Weakly anomalous diffusion with non-Gaussian propagators

NASA Astrophysics Data System (ADS)

Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.

2012-08-01

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.

Analyzing signal attenuation in PFG anomalous diffusion via a non-Gaussian phase distribution approximation approach by fractional derivatives.

PubMed

Lin, Guoxing

2016-11-21

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in nuclear magnetic resonance and magnetic resonance imaging. However, the interpretation of PFG anomalous diffusion is complicated. Moreover, the exact signal attenuation expression including the finite gradient pulse width effect has not been obtained based on fractional derivatives for PFG anomalous diffusion. In this paper, a new method, a Mainardi-Luchko-Pagnini (MLP) phase distribution approximation, is proposed to describe PFG fractional diffusion. MLP phase distribution is a non-Gaussian phase distribution. From the fractional derivative model, both the probability density function (PDF) of a spin in real space and the PDF of the spin's accumulating phase shift in virtual phase space are MLP distributions. The MLP phase distribution leads to a Mittag-Leffler function based PFG signal attenuation, which differs significantly from the exponential attenuation for normal diffusion and from the stretched exponential attenuation for fractional diffusion based on the fractal derivative model. A complete signal attenuation expression E α (-D f b α,β * ) including the finite gradient pulse width effect was obtained and it can handle all three types of PFG fractional diffusions. The result was also extended in a straightforward way to give a signal attenuation expression of fractional diffusion in PFG intramolecular multiple quantum coherence experiments, which has an n β dependence upon the order of coherence which is different from the familiar n 2 dependence in normal diffusion. The results obtained in this study are in agreement with the results from the literature. The results in this paper provide a set of new, convenient approximation formalisms to interpret complex PFG fractional diffusion experiments.

Anomalous Diffusion in a Trading Model

NASA Astrophysics Data System (ADS)

Khidzir, Sidiq Mohamad; Wan Abdullah, Wan Ahmad Tajuddin

2009-07-01

The result of the trading model by Chakrabarti et al. [1] is the wealth distribution with a mixed exponential and power law distribution. Based on the motivation of studying the dynamics behind the flow of money similar to work done by Brockmann [2, 3] we track the flow of money in this trading model to observe anomalous diffusion in the form of long waiting times and Levy Flights.

Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion

PubMed Central

Bodrova, Anna S.; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Safdari, Hadiseh; Sokolov, Igor M.; Metzler, Ralf

2016-01-01

It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. PMID:27462008

Inferring Diffusion Dynamics from FCS in Heterogeneous Nuclear Environments

PubMed Central

Tsekouras, Konstantinos; Siegel, Amanda P.; Day, Richard N.; Pressé, Steve

2015-01-01

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show—first using synthetic data—that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell’s nucleus as well as 2) in the cell’s cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins. PMID:26153697

Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions.

PubMed

Langlands, T A M; Henry, B I; Wearne, S L

2009-12-01

We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.

Conformable derivative approach to anomalous diffusion

NASA Astrophysics Data System (ADS)

Zhou, H. W.; Yang, S.; Zhang, S. Q.

2018-02-01

By using a new derivative with fractional order, referred to conformable derivative, an alternative representation of the diffusion equation is proposed to improve the modeling of anomalous diffusion. The analytical solutions of the conformable derivative model in terms of Gauss kernel and Error function are presented. The power law of the mean square displacement for the conformable diffusion model is studied invoking the time-dependent Gauss kernel. The parameters related to the conformable derivative model are determined by Levenberg-Marquardt method on the basis of the experimental data of chloride ions transportation in reinforced concrete. The data fitting results showed that the conformable derivative model agrees better with the experimental data than the normal diffusion equation. Furthermore, the potential application of the proposed conformable derivative model of water flow in low-permeability media is discussed.

A velocity-dependent anomalous radial transport model for (2-D, 2-V) kinetic transport codes

NASA Astrophysics Data System (ADS)

Bodi, Kowsik; Krasheninnikov, Sergei; Cohen, Ron; Rognlien, Tom

2008-11-01

Plasma turbulence constitutes a significant part of radial plasma transport in magnetically confined plasmas. This turbulent transport is modeled in the form of anomalous convection and diffusion coefficients in fluid transport codes. There is a need to model the same in continuum kinetic edge codes [such as the (2-D, 2-V) transport version of TEMPEST, NEO, and the code being developed by the Edge Simulation Laboratory] with non-Maxwellian distributions. We present an anomalous transport model with velocity-dependent convection and diffusion coefficients leading to a diagonal transport matrix similar to that used in contemporary fluid transport models (e.g., UEDGE). Also presented are results of simulations corresponding to radial transport due to long-wavelength ExB turbulence using a velocity-independent diffusion coefficient. A BGK collision model is used to enable comparison with fluid transport codes.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion.

