We quantified the ripple during asynchronous and conventional single-channel transcutaneous stimulation across a range of stimulation frequencies. The ripple was measured during 5 asynchronous stimulation protocols, 2 conventional stimulation protocols, and 3 volitional contractions in 12 healthy individuals. Conventional 40 Hz and asynchronous 16 Hz stimulation were found to induce contractions that were as smooth as volitional contractions. Asynchronous 8, 10, and 12 Hz stimulation induced contractions with significant ripple. Lower stimulation frequencies can reduce fatigue; however, they may also lead to increased ripple. Future efforts should study the relationship between force ripple and the smoothness of the evoked movements in addition to the relationship between stimulation frequency and NMES-induced fatigue to elucidate an optimal stimulation frequency for asynchronous stimulation. © 2014 Wiley Periodicals, Inc.

Learning-enhanced coupling between ripple oscillations in association cortices and hippocampus.

PubMed

Khodagholy, Dion; Gelinas, Jennifer N; Buzsáki, György

2017-10-20

Consolidation of declarative memories requires hippocampal-neocortical communication. Although experimental evidence supports the role of sharp-wave ripples in transferring hippocampal information to the neocortex, the exact cortical destinations and the physiological mechanisms of such transfer are not known. We used a conducting polymer-based conformable microelectrode array (NeuroGrid) to record local field potentials and neural spiking across the dorsal cortical surface of the rat brain, combined with silicon probe recordings in the hippocampus, to identify candidate physiological patterns. Parietal, midline, and prefrontal, but not primary cortical areas, displayed localized ripple (100 to 150 hertz) oscillations during sleep, concurrent with hippocampal ripples. Coupling between hippocampal and neocortical ripples was strengthened during sleep following learning. These findings suggest that ripple-ripple coupling supports hippocampal-association cortical transfer of memory traces. Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Participatory Action Research and Impact: An Ecological Ripples Perspective

ERIC Educational Resources Information Center

Trickett, Edison J.; Beehler, Sarah

2017-01-01

Assessment of the impact of varied forms of participatory research is enhanced by specific attention to the ripples, such work initiates in the social context. Ripples are defined as consequences either unintended or unanticipated by those carrying out the participatory research. Following a brief documentation of the range of reported ripples in…

Impact of cognitive stimulation on ripples within human epileptic and non-epileptic hippocampus.

PubMed

Brázdil, Milan; Cimbálník, Jan; Roman, Robert; Shaw, Daniel J; Stead, Matt M; Daniel, Pavel; Jurák, Pavel; Halámek, Josef

2015-07-25

Until now there has been no way of distinguishing between physiological and epileptic hippocampal ripples in intracranial recordings. In the present study we addressed this by investigating the effect of cognitive stimulation on interictal high frequency oscillations in the ripple range (80-250 Hz) within epileptic (EH) and non-epileptic hippocampus (NH). We analyzed depth EEG recordings in 10 patients with intractable epilepsy, in whom hippocampal activity was recorded initially during quiet wakefulness and subsequently during a simple cognitive task. Using automated detection of ripples based on amplitude of the power envelope, we analyzed ripple rate (RR) in the cognitive and resting period, within EH and NH. Compared to quiet wakefulness we observed a significant reduction of RR during cognitive stimulation in EH, while it remained statistically marginal in NH. Further, we investigated the direct impact of cognitive stimuli on ripples (i.e. immediately post-stimulus), which showed a transient statistically significant suppression of ripples in the first second after stimuli onset in NH only. Our results point to a differential reactivity of ripples within EH and NH to cognitive stimulation.

Facile characterization of ripple domains on exfoliated graphene.

PubMed

Choi, Jin Sik; Kim, Jin-Soo; Byun, Ik-Su; Lee, Duk Hyun; Hwang, In Rok; Park, Bae Ho; Choi, Taekjib; Park, Jeong Young; Salmeron, Miquel

2012-07-01

Ripples in graphene monolayers deposited on SiO(2)/Si wafer substrates were recently shown to give rise to friction anisotropy. High friction appears when the AFM tip slides in a direction perpendicular to the ripple crests and low friction when parallel. The direction of the ripple crest is, however, hard to determine as it is not visible in topographic images and requires elaborate measurements of friction as a function of angle. Here we report a simple method to characterize ripple crests by measuring the cantilever torsion signal while scanning in the non-conventional longitudinal direction (i.e., along the cantilever axis, as opposed to the usual friction measurement). The longitudinal torsion signal provides a much clearer ripple domain contrast than the conventional friction signal, while both signals show respective rotation angle dependences that can be explained using the torsion component of the normal reaction force exerted by the graphene ripples. We can also determine the ripple direction by comparing the contrast in torsion images obtained in longitudinal and lateral scans without sample rotation or complicated normalization.

Strategy of restraining ripple error on surface for optical fabrication.

PubMed

Wang, Tan; Cheng, Haobo; Feng, Yunpeng; Tam, Honyuen

2014-09-10

The influence from the ripple error to the high imaging quality is effectively reduced by restraining the ripple height. A method based on the process parameters and the surface error distribution is designed to suppress the ripple height in this paper. The generating mechanism of the ripple error is analyzed by polishing theory with uniform removal character. The relation between the processing parameters (removal functions, pitch of path, and dwell time) and the ripple error is discussed through simulations. With these, the strategy for diminishing the error is presented. A final process is designed and demonstrated on K9 work-pieces using the optimizing strategy with magnetorheological jet polishing. The form error on the surface is decreased from 0.216λ PV (λ=632.8  nm) and 0.039λ RMS to 0.03λ PV and 0.004λ RMS. And the ripple error is restrained well at the same time, because the ripple height is less than 6 nm on the final surface. Results indicate that these strategies are suitable for high-precision optical manufacturing.

Structure of the ripple phase in lecithin bilayers.

PubMed Central

Sun, W J; Tristram-Nagle, S; Suter, R M; Nagle, J F

1996-01-01

The phases of the x-ray form factors are derived for the ripple (Pbeta') thermodynamic phase in the lecithin bilayer system. By combining these phases with experimental intensity data, the electron density map of the ripple phase of dimyristoyl-phosphatidylcholine is constructed. The phases are derived by fitting the intensity data to two-dimensional electron density models, which are created by convolving an asymmetric triangular ripple profile with a transbilayer electron density profile. The robustness of the model method is indicated by the result that many different models of the transbilayer profile yield essentially the same phases, except for the weaker, purely ripple (0,k) peaks. Even with this residual ambiguity, the ripple profile is well determined, resulting in 19 angstroms for the ripple amplitude and 10 degrees and 26 degrees for the slopes of the major and the minor sides, respectively. Estimates for the bilayer head-head spacings show that the major side of the ripple is consistent with gel-like structure, and the minor side appears to be thinner with lower electron density. Images Fig. 1 Fig. 2 PMID:8692934

Two-dimensional converging-diverging rippled nozzles at transonic speeds. [performed in the Langley 16-Foot Transonic Tunnel

NASA Technical Reports Server (NTRS)

Carlson, John R.; Asbury, Scott C.

1994-01-01

An experimental investigation was performed in the Langley 16-Foot Transonic tunnel to determine the effects of external and internal flap rippling on the aerodynamics of a nonaxisymmetric nozzle. Data were obtained at several Mach numbers from static conditions to 1.2 over a range of nozzle pressure ratios. Nozzles with chordal boattail angles of 10, 20, and 30 degrees, with and without surface rippling, were tested. No effect on discharge coefficient due to surface rippling was observed. Internal thrust losses due to surface rippling were measured and attributed to a combination of additional internal skin friction and shock losses. External nozzle drag for the baseline configurations were generally less than that for the rippled configurations at all free-stream Mach numbers tested. The difference between the baseline and rippled nozzle drag levels generally increased with increasing boat tail angle. The thrust-minus-drag level for each rippled nozzle configuration was less than the equivalent baseline configuration for each Mach number at the design nozzle pressure ratio.

Assessing the inherent uncertainty of one-dimensional diffusions

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Cohen, Morrel H.

2013-01-01

In this paper we assess the inherent uncertainty of one-dimensional diffusion processes via a stochasticity classification which provides an à la Mandelbrot categorization into five states of uncertainty: infra-mild, mild, borderline, wild, and ultra-wild. Two settings are considered. (i) Stopped diffusions: the diffusion initiates from a high level and is stopped once it first reaches a low level; in this setting we analyze the inherent uncertainty of the diffusion's maximal exceedance above its initial high level. (ii) Stationary diffusions: the diffusion is in dynamical statistical equilibrium; in this setting we analyze the inherent uncertainty of the diffusion's equilibrium level. In both settings general closed-form analytic results are established, and their application is exemplified by stock prices in the stopped-diffusions setting, and by interest rates in the stationary-diffusions setting. These results provide a highly implementable decision-making tool for the classification of uncertainty in the context of one-dimensional diffusions.

Ripple-triggered stimulation of the locus coeruleus during post-learning sleep disrupts ripple/spindle coupling and impairs memory consolidation.

PubMed

Novitskaya, Yulia; Sara, Susan J; Logothetis, Nikos K; Eschenko, Oxana

2016-05-01

Experience-induced replay of neuronal ensembles occurs during hippocampal high-frequency oscillations, or ripples. Post-learning increase in ripple rate is predictive of memory recall, while ripple disruption impairs learning. Ripples may thus present a fundamental component of a neurophysiological mechanism of memory consolidation. In addition to system-level local and cross-regional interactions, a consolidation mechanism involves stabilization of memory representations at the synaptic level. Synaptic plasticity within experience-activated neuronal networks is facilitated by noradrenaline release from the axon terminals of the locus coeruleus (LC). Here, to better understand interactions between the system and synaptic mechanisms underlying "off-line" consolidation, we examined the effects of ripple-associated LC activation on hippocampal and cortical activity and on spatial memory. Rats were trained on a radial maze; after each daily learning session neural activity was monitored for 1 h via implanted electrode arrays. Immediately following "on-line" detection of ripple, a brief train of electrical pulses (0.05 mA) was applied to LC. Low-frequency (20 Hz) stimulation had no effect on spatial learning, while higher-frequency (100 Hz) trains transiently blocked generation of ripple-associated cortical spindles and caused a reference memory deficit. Suppression of synchronous ripple/spindle events appears to interfere with hippocampal-cortical communication, thereby reducing the efficiency of "off-line" memory consolidation. © 2016 Novitskaya et al.; Published by Cold Spring Harbor Laboratory Press.

Two different mechanisms associated with ripple-like oscillations (100-250 Hz) in the human epileptic subiculum in vitro

PubMed Central

Alvarado-Rojas, C; Huberfeld, G; Baulac, M; Clemenceau, S; Charpier, S; Miles, R; Menendez de la Prida, L; Le Van Quyen, M

2015-01-01

Transient high-frequency oscillations (150-600 Hz) in local field potential generated by human hippocampal and parahippocampal areas have been related to both physiological and pathological processes. The cellular basis and effects of normal and abnormal forms of high-frequency oscillations (HFO) has been controversial. Here, we searched for HFOs in slices of the subiculum prepared from human hippocampal tissue resected for treatment of pharmacoresistant epilepsy. HFOs occurred spontaneously in extracellular field potentials during interictal discharges (IID) and also during pharmacologically induced preictal discharges (PID) preceding ictal-like events. While most of these events might be considered pathological since they invaded the fast ripple band (>250 Hz), others were spectrally similar to physiological ripples (150-250 Hz). Do similar cellular mechanisms underly IID-ripples and PID-ripples? Are ripple-like oscillations a valid proxy of epileptogenesis in human TLE? With combined intra- or juxta-cellular and extracellular recordings, we showed that, despite overlapping spectral components, ripple-like IID and PID oscillations were associated with different cellular and synaptic mechanisms. IID-ripples were associated with rhythmic GABAergic and glutamatergic synaptic potentials with moderate neuronal firing. In contrast, PID-ripples were associated with depolarizing synaptic inputs frequently reaching the threshold for bursting in most cells. Thus ripple-like oscillations (100-250 Hz) in the human epileptic hippocampus are associated with different mechanisms for synchrony reflecting distinct dynamic changes in inhibition and excitation during interictal and pre-ictal states. PMID:25448920

Evaluation of Mandarin Chinese Speech Recognition in Adults with Cochlear Implants Using the Spectral Ripple Discrimination Test

PubMed Central

Dai, Chuanfu; Zhao, Zeqi; Zhang, Duo; Lei, Guanxiong

2018-01-01

Background The aim of this study was to explore the value of the spectral ripple discrimination test in speech recognition evaluation among a deaf (post-lingual) Mandarin-speaking population in China following cochlear implantation. Material/Methods The study included 23 Mandarin-speaking adult subjects with normal hearing (normal-hearing group) and 17 deaf adults who were former Mandarin-speakers, with cochlear implants (cochlear implantation group). The normal-hearing subjects were divided into men (n=10) and women (n=13). The spectral ripple discrimination thresholds between the groups were compared. The correlation between spectral ripple discrimination thresholds and Mandarin speech recognition rates in the cochlear implantation group were studied. Results Spectral ripple discrimination thresholds did not correlate with age (r=−0.19; p=0.22), and there was no significant difference in spectral ripple discrimination thresholds between the male and female groups (p=0.654). Spectral ripple discrimination thresholds of deaf adults with cochlear implants were significantly correlated with monosyllabic recognition rates (r=0.84; p=0.000). Conclusions In a Mandarin Chinese speaking population, spectral ripple discrimination thresholds of normal-hearing individuals were unaffected by both gender and age. Spectral ripple discrimination thresholds were correlated with Mandarin monosyllabic recognition rates of Mandarin-speaking in post-lingual deaf adults with cochlear implants. The spectral ripple discrimination test is a promising method for speech recognition evaluation in adults following cochlear implantation in China. PMID:29806954

Evaluation of Mandarin Chinese Speech Recognition in Adults with Cochlear Implants Using the Spectral Ripple Discrimination Test.

PubMed

Dai, Chuanfu; Zhao, Zeqi; Shen, Weidong; Zhang, Duo; Lei, Guanxiong; Qiao, Yuehua; Yang, Shiming

2018-05-28

BACKGROUND The aim of this study was to explore the value of the spectral ripple discrimination test in speech recognition evaluation among a deaf (post-lingual) Mandarin-speaking population in China following cochlear implantation. MATERIAL AND METHODS The study included 23 Mandarin-speaking adult subjects with normal hearing (normal-hearing group) and 17 deaf adults who were former Mandarin-speakers, with cochlear implants (cochlear implantation group). The normal-hearing subjects were divided into men (n=10) and women (n=13). The spectral ripple discrimination thresholds between the groups were compared. The correlation between spectral ripple discrimination thresholds and Mandarin speech recognition rates in the cochlear implantation group were studied. RESULTS Spectral ripple discrimination thresholds did not correlate with age (r=-0.19; p=0.22), and there was no significant difference in spectral ripple discrimination thresholds between the male and female groups (p=0.654). Spectral ripple discrimination thresholds of deaf adults with cochlear implants were significantly correlated with monosyllabic recognition rates (r=0.84; p=0.000). CONCLUSIONS In a Mandarin Chinese speaking population, spectral ripple discrimination thresholds of normal-hearing individuals were unaffected by both gender and age. Spectral ripple discrimination thresholds were correlated with Mandarin monosyllabic recognition rates of Mandarin-speaking in post-lingual deaf adults with cochlear implants. The spectral ripple discrimination test is a promising method for speech recognition evaluation in adults following cochlear implantation in China.

URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries.

PubMed

Drawert, Brian; Engblom, Stefan; Hellander, Andreas

2012-06-22

Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at an early stage of development. In this paper we demonstrate, in a series of examples with high relevance to the molecular systems biology community, that the proposed software framework is a useful tool for both practitioners and developers of spatial stochastic simulation algorithms. Through the combined efforts of algorithm development and improved modeling accuracy, increasingly complex biological models become feasible to study through computational methods. URDME is freely available at http://www.urdme.org.

Tests of oceanic stochastic parameterisation in a seasonal forecast system.

NASA Astrophysics Data System (ADS)

Cooper, Fenwick; Andrejczuk, Miroslaw; Juricke, Stephan; Zanna, Laure; Palmer, Tim

2015-04-01

Over seasonal time scales, our aim is to compare the relative impact of ocean initial condition and model uncertainty, upon the ocean forecast skill and reliability. Over seasonal timescales we compare four oceanic stochastic parameterisation schemes applied in a 1x1 degree ocean model (NEMO) with a fully coupled T159 atmosphere (ECMWF IFS). The relative impacts upon the ocean of the resulting eddy induced activity, wind forcing and typical initial condition perturbations are quantified. Following the historical success of stochastic parameterisation in the atmosphere, two of the parameterisations tested were multiplicitave in nature: A stochastic variation of the Gent-McWilliams scheme and a stochastic diffusion scheme. We also consider a surface flux parameterisation (similar to that introduced by Williams, 2012), and stochastic perturbation of the equation of state (similar to that introduced by Brankart, 2013). The amplitude of the stochastic term in the Williams (2012) scheme was set to the physically reasonable amplitude considered in that paper. The amplitude of the stochastic term in each of the other schemes was increased to the limits of model stability. As expected, variability was increased. Up to 1 month after initialisation, ensemble spread induced by stochastic parameterisation is greater than that induced by the atmosphere, whilst being smaller than the initial condition perturbations currently used at ECMWF. After 1 month, the wind forcing becomes the dominant source of model ocean variability, even at depth.

Utilization of independent component analysis for accurate pathological ripple detection in intracranial EEG recordings recorded extra- and intra-operatively.

PubMed

Shimamoto, Shoichi; Waldman, Zachary J; Orosz, Iren; Song, Inkyung; Bragin, Anatol; Fried, Itzhak; Engel, Jerome; Staba, Richard; Sharan, Ashwini; Wu, Chengyuan; Sperling, Michael R; Weiss, Shennan A

2018-01-01

To develop and validate a detector that identifies ripple (80-200 Hz) events in intracranial EEG (iEEG) recordings in a referential montage and utilizes independent component analysis (ICA) to eliminate or reduce high-frequency artifact contamination. Also, investigate the correspondence of detected ripples and the seizure onset zone (SOZ). iEEG recordings from 16 patients were first band-pass filtered (80-600 Hz) and Infomax ICA was next applied to derive the first independent component (IC1). IC1 was subsequently pruned, and an artifact index was derived to reduce the identification of high-frequency events introduced by the reference electrode signal. A Hilbert detector identified ripple events in the processed iEEG recordings using amplitude and duration criteria. The identified ripple events were further classified and characterized as true or false ripple on spikes, or ripples on oscillations by utilizing a topographical analysis to their time-frequency plot, and confirmed by visual inspection. The signal to noise ratio was improved by pruning IC1. The precision of the detector for ripple events was 91.27 ± 4.3%, and the sensitivity of the detector was 79.4 ± 3.0% (N = 16 patients, 5842 ripple events). The sensitivity and precision of the detector was equivalent in iEEG recordings obtained during sleep or intra-operatively. Across all the patients, true ripple on spike rates and also the rates of false ripple on spikes, that were generated due to filter ringing, classified the seizure onset zone (SOZ) with an area under the receiver operating curve (AUROC) of >76%. The magnitude and spectral content of true ripple on spikes generated in the SOZ was distinct as compared with the ripples generated in the NSOZ (p < .001). Utilizing ICA to analyze iEEG recordings in referential montage provides many benefits to the study of high-frequency oscillations. The ripple rates and properties defined using this approach may accurately delineate the seizure onset zone. Strategies to improve the spatial resolution of intracranial EEG and reduce artifact can help improve the clinical utility of HFO biomarkers. Copyright © 2017 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved.

On generic obstructions to recovering correct statistics from climate simulations: Homogenization for deterministic maps and multiplicative noise

NASA Astrophysics Data System (ADS)

Gottwald, Georg; Melbourne, Ian

2013-04-01

Whereas diffusion limits of stochastic multi-scale systems have a long and successful history, the case of constructing stochastic parametrizations of chaotic deterministic systems has been much less studied. We present rigorous results of convergence of a chaotic slow-fast system to a stochastic differential equation with multiplicative noise. Furthermore we present rigorous results for chaotic slow-fast maps, occurring as numerical discretizations of continuous time systems. This raises the issue of how to interpret certain stochastic integrals; surprisingly the resulting integrals of the stochastic limit system are generically neither of Stratonovich nor of Ito type in the case of maps. It is shown that the limit system of a numerical discretisation is different to the associated continuous time system. This has important consequences when interpreting the statistics of long time simulations of multi-scale systems - they may be very different to the one of the original continuous time system which we set out to study.

Stochastic approach and fluctuation theorem for charge transport in diodes

NASA Astrophysics Data System (ADS)

Gu, Jiayin; Gaspard, Pierre

2018-05-01

A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction stochastic partial differential equations and the electric field generated by the charges is determined with the Poisson equation. These equations are discretized in space for the numerical simulations of the mean density profiles, the mean electric potential, and the current-voltage characteristics. Moreover, the full counting statistics of the carrier current and the measured total current including the contribution of the displacement current are investigated. On the basis of local detailed balance, the fluctuation theorem is shown to hold for both currents.

Fabrication of rippled surfaces for diffraction gratings by plastic deformation of platinum foils and metallic glasses

NASA Astrophysics Data System (ADS)

Korsukov, V. E.; Malygin, G. A.; Korsukova, M. M.; Nyapshaev, I. A.; Obidov, B. A.

2015-12-01

Thin platinum foils and metallic glass ribbons with a fractal surface consisting of different-scale unidirectionally oriented ripples have been fabricated using special thermoplastic processing. The general fractal dimension of the rippled surface and dimensions along and across the ripples have been measured. The optical spectra of a PRK-4 lamp using rippled Pt(111) foils as reflective diffraction gratings have been determined. A model describing the mechanism of the formation of surface unidirectional fractal structures during deformation has been proposed.

Fabrication of large-scale ripples on fluorine-doped tin oxide films by femtosecond laser irradiation

NASA Astrophysics Data System (ADS)

Han, Yan-Hua; Li, Yan; Zhao, Xiu-Li; Qu, Shi-Liang

2014-09-01

The large-scale uniform self-organized ripples are fabricated on fluorine-doped tin oxide (FTO) coated glass by femtosecond laser. They can be smoothly linked in a horizontal line with the moving of XYZ stage by setting its velocity and the repetition rate of the laser. The ripple-to-ripple linking can also be realized through line-by-line scanning on a vertical level. The mechanism analysis shows that the seeding effect plays a key role in the linking of ripples.

Economic value analysis of the return from the Korean astronaut program and the science culture diffusion activity in Korea

NASA Astrophysics Data System (ADS)

Yi, Soyeon; Jang, Hyun-Jin; Lee, Hyo Suk; Yu, Jong-Phil; Kim, Soyeon; Lee, Joohee; Hur, Hee-Young

2013-06-01

In this study, we analyze the economic effects from the Korean Astronaut Program (KAP) and the subsequent Science Culture Diffusion Activity (SCDA). Korea has had a huge practical effect on the development of science and technology and has increased international awareness of Korea by producing Korea's first astronaut. There has also been a large, ripple effect on space related industries. In addition, the KAP has exercised a far-reaching influence on Korean society and culture by boosting all science and engineering and inspiring national pride. After the KAP, astronauts' outreach activities, such as lectures for the general public; interviews on television, newspapers and magazines; participating in children's science camps; and distributing publications and DVDs about astronaut program for general public, were instituted for diffusing science culture. Thus, positive effects such as the promotion of Korea's level of technology, student interest in science and engineering fields, and the expansion of the industrial base were reinforced after the KAP. This study is aimed at evaluating the economic significance and the value of return through analyzing the effects of the KAP and the subsequent Science Culture Diffusion Activity.