PubMed

López-Sánchez, Erick J; Romero, Juan M; Yépez-Martínez, Huitzilin

2017-09-01

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion

NASA Astrophysics Data System (ADS)

López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin

2017-09-01

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Inferring diffusion dynamics from FCS in heterogeneous nuclear environments.

PubMed

Tsekouras, Konstantinos; Siegel, Amanda P; Day, Richard N; Pressé, Steve

2015-07-07

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show-first using synthetic data-that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell's nucleus as well as 2) in the cell's cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Random walks exhibiting anomalous diffusion: elephants, urns and the limits of normality

NASA Astrophysics Data System (ADS)

Kearney, Michael J.; Martin, Richard J.

2018-01-01

A random walk model is presented which exhibits a transition from standard to anomalous diffusion as a parameter is varied. The model is a variant on the elephant random walk and differs in respect of the treatment of the initial state, which in the present work consists of a given number N of fixed steps. This also links the elephant random walk to other types of history dependent random walk. As well as being amenable to direct analysis, the model is shown to be asymptotically equivalent to a non-linear urn process. This provides fresh insights into the limiting form of the distribution of the walker’s position at large times. Although the distribution is intrinsically non-Gaussian in the anomalous diffusion regime, it gradually reverts to normal form when N is large under quite general conditions.

Wanted: A Positive Control for Anomalous Subdiffusion

PubMed Central

Saxton, Michael J.

2012-01-01

Anomalous subdiffusion in cells and model systems is an active area of research. The main questions are whether diffusion is anomalous or normal, and if it is anomalous, its mechanism. The subject is controversial, especially the hypothesis that crowding causes anomalous subdiffusion. Anomalous subdiffusion measurements would be strengthened by an experimental standard, particularly one able to cross-calibrate the different types of measurements. Criteria for a calibration standard are proposed. First, diffusion must be anomalous over the length and timescales of the different measurements. The length-scale is fundamental; the time scale can be adjusted through the viscosity of the medium. Second, the standard must be theoretically well understood, with a known anomalous subdiffusion exponent, ideally readily tunable. Third, the standard must be simple, reproducible, and independently characterizable (by, for example, electron microscopy for nanostructures). Candidate experimental standards are evaluated, including obstructed lipid bilayers; aqueous systems obstructed by nanopillars; a continuum percolation system in which a prescribed fraction of randomly chosen obstacles in a regular array is ablated; single-file diffusion in pores; transient anomalous subdiffusion due to binding of particles in arrays such as transcription factors in randomized DNA arrays; and computer-generated physical trajectories. PMID:23260043

Study of electron transport in a Hall thruster by axial–radial fully kinetic particle simulation

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

Cho, Shinatora, E-mail: choh.shinatora@jaxa.jp; Kubota, Kenichi; Funaki, Ikkoh

2015-10-15

Electron transport across a magnetic field in a magnetic-layer-type Hall thruster was numerically investigated for the future predictive modeling of Hall thrusters. The discharge of a 1-kW-class magnetic-layer-type Hall thruster designed for high-specific-impulse operation was modeled using an r-z two-dimensional fully kinetic particle code with and without artificial electron-diffusion models. The thruster performance results showed that both electron transport models captured the experimental result within discrepancies less than 20% in thrust and discharge current for all the simulated operation conditions. The electron cross-field transport mechanism of the so-called anomalous diffusion was self-consistently observed in the simulation without artificial diffusion models;more » the effective electron mobility was two orders of magnitude higher than the value obtained using the classical diffusion theory. To account for the self-consistently observed anomalous transport, the oscillation of plasma properties was speculated. It was suggested that the enhanced random-walk diffusion due to the velocity oscillation of low-frequency electron flow could explain the observed anomalous diffusion within an order of magnitude. The dominant oscillation mode of the electron flow velocity was found to be 20 kHz, which was coupled to electrostatic oscillation excited by global ionization instability.« less

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.