On the source of stochastic volatility: Evidence from CAC40 index options during the subprime crisis

NASA Astrophysics Data System (ADS)

Slim, Skander

2016-12-01

This paper investigates the performance of time-changed Lévy processes with distinct sources of return volatility variation for modeling cross-sectional option prices on the CAC40 index during the subprime crisis. Specifically, we propose a multi-factor stochastic volatility model: one factor captures the diffusion component dynamics and two factors capture positive and negative jump variations. In-sample and out-of-sample tests show that our full-fledged model significantly outperforms nested lower-dimensional specifications. We find that all three sources of return volatility variation, with different persistence, are needed to properly account for market pricing dynamics across moneyness, maturity and volatility level. Besides, the model estimation reveals negative risk premium for both diffusive volatility and downward jump intensity whereas a positive risk premium is found to be attributed to upward jump intensity.

Disentangling Random Motion and Flow in a Complex Medium

PubMed Central

Koslover, Elena F.; Chan, Caleb K.; Theriot, Julie A.

2016-01-01

We describe a technique for deconvolving the stochastic motion of particles from large-scale fluid flow in a dynamic environment such as that found in living cells. The method leverages the separation of timescales to subtract out the persistent component of motion from single-particle trajectories. The mean-squared displacement of the resulting trajectories is rescaled so as to enable robust extraction of the diffusion coefficient and subdiffusive scaling exponent of the stochastic motion. We demonstrate the applicability of the method for characterizing both diffusive and fractional Brownian motion overlaid by flow and analytically calculate the accuracy of the method in different parameter regimes. This technique is employed to analyze the motion of lysosomes in motile neutrophil-like cells, showing that the cytoplasm of these cells behaves as a viscous fluid at the timescales examined. PMID:26840734

Bistability: Requirements on Cell-Volume, Protein Diffusion, and Thermodynamics

PubMed Central

Endres, Robert G.

2015-01-01

Bistability is considered wide-spread among bacteria and eukaryotic cells, useful e.g. for enzyme induction, bet hedging, and epigenetic switching. However, this phenomenon has mostly been described with deterministic dynamic or well-mixed stochastic models. Here, we map known biological bistable systems onto the well-characterized biochemical Schlögl model, using analytical calculations and stochastic spatiotemporal simulations. In addition to network architecture and strong thermodynamic driving away from equilibrium, we show that bistability requires fine-tuning towards small cell volumes (or compartments) and fast protein diffusion (well mixing). Bistability is thus fragile and hence may be restricted to small bacteria and eukaryotic nuclei, with switching triggered by volume changes during the cell cycle. For large volumes, single cells generally loose their ability for bistable switching and instead undergo a first-order phase transition. PMID:25874711

MMS observations and hybrid simulations of rippled and reforming quasi-parallel shocks

NASA Astrophysics Data System (ADS)

Gingell, I.; Schwartz, S. J.; Burgess, D.; Johlander, A.; Russell, C. T.; Burch, J. L.; Ergun, R.; Fuselier, S. A.; Gershman, D. J.; Giles, B. L.; Goodrich, K.; Khotyaintsev, Y. V.; Lavraud, B.; Lindqvist, P. A.; Strangeway, R. J.; Trattner, K. J.; Torbert, R. B.; Wilder, F. D.

2017-12-01

Surface ripples, i.e. deviations in the nominal local shock orientation, are expected to propagate in the ramp and overshoot of collisionless shocks. These ripples have typically been associated with observations and simulations of quasi-perpendicular shocks. We present observations of a crossing of Earth's marginally quasi-parallel (θBn ˜ 45°) bow shock by the MMS spacecraft on 2015-11-27 06:01:44 UTC, for which we identify signatures consistent with a propagating surface ripple. In order to demonstrate the differences between ripples at quasi-perpendicular and quasi-parallel shocks, we also present two-dimensional hybrid simulations over a range of shock normal angles θBn under the observed solar wind conditions. We show that in the quasi-parallel cases surface ripples are transient phenomena modulated by the cyclic reformation of the shock front. These ripples develop faster than an ion gyroperiod and only during the period of the reformation cycle when a newly developed shock ramp is unaffected by turbulence in the foot. We conclude that the change of properties of the surface ripple observed by MMS while crossing Earth's quasi-parallel bow shock are consistent with the influence of cyclic reformation on shock structure. Given that both surface ripples and cyclic reformation are expected to affect the acceleration of electrons within the shock, the interaction of these phenomena and any other sources of shock non-stationary are important for models of particle acceleration. We therefore discuss signatures of electron heating and acceleration in several rippled shocks observed by MMS.

Reynolds Number Effect on Spatial Development of Viscous Flow Induced by Wave Propagation Over Bed Ripples

NASA Astrophysics Data System (ADS)

Dimas, Athanassios A.; Kolokythas, Gerasimos A.

Numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and appropriate bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme is used where central finite-differences, in the horizontal direction, and a pseudo-spectral approximation method with Chebyshev polynomials, in the vertical direction, are applied. A fractional time-step scheme is used for the temporal discretization. Over the rippled bed, the wave boundary layer thickness increases significantly, in comparison to the one over flat bed, due to flow separation at the ripple crests, which generates alternating circulation regions. The amplitude of the wall shear stress over the ripples increases with increasing ripple height or decreasing Reynolds number, while the corresponding friction force is insensitive to the ripple height change. The amplitude of the form drag forces due to dynamic and hydrostatic pressures increase with increasing ripple height but is insensitive to the Reynolds number change, therefore, the percentage of friction in the total drag force decreases with increasing ripple height or increasing Reynolds number.

Higher-order paraxial theory of the propagation of ring rippled laser beam in plasma: Relativistic ponderomotive regime

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

Purohit, Gunjan, E-mail: gunjan75@gmail.com; Rawat, Priyanka; Chauhan, Prashant

This article presents higher-order paraxial theory (non-paraxial theory) for the ring ripple formation on an intense Gaussian laser beam and its propagation in plasma, taking into account the relativistic-ponderomotive nonlinearity. The intensity dependent dielectric constant of the plasma has been determined for the main laser beam and ring ripple superimposed on the main laser beam. The dielectric constant of the plasma is modified due to the contribution of the electric field vector of ring ripple. Nonlinear differential equations have been formulated to examine the growth of ring ripple in plasma, self focusing of main laser beam, and ring rippled lasermore » beam in plasma using higher-order paraxial theory. These equations have been solved numerically for different laser intensities and plasma frequencies. The well established experimental laser and plasma parameters are used in numerical calculation. It is observed that the focusing of the laser beams (main and ring rippled) becomes fast in the nonparaxial region by expanding the eikonal and other relevant quantities up to the fourth power of r. The splitted profile of laser beam in the plasma is observed due to uneven focusing/defocusing of the axial and off-axial rays. The growths of ring ripple increase when the laser beam intensity increases. Furthermore, the intensity profile of ring rippled laser beam gets modified due to the contribution of growth rate.« less

Intelligent measurement and compensation of linear motor force ripple: a projection-based learning approach in the presence of noise

NASA Astrophysics Data System (ADS)

Liu, Yang; Song, Fazhi; Yang, Xiaofeng; Dong, Yue; Tan, Jiubin

2018-06-01

Due to their structural simplicity, linear motors are increasingly receiving attention for use in high velocity and high precision applications. The force ripple, as a space-periodic disturbance, however, would deteriorate the achievable dynamic performance. Conventional force ripple measurement approaches are time-consuming and have high requirements on the experimental conditions. In this paper, a novel learning identification algorithm is proposed for force ripple intelligent measurement and compensation. Existing identification schemes always use all the error signals to update the parameters in the force ripple. However, the error induced by noise is non-effective for force ripple identification, and even deteriorates the identification process. In this paper only the most pertinent information in the error signal is utilized for force ripple identification. Firstly, the effective error signals caused by the reference trajectory and the force ripple are extracted by projecting the overall error signals onto a subspace spanned by the physical model of the linear motor as well as the sinusoidal model of the force ripple. The time delay in the linear motor is compensated in the basis functions. Then, a data-driven approach is proposed to design the learning gain. It balances the trade-off between convergence speed and robustness against noise. Simulation and experimental results validate the proposed method and confirm its effectiveness and superiority.

Asynchronous ripple oscillations between left and right hippocampi during slow-wave sleep.

PubMed

Villalobos, Claudio; Maldonado, Pedro E; Valdés, José L

2017-01-01

Spatial memory, among many other brain processes, shows hemispheric lateralization. Most of the published evidence suggests that the right hippocampus plays a leading role in the manipulation of spatial information. Concurrently in the hippocampus, memory consolidation during sleep periods is one of the key steps in the formation of newly acquired spatial memory traces. One of the most characteristic oscillatory patterns in the hippocampus are sharp-wave ripple (SWR) complexes. Within this complex, fast-field oscillations or ripples have been demonstrated to be instrumental in the memory consolidation process. Since these ripples are relevant for the consolidation of memory traces associated with spatial navigation, and this process appears to be lateralized, we hypothesize that ripple events between both hippocampi would exhibit different temporal dynamics. We tested this idea by using a modified "split-hyperdrive" that allows us to record simultaneous LFPs from both right and left hippocampi of Sprague-Dawley rats during sleep. We detected individual events and found that during sleep periods these ripples exhibited a different occurrence patterns between hemispheres. Most ripple events were synchronous between intra- rather than inter-hemispherical recordings, suggesting that ripples in the hippocampus are independently generated and locally propagated within a specific hemisphere. In this study, we propose the ripples' lack of synchrony between left and right hippocampi as the putative physiological mechanism underlying lateralization of spatial memory.

Brain state-dependent recruitment of high-frequency oscillations in the human hippocampus.

PubMed

Billeke, Pablo; Ossandon, Tomas; Stockle, Marcelo; Perrone-Bertolotti, Marcela; Kahane, Philippe; Lachaux, Jean-Philippe; Fuentealba, Pablo

2017-09-01

Ripples are high-frequency bouts of coordinated hippocampal activity believed to be crucial for information transfer and memory formation. We used intracortical macroelectrodes to record neural activity in the human hippocampus of awake subjects undergoing surgical treatment for refractory epilepsy and distinguished two populations of ripple episodes based on their frequency spectrum. The phase-coupling of one population, slow ripples (90-110 Hz), to cortical delta oscillations was differentially modulated by cognitive task; whereas the second population, fast ripples (130-170 Hz), was not seemingly correlated to local neural activity. Furthermore, as cognitive tasks changed, the ongoing coordination of neural activity associated to slow ripples progressively augmented along the parahippocampal axis. Thus, during resting states, slow ripples were coordinated in restricted hippocampal territories; whereas during active states, such as attentionally-demanding tasks, high frequency activity emerged across the hippocampus and parahippocampal cortex, that was synchronized with slow ripples, consistent with ripples supporting information transfer and coupling anatomically distant regions. Hence, our results provide further evidence of neural diversity in hippocampal high-frequency oscillations and their association to cognitive processing in humans. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mechanisms for Selective Single-Cell Reactivation during Offline Sharp-Wave Ripples and Their Distortion by Fast Ripples.

PubMed

Valero, Manuel; Averkin, Robert G; Fernandez-Lamo, Ivan; Aguilar, Juan; Lopez-Pigozzi, Diego; Brotons-Mas, Jorge R; Cid, Elena; Tamas, Gabor; Menendez de la Prida, Liset

2017-06-21

Memory traces are reactivated selectively during sharp-wave ripples. The mechanisms of selective reactivation, and how degraded reactivation affects memory, are poorly understood. We evaluated hippocampal single-cell activity during physiological and pathological sharp-wave ripples using juxtacellular and intracellular recordings in normal and epileptic rats with different memory abilities. CA1 pyramidal cells participate selectively during physiological events but fired together during epileptic fast ripples. We found that firing selectivity was dominated by an event- and cell-specific synaptic drive, modulated in single cells by changes in the excitatory/inhibitory ratio measured intracellularly. This mechanism collapses during pathological fast ripples to exacerbate and randomize neuronal firing. Acute administration of a use- and cell-type-dependent sodium channel blocker reduced neuronal collapse and randomness and improved recall in epileptic rats. We propose that cell-specific synaptic inputs govern firing selectivity of CA1 pyramidal cells during sharp-wave ripples. Copyright © 2017 Elsevier Inc. All rights reserved.

Parvalbumin-positive interneurons mediate neocortical-hippocampal interactions that are necessary for memory consolidation

PubMed Central

Xia, Frances; Richards, Blake A; Tran, Matthew M; Josselyn, Sheena A

2017-01-01

Following learning, increased coupling between spindle oscillations in the medial prefrontal cortex (mPFC) and ripple oscillations in the hippocampus is thought to underlie memory consolidation. However, whether learning-induced increases in ripple-spindle coupling are necessary for successful memory consolidation has not been tested directly. In order to decouple ripple-spindle oscillations, here we chemogenetically inhibited parvalbumin-positive (PV+) interneurons, since their activity is important for regulating the timing of spiking activity during oscillations. We found that contextual fear conditioning increased ripple-spindle coupling in mice. However, inhibition of PV+ cells in either CA1 or mPFC eliminated this learning-induced increase in ripple-spindle coupling without affecting ripple or spindle incidence. Consistent with the hypothesized importance of ripple-spindle coupling in memory consolidation, post-training inhibition of PV+ cells disrupted contextual fear memory consolidation. These results indicate that successful memory consolidation requires coherent hippocampal-neocortical communication mediated by PV+ cells. PMID:28960176

Brownian aggregation rate of colloid particles with several active sites

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

Nekrasov, Vyacheslav M.; Yurkin, Maxim A.; Chernyshev, Andrei V., E-mail: chern@ns.kinetics.nsc.ru

2014-08-14

We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called “patchy particles”) are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shownmore » to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.« less

First-Passage-Time Distribution for Variable-Diffusion Processes

NASA Astrophysics Data System (ADS)

Barney, Liberty; Gunaratne, Gemunu H.

2017-05-01

First-passage-time distribution, which presents the likelihood of a stock reaching a pre-specified price at a given time, is useful in establishing the value of financial instruments and in designing trading strategies. First-passage-time distribution for Wiener processes has a single peak, while that for stocks exhibits a notable second peak within a trading day. This feature has only been discussed sporadically—often dismissed as due to insufficient/incorrect data or circumvented by conversion to tick time—and to the best of our knowledge has not been explained in terms of the underlying stochastic process. It was shown previously that intra-day variations in the market can be modeled by a stochastic process containing two variable-diffusion processes (Hua et al. in, Physica A 419:221-233, 2015). We show here that the first-passage-time distribution of this two-stage variable-diffusion model does exhibit a behavior similar to the empirical observation. In addition, we find that an extended model incorporating overnight price fluctuations exhibits intra- and inter-day behavior similar to those of empirical first-passage-time distributions.

A robust nonparametric framework for reconstruction of stochastic differential equation models

NASA Astrophysics Data System (ADS)

Rajabzadeh, Yalda; Rezaie, Amir Hossein; Amindavar, Hamidreza

2016-05-01

In this paper, we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series. The proposed method significantly improves the accuracy of the parameter estimation. In this framework, drift and diffusion coefficients are modeled through orthogonal Legendre polynomials. We employ the least squares regression approach along with the Euler-Maruyama approximation method to learn coefficients of stochastic model. Next, a numerical discrete construction of mean squared prediction error (MSPE) is established to calculate the order of Legendre polynomials in drift and diffusion terms. We show numerically that the new method is robust against the variation in sample size and sampling rate. The performance of our method in comparison with the kernel-based regression (KBR) method is demonstrated through simulation and real data. In case of real dataset, we test our method for discriminating healthy electroencephalogram (EEG) signals from epilepsy ones. We also demonstrate the efficiency of the method through prediction in the financial data. In both simulation and real data, our algorithm outperforms the KBR method.

Filter distortion effects on telemetry signal-to-noise ratio

NASA Technical Reports Server (NTRS)

Sadr, R.; Hurd, W.

1987-01-01

The effect of filtering on the Signal-to-Noise Ratio (SNR) of a coherently demodulated band-limited signal is determined in the presence of worse-case amplitude ripple. The problem is formulated mathematically as an optimization problem in the L2-Hilbert space. The form of the worst-cast amplitude ripple is specified, and the degradation in the SNR is derived in a closed form expression. It is shown that when the maximum passband amplitude ripple is 2 delta (peak to peak), the SNR is degraded by at most (1 - delta squared), even when the ripple is unknown or uncompensated. For example, an SNR loss of less than 0.01 dB due to amplitude ripple can be assured by keeping the amplitude ripple to under 0.42 dB.

Anisotropic Ripple Deformation in Phosphorene.

PubMed

Kou, Liangzhi; Ma, Yandong; Smith, Sean C; Chen, Changfeng

2015-05-07

Two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.

Particle acceleration at shocks with surface ripples

NASA Technical Reports Server (NTRS)

Decker, R. B.

1990-01-01

The present treatment of superthermal-ion acceleration on the surface of a fast-mode hydromagnetic shock gives attention to (1) small-amplitude surface ripples characterized by width L and amplitude A that are large relative to the energetic-ion gyroradius, and (2) shocks which are on average quasi-perpendicular. An investigation is made of the effects of the confinement, evolving geometry, and finite shock curvature associated with the ripple, by integrating along the orbits of the proton test particles. As an upstream magnetic field line convects through the surface ripple, it intersects the shock at two points, thereby forming a temporary magnetic trap. Flux-line profiles and angular distributions in a given ripple differ substantially, depending on the path it takes through the ripple and its distance from the shock.

Molecular finite-size effects in stochastic models of equilibrium chemical systems.

PubMed

Cianci, Claudia; Smith, Stephen; Grima, Ramon

2016-02-28

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

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

Chevalier, Michael W., E-mail: Michael.Chevalier@ucsf.edu; El-Samad, Hana, E-mail: Hana.El-Samad@ucsf.edu

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation timesmore » of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.« less

Variable-free exploration of stochastic models: a gene regulatory network example.

PubMed

Erban, Radek; Frewen, Thomas A; Wang, Xiao; Elston, Timothy C; Coifman, Ronald; Nadler, Boaz; Kevrekidis, Ioannis G

2007-04-21

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [R. Erban et al., J. Chem. Phys. 124, 084106 (2006)] the authors assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e., effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [R. Coifman et al., Proc. Natl. Acad. Sci. U.S.A. 102, 7426 (2005)] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free, coarse-grained computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.

Hybrid stochastic and deterministic simulations of calcium blips.

PubMed

Rüdiger, S; Shuai, J W; Huisinga, W; Nagaiah, C; Warnecke, G; Parker, I; Falcke, M

2007-09-15

Intracellular calcium release is a prime example for the role of stochastic effects in cellular systems. Recent models consist of deterministic reaction-diffusion equations coupled to stochastic transitions of calcium channels. The resulting dynamics is of multiple time and spatial scales, which complicates far-reaching computer simulations. In this article, we introduce a novel hybrid scheme that is especially tailored to accurately trace events with essential stochastic variations, while deterministic concentration variables are efficiently and accurately traced at the same time. We use finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. We describe the algorithmic approach and we demonstrate its efficiency compared to conventional methods. Our single-channel model matches experimental data and results in intriguing dynamics if calcium is used as charge carrier. Random openings of the channel accumulate in bursts of calcium blips that may be central for the understanding of cellular calcium dynamics.

MOLNs: A CLOUD PLATFORM FOR INTERACTIVE, REPRODUCIBLE, AND SCALABLE SPATIAL STOCHASTIC COMPUTATIONAL EXPERIMENTS IN SYSTEMS BIOLOGY USING PyURDME.

PubMed

Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas

2016-01-01

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments.

Rich stochastic dynamics of co-doped Er:Yb fluorescence upconversion nanoparticles in the presence of thermal, non-conservative, harmonic and optical forces

NASA Astrophysics Data System (ADS)

Nome, Rene A.; Sorbello, Cecilia; Jobbágy, Matías; Barja, Beatriz C.; Sanches, Vitor; Cruz, Joyce S.; Aguiar, Vinicius F.

2017-03-01

The stochastic dynamics of individual co-doped Er:Yb upconversion nanoparticles (UCNP) were investigated from experiments and simulations. The UCNP were characterized by high-resolution scanning electron microscopy, dynamic light scattering, and zeta potential measurements. Single UCNP measurements were performed by fluorescence upconversion micro-spectroscopy and optical trapping. The mean-square displacement (MSD) from single UCNP exhibited a time-dependent diffusion coefficient which was compared with Brownian dynamics simulations of a viscoelastic model of harmonically bound spheres. Experimental time-dependent two-dimensional trajectories of individual UCNP revealed correlated two-dimensional nanoparticle motion. The measurements were compared with stochastic trajectories calculated in the presence of a non-conservative rotational force field. Overall, the complex interplay of UCNP adhesion, thermal fluctuations and optical forces led to a rich stochastic behavior of these nanoparticles.

Parameters estimation using the first passage times method in a jump-diffusion model

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

Khaldi, K., E-mail: kkhaldi@umbb.dz; LIMOSE Laboratory, Boumerdes University, 35000; Meddahi, S., E-mail: samia.meddahi@gmail.com

2016-06-02

The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time (FPT method) generalized for all passage times (GPT method), in order to estimate the parameters of stochastic Jump-Diffusion process. (2) it compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the GPT method and those obtained by the moments method and the FPT method applied to the Merton Jump-Diffusion (MJD) model.

Minimization of torque ripple in ferrite-assisted synchronous reluctance motors by using asymmetric stator

NASA Astrophysics Data System (ADS)

Xu, Meimei; Liu, Guohai; Zhao, Wenxiang; Aamir, Nazir

2018-05-01

Torque ripple is one of the important issues for ferrite assisted synchronous reluctance motors (FASRMs). In this paper, an asymmetrical stator is proposed for the FASRM to reduce its torque ripple. In the proposed FASRM, an asymmetrical stator is designed by appropriately choosing the angle of the slot-opening shift. Meanwhile, its analytical torque expressions are derived. The results show that the proposed FASRM has an effective reduction in the cogging torque, reluctance torque ripple and total torque ripple. Moreover, it is easy to implement while the average torque is not sacrificed.

Influence of Magnetic Field Ripple on the Intrinsic Rotation of Tokamak Plasmas

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

Nave, M. F. F.; Johnson, T.; Eriksson, L.-G.

Using the unique capability of JET to monotonically change the amplitude of the magnetic field ripple, without modifying other relevant equilibrium conditions, the effect of the ripple on the angular rotation frequency of the plasma column was investigated under the conditions of no external momentum input. The ripple amplitude was varied from 0.08% to 1.5% in Ohmic and ion-cyclotron radio-frequency (ICRF) heated plasmas. In both cases the ripple causes counterrotation, indicating a strong torque due to nonambipolar transport of thermal ions and in the case of ICRF also fast ions.

The development of a modified spectral ripple test.

PubMed

Aronoff, Justin M; Landsberger, David M

2013-08-01

Poor spectral resolution can be a limiting factor for hearing impaired listeners, particularly for complex listening tasks such as speech understanding in noise. Spectral ripple tests are commonly used to measure spectral resolution, but these tests contain a number of potential confounds that can make interpretation of the results difficult. To measure spectral resolution while avoiding those confounds, a modified spectral ripple test with dynamically changing ripples was created, referred to as the spectral-temporally modulated ripple test (SMRT). This paper describes the SMRT and provides evidence that it is sensitive to changes in spectral resolution.

Diffusion in the special theory of relativity.

PubMed

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

Spiral diffusion of rotating self-propellers with stochastic perturbation

NASA Astrophysics Data System (ADS)

Nourhani, Amir; Ebbens, Stephen J.; Gibbs, John G.; Lammert, Paul E.