Anomalous Diffusion Approximation of Risk Processes in Operational Risk of Non-Financial Corporations

NASA Astrophysics Data System (ADS)

Magdziarz, M.; Mista, P.; Weron, A.

2007-05-01

We introduce an approximation of the risk processes by anomalous diffusion. In the paper we consider the case, where the waiting times between successive occurrences of the claims belong to the domain of attraction of alpha -stable distribution. The relationship between the obtained approximation and the celebrated fractional diffusion equation is emphasised. We also establish upper bounds for the ruin probability in the considered model and give some numerical examples.

Anomalous diffusion in a dynamical optical lattice

NASA Astrophysics Data System (ADS)

Zheng, Wei; Cooper, Nigel R.

2018-02-01

Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-André model which can cause localization of single-particle wave functions. We show that atomic wave packets in this dynamical lattice generically spread via anomalous diffusion, which can be tuned between superdiffusive and subdiffusive regimes. This anomalous diffusion arises from an interplay between Anderson localization and quantum fluctuations of the cavity field.

Anomalous transport in the crowded world of biological cells

NASA Astrophysics Data System (ADS)

Höfling, Felix; Franosch, Thomas

2013-04-01

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Fractional order analysis of Sephadex gel structures: NMR measurements reflecting anomalous diffusion

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Akpa, Belinda S.; Neuberger, Thomas; Webb, Andrew G.

2011-12-01

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-( bD) α], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4000 s mm -2). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

PubMed

Henry, B I; Langlands, T A M; Wearne, S L

2006-09-01

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Non-Brownian diffusion in lipid membranes: Experiments and simulations.

PubMed

Metzler, R; Jeon, J-H; Cherstvy, A G

2016-10-01

The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Anomalous diffusion and dynamics of fluorescence recovery after photobleaching in the random-comb model

NASA Astrophysics Data System (ADS)

Yuste, S. B.; Abad, E.; Baumgaertner, A.

2016-07-01

We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ ,P (ℓ ) ˜ℓ-(1 +α ) (α >0 ). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.

Fractional Dynamics of Single File Diffusion in Dusty Plasma Ring

NASA Astrophysics Data System (ADS)

Muniandy, S. V.; Chew, W. X.; Asgari, H.; Wong, C. S.; Lim, S. C.

2011-11-01

Single file diffusion (SFD) refers to the constrained motion of particles in quasi-one-dimensional channel such that the particles are unable to pass each other. Possible SFD of charged dust confined in biharmonic annular potential well with screened Coulomb interaction is investigated. Transition from normal diffusion to anomalous sub-diffusion behaviors is observed. Deviation from SFD's mean square displacement scaling behavior of 1/2-exponent may occur in strongly interacting systems. A phenomenological model based on fractional Langevin equation is proposed to account for the anomalous SFD behavior in dusty plasma ring.

Persistent-random-walk approach to anomalous transport of self-propelled particles

NASA Astrophysics Data System (ADS)

Sadjadi, Zeinab; Shaebani, M. Reza; Rieger, Heiko; Santen, Ludger

2015-06-01

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

Anomalous diffusion and scaling in coupled stochastic processes

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

Bel, Golan; Nemenman, Ilya

2009-01-01

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the Pocker-Planck the friction coefficient of the first depends on the state of the second. Integrating out the latter, we derive the Focker-Planck equation for the probability distribution of the former. This has the fonn of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well. Themore » diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standandard, diffusive Langevin descritpion.« less

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 < α , β ≤ 2 } based on the fractional derivative, has not been obtained, where α and β are time and space derivative orders. It is essential to derive a general PFG signal attenuation expression including the FGPW effect for PFG anisotropic anomalous diffusion research. In this paper, two recently developed modified-Bloch equations, the fractal differential modified-Bloch equation and the fractional integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.