2016-09-01

Translationally diffusive behavior arising from the combination of orientational diffusion and powered motion at microscopic scales is a known phenomenon, but the peculiarities of the evolution of expected position conditioned on initial position and orientation have been neglected. A theory is given of the spiral motion of the mean trajectory depending upon propulsion speed, angular velocity, orientational diffusion, and rate of random chirality reversal. We demonstrate the experimental accessibility of this effect using both tadpole-like and Janus sphere dimer rotating motors. Sensitivity of the mean trajectory to the kinematic parameters suggest that it may be a useful way to determine those parameters.

Discrimination of rippled-spectrum patterns in noise: A manifestation of compressive nonlinearity

PubMed Central

Milekhina, Olga N.; Nechaev, Dmitry I.; Klishin, Vladimir O.

2017-01-01

In normal-hearing listeners, rippled-spectrum discrimination was psychophysically investigated in both silence and with a simultaneous masker background using the following two paradigms: measuring the ripple density resolution with the phase-reversal test and measuring the ripple-shift threshold with the ripple-shift test. The 0.5-oct wide signal was centered on 2 kHz, the signal levels were 50 and 80 dB SPL, and the masker levels varied from 30 to 100 dB SPL. The baseline ripple density resolutions were 8.7 oct-1 and 8.6 oct-1 for the 50-dB and 80-dB signals, respectively. The baseline ripple shift thresholds were 0.015 oct and 0.018 oct for the 50-dB and 80-dB signals, respectively. The maskers were 0.5-oct noises centered on 2 kHz (on-frequency) or 0.75 to 1.25 oct below the signal (off-frequency maskers). The effects of the maskers were as follows: (i) both on- and low-frequency maskers reduced the ripple density resolution and increased the ripple shift thresholds, (ii) the masker levels at threshold (the ripple density resolution decrease down to 3 oct–1 or ripple shift threshold increased up to 0.1 oct) increased with increasing frequency spacing between the signal and masker, (iii) the masker levels at threshold were higher for the 80-dB signal than for the 50-dB signal, and (iv) the difference between the masker levels at threshold for the 50-dB and 80-dB signals decreased with increasing frequency spacing between the masker and signal. Within the 30-dB (from 50 to 80 dB SPL) signal level, the growth of the masker level at threshold was 27.8 dB for the on-frequency masker and 9 dB for the low-frequency masker. It is assumed that the difference between the on- and low-frequency masking of the rippled-spectrum discrimination reflects the cochlear compressive non-linearity. With this assumption, the compression was 0.3 dB/dB. PMID:28346538

Intrinsic trapping of stochastic sheared magnetic field lines

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

Negrea, M.; Petrisor, I.; Balescu, R.

2004-10-01

The decorrelation trajectory method is applied to the diffusion of magnetic field lines in a perturbed sheared slab magnetic configuration. Some interesting decorrelation trajectories for several values of the magnetic Kubo number and of the shear parameter are exhibited. The asymmetry of the decorrelation trajectories appears in comparison with those obtained in the purely electrostatic case studied in earlier work. The running and asymptotic diffusion tensor components are calculated and displayed.

The secular evolution of discrete quasi-Keplerian systems. II. Application to a multi-mass axisymmetric disc around a supermassive black hole

NASA Astrophysics Data System (ADS)

Fouvry, J.-B.; Pichon, C.; Chavanis, P.-H.

2018-01-01

A discrete self-gravitating quasi-Keplerian razor-thin axisymmetric stellar disc orbiting a massive black hole sees its orbital structure diffuse on secular timescales as a result of a self-induced resonant relaxation. In the absence of collective effects, such a process is described by the recently derived inhomogeneous multi-mass degenerate Landau equation. Relying on Gauss' method, we computed the associated drift and diffusion coefficients to characterise the properties of the resonant relaxation of razor-thin discs. For a disc-like configuration in our Galactic centre, we showed how this secular diffusion induces an adiabatic distortion of orbits and estimate the typical timescale of resonant relaxation. When considering a disc composed of multiple masses similarly distributed, we have illustrated how the population of lighter stars will gain eccentricity, driving it closer to the central black hole, provided the distribution function increases with angular momentum. The kinetic equation recovers as well the quenching of the resonant diffusion of a test star in the vicinity of the black hole (the "Schwarzschild barrier") as a result of the divergence of the relativistic precessions. The dual stochastic Langevin formulation yields consistent results and offers a versatile framework in which to incorporate other stochastic processes.

Use of forecasting signatures to help distinguish periodicity, randomness, and chaos in ripples and other spatial patterns

USGS Publications Warehouse

Rubin, D.M.

1992-01-01

Forecasting of one-dimensional time series previously has been used to help distinguish periodicity, chaos, and noise. This paper presents two-dimensional generalizations for making such distinctions for spatial patterns. The techniques are evaluated using synthetic spatial patterns and then are applied to a natural example: ripples formed in sand by blowing wind. Tests with the synthetic patterns demonstrate that the forecasting techniques can be applied to two-dimensional spatial patterns, with the same utility and limitations as when applied to one-dimensional time series. One limitation is that some combinations of periodicity and randomness exhibit forecasting signatures that mimic those of chaos. For example, sine waves distorted with correlated phase noise have forecasting errors that increase with forecasting distance, errors that, are minimized using nonlinear models at moderate embedding dimensions, and forecasting properties that differ significantly between the original and surrogates. Ripples formed in sand by flowing air or water typically vary in geometry from one to another, even when formed in a flow that is uniform on a large scale; each ripple modifies the local flow or sand-transport field, thereby influencing the geometry of the next ripple downcurrent. Spatial forecasting was used to evaluate the hypothesis that such a deterministic process - rather than randomness or quasiperiodicity - is responsible for the variation between successive ripples. This hypothesis is supported by a forecasting error that increases with forecasting distance, a greater accuracy of nonlinear relative to linear models, and significant differences between forecasts made with the original ripples and those made with surrogate patterns. Forecasting signatures cannot be used to distinguish ripple geometry from sine waves with correlated phase noise, but this kind of structure can be ruled out by two geometric properties of the ripples: Successive ripples are highly correlated in wavelength, and ripple crests display dislocations such as branchings and mergers. ?? 1992 American Institute of Physics.

Wave-induced ripple development in mixed clay-sand substrates

NASA Astrophysics Data System (ADS)

Wu, Xuxu; Parsons, Daniel; Baas, Jaco H.; Mouazé, Dominique; McLelland, Stuart; Amoudry, Laurent; Eggenhuisen, Jorris; Cartigny, Matthieu; Ruessink, Gerben

2016-04-01

This paper reports on a series of experiments that aim to provide a fuller understanding of ripple development within clay-sand mixture substrates under oscillatory flow conditions. The work was conducted in the Total Environment Simulator at the University of Hull and constituted 6 separate runs, in which 5 runs were conducted under identical sets of regular waves (an additional run was conducted under irregular waves, but is not discussed in present paper). The bed content was systematically varied in its composition ranging from a pure sand bed through to a bed comprising 7.4% clay. A series of state-of-the-art measurements were employed to quantify interactions of near-bed hydrodynamics, sediment transport, and turbulence over rippled beds formed by wave action, during and after, each run. The experimental results demonstrate the significant influence of the amount of cohesive clay materials in the substrate on ripple evolution under waves. Most importantly, addition of clay in the bed dramatically slowed down the rate of ripple development and evolution. The equilibrium time of each run increased exponentially from 30 minutes under the control conditions of a pure sand bed, rising to ~350 minutes for the bed with the highest fraction of clay. The paper discusses the slower ripple growth rates with higher cohesive fractions, via an influence on critical shear, but highlights that the end equilibrium size of ripples is found to be independent of increasing substrate clay fraction. The suspended particles mass (SPM) concentration indicates that clay particles were suspended and winnowed by wave action. Additionally, laser granulometry of the final substrates verified that ripple crests were composed of pure sand layers that were absent at ripple troughs, reflecting a relatively higher winnowing efficiency at wave ripples crest. The winnowing process and its efficiency is inexorably linked to wave ripple development and evolution. The implications of the results for sediment dynamics in mixed-bed substrates are highlighted and discussed.

Nanostructures on fused silica surfaces produced by ion beam sputtering with Al co-deposition

NASA Astrophysics Data System (ADS)

Liu, Ying; Hirsch, Dietmar; Fechner, Renate; Hong, Yilin; Fu, Shaojun; Frost, Frank; Rauschenbach, Bernd

2018-01-01

The ion beam sputtering (IBS) of smooth mono-elemental Si with impurity co-deposition is extended to a pre-rippled binary compound surface of fused silica (SiO2). The dependence of the rms roughness and the deposited amount of Al on the distance from the Al source under Ar+ IBS with Al co-deposition was investigated on smooth SiO2, pre-rippled SiO2, and smooth Si surfaces, using atomic force microscopy and X-ray photoelectron spectroscopy. Although the amounts of Al deposited on these three surfaces all decreased with increasing distance from the Al target, the morphology and rms roughness of the smooth Si surface did not demonstrate a strong distance dependence. In contrast to smooth Si, the rms roughness of both the smooth and pre-rippled SiO2 surfaces exhibited a similar distance evolution trend of increasing, decreasing, and final stabilization at the distance where the results were similar to those obtained without Al co-deposition. However, the pre-rippled SiO2 surfaces showed a stronger modulation of rms roughness than the smooth surfaces. At the incidence angles of 60° and 70°, dot-decorated ripples and roof-tiles were formed on the smooth SiO2 surfaces, respectively, whereas nanostructures of closely aligned grains and blazed facets were generated on the pre-rippled SiO2, respectively. The combination of impurity co-deposition with pre-rippled surfaces was found to facilitate the formation of novel types of nanostructures and morphological growth. The initial ripples act as a template to guide the preferential deposition of Al on the tops of the ripples or the ripple sides facing the Al wedge, but not in the valleys between the ripples, leading to 2D grains and quasi-blazed grating, which offer significant promise in optical applications. The rms roughness enhancement is attributed not to AlSi, but to AlOxFy compounds originating mainly from the Al source.

Large Ripples on Earth and Mars

NASA Technical Reports Server (NTRS)

Williams, S. H.; Zimbelman, J. R.; Ward, A. W.

2002-01-01

Aeolian ripples on Earth with wavelengths greater than 50 cm have distinctive attributes, that should be helpful in interpreting ripple-like features on Mars. Additional information is contained in the original extended abstract.

Martian Dune Ripples as Indicators of Recent Surface Wind Patterns

NASA Astrophysics Data System (ADS)

Johnson, M.; Zimbelman, J. R.

2015-12-01

Sand dunes have been shown to preserve the most recent wind patterns in their ripple formations. This investigation continues the manual documentation of ripples on Martian dunes in order to assess surface wind flow. Study sites investigated must have clear HiRISE frames and be able to represent diverse locations across the surface, decided primarily by their spread of latitude and longitude values. Additionally, frames with stereo pairs are preferred because of their ability to create digital terrain models. This will assist in efforts to relate dune slopes and obstacles to ripple patterns. The search and analysis period resulted in 40 study sites with mapped ripples. Lines were drawn perpendicular to ripple crests across three adjacent ripples in order to document both ripple wavelength from line length and inferred wind direction from azimuth. It is not possible to infer a unique wind direction from ripple orientation alone and therefore these inferred directions have a 180 degree ambiguity. Initial results from all study sites support previous observations that the Martian surface has many dune types in areas with adequate sand supply. The complexity of ripple patterns varies greatly across sites as well as within individual sites. Some areas of uniform directionality for hundreds of kilometers suggest a unimodal wind regime while overlapping patterns suggest multiple dominant winds or seasonally varying winds. In most areas, form flow related to dune shape seems to have a large effect on orientation and must be considered along with the dune type. As long as the few steep slip faces on these small dunes are avoided, form flow can be considered the dominant cause of deviation from the regional wind direction. Regional results, wind roses, and comparisons to previous work will be presented for individual sites.

Correction to verdonck and tuerlinckx (2014).

PubMed

2015-01-01

Reports an error in "The Ising Decision Maker: A binary stochastic network for choice response time" by Stijn Verdonck and Francis Tuerlinckx (Psychological Review, 2014[Jul], Vol 121[3], 422-462). An inaccurate assumption in Appendix B (provided in the erratum) led to an oversimplified result in Equation 18 (the diffusion equations associated with the microscopically defined dynamics). The authors sincerely thank Rani Moran for making them aware of the problem. Only the expression of the diffusion coefficient D is incorrect, and should be changed, as indicated in the erratum. Both the cause of the problem and the solution are also explained in the erratum. (The following abstract of the original article appeared in record 2014-31650-006.) The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

A statistical mechanics approach to computing rare transitions in multi-stable turbulent geophysical flows

NASA Astrophysics Data System (ADS)

Laurie, J.; Bouchet, F.

2012-04-01

Many turbulent flows undergo sporadic random transitions, after long periods of apparent statistical stationarity. For instance, paths of the Kuroshio [1], the Earth's magnetic field reversal, atmospheric flows [2], MHD experiments [3], 2D turbulence experiments [4,5], 3D flows [6] show this kind of behavior. The understanding of this phenomena is extremely difficult due to the complexity, the large number of degrees of freedom, and the non-equilibrium nature of these turbulent flows. It is however a key issue for many geophysical problems. A straightforward study of these transitions, through a direct numerical simulation of the governing equations, is nearly always impracticable. This is mainly a complexity problem, due to the large number of degrees of freedom involved for genuine turbulent flows, and the extremely long time between two transitions. In this talk, we consider two-dimensional and geostrophic turbulent models, with stochastic forces. We consider regimes where two or more attractors coexist. As an alternative to direct numerical simulation, we propose a non-equilibrium statistical mechanics approach to the computation of this phenomenon. Our strategy is based on large deviation theory [7], derived from a path integral representation of the stochastic process. Among the trajectories connecting two non-equilibrium attractors, we determine the most probable one. Moreover, we also determine the transition rates, and in which cases this most probable trajectory is a typical one. Interestingly, we prove that in the class of models we consider, a mechanism exists for diffusion over sets of connected attractors. For the type of stochastic forces that allows this diffusion, the transition between attractors is not a rare event. It is then very difficult to characterize the flow as bistable. However for another class of stochastic forces, this diffusion mechanism is prevented, and genuine bistability or multi-stability is observed. We discuss how these results are probably connected to the long debated existence of multi-stability in the atmosphere and oceans.

Large wind ripples on Mars: A record of atmospheric evolution

NASA Astrophysics Data System (ADS)

Lapotre, M. G. A.; Ewing, R. C.; Lamb, M. P.; Fischer, W. W.; Grotzinger, J. P.; Rubin, D. M.; Lewis, K. W.; Ballard, M. J.; Day, M.; Gupta, S.; Banham, S. G.; Bridges, N. T.; Des Marais, D. J.; Fraeman, A. A.; Grant, J. A.; Herkenhoff, K. E.; Ming, D. W.; Mischna, M. A.; Rice, M. S.; Sumner, D. A.; Vasavada, A. R.; Yingst, R. A.

2016-07-01

Wind blowing over sand on Earth produces decimeter-wavelength ripples and hundred-meter- to kilometer-wavelength dunes: bedforms of two distinct size modes. Observations from the Mars Science Laboratory Curiosity rover and the Mars Reconnaissance Orbiter reveal that Mars hosts a third stable wind-driven bedform, with meter-scale wavelengths. These bedforms are spatially uniform in size and typically have asymmetric profiles with angle-of-repose lee slopes and sinuous crest lines, making them unlike terrestrial wind ripples. Rather, these structures resemble fluid-drag ripples, which on Earth include water-worked current ripples, but on Mars instead form by wind because of the higher kinematic viscosity of the low-density atmosphere. A reevaluation of the wind-deposited strata in the Burns formation (about 3.7 billion years old or younger) identifies potential wind-drag ripple stratification formed under a thin atmosphere.

Influence of group-delay ripple on timing jitter induced by SPM and IXPM in systems with dispersion compensated by CFBG

NASA Astrophysics Data System (ADS)

Qin, Xi; Cao, Jihong; Chen, Yong; Zhang, Feng; Jian, Shuisheng

2007-08-01

An analytical expression was proposed to analyze the influence of group-delay ripple (GDR) on timing jitter induced by self-phase modulation (SPM) and intra-channel cross-phase modulation (IXPM) in pseudo-linear transmission systems when dispersion was compensated by chirped fiber Bragg grating (CFBG). Effects of ripple amplitude, period, and phase on timing jitter were discussed by theoretical and numerical analysis in detail. The results show that the influence of GDR on timing jitter changes linearly with the amplitude of GDR and whether it decreases or increases the timing jitter relies on the ripple period and ripple phase. Timing jitter induced by SPM and IXPM could be suppressed totally by adjusting the relative phase between the center frequency of the pulse and the ripples.

The properties and causes of rippling in quasi-perpendicular collisionless shock fronts

NASA Astrophysics Data System (ADS)

Lowe, R. E.; Burgess, D.

2003-03-01

The overall structure of quasi-perpendicular, high Mach number collisionless shocks is controlled to a large extent by ion reflection at the shock ramp. Departure from a strictly one-dimensional structure is indicated by simulation results showing that the surface of such shocks is rippled, with variations in the density and all field components. We present a detailed analysis of these shock ripples, using results from a two-dimensional hybrid (particle ions, electron fluid) simulation. The process that generates the ripples is poorly understood, because the large gradients at the shock ramp make it difficult to identify instabilities. Our analysis reveals new features of the shock ripples, which suggest the presence of a surface wave mode dominating the shock normal magnetic field component of the ripples, as well as whistler waves excited by reflected ions.

Mechanics of wind ripple stratigraphy.

PubMed

Forrest, S B; Haff, P K

1992-03-06

Stratigraphic patterns preserved under translating surface undulations or ripples in a depositional eolian environment are computed on a grain by grain basis using physically based cellular automata models. The spontaneous appearance, growth, and motion of the simulated ripples correspond in many respects to the behavior of natural ripples. The simulations show that climbing strata can be produced by impact alone; direct action of fluid shear is unnecessary. The model provides a means for evaluating the connection between mechanical processes occurring in the paleoenvironment during deposition and the resulting stratigraphy preserved in the geologic column: vertical compression of small laminae above a planar surface indicates nascent ripple growth; supercritical laminae are associated with unusually intense deposition episodes; and a plane erosion surface separating sets of well-developed laminae is consistent with continued migration of mature ripples during a hiatus in deposition.

Large wind ripples on Mars: A record of atmospheric evolution

USGS Publications Warehouse

Lapotre, M G; Ewing, R C; Lamb, M P; Fischer, W W; Grotzinger, J P; Rubin, D M; Lewis, K W; Ballard, M; Day, Mitch D.; Gupta, S.; Banham, S G; Bridges, N T; Des Marais, D J; Fraeman, A A; Grant, J A; Herkenhoff, Kenneth E.; Ming, D W; Mischna, M A; Rice, M S; Sumner, D A; Vasavada, A R; Yingst, R A

2016-01-01

Wind blowing over sand on Earth produces decimeter-wavelength ripples and hundred-meter– to kilometer-wavelength dunes: bedforms of two distinct size modes. Observations from the Mars Science Laboratory Curiosity rover and the Mars Reconnaissance Orbiter reveal that Mars hosts a third stable wind-driven bedform, with meter-scale wavelengths. These bedforms are spatially uniform in size and typically have asymmetric profiles with angle-of-repose lee slopes and sinuous crest lines, making them unlike terrestrial wind ripples. Rather, these structures resemble fluid-drag ripples, which on Earth include water-worked current ripples, but on Mars instead form by wind because of the higher kinematic viscosity of the low-density atmosphere. A reevaluation of the wind-deposited strata in the Burns formation (about 3.7 billion years old or younger) identifies potential wind-drag ripple stratification formed under a thin atmosphere.

Anisotropic ripple deformation in phosphorene

DOE PAGES

Kou, Liangzhi; Ma, Yandong; Smith, Sean C.; ...

2015-04-07

Here, two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS 2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classicalmore » elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.« less

Anisotropic ripple deformation in phosphorene

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

Kou, Liangzhi; Ma, Yandong; Smith, Sean C.

Here, two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS 2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classicalmore » elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.« less

Temperature-Controlled High-Speed AFM: Real-Time Observation of Ripple Phase Transitions.

PubMed

Takahashi, Hirohide; Miyagi, Atsushi; Redondo-Morata, Lorena; Scheuring, Simon

2016-11-01

With nanometer lateral and Angstrom vertical resolution, atomic force microscopy (AFM) has contributed unique data improving the understanding of lipid bilayers. Lipid bilayers are found in several different temperature-dependent states, termed phases; the main phases are solid and fluid phases. The transition temperature between solid and fluid phases is lipid composition specific. Under certain conditions some lipid bilayers adopt a so-called ripple phase, a structure where solid and fluid phase domains alternate with constant periodicity. Because of its narrow regime of existence and heterogeneity ripple phase and its transition dynamics remain poorly understood. Here, a temperature control device to high-speed atomic force microscopy (HS-AFM) to observe dynamics of phase transition from ripple phase to fluid phase reversibly in real time is developed and integrated. Based on HS-AFM imaging, the phase transition processes from ripple phase to fluid phase and from ripple phase to metastable ripple phase to fluid phase could be reversibly, phenomenologically, and quantitatively studied. The results here show phase transition hysteresis in fast cooling and heating processes, while both melting and condensation occur at 24.15 °C in quasi-steady state situation. A second metastable ripple phase with larger periodicity is formed at the ripple phase to fluid phase transition when the buffer contains Ca 2+ . The presented temperature-controlled HS-AFM is a new unique experimental system to observe dynamics of temperature-sensitive processes at the nanoscopic level. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Coarsening of ion-beam-induced surface ripple in Si: Nonlinear effect vs. geometrical shadowing

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

Datta, Debi Prasad; Chini, Tapas Kumar

The temporal evolution of a periodic ripple pattern on a silicon surface undergoing erosion by 30 keV argon ion bombardment has been studied for two angles of ion incidence of 60 deg. and 70 deg. using ex situ atomic force microscopy (AFM) in ambient condition. The roughness amplitude (w) grows exponentially with sputtering time for both the angle of ion incidence followed by a slow growth process that saturates eventually with almost constant amplitude. Within the exponential growth regime of amplitude, however, ripple wavelength (l) remains constant initially and increases subsequently as a power law fashion l{proportional_to}t{sup n}, where n=0.47{+-}0.02more » for a 60 deg. angle of ion incidence followed by a saturation. Wavelength coarsening was also observed for 70 deg. but ordering in the periodic ripple pattern is destroyed quickly for 70 deg. as compared to 60 deg. . The ripple orientation, average ripple wavelength at the initial stage of ripple evolution, and the exponential growth of ripple amplitude can be described by a linear continuum model. While the wavelength coarsening could possibly be explained in the light of recent hydrodynamic model based continuum theory, the subsequent saturation of wavelength and amplitude was attributed to the effect of geometrical shadowing. This is an experimental result that probably gives a hint about the upper limit of the energy of ion beam rippling for applying the recently developed type of nonlinear continuum model.« less

Adaptive two-regime method: Application to front propagation

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

Robinson, Martin, E-mail: martin.robinson@maths.ox.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk; Flegg, Mark, E-mail: mark.flegg@monash.edu

2014-03-28

The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser lattice-based models. The ATRM is a generalization of the previously developed Two-Regime Method [Flegg et al., J. R. Soc., Interface 9, 859 (2012)] to multiscale problems which require a dynamic selection of regions where detailed Brownian dynamics simulation is used. Typical applications include a front propagation or spatio-temporal oscillations. In this paper, the ATRM is used for an in-depth study of front propagation in a stochastic reaction-diffusion system which has its mean-field model given in termsmore » of the Fisher equation [R. Fisher, Ann. Eugen. 7, 355 (1937)]. It exhibits a travelling reaction front which is sensitive to stochastic fluctuations at the leading edge of the wavefront. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on lattice-based models, but there has been limited progress using off-lattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher mean-field model. By modelling only the wavefront itself with the off-lattice model, it is shown that the ATRM leads to the same Fisher wave results as purely off-lattice models, but at a fraction of the computational cost. The error analysis of the ATRM is also presented for a morphogen gradient model.« less

Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles

NASA Astrophysics Data System (ADS)

Katsoulakis, Markos A.; Vlachos, Dionisios G.

2003-11-01

We derive a hierarchy of successively coarse-grained stochastic processes and associated coarse-grained Monte Carlo (CGMC) algorithms directly from the microscopic processes as approximations in larger length scales for the case of diffusion of interacting particles on a lattice. This hierarchy of models spans length scales between microscopic and mesoscopic, satisfies a detailed balance, and gives self-consistent fluctuation mechanisms whose noise is asymptotically identical to the microscopic MC. Rigorous, detailed asymptotics justify and clarify these connections. Gradient continuous time microscopic MC and CGMC simulations are compared under far from equilibrium conditions to illustrate the validity of our theory and delineate the errors obtained by rigorous asymptotics. Information theory estimates are employed for the first time to provide rigorous error estimates between the solutions of microscopic MC and CGMC, describing the loss of information during the coarse-graining process. Simulations under periodic boundary conditions are used to verify the information theory error estimates. It is shown that coarse-graining in space leads also to coarse-graining in time by q2, where q is the level of coarse-graining, and overcomes in part the hydrodynamic slowdown. Operation counting and CGMC simulations demonstrate significant CPU savings in continuous time MC simulations that vary from q3 for short potentials to q4 for long potentials. Finally, connections of the new coarse-grained stochastic processes to stochastic mesoscopic and Cahn-Hilliard-Cook models are made.

Adaptive output-feedback control for switched stochastic uncertain nonlinear systems with time-varying delay.

PubMed

Song, Zhibao; Zhai, Junyong

2018-04-01

This paper addresses the problem of adaptive output-feedback control for a class of switched stochastic time-delay nonlinear systems with uncertain output function, where both the control coefficients and time-varying delay are unknown. The drift and diffusion terms are subject to unknown homogeneous growth condition. By virtue of adding a power integrator technique, an adaptive output-feedback controller is designed to render that the closed-loop system is bounded in probability, and the state of switched stochastic nonlinear system can be globally regulated to the origin almost surely. A numerical example is provided to demonstrate the validity of the proposed control method. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Nearly axisymmetric hot plasmas in a highly rippled tokamak

NASA Astrophysics Data System (ADS)

Bellan, Paul

2002-11-01

Tokamak ohmic heating current flowing along toroidally rippled flux surfaces results in a poloidal torque. Since pressure gradients cannot offset torques, the torque drives plasma flows which convect plasma toroidally from ripple necks (high B_pol^2) to ripple bulges (low B_pol^2). Stagnation of the oppositely directed toroidal flows at the ripple bulges thermalizes the directed flow velocity ˜ B_pol/μ_0ρ , giving β _pol ˜1. These flows also convect frozen-in poloidal field lines which accumulate at the bulges enhancing the pinch force there and so reducing the bulge. Thus, a nearly axisymmetric β_pol ˜1 equilibrium is achieved using only a few TF coils. Particles bouncing in step between approaching flows will be Fermi accelerated to form a high energy tail. The ST tokamak magnetic mountain experiment [1] showed that, compared to a 1.8% ripple configuration, a 28% ripple configuration had four times the neutron production, and only a modest degradation of overall confinement; the former is consistent with the notion of Fermi acceleration of particles bouncing between colliding toroidal flows and the latter is consistent with ripple reduction due to toroidal convection of poloidal field lines. [1] W. Stodiek et al, Proc. 4th Intl. Conf. Plasma Phys. and Contr. Nuc. Fusion Res., (Madison, 1971), Vol. 1, p. 465

Observations of the Space-time Structure of Flow, Vorticity and Stress over Orbital-scale Ripples

NASA Astrophysics Data System (ADS)

Hare, J.; Hay, A. E.; Cheel, R. A.; Zedel, L. J.

2012-12-01

Results are presented from a laboratory investigation of the spatial and temporal structure at turbulence-resolving scales of the flow, vorticity and stress over equilibrium orbital-scale sand ripples. The ripples were created in 0.153 mm median diameter sand, at 10 s period and an excursion of 0.5 m, using the oscillating tray apparatus described in Hay et al. (JGR-Oceans, 2012). Vertical profiles of velocity above the bed were obtained at 40 Hz and 3 mm vertical resolution using a wide-band coherent Doppler profiler (MFDop). Through runs at different positions of the MFDop relative to a particular ripple crest, phase-averaged measures of the flow over a full ripple wavelength were obtained as a function of phase during the forcing cycle. These measurements are used to determine the formation of the lee vortex and the position of the point of reattachment. Estimates of the phase-averaged bottom stress (obtained using the vertical integral of the defect acceleration, the Reynolds stress and the law-of-the-wall) as a function of position along the ripple profile are inter-compared.Phase-averaged horizontal velocity over one ripple where the black line indicates the sediment-water interface. Phase-averaged vertical velocity over one ripple where the black line indicates the sediment-water interface.

Comparing spatial tuning curves, spectral ripple resolution, and speech perception in cochlear implant users.

PubMed

Anderson, Elizabeth S; Nelson, David A; Kreft, Heather; Nelson, Peggy B; Oxenham, Andrew J

2011-07-01

Spectral ripple discrimination thresholds were measured in 15 cochlear-implant users with broadband (350-5600 Hz) and octave-band noise stimuli. The results were compared with spatial tuning curve (STC) bandwidths previously obtained from the same subjects. Spatial tuning curve bandwidths did not correlate significantly with broadband spectral ripple discrimination thresholds but did correlate significantly with ripple discrimination thresholds when the rippled noise was confined to an octave-wide passband, centered on the STC's probe electrode frequency allocation. Ripple discrimination thresholds were also measured for octave-band stimuli in four contiguous octaves, with center frequencies from 500 Hz to 4000 Hz. Substantial variations in thresholds with center frequency were found in individuals, but no general trends of increasing or decreasing resolution from apex to base were observed in the pooled data. Neither ripple nor STC measures correlated consistently with speech measures in noise and quiet in the sample of subjects in this study. Overall, the results suggest that spectral ripple discrimination measures provide a reasonable measure of spectral resolution that correlates well with more direct, but more time-consuming, measures of spectral resolution, but that such measures do not always provide a clear and robust predictor of performance in speech perception tasks. © 2011 Acoustical Society of America

Comparing spatial tuning curves, spectral ripple resolution, and speech perception in cochlear implant users

PubMed Central

Anderson, Elizabeth S.; Nelson, David A.; Kreft, Heather; Nelson, Peggy B.; Oxenham, Andrew J.

2011-01-01

Spectral ripple discrimination thresholds were measured in 15 cochlear-implant users with broadband (350–5600 Hz) and octave-band noise stimuli. The results were compared with spatial tuning curve (STC) bandwidths previously obtained from the same subjects. Spatial tuning curve bandwidths did not correlate significantly with broadband spectral ripple discrimination thresholds but did correlate significantly with ripple discrimination thresholds when the rippled noise was confined to an octave-wide passband, centered on the STC’s probe electrode frequency allocation. Ripple discrimination thresholds were also measured for octave-band stimuli in four contiguous octaves, with center frequencies from 500 Hz to 4000 Hz. Substantial variations in thresholds with center frequency were found in individuals, but no general trends of increasing or decreasing resolution from apex to base were observed in the pooled data. Neither ripple nor STC measures correlated consistently with speech measures in noise and quiet in the sample of subjects in this study. Overall, the results suggest that spectral ripple discrimination measures provide a reasonable measure of spectral resolution that correlates well with more direct, but more time-consuming, measures of spectral resolution, but that such measures do not always provide a clear and robust predictor of performance in speech perception tasks. PMID:21786905

Ripple-aware optical proximity correction fragmentation for back-end-of-line designs

NASA Astrophysics Data System (ADS)

Wang, Jingyu; Wilkinson, William

2018-01-01

Accurate characterization of image rippling is critical in early detection of back-end-of-line (BEOL) patterning weakpoints, as most defects are strongly associated with excessive rippling that does not get effectively compensated by optical proximity correction (OPC). We correlate image contour with design shapes to account for design geometry-dependent rippling signature, and explore the best practice of OPC fragmentation for BEOL geometries. Specifically, we predict the optimum contour as allowed by the lithographic process and illumination conditions and locate ripple peaks, valleys, and inflection points. This allows us to identify potential process weakpoints and segment the mask accordingly to achieve the best correction results.

Controlled ripple texturing of suspended graphene and ultrathin graphite membranes.

PubMed

Bao, Wenzhong; Miao, Feng; Chen, Zhen; Zhang, Hang; Jang, Wanyoung; Dames, Chris; Lau, Chun Ning

2009-09-01

Graphene is nature's thinnest elastic material and displays exceptional mechanical and electronic properties. Ripples are an intrinsic feature of graphene sheets and are expected to strongly influence electronic properties by inducing effective magnetic fields and changing local potentials. The ability to control ripple structure in graphene could allow device design based on local strain and selective bandgap engineering. Here, we report the first direct observation and controlled creation of one- and two-dimensional periodic ripples in suspended graphene sheets, using both spontaneously and thermally generated strains. We are able to control ripple orientation, wavelength and amplitude by controlling boundary conditions and making use of graphene's negative thermal expansion coefficient (TEC), which we measure to be much larger than that of graphite. These results elucidate the ripple formation process, which can be understood in terms of classical thin-film elasticity theory. This should lead to an improved understanding of suspended graphene devices, a controlled engineering of thermal stress in large-scale graphene electronics, and a systematic investigation of the effect of ripples on the electronic properties of graphene.

Directional bottom roughness associated with waves, currents, and ripples

USGS Publications Warehouse

Sherwood, Christopher R.; Rosati, Julie D.; Wang, Ping; Roberts, Tiffany M.

2011-01-01

Roughness lengths are used in wave-current bottom boundary layer models to parameterize drag associated with grain roughness, the effect of saltating grains during sediment transport, and small-scale bottom topography (ripples and biogenic features). We made field measurements of flow parameters and recorded sonar images of ripples at the boundary of a sorted-bedform at ~12-m depth on the inner shelf for a range of wave and current conditions over two months. We compared estimates of apparent bottom roughness inferred from the flow measurements with bottom roughness calculated using ripple geometry and the Madsen (1994) one-dimensional (vertical) wave-current bottom boundary layer model. One result of these comparisons was that the model over predicted roughness of flow from the dormant large ripples when waves were small. We developed a correction to the ripple-roughness model that incorporates an apparent ripple wavelength related to the combined wave-current flow direction. This correction provides a slight improvement for low-wave conditions, but does not address several other differences between observations and the modeled roughness.

Anomalous transport and stochastic processes

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

Balescu, R.

1996-03-01

The relation between kinetic transport theory and theory of stochastic processes is reviewed. The Langevin equation formalism provides important, but rather limited information about diffusive processes. A quite promising new approach to modeling complex situations, such as transport in incompletely destroyed magnetic surfaces, is provided by the theory of Continuous Time Random Walks (CTRW), which is presented in some detail. An academic test problem is discussed in great detail: transport of particles in a fluctuating magnetic field, in the limit of infinite perpendicular correlation length. The well-known subdiffusive behavior of the Mean Square Displacement (MSD), proportional to t{sup 1/2}, ismore » recovered by a CTRW, but the complete density profile is not. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW. 16 refs., 3 figs.« less

Stochastic models for tumoral growth

NASA Astrophysics Data System (ADS)

Escudero, Carlos

2006-02-01

Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border and the surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are reported in this paper in order to correctly model the physical properties of tumoral growth in (1+1) and (2+1) dimensions. The advantage of these models is that they reproduce the correct geometry of the tumor and are defined in terms of polar variables. An analysis of these models allows us to quantitatively estimate the response of the tumor to an unfavorable perturbation during growth.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

PubMed

García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G

2017-08-01

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

Stochastic Analysis of Reaction–Diffusion Processes

PubMed Central

Hu, Jifeng; Kang, Hye-Won

2013-01-01

Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartment size for simulating reaction–diffusion systems and introduce a measure of fluctuations in a discretized system. We then describe a new computational algorithm for implementing a modified Gillespie method for compartmental systems in which reactions are aggregated into equivalence classes and computational cells are searched via an optimized tree structure. Finally, we discuss several examples that illustrate the issues that have to be addressed in general systems. PMID:23719732

Direct imaging of atomic-scale ripples in few-layer graphene.

PubMed

Wang, Wei L; Bhandari, Sagar; Yi, Wei; Bell, David C; Westervelt, Robert; Kaxiras, Efthimios

2012-05-09

Graphene has been touted as the prototypical two-dimensional solid of extraordinary stability and strength. However, its very existence relies on out-of-plane ripples as predicted by theory and confirmed by experiments. Evidence of the intrinsic ripples has been reported in the form of broadened diffraction spots in reciprocal space, in which all spatial information is lost. Here we show direct real-space images of the ripples in a few-layer graphene (FLG) membrane resolved at the atomic scale using monochromated aberration-corrected transmission electron microscopy (TEM). The thickness of FLG amplifies the weak local effects of the ripples, resulting in spatially varying TEM contrast that is unique up to inversion symmetry. We compare the characteristic TEM contrast with simulated images based on accurate first-principles calculations of the scattering potential. Our results characterize the ripples in real space and suggest that such features are likely common in ultrathin materials, even in the nanometer-thickness range.

Angular tuning of the magnetic birefringence in rippled cobalt films

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

Arranz, Miguel A., E-mail: MiguelAngel.Arranz@uclm.es; Colino, José M.

We report the measurement of magnetically induced birefringence in rippled Co films. For this purpose, the magneto-optical properties of ion beam eroded ferromagnetic films were studied using Kerr magnetometry and magnetic birefringence in the transmitted light intensity. Upon sufficient ion sculpting, these ripple surface nanostructures developed a defined uniaxial anisotropy in the in-plane magnetization, finely tuning the magnetic birefringence effect. We have studied its dependence on the relative orientation between the ripple direction and the magnetic field, and found this effect to be dramatically correlated with the capability to neatly distinguish the mechanisms for the in-plane magnetization reversal, i.e., rotationmore » and nucleation. This double refraction corresponds univocally to the two magnetization axes, parallel and perpendicular to the ripples direction. We have also observed that tuned birefringence in stack assemblies of rippled Co films, which enables us to technically manipulate the number and direction of refraction axes.« less

Pyramidal cell-interneuron interactions underlie hippocampal ripple oscillations.

PubMed

Stark, Eran; Roux, Lisa; Eichler, Ronny; Senzai, Yuta; Royer, Sebastien; Buzsáki, György

2014-07-16

High-frequency ripple oscillations, observed most prominently in the hippocampal CA1 pyramidal layer, are associated with memory consolidation. The cellular and network mechanisms underlying the generation, frequency control, and spatial coherence of the rhythm are poorly understood. Using multisite optogenetic manipulations in freely behaving rodents, we found that depolarization of a small group of nearby pyramidal cells was sufficient to induce high-frequency oscillations, whereas closed-loop silencing of pyramidal cells or activation of parvalbumin- (PV) or somatostatin-immunoreactive interneurons aborted spontaneously occurring ripples. Focal pharmacological blockade of GABAA receptors abolished ripples. Localized PV interneuron activation paced ensemble spiking, and simultaneous induction of high-frequency oscillations at multiple locations resulted in a temporally coherent pattern mediated by phase-locked interneuron spiking. These results constrain competing models of ripple generation and indicate that temporally precise local interactions between excitatory and inhibitory neurons support ripple generation in the intact hippocampus. Copyright © 2014 Elsevier Inc. All rights reserved.

Pyramidal Cell-Interneuron Interactions Underlie Hippocampal Ripple Oscillations

PubMed Central

Stark, Eran; Roux, Lisa; Eichler, Ronny; Senzai, Yuta; Royer, Sebastien; Buzsáki, György

2015-01-01

SUMMARY High-frequency ripple oscillations, observed most prominently in the hippocampal CA1 pyramidal layer, are associated with memory consolidation. The cellular and network mechanisms underlying the generation, frequency control, and spatial coherence of the rhythm are poorly understood. Using multisite optogenetic manipulations in freely behaving rodents, we found that depolarization of a small group of nearby pyramidal cells was sufficient to induce high-frequency oscillations, whereas closed-loop silencing of pyramidal cells or activation of parvalbumin-(PV) or somatostatin-immunoreactive interneurons aborted spontaneously occurring ripples. Focal pharmacological blockade of GABAA receptors abolished ripples. Localized PV inter-neuron activation paced ensemble spiking, and simultaneous induction of high-frequency oscillations at multiple locations resulted in a temporally coherent pattern mediated by phase-locked inter-neuron spiking. These results constrain competing models of ripple generation and indicate that temporally precise local interactions between excitatory and inhibitory neurons support ripple generation in the intact hippocampus. PMID:25033186

Ripple/Carcinoid pattern sebaceoma with apocrine differentiation.

PubMed

Misago, Noriyuki; Narisawa, Yutaka

2011-02-01

Sebaceoma is a benign sebaceous neoplasm, which has been reported to show characteristic growth patterns, such as, ripple, labyrinthine/sinusoidal, and carcinoid-like patterns. Another recent finding regarding in sebaceoma is the observation of apocrine differentiation within the sebaceoma lesion. This report describes a case of carcinoid (a partial ripple and labyrinthine) pattern sebaceoma with apocrine differentiation with a literature review and immunohistochemical studies. The various characteristic growth patterns in sebaceoma were suggested to simply be variations of the same growth pattern arranged in cords, namely, a unified term "ripple/carcinoid pattern." The primitive sebaceous germinative cells in sebaceoma may still have the ability to undergo apocrine differentiation. Most of the reports so far on sebaceoma with apocrine differentiation, including the present case, describe a ripple/carcinoid pattern, thus suggesting that ripple/carcinoid pattern sebaceoma is composed of more primitive sebaceous germinative cells than conventional sebaceoma.

Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation.

PubMed

Erban, Radek; Kevrekidis, Ioannis G; Adalsteinsson, David; Elston, Timothy C

2006-02-28

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy Phi and of a state-dependent effective diffusion coefficient D that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.

Correlation between the ripple phase and stripe domains in membranes.

PubMed

Bernchou, Uffe; Midtiby, Henrik; Ipsen, John Hjort; Simonsen, Adam Cohen

2011-12-01

We investigate the relationship between stripe domains and the ripple phase in membranes. These have previously been observed separately without being linked explicitly. Past results have demonstrated that solid and ripple phases exhibit rich textural patterns related to the orientational order of tilted lipids and the orientation of ripple corrugations. Here we reveal a highly complex network pattern of ripple and solid domains in DLPC, DPPC bilayers with structures covering length scales from 10 nm to 100 μm. Using spincoated double supported membranes we investigate domains by correlated AFM and fluorescence microscopy. Cooling experiments demonstrate the mode of nucleation and growth of stripe domains enriched in the fluorescent probe. Concurrent AFM imaging reveals that these stripe domains have a one-to-one correspondence with a rippled morphology running parallel to the stripe direction. Both thin and thick stripe domains are observed having ripple periods of 13.5±0.2 nm and 27.4±0.6 nm respectively. These are equivalent to previously observed asymmetric/equilibrium and symmetric/metastable ripple phases, respectively. Thin stripes grow from small solid domains and grow predominantly in length with a speed of ~3 times that of the thick stripes. Thick stripes grow by templating on the sides of thinner stripes or can emerge directly from the fluid phase. Bending and branching angles of stripes are in accordance with an underlying six fold lattice. We discuss mechanisms for the nucleation and growth of ripples and discuss a generic phase diagram that may partly rationalize the coexistence of metastable and stable phases. Copyright © 2011 Elsevier B.V. All rights reserved.

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

Duncan, Andrew, E-mail: a.duncan@imperial.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk; Zygalakis, Konstantinos, E-mail: k.zygalakis@ed.ac.uk

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when onemore » or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.« less

Microalgal mediation of ripple mobility.

PubMed

Friend, P L; Lucas, C H; Holligan, P M; Collins, M B

2008-01-01

The interaction between physical and biological factors responsible for the cessation of ripple migration on a sandy intertidal flat was examined during a microalgal bloom period in late winter/early spring, as part of a wider study into the biostabilisation of intertidal sediments. Ripple positions and ripple geometry were monitored, and surface sediment was sampled, at weekly intervals over a 5-week period. Ripples remained in the same position for at least 4 weeks, during which time there was a progressive reduction in bedform height (smoothing) and deposition of some 1.5 cm sediment, mainly in the ripple troughs (surface levelling). The mean chlorophyll a (chl a) sediment content was 6.0 microg gDW(-1) (DW: dry weight) (0-1 mm depth fraction), with a maximum value of 7.4 microg gDW(-1) half way through the bloom. Mean colloidal-S carbohydrate (S: saline extraction) content was 131 microg GE gDW(-1) (GE: glucose equivalent) (0-1 mm), with a maximum of 261 microg GE gDW(-1 )towards the end of the bloom. Important accessory pigments were peridinin (indicative of dinophytes) and fucoxanthin (diatoms). Stepwise multiple regression showed that peridinin was the best predictor of chl a. For the first time, in situ evidence for the mediation of (wave) ripple migration by microalgae is provided. Results indicate that diatoms, and quite possibly dinophytes, can have a significant effect on intertidal flat ripple mobility on a temporal scale of weeks. In addition, microalgal effects appear capable of effecting a reduction in bed roughness on a spatial scale of up to 10(-2 )m, with a subsequent reduction in bottom stress and bed erodability. It is suggested that a unique combination of environmental conditions, in conjunction with the microalgal bloom(s), promoted the initial cessation of ripple movement, and that stationary-phase, diatom-derived extracellular polymeric substances (EPS) (and possibly dinophyte-derived EPS) may have prolonged the condition. It is reasonable to suppose that ripple stabilisation by similar processes may have contributed to ripple mark preservation in the geological record. A conceptual model of sandy intertidal flat processes is presented, illustrating two conditions: (i) a low EPS/microalgae sediment content with low ripple stabilisation and preservation potential; and (ii) a high EPS/microalgae content with higher preservation potential.

Fractional Brownian motors and stochastic resonance

NASA Astrophysics Data System (ADS)

Goychuk, Igor; Kharchenko, Vasyl

2012-05-01

We study fluctuating tilt Brownian ratchets based on fractional subdiffusion in sticky viscoelastic media characterized by a power law memory kernel. Unlike the normal diffusion case, the rectification effect vanishes in the adiabatically slow modulation limit and optimizes in a driving frequency range. It is shown also that the anomalous rectification effect is maximal (stochastic resonance effect) at optimal temperature and can be of surprisingly good quality. Moreover, subdiffusive current can flow in the counterintuitive direction upon a change of temperature or driving frequency. The dependence of anomalous transport on load exhibits a remarkably simple universality.

Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck approximation.

PubMed

Riegert, Anja; Baba, Nilüfer; Gelfert, Katrin; Just, Wolfram; Kantz, Holger

2005-02-11

The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.

Python-based geometry preparation and simulation visualization toolkits for STEPS

PubMed Central

Chen, Weiliang; De Schutter, Erik

2014-01-01

STEPS is a stochastic reaction-diffusion simulation engine that implements a spatial extension of Gillespie's Stochastic Simulation Algorithm (SSA) in complex tetrahedral geometries. An extensive Python-based interface is provided to STEPS so that it can interact with the large number of scientific packages in Python. However, a gap existed between the interfaces of these packages and the STEPS user interface, where supporting toolkits could reduce the amount of scripting required for research projects. This paper introduces two new supporting toolkits that support geometry preparation and visualization for STEPS simulations. PMID:24782754

Finite-Dimensional Representations for Controlled Diffusions with Delay

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

Federico, Salvatore, E-mail: salvatore.federico@unimi.it; Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr

2015-02-15

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

Quantum cybernetics: a new perspective for Nelson's stochastic theory, nonlocality, and the Klein-Gordon equation

NASA Astrophysics Data System (ADS)

Grössing, Gerhard

2002-04-01

The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a “particle”, which is both passively affected by, and actively affecting, a diffusion process of its generally nonlocal environment. This indicates circularly causal, or “cybernetic”, relationships between “particles” and their surroundings. Moreover, in the relativistic domain, the original stochastic theory of Nelson is shown to hold as a limiting case only, i.e., for a vanishing quantum potential.

Nonlocal theory of electromagnetic wave decay into two electromagnetic waves in a rippled density plasma channel

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

Sati, Priti; Tripathi, V. K.

Parametric decay of a large amplitude electromagnetic wave into two electromagnetic modes in a rippled density plasma channel is investigated. The channel is taken to possess step density profile besides a density ripple of axial wave vector. The density ripple accounts for the momentum mismatch between the interacting waves and facilitates nonlinear coupling. For a given pump wave frequency, the requisite ripple wave number varies only a little w.r.t. the frequency of the low frequency decay wave. The radial localization of electromagnetic wave reduces the growth rate of the parametric instability. The growth rate decreases with the frequency of lowmore » frequency electromagnetic wave.« less

Prediction of Ripple Properties in Shelf Seas. Mark 2 Predictor for Time Evolution

DTIC Science & Technology

2005-12-01

respectively. It is seen in Figure 15 that the time -evolving ripple predictor manages to predict many of the features seen in the data: the growth from a...UNCLASSIFIED Prediction of Ripple Properties in Shelf Seas Mark 2 Predictor for Time Evolution Final Technical Report Prepared for US Office of Naval...distribution is unlimited j~j HR Wallingford UNCLASSIFIED Prediction of Ripple Properties in Shelf Seas Mark 2 Predictor for Time Evolution

[SPECIFIC DIAGNOSTIC SIGNIFICANCE OF "RIPPLE SIGN" OF MEDIAL FEMORAL CONDYLE UNDER ARTHROSCOPE IN MEDIAL LONGITUDINAL MENISCAL TEARS].

PubMed

Ren Shiyou; Sun, Limang; Chen, Guofei; Jiang, Changqing; Zhang, Xintao; Zhang Wentao

2015-01-01

To investigate the reliability of the "ripple sign" on the upper surface of the medial femoral condyle in the diagnosis of medial longitudinal meniscal tears under arthroscope. Between June 2013 and June 2014, 56 patients with knee injuries were included. There were 35 males and 21 females with an average age of 22.2 years (range, 12-38 years). The causes of injury were sports in 40 cases, falling in 10 cases, and traffic accident in 6 cases. The injury was located at the left knee in 22 cases and at the right knee in 34 cases. The disease duration was 10-40 days (mean, 20.2 days). Of 56 patients, 15 cases had simple medial meniscal injury; 41 cases had combined injuries, including anterior cruciate ligament injury in 38 cases, posterior cruciate ligament injury in 2 cases, and patellar dislocation in 1 case. The "ripple sign" was observed under arthroscope before operation. Repair of medial meniscal injury and reconstruction of cruciate ligament were performed. The positive "ripple sign" was seen under arthroscope in all patients, who were diagnosed to have longitudinal meniscal tears, including 23 cases of mild "ripple sign" , 28 cases of moderate "ripple sign", and 5 cases of severe "ripple sign". The "ripple sign" on the upper surface of the medial femoral condyle is a reliable diagnostic evidence of medial longitudinal meniscal tears.

Asynchronous ripple oscillations between left and right hippocampi during slow-wave sleep

PubMed Central

Villalobos, Claudio

2017-01-01

Spatial memory, among many other brain processes, shows hemispheric lateralization. Most of the published evidence suggests that the right hippocampus plays a leading role in the manipulation of spatial information. Concurrently in the hippocampus, memory consolidation during sleep periods is one of the key steps in the formation of newly acquired spatial memory traces. One of the most characteristic oscillatory patterns in the hippocampus are sharp-wave ripple (SWR) complexes. Within this complex, fast-field oscillations or ripples have been demonstrated to be instrumental in the memory consolidation process. Since these ripples are relevant for the consolidation of memory traces associated with spatial navigation, and this process appears to be lateralized, we hypothesize that ripple events between both hippocampi would exhibit different temporal dynamics. We tested this idea by using a modified "split-hyperdrive" that allows us to record simultaneous LFPs from both right and left hippocampi of Sprague-Dawley rats during sleep. We detected individual events and found that during sleep periods these ripples exhibited a different occurrence patterns between hemispheres. Most ripple events were synchronous between intra- rather than inter-hemispherical recordings, suggesting that ripples in the hippocampus are independently generated and locally propagated within a specific hemisphere. In this study, we propose the ripples’ lack of synchrony between left and right hippocampi as the putative physiological mechanism underlying lateralization of spatial memory. PMID:28158285

Seabed ripple morphology and surficial sediment size at the SAX04 experiments near Fort Walton Beach, Florida, fall 2004

USGS Publications Warehouse

Hanes, Daniel M.; Erikson, Li H.; Lescinski, Jamie M.R.; Harney, Jodi N.; Carter, Carissa L.; Hatcher, Gerry A.; Lacy, Jessica R.; Rubin, David M.

2007-01-01

Data presented in this report originates from measurements obtained off the Florida coast (fig. 1) as part of the Sediment Acoustics Experiment (SAX04) and Ripples Department Research Initiative (DRI) (Office of Naval Research (ONR), Critical Benthic Environmental Processes and Modeling, Long Range BAA 04-001, Sept. 10, 2003). The aim of this document is to present methods employed to extract data and the resulting measured ripple characteristics (ripple height, wavelength, and orientation) and seabed grain sizes. Application and analysis of the data with respect to hydro- and morphodynamics will be addressed in subsequent reports. Sediment transport in the coastal region is a complex process involving interactions between flow dynamics, sediments, and bedforms. Sediment type and bed geometry directly influence entrainment of sediments into suspension, and at sites where ripples occur (sand formations on the order of several cm high and less than two meter long wavelengths), the understanding of ripple dynamics is an essential component in improving sediment transport models. To gain a better understanding and ability to predict sediment transport, a field study was undertaken to investigate morphology, orientation, and dynamics of ripples on the seafloor. The data obtained from the field campaign also supports an on-going effort to study the effects of ripples on low grazing acoustic penetration into sandy marine sediments for the detection of objects, such as mines (Jackson and others, 2002).

PROBABILISTIC CHARACTERIZATION OF ATMOSPHERIC TRANSPORT AND DIFFUSION

EPA Science Inventory

The observed scatter of observations about air quality model predictions stems from a combination of naturally occurring stochastic variations that are impossible for any model to explicitly simulate and variations arising from limitations in our knowledge and from imperfect inpu...

Coordinated Interaction between Hippocampal Sharp-Wave Ripples and Anterior Cingulate Unit Activity

PubMed Central

2016-01-01

Hippocampal–cortical interaction during sleep promotes transformation of memory for long-term storage in the cortex. In particular, hippocampal sharp-wave ripple-associated neural activation is important for this transformation during slow-wave sleep. The anterior cingulate cortex (ACC) has been shown to be crucial for expression and likely storage of long-term memory. However, little is known about how ACC activity is influenced by hippocampal ripple activity during sleep. We report here about coordinated interactions between hippocampal ripple activity and ACC neural firings. By recording from the ACC and hippocampal CA1 simultaneously in mice, we found that almost all ACC neurons showed increased activity before hippocampal ripple activity; moreover, a subpopulation (17%) displayed a further activation immediately after ripple activity. This postripple activation of ACC neurons correlated positively with ripple amplitude, and the same neurons were excited upon electrical stimulation of the CA1. Interestingly, the preripple activation of ACC neurons was present during the sleep state, but not during the awake state. These results suggest intimate interactions between hippocampal sharp-wave ripples and ACC neurons in a state-dependent manner. Importantly, sharp-wave ripples and associated activation appear to regulate activity of a small population of ACC neurons, a process that may play a critical role in memory consolidation. SIGNIFICANCE STATEMENT The hippocampus communicates with the cortex for memory transformation. Memories of previous experiences become less dependent on the hippocampus and increasingly dependent on cortical areas, such as the anterior cingulate cortex (ACC). However, little evidence is available to directly support this hippocampus-to-cortex information transduction hypothesis of memory consolidation. Here we show that a subpopulation of ACC neurons becomes active just after hippocampal ripple activity, and that electrical stimulation of the hippocampus excites the same ACC neurons. In addition, the majority of ACC neurons are activated just before ripple activity during the sleep state, but not during the awake state. These results provide evidence supporting the hypothesis of hippocampus-to-cortex information flow for memory consolidation as well as reciprocal interaction between the hippocampus and the cortex. PMID:27733616

Ripples and Dunes in the Syrtis Major Region of Mars, as Revealed in MOC Images

NASA Technical Reports Server (NTRS)

Zimbelman, J. R.; Wilson, S.

2002-01-01

Six categories of ripple-like aeolian bedforms have been identified in MOC images, and their physical attributes are compared to large ripples on Earth. Additional information is contained in the original extended abstract.

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

NASA Astrophysics Data System (ADS)

Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

2018-02-01

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

Formation and characterization of perpendicular mode Si ripples by glancing angle O{sub 2}{sup +} sputtering at room temperature

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

Mollick, S. A.; Ghose, D.

Off-normal low energy ion beam sputtering of solid surfaces often leads to morphological instabilities resulting in the spontaneous formation of ripple structures in nanometer length scales. In the case of Si surfaces at ambient temperature, ripple formation is found to take place normally at lower incident angles with the wave vector parallel to the ion beam direction. The absence of ripple pattern on Si surface at larger angles is due to the dominance of ion beam polishing effect. We have shown that a gentle chemical roughening of the starting surface morphology can initiate ripple pattern under grazing incidence ion beammore » sputtering (theta>64 deg. with respect to the surface normal), where the ripple wave vector is perpendicular to the ion beam direction. The characteristics of the perpendicular mode ripples are studied as a function of pristine surface roughness (2-30 nm) and projectile fluence (5x10{sup 16}-1.5x10{sup 18} O atoms cm{sup -2}). The quality of the morphological structure is assessed from the analysis of ion induced topological defects.« less

Hippocampal CA1 Ripples as Inhibitory Transients

PubMed Central

Krishnan, Giri P; Fellous, Jean-Marc; Bazhenov, Maxim

2016-01-01

Memories are stored and consolidated as a result of a dialogue between the hippocampus and cortex during sleep. Neurons active during behavior reactivate in both structures during sleep, in conjunction with characteristic brain oscillations that may form the neural substrate of memory consolidation. In the hippocampus, replay occurs within sharp wave-ripples: short bouts of high-frequency activity in area CA1 caused by excitatory activation from area CA3. In this work, we develop a computational model of ripple generation, motivated by in vivo rat data showing that ripples have a broad frequency distribution, exponential inter-arrival times and yet highly non-variable durations. Our study predicts that ripples are not persistent oscillations but result from a transient network behavior, induced by input from CA3, in which the high frequency synchronous firing of perisomatic interneurons does not depend on the time scale of synaptic inhibition. We found that noise-induced loss of synchrony among CA1 interneurons dynamically constrains individual ripple duration. Our study proposes a novel mechanism of hippocampal ripple generation consistent with a broad range of experimental data, and highlights the role of noise in regulating the duration of input-driven oscillatory spiking in an inhibitory network. PMID:27093059

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Rolling Ripple

NASA Technical Reports Server (NTRS)

2006-01-01

NASA's Mars Exploration Rover Opportunity continues to cut southward across a plain marked by large sand ripples and a pavement of outcrop rock. The ripple in the center of the image shows a distinct pattern of banding, which the science team hopes to investigate more closely during the trek through this terrain. The banding and other features have inspired a hypothesis that Meridiani ripples are old features that are currently being eroded, and not transported, by wind. This navigation camera image was taken on Opportunity's sol 795, April 19, 2006.

Scaling results for the magnetic field line trajectories in the stochastic layer near the separatrix in divertor tokamaks with high magnetic shear using the higher shear map

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh; Ali, Halima; Farhat, Hamidullah

2009-07-01

Extra terms are added to the generating function of the simple map (Punjabi et al 1992 Phys. Rev. Lett. 69 3322) to adjust shear of magnetic field lines in divertor tokamaks. From this new generating function, a higher shear map is derived from a canonical transformation. A continuous analog of the higher shear map is also derived. The method of maps (Punjabi et al 1994 J. Plasma Phys. 52 91) is used to calculate the average shear, stochastic broadening of the ideal separatrix near the X-point in the principal plane of the tokamak, loss of poloidal magnetic flux from inside the ideal separatrix, magnetic footprint on the collector plate, and its area, and the radial diffusion coefficient of magnetic field lines near the X-point. It is found that the width of the stochastic layer near the X-point and the loss of poloidal flux from inside the ideal separatrix scale linearly with average shear. The area of magnetic footprints scales roughly linearly with average shear. Linear scaling of the area is quite good when the average shear is greater than or equal to 1.25. When the average shear is in the range 1.1-1.25, the area of the footprint fluctuates (as a function of average shear) and scales faster than linear scaling. Radial diffusion of field lines near the X-point increases very rapidly by about four orders of magnitude as average shear increases from about 1.15 to 1.5. For higher values of average shear, diffusion increases linearly, and comparatively very slowly. The very slow scaling of the radial diffusion of the field can flatten the plasma pressure gradient near the separatrix, and lead to the elimination of type-I edge localized modes.

Phenomenology and energetics of diffusion across cell phase states.

PubMed

Ashrafuzzaman, Md

2015-11-01

Cell based transport properties have been mathematically addressed. Cell contained cross boundary diffusion of materials has been explained using valid formalisms and related analytical expressions have been developed. Various distinguishable physical structures and their properties raise different general structure specific diffusion mechanisms and controlled transport related parameters. Some of these parameters play phenomenological roles and some cause regulatory effects. The cell based compartments may be divided into three major physical phase states namely liquid, plasma and solid phase states. Transport of ions, nutrients, small molecules like proteins, etc. across inter phase states and intraphase states follows general transport related formalisms. Creation of some localized permanent and/or temporary structures e.g., ion channels, clustering of constituents, etc. and the transitions between such structures appear as regulators of the transport mechanisms. In this article, I have developed mainly a theoretical analysis of the commonly observed cell transport phenomena. I have attempted to develop formalisms on general cell based diffusion followed by a few numerical computations to address the analytical expression phenomenologically. I have then extended the analysis to adopting with the local structure originated energetics. Independent or correlated molecular transport naturally relies on some general parameters that define the nature of local cell environment as well as on some occasionally raised or transiently active stochastic resonance due to localized interactions. Short and long range interaction energies play crucial roles in this regard. Physical classification of cellular compartments has led us developing analytical expressions on both biologically observed diffusion mechanisms and the diffusions's occasional stochasticity causing energetics. These analytical expressions help us address the diffusion phenomena generally considering the physical properties of the biostructures across the diffusion pathways. A specific example case of single molecule transport and localized interaction energetics in a specific cell phase has been utilized to address the diffusion quite clearly. This article helps to address the mechanisms of cell based diffusion and nutrient movements and thus helps develop strategic templates to manipulate the diffusion mechanisms. Application of the theoretical knowledge into designing or discovering drugs or small molecule inhibitors targeting cell based structures may open up new avenues in biomedical sciences.

Hearing Sensitivity to Shifts of Rippled-Spectrum Sound Signals in Masking Noise.

PubMed

Nechaev, Dmitry I; Milekhina, Olga N; Supin, Alexander Ya

2015-01-01

The goal of the study was to enlarge knowledge of discrimination of complex sound signals by the auditory system in masking noise. For that, influence of masking noise on detection of shift of rippled spectrum was studied in normal listeners. The signal was a shift of ripple phase within a 0.5-oct wide rippled spectrum centered at 2 kHz. The ripples were frequency-proportional (throughout the band, ripple spacing was a constant proportion of the ripple center frequency). Simultaneous masker was a 0.5-oct noise below-, on-, or above the signal band. Both the low-frequency (center frequency 1 kHz) and on-frequency (the same center frequency as for the signal) maskers increased the thresholds for detecting ripple phase shift. However, the threshold dependence on the masker level was different for these two maskers. For the on-frequency masker, the masking effect primarily depended on the masker/signal ratio: the threshold steeply increased at a ratio of 5 dB, and no shift was detectable at a ratio of 10 dB. For the low-frequency masker, the masking effect primarily depended on the masker level: the threshold increased at a masker level of 80 dB SPL, and no shift was detectable at a masker level of 90 dB (for a signal level of 50 dB) or 100 dB (for a signal level of 80 dB). The high-frequency masker had little effect. The data were successfully simulated using an excitation-pattern model. In this model, the effect of the on-frequency masker appeared to be primarily due to a decrease of ripple depth. The effect of the low-frequency masker appeared due to widening of the auditory filters at high sound levels.

Maintaining Stability During a Conducted-Ripple EMC Test

NASA Technical Reports Server (NTRS)

Vorperian, Vatche

2007-01-01

An improved technique, and electronic circuitry to implement the technique, have been developed for a military-standard electromagnetic-compatibility (EMC) test in which one analyzes susceptibility to low-frequency ripple conducted into the equipment under test via a DC power line. In the traditional technique for performing the particular test, the ripple is coupled onto the DC power line via a transformer. Depending upon some design details of the equipment under test, the inductance of the transformer can contribute a degree of instability that results in an oscillation of amplitude large enough to destroy the equipment. It is usually possible to suppress the oscillation by connecting a damping resistor to the primary terminals of the ripple-injection transformer. However, it is important to emphasize the usually in the preceding sentence: sometimes, the resistive damping becomes insufficient to suppress destructive oscillation. In addition, undesirably, the resistor contributes to power dissipation and power demand, and thereby also necessitates the use of a larger ripple voltage amplifier. Yet another disadvantage of the transformer-coupling technique is that the transformer introduces low-frequency distortion of the injected ripple voltage. The improved technique makes it possible to inject ripple with very low distortion at low frequency, without inducing oscillation. In this technique, a transformer is not used: Instead, power is fed to the equipment under test via series power field-effect transistors (FETs) controlled by a summing operational amplifier. One of the inputs to the amplifier controls the DC component of the power-line voltage; the other input, generated by an external oscillator, controls the ripple component. The circuitry for implementing this technique includes panel displays, an internal power supply for the operational amplifier and panel displays, and amplitude controls for the DC and ripple powerline voltage components.

Hearing Sensitivity to Shifts of Rippled-Spectrum Sound Signals in Masking Noise

PubMed Central

Nechaev, Dmitry I.; Milekhina, Olga N.; Supin, Alexander Ya.

2015-01-01

The goal of the study was to enlarge knowledge of discrimination of complex sound signals by the auditory system in masking noise. For that, influence of masking noise on detection of shift of rippled spectrum was studied in normal listeners. The signal was a shift of ripple phase within a 0.5-oct wide rippled spectrum centered at 2 kHz. The ripples were frequency-proportional (throughout the band, ripple spacing was a constant proportion of the ripple center frequency). Simultaneous masker was a 0.5-oct noise below-, on-, or above the signal band. Both the low-frequency (center frequency 1 kHz) and on-frequency (the same center frequency as for the signal) maskers increased the thresholds for detecting ripple phase shift. However, the threshold dependence on the masker level was different for these two maskers. For the on-frequency masker, the masking effect primarily depended on the masker/signal ratio: the threshold steeply increased at a ratio of 5 dB, and no shift was detectable at a ratio of 10 dB. For the low-frequency masker, the masking effect primarily depended on the masker level: the threshold increased at a masker level of 80 dB SPL, and no shift was detectable at a masker level of 90 dB (for a signal level of 50 dB) or 100 dB (for a signal level of 80 dB). The high-frequency masker had little effect. The data were successfully simulated using an excitation-pattern model. In this model, the effect of the on-frequency masker appeared to be primarily due to a decrease of ripple depth. The effect of the low-frequency masker appeared due to widening of the auditory filters at high sound levels. PMID:26462066

Wavelength selection of rolling-grain ripples in the laboratory

NASA Astrophysics Data System (ADS)

Rousseaux, Germain; Stegner, Alexandre; Wesfreid, José Eduardo

2004-03-01

We have performed an experimental study, at very high resolution, of the wavelength selection and the evolution of rolling-grain ripples. A clear distinction is made between the flat sand bed instability and the ripple coarsening. The observation of the initial wavelength for the rolling-grain ripples is only possible close to the threshold for movement which imposes a constraint on the parameters. Moreover, we have proposed a law for the selection of the unstable wavelength under the latter constraint. Our results suggest that the initial wavelength depends on the amplitude of oscillation, the grain diameter, and the Stokes layer. Besides, during the coarsening, we observe no self-similarity of the ripple shape and for few cases a logarithmic growth of the wavelength.

High performance ripple feedback for the buck unity-power-factor rectifier

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

Lo, Y.W.; King, R.J.

1995-03-01

The buck unity-power-factor rectifier has harmonic-free input current with complete load regulation down to zero output voltage. A new ``nonlinear ripple feedback`` is proposed which exactly cancels the spoiling effect of dc-side current ripple on the low-distortion ac line current waveforms, even for large amounts of ripple. This cancellation is independent of operating point and readily implemented with analog hardware, thereby permitting economies in the design of the dc filter while maintaining harmonic-free operation. Both large-signal and incremental analyses of the rectifier are given. Confirming experimental results from a 1-kW 48-V isolated battery charger operating with current-ripple levels ranging frommore » 50% to discontinuous-conduction-mode operation are given.« less

Real time algorithms for sharp wave ripple detection.

PubMed

Sethi, Ankit; Kemere, Caleb

2014-01-01

Neural activity during sharp wave ripples (SWR), short bursts of co-ordinated oscillatory activity in the CA1 region of the rodent hippocampus, is implicated in a variety of memory functions from consolidation to recall. Detection of these events in an algorithmic framework, has thus far relied on simple thresholding techniques with heuristically derived parameters. This study is an investigation into testing and improving the current methods for detection of SWR events in neural recordings. We propose and profile methods to reduce latency in ripple detection. Proposed algorithms are tested on simulated ripple data. The findings show that simple realtime algorithms can improve upon existing power thresholding methods and can detect ripple activity with latencies in the range of 10-20 ms.

Stochastic thermodynamics across scales: Emergent inter-attractoral discrete Markov jump process and its underlying continuous diffusion

NASA Astrophysics Data System (ADS)

Santillán, Moisés; Qian, Hong

2013-01-01

We investigate the internal consistency of a recently developed mathematical thermodynamic structure across scales, between a continuous stochastic nonlinear dynamical system, i.e., a diffusion process with Langevin and Fokker-Planck equations, and its emergent discrete, inter-attractoral Markov jump process. We analyze how the system’s thermodynamic state functions, e.g. free energy F, entropy S, entropy production ep, free energy dissipation Ḟ, etc., are related when the continuous system is described with coarse-grained discrete variables. It is shown that the thermodynamics derived from the underlying, detailed continuous dynamics gives rise to exactly the free-energy representation of Gibbs and Helmholtz. That is, the system’s thermodynamic structure is the same as if one only takes a middle road and starts with the natural discrete description, with the corresponding transition rates empirically determined. By natural we mean in the thermodynamic limit of a large system, with an inherent separation of time scales between inter- and intra-attractoral dynamics. This result generalizes a fundamental idea from chemistry, and the theory of Kramers, by incorporating thermodynamics: while a mechanical description of a molecule is in terms of continuous bond lengths and angles, chemical reactions are phenomenologically described by a discrete representation, in terms of exponential rate laws and a stochastic thermodynamics.

The Stochastic Dynamics of Filopodial Growth

NASA Astrophysics Data System (ADS)

Papoian, Garegin A.; Lan, Yueheng; Zhuravlev, Pavel

2008-03-01

A filopodium is a cytoplasmic projection, exquisitely built and regulated, which extends from the leading edge of the migrating cell, exploring the cell's neighborhood. Commonly, filopodia grow and retract after their initiation, exhibiting rich dynamical behaviors. We model the growth of a filopodium based on a stochastic description which incorporates mechanical, physical and biochemical components. Our model provides a full stochastic treatment of the actin monomer diffusion and polymerization of each individual actin filament under stress of the fluctuating membrane. We have investigated the length distribution of individual filaments in a growing filopodium and studied how it depends on various physical parameters. The distribution of filament lengths turned out to be narrow, which we explained by the negative feedback created by the membrane load and monomeric G-actin gradient. We also discovered that filopodial growth is strongly diminished upon increasing retrograde flow, suggesting that regulating the retrograde flow rate would be a highly efficient way to control filopodial extension dynamics. The filopodial length increases as the membrane fluctuations decrease, which we attributed to the unequal loading of the mem- brane force among individual filaments, which, in turn, results in larger average polymerization rates. We also observed significant diffusional noise of G-actin monomers, which leads to smaller G-actin flux along the filopodial tube compared with the prediction using the diffusion equation.

Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches

PubMed Central

Taylor, P. R.; Baker, R. E.; Simpson, M. J.; Yates, C. A.

2016-01-01

Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are ‘compartment-based’: the domain is discretized into compartments, and particles can jump between these compartments. Volume-excluding effects (crowding) can be incorporated by blocking movement with some probability. Recent work has established the connection between fine- and coarse-grained models incorporating volume exclusion, but only for uniform lattices. In this paper, we consider non-uniform, hybrid lattices that incorporate both fine- and coarse-grained regions, and present two different approaches to describe the interface of the regions. We test both techniques in a range of scenarios to establish their accuracy, benchmarking against fine-grained models, and show that the hybrid models developed in this paper can be significantly faster to simulate than the fine-grained models in certain situations and are at least as fast otherwise. PMID:27383421

Lagrangian analysis by clustering. An example in the Nordic Seas.

NASA Astrophysics Data System (ADS)

Koszalka, Inga; Lacasce, Joseph H.

2010-05-01

We propose a new method for obtaining average velocities and eddy diffusivities from Lagrangian data. Rather than grouping the drifter-derived velocities in uniform geographical bins, as is commonly done, we group a specified number of nearest-neighbor velocities. This is done via a clustering algorithm operating on the instantaneous positions of the drifters. Thus it is the data distribution itself which determines the positions of the averages and the areal extent of the clusters. A major advantage is that because the number of members is essentially the same for all clusters, the statistical accuracy is more uniform than with geographical bins. We illustrate the technique using synthetic data from a stochastic model, employing a realistic mean flow. The latter is an accurate representation of the surface currents in the Nordic Seas and is strongly inhomogeneous in space. We use the clustering algorithm to extract the mean velocities and diffusivities (both of which are known from the stochastic model). We also compare the results to those obtained with fixed geographical bins. Clustering is more successful at capturing spatial variability of the mean flow and also improves convergence in the eddy diffusivity estimates. We discuss both the future prospects and shortcomings of the new method.

75 FR 29238 - Proposed Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2010-05-25

... River). with Pot Ripple Creek Henry County. to approximately 0.5 mile upstream of the confluence with Pot Ripple Creek. Boiling Branch (Backwater effects From the confluence None +481 Unincorporated Areas... Drennon Road. Pot Ripple Creek (Backwater effects From the confluence None +488 Unincorporated Areas of...

Adhesion modification of neural stem cells induced by nanoscale ripple patterns

NASA Astrophysics Data System (ADS)

Pedraz, P.; Casado, S.; Rodriguez, V.; Giordano, M. C.; Buatier de Mongeot, F.; Ayuso-Sacido, A.; Gnecco, E.

2016-03-01

We have studied the influence of anisotropic nanopatterns (ripples) on the adhesion and morphology of mouse neural stem cells (C17.2) on glass substrates using cell viability assay, optical microscopy and atomic force microscopy. The ripples were produced by defocused ion beam sputtering with inert Ar ions, which physically remove atoms from the surface at the energy of 800 eV. The ripple periodicity (∼200 nm) is comparable to the thickness of the cytoplasmatic microspikes (filopodia) which link the stem cells to the substrate. All methods show that the cell adhesion is significantly lowered compared to the same type of cells on flat glass surfaces. Furthermore, the AFM analysis reveals that the filopodia tend to be trapped parallel or perpendicular to the ripples, which limits the spreading of the stem cell on the rippled substrate. This opens the perspective of controlling the micro-adhesion of stem cells and the orientation of their filopodia by tuning the anisotropic substrate morphology without chemical reactions occurring at the surface.

Dominant source of disorder in graphene: charged impurities or ripples?

NASA Astrophysics Data System (ADS)

Fan, Zheyong; Uppstu, Andreas; Harju, Ari

2017-06-01

Experimentally produced graphene sheets exhibit a wide range of mobility values. Both extrinsic charged impurities and intrinsic ripples (corrugations) have been suggested to induce long-range disorder in graphene and could be a candidate for the dominant source of disorder. Here, using large-scale molecular dynamics and quantum transport simulations, we find that the hopping disorder and the gauge and scalar potentials induced by the ripples are short-ranged, in strong contrast with predictions by continuous models, and the transport fingerprints of the ripple disorder are very different from those of charged impurities. We conclude that charged impurities are the dominant source of disorder in most graphene samples, whereas scattering by ripples is mainly relevant in the high carrier density limit of ultraclean graphene samples (with a charged impurity concentration less than about 10 ppm) at room and higher temperatures. Our finding is valuable to theoretical modelling of transport properties of not only graphene, but also other two-dimensional materials, as the thermal ripples are universal.

Diversity of sharp-wave-ripple LFP signatures reveals differentiated brain-wide dynamical events.

PubMed

Ramirez-Villegas, Juan F; Logothetis, Nikos K; Besserve, Michel

2015-11-17

Sharp-wave-ripple (SPW-R) complexes are believed to mediate memory reactivation, transfer, and consolidation. However, their underlying neuronal dynamics at multiple scales remains poorly understood. Using concurrent hippocampal local field potential (LFP) recordings and functional MRI (fMRI), we study local changes in neuronal activity during SPW-R episodes and their brain-wide correlates. Analysis of the temporal alignment between SPW and ripple components reveals well-differentiated SPW-R subtypes in the CA1 LFP. SPW-R-triggered fMRI maps show that ripples aligned to the positive peak of their SPWs have enhanced neocortical metabolic up-regulation. In contrast, ripples occurring at the trough of their SPWs relate to weaker neocortical up-regulation and absent subcortical down-regulation, indicating differentiated involvement of neuromodulatory pathways in the ripple phenomenon mediated by long-range interactions. To our knowledge, this study provides the first evidence for the existence of SPW-R subtypes with differentiated CA1 activity and metabolic correlates in related brain areas, possibly serving different memory functions.

Anomalous behavior in temporal evolution of ripple wavelength under medium energy Ar{sup +}-ion bombardment on Si: A case of initial wavelength selection

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

Garg, Sandeep Kumar; Inter-University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi 110 067; Cuerno, Rodolfo

We have studied the early stage dynamics of ripple patterns on Si surfaces, in the fluence range of 1–3 × 10{sup 18} ions cm{sup −2}, as induced by medium energy Ar{sup +}-ion irradiation at room temperature. Under our experimental conditions, the ripple evolution is found to be in the linear regime, while a clear decreasing trend in the ripple wavelength is observed up to a certain time (fluence). Numerical simulations of a continuum model of ion-sputtered surfaces suggest that this anomalous behavior is due to the relaxation of the surface features of the experimental pristine surface during the initial stage of patternmore » formation. The observation of this hitherto unobserved behavior of the ripple wavelength seems to have been enabled by the use of medium energy ions, where the ripple wavelengths are found to be order(s) of magnitude larger than those at lower ion energies.« less

Spontaneous ripple formation in phosphorene: electronic properties and possible applications.

PubMed

Zhou, Yungang; Yang, Li; Zu, Xiaotao; Gao, Fei

2016-06-09

According to the Mermin-Wagner theorem and theory of elasticity, long-range order in two-dimensional (2D) crystals will be inevitably destroyed due to a thermal fluctuation. Thus, a 2D lattice prefers a corrugation meaning that a 2D crystal is easy to present a ripple. In this work, we, via employing ab initio molecular dynamics (AIMD) simulations, for the first time evidenced that the inherent dynamics of phosphorene would lead to a spontaneous formation of ripples at room temperature. The height of a ripple closely associates with the temperature and the width. Via density functional theory (DFT) calculations, we further demonstrated that the emergence of ripples would remarkably reduce the bandgap of phosphorene. Via the construction of the unique phosphorene structure, we finally found that such a rippled structure is expected to be used in the light-emitting field. These results give us further knowledge of phosphorene, which goes beyond the current scope of phosphorene limited to the flat lattice.

Cochlear implant users' spectral ripple resolution.

PubMed

Jeon, Eun Kyung; Turner, Christopher W; Karsten, Sue A; Henry, Belinda A; Gantz, Bruce J

2015-10-01

This study revisits the issue of the spectral ripple resolution abilities of cochlear implant (CI) users. The spectral ripple resolution of recently implanted CI recipients (implanted during the last 10 years) were compared to those of CI recipients implanted 15 to 20 years ago, as well as those of normal-hearing and hearing-impaired listeners from previously published data from Henry, Turner, and Behrens [J. Acoust. Soc. Am. 118, 1111-1121 (2005)]. More recently, implanted CI recipients showed significantly better spectral ripple resolution. There is no significant difference in spectral ripple resolution for these recently implanted subjects compared to hearing-impaired (acoustic) listeners. The more recently implanted CI users had significantly better pre-operative speech perception than previously reported CI users. These better pre-operative speech perception scores in CI users from the current study may be related to better performance on the spectral ripple discrimination task; however, other possible factors such as improvements in internal and external devices cannot be excluded.

Diversity of sharp-wave–ripple LFP signatures reveals differentiated brain-wide dynamical events

PubMed Central

Ramirez-Villegas, Juan F.; Logothetis, Nikos K.; Besserve, Michel

2015-01-01

Sharp-wave–ripple (SPW-R) complexes are believed to mediate memory reactivation, transfer, and consolidation. However, their underlying neuronal dynamics at multiple scales remains poorly understood. Using concurrent hippocampal local field potential (LFP) recordings and functional MRI (fMRI), we study local changes in neuronal activity during SPW-R episodes and their brain-wide correlates. Analysis of the temporal alignment between SPW and ripple components reveals well-differentiated SPW-R subtypes in the CA1 LFP. SPW-R–triggered fMRI maps show that ripples aligned to the positive peak of their SPWs have enhanced neocortical metabolic up-regulation. In contrast, ripples occurring at the trough of their SPWs relate to weaker neocortical up-regulation and absent subcortical down-regulation, indicating differentiated involvement of neuromodulatory pathways in the ripple phenomenon mediated by long-range interactions. To our knowledge, this study provides the first evidence for the existence of SPW-R subtypes with differentiated CA1 activity and metabolic correlates in related brain areas, possibly serving different memory functions. PMID:26540729

Cochlear implant users' spectral ripple resolution

PubMed Central

Jeon, Eun Kyung; Turner, Christopher W.; Karsten, Sue A.; Henry, Belinda A.; Gantz, Bruce J.

2015-01-01

This study revisits the issue of the spectral ripple resolution abilities of cochlear implant (CI) users. The spectral ripple resolution of recently implanted CI recipients (implanted during the last 10 years) were compared to those of CI recipients implanted 15 to 20 years ago, as well as those of normal-hearing and hearing-impaired listeners from previously published data from Henry, Turner, and Behrens [J. Acoust. Soc. Am. 118, 1111–1121 (2005)]. More recently, implanted CI recipients showed significantly better spectral ripple resolution. There is no significant difference in spectral ripple resolution for these recently implanted subjects compared to hearing-impaired (acoustic) listeners. The more recently implanted CI users had significantly better pre-operative speech perception than previously reported CI users. These better pre-operative speech perception scores in CI users from the current study may be related to better performance on the spectral ripple discrimination task; however, other possible factors such as improvements in internal and external devices cannot be excluded. PMID:26520316

Semiclassical stochastic mechanics for the Coulomb potential with applications to modelling dark matter

NASA Astrophysics Data System (ADS)

Neate, Andrew; Truman, Aubrey

2016-05-01

Little is known about dark matter particles save that their most important interactions with ordinary matter are gravitational and that, if they exist, they are stable, slow moving and relatively massive. Based on these assumptions, a semiclassical approximation to the Schrödinger equation under the action of a Coulomb potential should be relevant for modelling their behaviour. We investigate the semiclassical limit of the Schrödinger equation for a particle of mass M under a Coulomb potential in the context of Nelson's stochastic mechanics. This is done using a Freidlin-Wentzell asymptotic series expansion in the parameter ɛ = √{ ħ / M } for the Nelson diffusion. It is shown that for wave functions ψ ˜ exp((R + iS)/ɛ2) where R and S are real valued, the ɛ = 0 behaviour is governed by a constrained Hamiltonian system with Hamiltonian Hr and constraint Hi = 0 where the superscripts r and i denote the real and imaginary parts of the Bohr correspondence limit of the quantum mechanical Hamiltonian, independent of Nelson's ideas. Nelson's stochastic mechanics is restored in dealing with the nodal surface singularities and by computing (correct to first order in ɛ) the relevant diffusion process in terms of Jacobi fields thereby revealing Kepler's laws in a new light. The key here is that the constrained Hamiltonian system has just two solutions corresponding to the forward and backward drifts in Nelson's stochastic mechanics. We discuss the application of this theory to modelling dark matter particles under the influence of a large gravitating point mass.

Backward-stochastic-differential-equation approach to modeling of gene expression

NASA Astrophysics Data System (ADS)

Shamarova, Evelina; Chertovskih, Roman; Ramos, Alexandre F.; Aguiar, Paulo

2017-03-01

In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological conditions (e.g., protein concentrations) that preceded an experimentally measured event of interest (e.g., mitosis, apoptosis, etc.).

MOLNs: A CLOUD PLATFORM FOR INTERACTIVE, REPRODUCIBLE, AND SCALABLE SPATIAL STOCHASTIC COMPUTATIONAL EXPERIMENTS IN SYSTEMS BIOLOGY USING PyURDME

PubMed Central

Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas

2017-01-01

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments. PMID:28190948

Backward-stochastic-differential-equation approach to modeling of gene expression.

PubMed

Shamarova, Evelina; Chertovskih, Roman; Ramos, Alexandre F; Aguiar, Paulo

2017-03-01

In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological conditions (e.g., protein concentrations) that preceded an experimentally measured event of interest (e.g., mitosis, apoptosis, etc.).

Higher-order stochastic differential equations and the positive Wigner function

NASA Astrophysics Data System (ADS)

Drummond, P. D.

2017-12-01

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

Stochastic DT-MRI connectivity mapping on the GPU.

PubMed

McGraw, Tim; Nadar, Mariappan

2007-01-01

We present a method for stochastic fiber tract mapping from diffusion tensor MRI (DT-MRI) implemented on graphics hardware. From the simulated fibers we compute a connectivity map that gives an indication of the probability that two points in the dataset are connected by a neuronal fiber path. A Bayesian formulation of the fiber model is given and it is shown that the inversion method can be used to construct plausible connectivity. An implementation of this fiber model on the graphics processing unit (GPU) is presented. Since the fiber paths can be stochastically generated independently of one another, the algorithm is highly parallelizable. This allows us to exploit the data-parallel nature of the GPU fragment processors. We also present a framework for the connectivity computation on the GPU. Our implementation allows the user to interactively select regions of interest and observe the evolving connectivity results during computation. Results are presented from the stochastic generation of over 250,000 fiber steps per iteration at interactive frame rates on consumer-grade graphics hardware.

Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism

NASA Astrophysics Data System (ADS)

Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.

2015-04-01

We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.

Extracellular calcium controls the expression of two different forms of ripple-like hippocampal oscillations.

PubMed

Aivar, Paloma; Valero, Manuel; Bellistri, Elisa; Menendez de la Prida, Liset

2014-02-19

Hippocampal high-frequency oscillations (HFOs) are prominent in physiological and pathological conditions. During physiological ripples (100-200 Hz), few pyramidal cells fire together coordinated by rhythmic inhibitory potentials. In the epileptic hippocampus, fast ripples (>200 Hz) reflect population spikes (PSs) from clusters of bursting cells, but HFOs in the ripple and the fast ripple range are vastly intermixed. What is the meaning of this frequency range? What determines the expression of different HFOs? Here, we used different concentrations of Ca(2+) in a physiological range (1-3 mM) to record local field potentials and single cells in hippocampal slices from normal rats. Surprisingly, we found that this sole manipulation results in the emergence of two forms of HFOs reminiscent of ripples and fast ripples recorded in vivo from normal and epileptic rats, respectively. We scrutinized the cellular correlates and mechanisms underlying the emergence of these two forms of HFOs by combining multisite, single-cell and paired-cell recordings in slices prepared from a rat reporter line that facilitates identification of GABAergic cells. We found a major effect of extracellular Ca(2+) in modulating intrinsic excitability and disynaptic inhibition, two critical factors shaping network dynamics. Moreover, locally modulating the extracellular Ca(2+) concentration in an in vivo environment had a similar effect on disynaptic inhibition, pyramidal cell excitability, and ripple dynamics. Therefore, the HFO frequency band reflects a range of firing dynamics of hippocampal networks.

Stochastically gated local and occupation times of a Brownian particle

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.

2017-01-01

We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected. In both scenarios, the gate randomly switches between the open and closed states according to a two-state Markov process. We derive a stochastic, backward Fokker-Planck equation (FPE) for the moment-generating function of the two types of gated Brownian functional, given a particular realization of the stochastic gate, and analyze the resulting stochastic FPE using a moments method recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment-generating function, averaged with respect to realizations of the stochastic gate.

Weak Galilean invariance as a selection principle for coarse-grained diffusive models.

PubMed

Cairoli, Andrea; Klages, Rainer; Baule, Adrian

2018-05-29

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

76 FR 35119 - Final Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2011-06-16

... (backwater effects from From the confluence with Pot +488 Unincorporated Areas of Kentucky River). Ripple Creek to Henry County. approximately 0.5 mile upstream of the confluence with Pot Ripple Creek. Boiling... Ripple Creek (backwater effects From the confluence with the +488 Unincorporated Areas of from Kentucky...

Lagrangian particles with mixing. I. Simulating scalar transport

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2009-06-01

The physical similarity and mathematical equivalence of continuous diffusion and particle random walk forms one of the cornerstones of modern physics and the theory of stochastic processes. The randomly walking particles do not need to posses any properties other than location in physical space. However, particles used in many models dealing with simulating turbulent transport and turbulent combustion do posses a set of scalar properties and mixing between particle properties is performed to reflect the dissipative nature of the diffusion processes. We show that the continuous scalar transport and diffusion can be accurately specified by means of localized mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. Particles with scalar properties and localized mixing represent an alternative formulation for the process, which is selected to represent the continuous diffusion. Simulating diffusion by Lagrangian particles with mixing involves three main competing requirements: minimizing stochastic uncertainty, minimizing bias introduced by numerical diffusion, and preserving independence of particles. These requirements are analyzed for two limited cases of mixing between two particles and mixing between a large number of particles. The problem of possible dependences between particles is most complicated. This problem is analyzed using a coupled chain of equations that has similarities with Bogolubov-Born-Green-Kirkwood-Yvon chain in statistical physics. Dependences between particles can be significant in close proximity of the particles resulting in a reduced rate of mixing. This work develops further ideas introduced in the previously published letter [Phys. Fluids 19, 031702 (2007)]. Paper I of this work is followed by Paper II [Phys. Fluids 19, 065102 (2009)] where modeling of turbulent reacting flows by Lagrangian particles with localized mixing is specifically considered.

Diffusion within the cytoplasm: a mesoscale model of interacting macromolecules.

PubMed

Trovato, Fabio; Tozzini, Valentina

2014-12-02

Recent experiments carried out in the dense cytoplasm of living cells have highlighted the importance of proteome composition and nonspecific intermolecular interactions in regulating macromolecule diffusion and organization. Despite this, the dependence of diffusion-interaction on physicochemical properties such as the degree of poly-dispersity and the balance between steric repulsion and nonspecific attraction among macromolecules was not systematically addressed. In this work, we study the problem of diffusion-interaction in the bacterial cytoplasm, combining theory and experimental data to build a minimal coarse-grained representation of the cytoplasm, which also includes, for the first time to our knowledge, the nucleoid. With stochastic molecular-dynamics simulations of a virtual cytoplasm we are able to track the single biomolecule motion, sizing from 3 to 80 nm, on submillisecond-long trajectories. We demonstrate that the size dependence of diffusion coefficients, anomalous exponents, and the effective viscosity experienced by biomolecules in the cytoplasm is fine-tuned by the intermolecular interactions. Accounting only for excluded volume in these potentials gives a weaker size-dependence than that expected from experimental data. On the contrary, adding nonspecific attraction in the range of 1-10 thermal energy units produces a stronger variation of the transport properties at growing biopolymer sizes. Normal and anomalous diffusive regimes emerge straightforwardly from the combination of high macromolecular concentration, poly-dispersity, stochasticity, and weak nonspecific interactions. As a result, small biopolymers experience a viscous cytoplasm, while the motion of big ones is jammed because the entanglements produced by the network of interactions and the entropic effects caused by poly-dispersity are stronger. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Logistical constraints lead to an intermediate optimum in outbreak response vaccination

PubMed Central

Shea, Katriona; Ferrari, Matthew

2018-01-01

Dynamic models in disease ecology have historically evaluated vaccination strategies under the assumption that they are implemented homogeneously in space and time. However, this approach fails to formally account for operational and logistical constraints inherent in the distribution of vaccination to the population at risk. Thus, feedback between the dynamic processes of vaccine distribution and transmission might be overlooked. Here, we present a spatially explicit, stochastic Susceptible-Infected-Recovered-Vaccinated model that highlights the density-dependence and spatial constraints of various diffusive strategies of vaccination during an outbreak. The model integrates an agent-based process of disease spread with a partial differential process of vaccination deployment. We characterize the vaccination response in terms of a diffusion rate that describes the distribution of vaccination to the population at risk from a central location. This generates an explicit trade-off between slow diffusion, which concentrates effort near the central location, and fast diffusion, which spreads a fixed vaccination effort thinly over a large area. We use stochastic simulation to identify the optimum vaccination diffusion rate as a function of population density, interaction scale, transmissibility, and vaccine intensity. Our results show that, conditional on a timely response, the optimal strategy for minimizing outbreak size is to distribute vaccination resource at an intermediate rate: fast enough to outpace the epidemic, but slow enough to achieve local herd immunity. If the response is delayed, however, the optimal strategy for minimizing outbreak size changes to a rapidly diffusive distribution of vaccination effort. The latter may also result in significantly larger outbreaks, thus suggesting a benefit of allocating resources to timely outbreak detection and response. PMID:29791432

Impact of typical steady-state conditions and transient conditions on flow ripple and its test accuracy for axial piston pump

NASA Astrophysics Data System (ADS)

Xu, Bing; Hu, Min; Zhang, Junhui

2015-09-01

The current research about the flow ripple of axial piston pump mainly focuses on the effect of the structure of parts on the flow ripple. Therein, the structure of parts are usually designed and optimized at rated working conditions. However, the pump usually has to work in large-scale and time-variant working conditions. Therefore, the flow ripple characteristics of pump and analysis for its test accuracy with respect to variant steady-state conditions and transient conditions in a wide range of operating parameters are focused in this paper. First, a simulation model has been constructed, which takes the kinematics of oil film within friction pairs into account for higher accuracy. Afterwards, a test bed which adopts Secondary Source Method is built to verify the model. The simulation and tests results show that the angular position of the piston, corresponding to the position where the peak flow ripple is produced, varies with the different pressure. The pulsating amplitude and pulsation rate of flow ripple increase with the rise of pressure and the variation rate of pressure. For the pump working at a constant speed, the flow pulsation rate decreases dramatically with the increasing speed when the speed is less than 27.78% of the maximum speed, subsequently presents a small decrease tendency with the speed further increasing. With the rise of the variation rate of speed, the pulsating amplitude and pulsation rate of flow ripple increase. As the swash plate angle augments, the pulsating amplitude of flow ripple increases, nevertheless the flow pulsation rate decreases. In contrast with the effect of the variation of pressure, the test accuracy of flow ripple is more sensitive to the variation of speed. It makes the test accuracy above 96.20% available for the pulsating amplitude of pressure deviating within a range of ±6% from the mean pressure. However, with a variation of speed deviating within a range of ±2% from the mean speed, the attainable test accuracy of flow ripple is above 93.07%. The model constructed in this research proposes a method to determine the flow ripple characteristics of pump and its attainable test accuracy under the large-scale and time-variant working conditions. Meanwhile, a discussion about the variation of flow ripple and its obtainable test accuracy with the conditions of the pump working in wide operating ranges is given as well.

Automatic Detection of Sand Ripple Features in Sidescan Sonar Imagery

DTIC Science & Technology

2014-07-09

Among the features used in forensic scientific fingerprint analysis are terminations or bifurcations of print ridges. Sidescan sonar imagery of ripple...always be pathological cases. The size of the blocks of pixels used in determining the ripple wavelength is evident in the output images on the right in

Unidirectional flow over asymmetric and symmetric ripples

NASA Astrophysics Data System (ADS)

Wiberg, Patricia L.; Nelson, Jonathan M.

1992-08-01

An LDV-equipped flume has yielded detailed measurements of velocity and turbulence over fixed sets of two-dimensional symmetric and asymmetric ripples. The measured velocities over the ripples are compared with the Nelson and Smith (1989)results for flow over larger-scale dunes; the new results are larger in the outer region of the flow, and the velocity profiles exhibit no sharp inflection at the top of the lowest wake. A model for flow over bedforms which has yielded excellent agreement with dune measurements is presently modified to better represent the observed flow over ripples.

Rolling Ripple

NASA Image and Video Library

2006-05-01

NASA's Mars Exploration Rover Opportunity continues to cut southward across a plain marked by large sand ripples and a pavement of outcrop rock. The ripple in the center of the image shows a distinct pattern of banding, which the science team hopes to investigate more closely during the trek through this terrain. The banding and other features have inspired a hypothesis that Meridiani ripples are old features that are currently being eroded, and not transported, by wind. This navigation camera image was taken on Opportunity's sol 795, April 19, 2006. http://photojournal.jpl.nasa.gov/catalog/PIA08424

Single- and multi-pulse formation of surface structures under static femtosecond irradiation

NASA Astrophysics Data System (ADS)

Guillermin, M.; Garrelie, F.; Sanner, N.; Audouard, E.; Soder, H.

2007-07-01

Femtosecond surface structure modifications are investigated under irradiation with laser pulses of 150 fs at 800 nm, on copper and silicon. We report sub-wavelength periodic structures formation (ripples) with a periodicity of 500 nm for both materials. These ripples are perpendicular to the laser polarization and can be obtained with only one pulse. The formation of these ripples corresponds to a fluence threshold of 1 J/cm 2 for copper and 0.15 J/cm 2 for silicon. We find several morphologies when more pulses are applied: larger ripples parallel to the polarization are formed with a periodicity of 1 μm and degenerate into a worm-like morphology with a higher number of pulses. In addition, walls of deep holes also show sub-wavelength and large ripples.

Orientation of ripples induced by ultrafast laser pulses on copper in different liquids

NASA Astrophysics Data System (ADS)

Maragkaki, Stella; Elkalash, Abdallah; Gurevich, Evgeny L.

2017-12-01

Formation of laser-induced periodic surface structures (LIPSS or ripples) was studied on a metallic surface of polished copper using irradiation with multiple femtosecond laser pulses in different environmental conditions (air, water, ethanol and methanol). Uniform LIPSS have been achieved by controlling the peak fluence and the overlapping rate. Ripples in both orientations, perpendicular and parallel to laser polarization, were observed in all liquids simultaneously. The orientation of these ripples in the center of the ablated line was changing with the incident light intensity. For low intensities the orientation of the ripples is perpendicular to the laser polarization, whereas for high intensities it turns parallel to it without considerable changes in the period. Multi-directional LIPSS formation was also observed for moderate peak fluence in liquid environments.

Modulations of anisotropic optical transmission on alumina-doped zinc oxide surface by femtosecond laser induced ripples

NASA Astrophysics Data System (ADS)

Lu, Yanhui; Jiang, Lan; Sun, Jingya; Cao, Qiang; Wang, Qingsong; Han, Weina; Lu, Yongfeng

2018-04-01

This study demonstrated that femtosecond-laser-induced ripples on an alumina-doped zinc oxide (AZO) film with space intervals of approximately 340 and 660 nm exhibit modulations of anisotropic optical transmission. At low laser fluence, ripples can not affect the original absorption peak of AZO film, but at higher laser fluence, the absorption peak of AZO film is disappeared due to the modulation by femtosecond laser induced ripples. Moreover, the relationship between the anisotropic optical transmission and the features of nanostructures is discussed. Ripples with a space interval of approximately 660 nm have a higher ability to block light than nanostructures with a space interval of approximately 340 nm. These observations indicate that anisotropic optical transmission has potential applications in the field of optoelectronics.

Laboratory Observations of Sand Ripple Evolution in a Small Oscillatory Flow Tunnel

NASA Astrophysics Data System (ADS)

Calantoni, J.; Palmsten, M. L.; Chu, J.; Landry, B. J.; Penko, A.

2014-12-01

The dynamics of sand ripples are vital to understanding numerous coastal processes such as sediment transport, wave attenuation, boundary layer development, and seafloor acoustic properties. Experimental work was conducted in a small oscillatory flow tunnel at the Sediment Dynamics Laboratory at the Naval Research Laboratory, Stennis Space Center. Six different monochromatic oscillatory forcings, three with velocity asymmetry and three without, were used to investigate sand ripple dynamics using a unimodal grain size distribution with D50=0.65 mm. The experiments represent an extension of previous work using bimodal grain size distributions. A DSLR camera with a 180-degree fisheye lens collected images of the sediment bed profile every 2 seconds to resolve changes in ripple geometries and migration rates resulting from the different flow conditions for over 127 hours (229,388 images). Matlab © algorithms undistorted the fisheye images and quantified the ripple geometries, wavelengths, heights, and migration rates as a function of flow forcing. The mobility number was kept nearly constant by increasing and decreasing the semi-excursion amplitude and the wave frequency, respectively. We observed distinct changes in ripple geometry and migration rate for the pair of oscillatory forcings having nearly identical mobility numbers. The results suggested that the commonly used mobility number might not be appropriate to characterize ripple geometry or migration rates.

MMS Observations and Hybrid Simulations of Surface Ripples at a Marginally Quasi-Parallel Shock

NASA Astrophysics Data System (ADS)

Gingell, Imogen; Schwartz, Steven J.; Burgess, David; Johlander, Andreas; Russell, Christopher T.; Burch, James L.; Ergun, Robert E.; Fuselier, Stephen; Gershman, Daniel J.; Giles, Barbara L.; Goodrich, Katherine A.; Khotyaintsev, Yuri V.; Lavraud, Benoit; Lindqvist, Per-Arne; Strangeway, Robert J.; Trattner, Karlheinz; Torbert, Roy B.; Wei, Hanying; Wilder, Frederick

2017-11-01

Simulations and observations of collisionless shocks have shown that deviations of the nominal local shock normal orientation, that is, surface waves or ripples, are expected to propagate in the ramp and overshoot of quasi-perpendicular shocks. Here we identify signatures of a surface ripple propagating during a crossing of Earth's marginally quasi-parallel (θBn˜45∘) or quasi-parallel bow shock on 27 November 2015 06:01:44 UTC by the Magnetospheric Multiscale (MMS) mission and determine the ripple's properties using multispacecraft methods. Using two-dimensional hybrid simulations, we confirm that surface ripples are a feature of marginally quasi-parallel and quasi-parallel shocks under the observed solar wind conditions. In addition, since these marginally quasi-parallel and quasi-parallel shocks are expected to undergo a cyclic reformation of the shock front, we discuss the impact of multiple sources of nonstationarity on shock structure. Importantly, ripples are shown to be transient phenomena, developing faster than an ion gyroperiod and only during the period of the reformation cycle when a newly developed shock ramp is unaffected by turbulence in the foot. We conclude that the change in properties of the ripple observed by MMS is consistent with the reformation of the shock front over a time scale of an ion gyroperiod.

Electromagnetic processes during phase commutation in field regulated reluctance machine

NASA Astrophysics Data System (ADS)

Shishkov, A. N.; Sychev, D. A.; Zemlyansky, A. A.; Krupnova, M. N.; Funk, T. A.; Ishmet'eva, V. D.

2018-03-01

The processes of currents switching in stator windings have been explained by the existence of the electromagnetic torque ripples in the electric drive with the field-regulated reluctance machine. The maximum value of ripples in the open loop control system for the six-phase machine can reach 20 percent from the developed electromagnetic torque. This method allows one to make calculation of ripple spike towards average torque developed by the electromotor for the different number of phases. Application of a trapezoidal form of current at six phases became the solution. In case of a less number of phases than six, a ripple spike considerably increases, which is inadmissible. On the other hand, increasing the number of phases tends to the increase of the semiconductor inverter external dimensions based on the inconspicuous decreasing of a ripple spike. The creation and usage of high-speed control loops of current (HCLC) have been recommended for a reduction of the electromagnetic torque’s ripple level, as well as the appliance of positive current feedback in switching phase currents. This decision allowed one to receive a mean value of the torque more than 10%, compared to system without change, to reduce greatly ripple spike of the electromagnetic torque. The possibility of the electric drive effective operation with FRRM in emergency operation has been shown.

Configuration of ripple domains and their topological defects formed under local mechanical stress on hexagonal monolayer graphene.

PubMed

Park, Yeonggu; Choi, Jin Sik; Choi, Taekjib; Lee, Mi Jung; Jia, Quanxi; Park, Minwoo; Lee, Hoonkyung; Park, Bae Ho

2015-03-24

Ripples in graphene are extensively investigated because they ensure the mechanical stability of two-dimensional graphene and affect its electronic properties. They arise from spontaneous symmetry breaking and are usually manifested in the form of domains with long-range order. It is expected that topological defects accompany a material exhibiting long-range order, whose functionality depends on characteristics of domains and topological defects. However, there remains a lack of understanding regarding ripple domains and their topological defects formed on monolayer graphene. Here we explore configuration of ripple domains and their topological defects in exfoliated monolayer graphenes on SiO2/Si substrates using transverse shear microscope. We observe three-color domains with three different ripple directions, which meet at a core. Furthermore, the closed domain is surrounded by an even number of cores connected together by domain boundaries, similar to topological vortex and anti-vortex pairs. In addition, we have found that axisymmetric three-color domains can be induced around nanoparticles underneath the graphene. This fascinating configuration of ripple domains may result from the intrinsic hexagonal symmetry of two-dimensional graphene, which is supported by theoretical simulation using molecular dynamics. Our findings are expected to play a key role in understanding of ripple physics in graphene and other two-dimensional materials.

Two Sizes of Ripples on Surface of Martian Sand Dune

NASA Image and Video Library

2016-06-30

Two sizes of wind-sculpted ripples are evident in this view of the top surface of a Martian sand dune. Sand dunes and the smaller type of ripples also exist on Earth. The larger ripples -- roughly 10 feet (3 meters) apart -- are a type not seen on Earth nor previously recognized as a distinct type on Mars. The Mast Camera (Mastcam) on NASA's Curiosity Mars rover took the multiple component images of this scene on Dec. 13, 2015, during the 1,192nd Martian day, or sol, of the rover's work on Mars. That month, Curiosity was conducting the first close-up investigation ever made of active sand dunes anywhere other than Earth. The larger ripples have distinctive sinuous crest lines, compared to the smaller ripples. The location is part of "Namib Dune" in the Bagnold Dune Field, which forms a dark band along the northwestern flank of Mount Sharp. The component images were taken in early morning at this site, with the camera looking in the direction of the sun. This mosaic combining the images has been processed to brighten it and make the ripples more visible. The sand is very dark, both from the morning shadows and from the intrinsic darkness of the minerals that dominate its composition. http://photojournal.jpl.nasa.gov/catalog/PIA20755

Implications of Pulser Voltage Ripple

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

Barnard, J J

In a recent set of measurements obtained by G. Kamin, W. Manning, A. Molvik, and J. Sullivan, the voltage waveform of the diode pulser had a ripple of approximately {+-}1.3% of the 65 kV flattop voltage, and the beam current had a larger corresponding ripple of approximately {+-}8.4% of the 1.5 mA average current at the location of the second Faraday cup, approximately 1.9 m downstream from the ion source. The period of the ripple was about 1 {mu}s. It was initially unclear whether this large current ripple was in fact a true measurement of the current or a spuriousmore » measurement of noise produced by the pulser electronics. The purpose of this note is to provide simulations which closely match the experimental results and thereby corroborate the physical nature of those measurements, and to provide predictions of the amplitude of the current ripples as they propagate to the end of linear transport section. Additionally analytic estimates are obtained which lend some insight into the nature of the current fluctuations and to provide an estimate of what the maximum amplitude of the current fluctuations are expected to be, and conversely what initial ripple in the voltage source is allowed, given a smaller acceptable tolerance on the line charge density.« less

Basilar-membrane interference patterns from multiple internal reflection of cochlear traveling waves.

PubMed

Shera, Christopher A; Cooper, Nigel P

2013-04-01

At low stimulus levels, basilar-membrane (BM) mechanical transfer functions in sensitive cochleae manifest a quasiperiodic rippling pattern in both amplitude and phase. Analysis of the responses of active cochlear models suggests that the rippling is a mechanical interference pattern created by multiple internal reflection within the cochlea. In models, the interference arises when reverse-traveling waves responsible for stimulus-frequency otoacoustic emissions (SFOAEs) reflect off the stapes on their way to the ear canal, launching a secondary forward-traveling wave that combines with the primary wave produced by the stimulus. Frequency-dependent phase differences between the two waves then create the rippling pattern measurable on the BM. Measurements of BM ripples and SFOAEs in individual chinchilla ears demonstrate that the ripples are strongly correlated with the acoustic interference pattern measured in ear-canal pressure, consistent with a common origin involving the generation of SFOAEs. In BM responses to clicks, the ripples appear as temporal fine structure in the response envelope (multiple lobes, waxing and waning). Analysis of the ripple spacing and response phase gradients provides a test for the role of fast- and slow-wave modes of reverse energy propagation within the cochlea. The data indicate that SFOAE delays are consistent with reverse slow-wave propagation but much too long to be explained by fast waves.

Stochastic Physicochemical Dynamics

NASA Astrophysics Data System (ADS)

Tsekov, R.

2001-02-01

Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic fluctuations. The range of validity of the Boltzmann-Einstein principle is also discussed and a generalized alternative is proposed. Both expressions coincide in the small fluctuation limit, providing a normal distribution density. Fluctuation Stability of Thin Liquid Films: Memory effect of Brownian motion in an incompressible fluid is studied. The reasoning is based on the Mori-Zwanzig formalism and a new formulation of the Langevin force as a result of collisions between an effective and the Brownian particles. Thus, the stochastic force autocorrelation function with finite dispersion and the corresponding Brownian particle velocity autocorrelation function are obtained. It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for description of the film drainage and classifies all the known results from the literature. The obtained general expression for the thinning rate is a heuristic one and predicts variety of drainage models, which are even difficult to simulate in practice. It is a typical example of a scaling law, which explains the origin of the complicate dependence of the thinning rate on the film radius. On the basis of the theory of stochastic processes the evolution of the spatial correlation function of the surface waves on a thin liquid film as well as the corresponding root mean square amplitude A(t) and number of uncorrelated subdomains N(t) are obtained. A formulation of the life time of unstable nonthinning films is proposed, based on the evolution of A and N. It is shown that the presence of uncorrelated subdomains shortens the life time of the film. Some numerical results for A(t) and N(t) at different film thicknesses h and areas S, are demonstrated, taking into account only van der Waals and capillary forces. Resonant Diffusion in Molecular Solid Structures: A new approach to Brownian motion of atomic clusters on solid surfaces is developed. The main topic discussed is the dependence of the diffusion coefficient on the fit between the surface static potential and the internal cluster configuration. It is shown this dependence is non-monotonous, which is the essence of the so-called resonant diffusion. Assuming quicker inner motion of the cluster than its translation, adiabatic separation of these variables is possible and a relatively simple expression for the diffusion coefficient is obtained. In this way, the role of cluster vibrations is accounted for, thus leading to a more complex resonance in the cluster surface mobility. Diffusion of normal alkanes in one-dimensional zeolites is theoretically studied on the basis of the stochastic equation formalism. The calculated diffusion coefficient accounts for the vibrations of the diffusing molecule and zeolite framework, molecule-zeolite interaction, and specific structure of the zeolite. It is shown that when the interaction potential is predominantly determined by the zeolite pore structure, the diffusion coefficient varies periodically with the number of carbon atoms of the alkane molecule, a phenomenon called resonant diffusion. A criterion for observable resonance is obtained from the balance between the interaction potentials of the molecule due to the atomic and pore structures of the zeolite. It shows that the diffusion is not resonant in zeolites without pore structure, such as ZSM-12. Moreover, even in zeolites with developed pore structure no resonant dependence of the diffusion constant can be detected if the pore structure energy barriers are not at least three times higher than the atomic structure energy barriers. The role of the alkane molecule vibrations is examined as well and a surprising effect of suppression of the diffusion in comparison with the case of a rigid molecule is observed. This effect is explained with the balance between the static and dynamic interaction of the molecule and zeolite. Catalytic Kinetics of Chemical Dissociation: A unified description of the catalytic effect of Cu-exchanged zeolites is proposed for the decomposition of NO. A general expression for the rate constant of NO decomposition is obtained by assuming that the rate-determining step consists of the transferring of a single atom associated with breaking of the N-O bond. The analysis is performed on the base of the generalized Langevin equation and takes into account both the potential interactions in the system and the memory effects due to the zeolite vibrations. Two different mechanisms corresponding to monomolecular and bimolecular NO decomposition are discussed. The catalytic effect in the monomolecular mechanism is related to both the Cu+ ions and zeolite O-vacancies, while in the case of the bimolecular mechanism the zeolite contributes through dissipation only. The comparison of the theoretically calculated rate constants with experimental results reveals additional information about the geometric and energetic characteristics of the active centers and confirms the logic of the proposed models.

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone

2018-03-01

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas in two dimensions, viz. to the Kob-Andersen model on the square lattice.

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

PubMed Central

Orio, Patricio; Soudry, Daniel

2012-01-01

Background The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled gating particles, while the DA was modeled using uncoupled gating particles. Implementations of DA with coupled particles, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. Main Contributions We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable – allowing an easy, transparent and efficient DA implementation, avoiding unnecessary approximations. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods, except when short time steps or low channel numbers were used. PMID:22629320

Kinetic Monte Carlo simulation of self-organized pattern formation induced by ion beam sputtering using crater functions

NASA Astrophysics Data System (ADS)

Yang, Zhangcan; Lively, Michael A.; Allain, Jean Paul

2015-02-01

The production of self-organized nanostructures by ion beam sputtering has been of keen interest to researchers for many decades. Despite numerous experimental and theoretical efforts to understand ion-induced nanostructures, there are still many basic questions open to discussion, such as the role of erosion or curvature-dependent sputtering. In this work, a hybrid MD/kMC (molecular dynamics/kinetic Monte Carlo) multiscale atomistic model is developed to investigate these knowledge gaps, and its predictive ability is validated across the experimental parameter space. This model uses crater functions, which were obtained from MD simulations, to model the prompt mass redistribution due to single-ion impacts. Defect migration, which is missing from previous models that use crater functions, is treated by a kMC Arrhenius method. Using this model, a systematic study was performed for silicon bombarded by Ar+ ions of various energies (100 eV, 250 eV, 500 eV, 700 eV, and 1000 eV) at incidence angles of 0∘ to 80∘. The simulation results were compared with experimental findings, showing good agreement in many aspects of surface evolution, such as the phase diagram. The underestimation of the ripple wavelength by the simulations suggests that surface diffusion is not the main smoothening mechanism for ion-induced pattern formation. Furthermore, the simulated results were compared with moment-description continuum theory and found to give better results, as the simulation did not suffer from the same mathematical inconsistencies as the continuum model. The key finding was that redistributive effects are dominant in the formation of flat surfaces and parallel-mode ripples, but erosive effects are dominant at high angles when perpendicular-mode ripples are formed. Ion irradiation with simultaneous sample rotation was also simulated, resulting in arrays of square-ordered dots. The patterns obtained from sample rotation were strongly correlated to the rotation speed and to the pattern types formed without sample rotation, and a critical value of about 5 rpm was found between disordered ripples and square-ordered dots. Finally, simulations of dual-beam sputtering were performed, with the resulting patterns determined by the flux ratio of the two beams and the pattern types resulting from single-beam sputtering under the same conditions.

Resist image quality control via acid diffusion constant and/or photodecomposable quencher concentration in the fabrication of 11 nm half-pitch line-and-space patterns using extreme-ultraviolet lithography

NASA Astrophysics Data System (ADS)

Kozawa, Takahiro; Santillan, Julius Joseph; Itani, Toshiro

2018-05-01

Extreme-ultraviolet (EUV) lithography will be applied to the high-volume production of semiconductor devices with 16 nm half-pitch resolution and is expected to be extended to that of devices with 11 nm half-pitch resolution. With the reduction in the feature sizes, the control of acid diffusion becomes a significant concern. In this study, the dependence of resist image quality on T PEB D acid and photodecomposable quencher concentration was investigated by the Monte Carlo method on the basis of the sensitization and reaction mechanisms of chemically amplified EUV resists. Here, T PEB and D acid are the postexposure baking (PEB) time and the acid diffusion constant, respectively. The resist image quality of 11 nm line-and-space patterns is discussed in terms of line edge roughness (LER) and stochastic defect generation. For the minimization of LER, it is necessary to design and control not only the photodecomposable quencher concentration but also T PEB D acid. In this case, D acid should be adjusted to be 0.3–1.5 nm2 s‑1 for a PEB time of 60 s with optimization of the balance among LER and stochastic pinching and bridging. Even if it is difficult to decrease D acid to the range of 0.3–1.5 nm2 s‑1, the image quality can still be controlled via only the photodecomposable quencher concentration, although LER and stochastic pinching and bridging are slightly increased. In this case, accurate control of the photodecomposable quencher concentration and the reduction in the initial standard deviation of the number of protected units are required.

On the anisotropic advection-diffusion equation with time dependent coefficients

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

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE PAGES

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

2017-02-01

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

Taming stochastic bifurcations in fractional-order systems via noise and delayed feedback

NASA Astrophysics Data System (ADS)

Sun, Zhongkui; Zhang, Jintian; Yang, Xiaoli; Xu, Wei

2017-08-01

The dynamics in fractional-order systems have been widely studied during the past decade due to the potential applications in new materials and anomalous diffusions, but the investigations have been so far restricted to a fractional-order system without time delay(s). In this paper, we report the first study of random responses of fractional-order system coupled with noise and delayed feedback. Stochastic averaging method has been utilized to determine the stationary probability density functions (PDFs) by means of the principle of minimum mean-square error, based on which stochastic bifurcations could be identified through recognizing the shape of the PDFs. It has been found that by changing the fractional order the shape of the PDFs can switch from unimodal distribution to bimodal one, or from bimodal distribution to unimodal one, thus announcing the onset of stochastic bifurcation. Further, we have demonstrated that by merely modulating the time delay, the feedback strengths, or the noise intensity, the shapes of PDFs can transit between a single peak and a double peak. Therefore, it provides an efficient candidate to control, say, induce or suppress, the stochastic bifurcations in fractional-order systems.

Prediction of nonlinear evolution character of energetic-particle-driven instabilities

DOE PAGES

Duarte, Vinicius N.; Berk, H. L.; Gorelenkov, N. N.; ...

2017-03-17

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. Furthermore, the latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation.

PubMed

Huang, Yong; Tao, Gang

2014-09-01

The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.

Prediction of nonlinear evolution character of energetic-particle-driven instabilities

NASA Astrophysics Data System (ADS)

Duarte, V. N.; Berk, H. L.; Gorelenkov, N. N.; Heidbrink, W. W.; Kramer, G. J.; Nazikian, R.; Pace, D. C.; Podestà, M.; Tobias, B. J.; Van Zeeland, M. A.

2017-05-01

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation

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

Huang, Yong, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn; Tao, Gang, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn

2014-09-01

The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.

Doi-Peliti path integral methods for stochastic systems with partial exclusion

NASA Astrophysics Data System (ADS)

Greenman, Chris D.

2018-09-01

Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then utilized to construct path integral formulations of factorial moments. We show that for many models of interest, a Magnus expansion is required to construct a suitable action, meaning actions containing a finite number of terms are not always feasible. However, for such systems, perturbative techniques are still viable, and for some examples, including carrying capacity population dynamics, and diffusion with partial exclusion, the expansions are exactly summable.

Gap junction networks can generate both ripple-like and fast ripple-like oscillations

PubMed Central

Simon, Anna; Traub, Roger D.; Vladimirov, Nikita; Jenkins, Alistair; Nicholson, Claire; Whittaker, Roger G.; Schofield, Ian; Clowry, Gavin J.; Cunningham, Mark O.; Whittington, Miles A.

2014-01-01

Fast ripples (FRs) are network oscillations, defined variously as having frequencies of > 150 to > 250 Hz, with a controversial mechanism. FRs appear to indicate a propensity of cortical tissue to originate seizures. Here, we demonstrate field oscillations, at up to 400 Hz, in spontaneously epileptic human cortical tissue in vitro, and present a network model that could explain FRs themselves, and their relation to ‘ordinary’ (slower) ripples. We performed network simulations with model pyramidal neurons, having axons electrically coupled. Ripples (< 250 Hz) were favored when conduction of action potentials, axon to axon, was reliable. Whereas ripple population activity was periodic, firing of individual axons varied in relative phase. A switch from ripples to FRs took place when an ectopic spike occurred in a cell coupled to another cell, itself multiply coupled to others. Propagation could then start in one direction only, a condition suitable for re-entry. The resulting oscillations were > 250 Hz, were sustained or interrupted, and had little jitter in the firing of individual axons. The form of model FR was similar to spontaneously occurring FRs in excised human epileptic tissue. In vitro, FRs were suppressed by a gap junction blocker. Our data suggest that a given network can produce ripples, FRs, or both, via gap junctions, and that FRs are favored by clusters of axonal gap junctions. If axonal gap junctions indeed occur in epileptic tissue, and are mediated by connexin 26 (recently shown to mediate coupling between immature neocortical pyramidal cells), then this prediction is testable. PMID:24118191

Gap junction networks can generate both ripple-like and fast ripple-like oscillations.

PubMed

Simon, Anna; Traub, Roger D; Vladimirov, Nikita; Jenkins, Alistair; Nicholson, Claire; Whittaker, Roger G; Schofield, Ian; Clowry, Gavin J; Cunningham, Mark O; Whittington, Miles A

2014-01-01

Fast ripples (FRs) are network oscillations, defined variously as having frequencies of > 150 to > 250 Hz, with a controversial mechanism. FRs appear to indicate a propensity of cortical tissue to originate seizures. Here, we demonstrate field oscillations, at up to 400 Hz, in spontaneously epileptic human cortical tissue in vitro, and present a network model that could explain FRs themselves, and their relation to 'ordinary' (slower) ripples. We performed network simulations with model pyramidal neurons, having axons electrically coupled. Ripples (< 250 Hz) were favored when conduction of action potentials, axon to axon, was reliable. Whereas ripple population activity was periodic, firing of individual axons varied in relative phase. A switch from ripples to FRs took place when an ectopic spike occurred in a cell coupled to another cell, itself multiply coupled to others. Propagation could then start in one direction only, a condition suitable for re-entry. The resulting oscillations were > 250 Hz, were sustained or interrupted, and had little jitter in the firing of individual axons. The form of model FR was similar to spontaneously occurring FRs in excised human epileptic tissue. In vitro, FRs were suppressed by a gap junction blocker. Our data suggest that a given network can produce ripples, FRs, or both, via gap junctions, and that FRs are favored by clusters of axonal gap junctions. If axonal gap junctions indeed occur in epileptic tissue, and are mediated by connexin 26 (recently shown to mediate coupling between immature neocortical pyramidal cells), then this prediction is testable. © 2013 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.

Wavelength selection and symmetry breaking in orbital wave ripples

NASA Astrophysics Data System (ADS)

Nienhuis, Jaap H.; Perron, J. Taylor; Kao, Justin C. T.; Myrow, Paul M.

2014-10-01

Sand ripples formed by waves have a uniform wavelength while at equilibrium and develop defects while adjusting to changes in the flow. These patterns arise from the interaction of the flow with the bed topography, but the specific mechanisms have not been fully explained. We use numerical flow models and laboratory wave tank experiments to explore the origins of these patterns. The wavelength of "orbital" wave ripples (λ) is directly proportional to the oscillating flow's orbital diameter (d), with many experimental and field studies finding λ/d ≈ 0.65. We demonstrate a coupling that selects this ratio: the maximum length of the flow separation zone downstream of a ripple crest equals λ when λ/d ≈ 0.65. We show that this condition maximizes the growth rate of ripples. Ripples adjusting to changed flow conditions develop defects that break the bed's symmetry. When d is shortened sufficiently, two new incipient crests appear in every trough, but only one grows into a full-sized crest. Experiments have shown that the same side (right or left) wins in every trough. We find that this occurs because incipient secondary crests slow the flow and encourage the growth of crests on the next flank. Experiments have also shown that when d is lengthened, ripple crests become increasingly sinuous and eventually break up. We find that this occurs because crests migrate preferentially toward the nearest adjacent crest, amplifying any initial sinuosity. Our results reveal the mechanisms that form common wave ripple patterns and highlight interactions among unsteady flows, sediment transport, and bed topography.

FAST TRACK COMMUNICATION: Quantum anomalies and linear response theory

NASA Astrophysics Data System (ADS)

Sela, Itamar; Aisenberg, James; Kottos, Tsampikos; Cohen, Doron

2010-08-01

The analysis of diffusive energy spreading in quantized chaotic driven systems leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation, a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient D that is proportional to the intensity ɛ2 of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time tɛ, and a self-generated (intrinsic) dephasing process leads to nonlinear dependence of D on ɛ2.

A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm.

PubMed

Barrera, Antonio; Román-Román, Patricia; Torres-Ruiz, Francisco

2018-01-01

A stochastic diffusion process, whose mean function is a hyperbolastic curve of type I, is presented. The main characteristics of the process are studied and the problem of maximum likelihood estimation for the parameters of the process is considered. To this end, the firefly metaheuristic optimization algorithm is applied after bounding the parametric space by a stagewise procedure. Some examples based on simulated sample paths and real data illustrate this development. Copyright © 2017 Elsevier B.V. All rights reserved.

Diffusion limit of Lévy-Lorentz gas is Brownian motion

NASA Astrophysics Data System (ADS)

Magdziarz, Marcin; Szczotka, Wladyslaw

2018-07-01

In this paper we analyze asymptotic behaviour of a stochastic process called Lévy-Lorentz gas. This process is aspecial kind of continuous-time random walk in which walker moves in the fixed environment composed of scattering points. Upon each collision the walker performs a flight to the nearest scattering point. This type of dynamics is observed in Lévy glasses or long quenched polymers. We show that the diffusion limit of Lévy-Lorentz gas with finite mean distance between scattering centers is the standard Brownian motion. Thus, for long times the behaviour of the Lévy-Lorentz gas is close to the diffusive regime.

Ripples in the Ripples

NASA Technical Reports Server (NTRS)

2004-01-01

This image taken by the Mars Exploration Rover Opportunity shows the dunes that line the floor of 'Endurance Crater.' Small-scale ripples on top of the larger dune waves suggest that these dunes may have been active in geologically recent times. The image was taken by the rover's panoramic camera on sol 198 (August 14, 2004).

On ripple-load, stress-corrosion, and sustained-load cracking behavior in a high strength beta titanium alloy

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

Pao, P.S.; Meyn, D.A.; Bayles, R.A.

1997-06-01

Both overaged and peakaged TIMETAL 21S beta titanium alloys exhibit significant ripple-load cracking susceptibility in salt water and in ambient air environments. At R = 0.90, the ripple-load cracking thresholds of the overaged alloy are 67% and 72% lower than the stress-corrosion cracking and sustained-load cracking thresholds. For the peakaged alloy, the reductions are 55% and 61%. The stress-corrosion cracking threshold in salt water and the sustained-load cracking threshold in air of peakaged TIMETAL 21S are significantly lower while the ripple-load cracking threshold is slightly lower than those of the overaged alloy. The stress-corrosion cracking, sustained-load cracking, and ripple-load crackingmore » resistance of peakaged TIMETAL 21S are significantly inferior to those of both beta-annealed Ti-6Al-4V and Ti-15V-3Cr-3Al-3Sn. The ripple-load cracking resistance of overaged TIMETAL 21S, though better than Ti-15V-3Cr-3Al-3Sn, is still inferior than that of beta-annealed Ti-6Al-4V.« less

Hierarchical thermoplastic rippled nanostructures regulate Schwann cell adhesion, morphology and spatial organization.

PubMed

Masciullo, Cecilia; Dell'Anna, Rossana; Tonazzini, Ilaria; Böettger, Roman; Pepponi, Giancarlo; Cecchini, Marco

2017-10-12

Periodic ripples are a variety of anisotropic nanostructures that can be realized by ion beam irradiation on a wide range of solid surfaces. Only a few authors have investigated these surfaces for tuning the response of biological systems, probably because it is challenging to directly produce them in materials that well sustain long-term cellular cultures. Here, hierarchical rippled nanotopographies with a lateral periodicity of ∼300 nm are produced from a gold-irradiated germanium mold in polyethylene terephthalate (PET), a biocompatible polymer approved by the US Food and Drug Administration for clinical applications, by a novel three-step embossing process. The effects of nano-ripples on Schwann Cells (SCs) are studied in view of their possible use for nerve-repair applications. The data demonstrate that nano-ripples can enhance short-term SC adhesion and proliferation (3-24 h after seeding), drive their actin cytoskeleton spatial organization and sustain long-term cell growth. Notably, SCs are oriented perpendicularly with respect to the nanopattern lines. These results provide information about the possible use of hierarchical nano-rippled elements for nerve-regeneration protocols.

A new adaptive self-tuning Fourier coefficients algorithm for periodic torque ripple minimization in permanent magnet synchronous motors (PMSM).

PubMed

Gómez-Espinosa, Alfonso; Hernández-Guzmán, Víctor M; Bandala-Sánchez, Manuel; Jiménez-Hernández, Hugo; Rivas-Araiza, Edgar A; Rodríguez-Reséndiz, Juvenal; Herrera-Ruíz, Gilberto

2013-03-19

A New Adaptive Self-Tuning Fourier Coefficients Algorithm for Periodic Torque Ripple Minimization in Permanent Magnet Synchronous Motors (PMSM) Torque ripple occurs in Permanent Magnet Synchronous Motors (PMSMs) due to the non-sinusoidal flux density distribution around the air-gap and variable magnetic reluctance of the air-gap due to the stator slots distribution. These torque ripples change periodically with rotor position and are apparent as speed variations, which degrade the PMSM drive performance, particularly at low speeds, because of low inertial filtering. In this paper, a new self-tuning algorithm is developed for determining the Fourier Series Controller coefficients with the aim of reducing the torque ripple in a PMSM, thus allowing for a smoother operation. This algorithm adjusts the controller parameters based on the component's harmonic distortion in time domain of the compensation signal. Experimental evaluation is performed on a DSP-controlled PMSM evaluation platform. Test results obtained validate the effectiveness of the proposed self-tuning algorithm, with the Fourier series expansion scheme, in reducing the torque ripple.

Continuous-time mean-variance portfolio selection with value-at-risk and no-shorting constraints

NASA Astrophysics Data System (ADS)

Yan, Wei

2012-01-01

An investment problem is considered with dynamic mean-variance(M-V) portfolio criterion under discontinuous prices which follow jump-diffusion processes according to the actual prices of stocks and the normality and stability of the financial market. The short-selling of stocks is prohibited in this mathematical model. Then, the corresponding stochastic Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and the solution of the stochastic HJB equation based on the theory of stochastic LQ control and viscosity solution is obtained. The efficient frontier and optimal strategies of the original dynamic M-V portfolio selection problem are also provided. And then, the effects on efficient frontier under the value-at-risk constraint are illustrated. Finally, an example illustrating the discontinuous prices based on M-V portfolio selection is presented.

A framework for discrete stochastic simulation on 3D moving boundary domains

DOE PAGES

Drawert, Brian; Hellander, Stefan; Trogdon, Michael; ...

2016-11-14

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. Finally, we demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formationmore » during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.« less

A common stochastic accumulator with effector-dependent noise can explain eye-hand coordination

PubMed Central

Gopal, Atul; Viswanathan, Pooja

2015-01-01

The computational architecture that enables the flexible coupling between otherwise independent eye and hand effector systems is not understood. By using a drift diffusion framework, in which variability of the reaction time (RT) distribution scales with mean RT, we tested the ability of a common stochastic accumulator to explain eye-hand coordination. Using a combination of behavior, computational modeling and electromyography, we show how a single stochastic accumulator to threshold, followed by noisy effector-dependent delays, explains eye-hand RT distributions and their correlation, while an alternate independent, interactive eye and hand accumulator model does not. Interestingly, the common accumulator model did not explain the RT distributions of the same subjects when they made eye and hand movements in isolation. Taken together, these data suggest that a dedicated circuit underlies coordinated eye-hand planning. PMID:25568161

Entropy production in mesoscopic stochastic thermodynamics: nonequilibrium kinetic cycles driven by chemical potentials, temperatures, and mechanical forces

NASA Astrophysics Data System (ADS)

Qian, Hong; Kjelstrup, Signe; Kolomeisky, Anatoly B.; Bedeaux, Dick

2016-04-01

Nonequilibrium thermodynamics (NET) investigates processes in systems out of global equilibrium. On a mesoscopic level, it provides a statistical dynamic description of various complex phenomena such as chemical reactions, ion transport, diffusion, thermochemical, thermomechanical and mechanochemical fluxes. In the present review, we introduce a mesoscopic stochastic formulation of NET by analyzing entropy production in several simple examples. The fundamental role of nonequilibrium steady-state cycle kinetics is emphasized. The statistical mechanics of Onsager’s reciprocal relations in this context is elucidated. Chemomechanical, thermomechanical, and enzyme-catalyzed thermochemical energy transduction processes are discussed. It is argued that mesoscopic stochastic NET in phase space provides a rigorous mathematical basis of fundamental concepts needed for understanding complex processes in chemistry, physics and biology. This theory is also relevant for nanoscale technological advances.

On the generation of log-Lévy distributions and extreme randomness

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2011-10-01

The log-normal distribution is prevalent across the sciences, as it emerges from the combination of multiplicative processes and the central limit theorem (CLT). The CLT, beyond yielding the normal distribution, also yields the class of Lévy distributions. The log-Lévy distributions are the Lévy counterparts of the log-normal distribution, they appear in the context of ultraslow diffusion processes, and they are categorized by Mandelbrot as belonging to the class of extreme randomness. In this paper, we present a natural stochastic growth model from which both the log-normal distribution and the log-Lévy distributions emerge universally—the former in the case of deterministic underlying setting, and the latter in the case of stochastic underlying setting. In particular, we establish a stochastic growth model which universally generates Mandelbrot’s extreme randomness.

Roles of effective helical ripple rates in nonlinear stability of externally induced magnetic islands

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

Nishimura, Seiya, E-mail: n-seiya@kobe-kosen.ac.jp

Magnetic islands are externally produced by resonant magnetic perturbations (RMPs) in toroidal plasmas. Spontaneous annihilation of RMP-induced magnetic islands called self-healing has been observed in helical systems. A possible mechanism of the self-healing is shielding of RMP penetration by helical ripple-induced neoclassical flows, which give rise to neoclassical viscous torques. In this study, effective helical ripple rates in multi-helicity helical systems are revisited, and a multi-helicity effect on the self-healing is investigated, based on a theoretical model of rotating magnetic islands. It is confirmed that effective helical ripple rates are sensitive to magnetic axis positions. It is newly found thatmore » self-healing thresholds also strongly depend on magnetic axis positions, which is due to dependence of neoclassical viscous torques on effective helical ripple rates.« less

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

NASA Astrophysics Data System (ADS)

Hâkansson, P.; Mella, M.; Bressanini, Dario; Morosi, Gabriele; Patrone, Marta

2006-11-01

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with Itô calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Itô calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.

Stochastic resetting in backtrack recovery by RNA polymerases

NASA Astrophysics Data System (ADS)

Roldán, Édgar; Lisica, Ana; Sánchez-Taltavull, Daniel; Grill, Stephan W.

2016-06-01

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally inactive backtracked state is determined by a kinetic competition between one-dimensional diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of one-dimensional diffusion is large compared to the rate of cleavage.

Electron transport in the stochastic fields of the reversed-field pinch

NASA Astrophysics Data System (ADS)

Kim, Myung-Hee; Punjabi, Alkesh

1996-08-01

We employ the Monte Carlo method for the calculation of anomalous transport developed by Punjabi and Boozer to calculate the particle diffusion coefficient for electrons in the stochastic magnetic fields of the reversed-field pinch (RFP). in the Monte Carlo calculations represented here, the transport mechanism is the loss of magnetic surfaces due to resistive perturbations. The equilibrium magnetic fields are represented by the Bessel function model for the RFP. The diffusion coefficient D is calculated as a function of a, the amplitude of the perturbation. We see three regimes as the amplitude of the tearing modes is increased: the Rechester—Rosenbluth regime where D scales as a2 the anomalous regime where D scales more rapidly than a2 and the Mynick—Krornmes regime where D scales more slowly than a2. Inclusion of the effects of loop voltage on the particle drift orbits in the RFP does not affect the intervals in the amplitude a where these regimes operate.

Positive feedback can lead to dynamic nanometer-scale clustering on cell membranes

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

Wehrens, Martijn; Rein ten Wolde, Pieter; Mugler, Andrew, E-mail: amugler@purdue.edu

2014-11-28

Clustering of molecules on biological membranes is a widely observed phenomenon. A key example is the clustering of the oncoprotein Ras, which is known to be important for signal transduction in mammalian cells. Yet, the mechanism by which Ras clusters form and are maintained remains unclear. Recently, it has been discovered that activated Ras promotes further Ras activation. Here we show using particle-based simulation that this positive feedback is sufficient to produce persistent clusters of active Ras molecules at the nanometer scale via a dynamic nucleation mechanism. Furthermore, we find that our cluster statistics are consistent with experimental observations ofmore » the Ras system. Interestingly, we show that our model does not support a Turing regime of macroscopic reaction-diffusion patterning, and therefore that the clustering we observe is a purely stochastic effect, arising from the coupling of positive feedback with the discrete nature of individual molecules. These results underscore the importance of stochastic and dynamic properties of reaction diffusion systems for biological behavior.« less

Laboratory Experiments of Sand Ripples with Bimodal Size Distributions Under Asymmetric Oscillatory Flows

NASA Astrophysics Data System (ADS)

Calantoni, J.; Landry, B. J.

2010-12-01

The dynamics of sand ripples are vital to understanding numerous coastal processes such as sediment transport, wave attenuation, boundary layer development, and seafloor acoustic properties. Though significant laboratory research has been conducted to elucidate oscillatory flow morphodynamics under various constant and transient forcing conditions, the majority of the previous experiments were conducted only for beds with unimodal size distributions of sediment. Recent oscillatory flow experiments as well as past laboratory observations in uniform flows suggest that the presence of heterogeneous size sand compositions may significantly impact ripple morphology, resulting in a variety of observable effects (e.g., sediment sorting, bed armoring, and altered transport rates). Experimental work was conducted in a small oscillatory flow tunnel at the Sediment Dynamics Laboratory at the Naval Research Laboratory, Stennis Space Center. Three different monochromatic oscillatory forcings having velocity asymmetry were used to study sand ripple dynamics over five bimodal and two unimodal sediment beds. The seven different mixtures were composed using two unimodal sands of different colors (blue/white) and median grain diameters (d=0.31 mm / d=0.65 mm) combined into various mixtures by mass (i.e., 0/100; 10/90; 25/75; 50/50; 75/25; 90/10; and 100/0 which denotes mass percentage of blue/white sand, respectively, within each mixture). High-definition video of the sediment bed profile was acquired in conjunction with sediment trap measurements to resolve differences in ripple geometries, migration and evolution rates due to the different sediment mixtures and flow conditions. Observational findings clearly illustrate sediment stratification within ripple crests and the depth of the active mixing layer in addition to supporting sediment sorting in previous research on symmetric oscillatory flows in which the larger grains collect on top of ripple crests and smaller grains in the troughs. Preliminary quantitative results illuminate variations in equilibrium ripple geometry, ripple migration rates, and transition time scales between equilibrium states, all as functions of the sediment size mixture and flow forcing.

Evaluation of beam delivery and ripple filter design for non-isocentric proton and carbon ion therapy.

PubMed

Grevillot, L; Stock, M; Vatnitsky, S

2015-10-21

This study aims at selecting and evaluating a ripple filter design compatible with non-isocentric proton and carbon ion scanning beam treatment delivery for a compact nozzle. The use of non-isocentric treatments when the patient is shifted as close as possible towards the nozzle exit allows for a reduction in the air gap and thus an improvement in the quality of scanning proton beam treatment delivery. Reducing the air gap is less important for scanning carbon ions, but ripple filters are still necessary for scanning carbon ion beams to reduce the number of energy steps required to deliver homogeneous SOBP. The proper selection of ripple filters also allows a reduction in the possible transverse and depth-dose inhomogeneities that could appear in non-isocentric conditions in particular. A thorough review of existing ripple filter designs over the past 16 years is performed and a design for non-isocentric treatment delivery is presented. A unique ripple filter quality index (QIRiFi) independent of the particle type and energy and representative of the ratio between energy modulation and induced scattering is proposed. The Bragg peak width evaluated at the 80% dose level (BPW80) is proposed to relate the energy modulation of the delivered Bragg peaks and the energy layer step size allowing the production of homogeneous SOBP. Gate/Geant4 Monte Carlo simulations have been validated for carbon ion and ripple filter simulations based on measurements performed at CNAO and subsequently used for a detailed analysis of the proposed ripple filter design. A combination of two ripple filters in a series has been validated for non-isocentric delivery and did not show significant transverse and depth-dose inhomogeneities. Non-isocentric conditions allow a significant reduction in the spot size at the patient entrance (up to 350% and 200% for protons and carbon ions with range shifter, respectively), and therefore in the lateral penumbra in the patients.