PubMed

Ingo, Carson; Magin, Richard L; Parrish, Todd B

2014-11-01

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

Crossover from anomalous to normal diffusion in porous media

NASA Astrophysics Data System (ADS)

Aarão Reis, F. D. A.; di Caprio, Dung

2014-06-01

Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover to long-time normal diffusion is observed in most samples. The anomalous concentration profile remains at long times in very porous solids if the walker steps are restricted to nearest neighbors and is accompanied with subdiffusion features. These findings are correlated with a decay of the explored area with z. The study of RW of tracer particles left at the internal part of the solid rules out an interpretation by diffusion equations with position-dependent coefficients. A model of RW in a tube of decreasing cross section explains those results by showing long crossovers from an effective subdiffusion regime to an asymptotic normal diffusion. The crossover position and density are analytically calculated for a tube with area decreasing exponentially with z and show good agreement with numerical data. The anomalous decay of the concentration profile is interpreted as a templating effect of the tube shape on the total number of diffusing particles at each depth, while the volumetric concentration in the actually explored porous region may not have significant decay. These results may explain the anomalous diffusion of metal atoms in porous deposits observed in recent works. They also confirm the difficulty in interpreting experimental or computational data on anomalous transport reported in recent works, particularly if only the concentration profiles are measured.

Anomalous diffusion of poly(ethylene oxide) in agarose gels.

PubMed

Brenner, Tom; Matsukawa, Shingo

2016-11-01

We report on the effect of probe size and diffusion time of poly(ethylene) oxide in agarose gels. Time-dependence of the diffusion coefficient, reflecting anomalous diffusion, was observed for poly(ethylene) oxide chains with hydrodynamic radii exceeding about 20nm at an agarose concentration of 2%. The main conclusion is that the pore distribution includes pores that are only several nm across, in agreement with scattering reports in the literature. Interpretation of the diffusion coefficient dependence on the probe size based on a model of entangled rigid rods yielded a rod length of 72nm. Copyright © 2016. Published by Elsevier B.V.

Anomalous diffusion for bed load transport with a physically-based model

NASA Astrophysics Data System (ADS)

Fan, N.; Singh, A.; Foufoula-Georgiou, E.; Wu, B.

2013-12-01

Diffusion of bed load particles shows both normal and anomalous behavior for different spatial-temporal scales. Understanding and quantifying these different types of diffusion is important not only for the development of theoretical models of particle transport but also for practical purposes, e.g., river management. Here we extend a recently proposed physically-based model of particle transport by Fan et al. [2013] to further develop an Episodic Langevin equation (ELE) for individual particle motion which reproduces the episodic movement (start and stop) of sediment particles. Using the proposed ELE we simulate particle movements for a large number of uniform size particles, incorporating different probability distribution functions (PDFs) of particle waiting time. For exponential PDFs of waiting times, particles reveal ballistic motion in short time scales and turn to normal diffusion at long time scales. The PDF of simulated particle travel distances also shows a change in its shape from exponential to Gamma to Gaussian with a change in timescale implying different diffusion scaling regimes. For power-law PDF (with power - μ) of waiting times, the asymptotic behavior of particles at long time scales reveals both super-diffusion and sub-diffusion, however, only very heavy tailed waiting times (i.e. 1.0 < μ < 1.5) could result in sub-diffusion. We suggest that the contrast between our results and previous studies (for e.g., studies based on fractional advection-diffusion models of thin/heavy tailed particle hops and waiting times) results could be due the assumption in those studies that the hops are achieved instantaneously, but in reality, particles achieve their hops within finite times (as we simulate here) instead of instantaneously, even if the hop times are much shorter than waiting times. In summary, this study stresses on the need to rethink the alternative models to the previous models, such as, fractional advection-diffusion equations, for studying the anomalous diffusion of bed load particles. The implications of these results for modeling sediment transport are discussed.

Diffusion of a particle in the spatially correlated exponential random energy landscape: Transition from normal to anomalous diffusion.

PubMed

Novikov, S V

2018-01-14

Diffusive transport of a particle in a spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime for the 1D transport model and found that for slow decaying correlation functions the diffusivity becomes singular at some particular temperature higher than the temperature of the transition to the true non-equilibrium dispersive transport regime. It means that the diffusion becomes anomalous and does not follow the usual ∝ t 1/2 law. In such situation, the fully developed non-equilibrium regime emerges in two stages: first, at some temperature there is the transition from the normal to anomalous diffusion, and then at lower temperature the average velocity for the infinite medium goes to zero, thus indicating the development of the true dispersive regime. Validity of the Einstein relation is discussed for the situation where the diffusivity does exist. We provide also some arguments in favor of conservation of the major features of the new transition scenario in higher dimensions.

Multiple Diffusion Mechanisms Due to Nanostructuring in Crowded Environments

PubMed Central

Sanabria, Hugo; Kubota, Yoshihisa; Waxham, M. Neal

2007-01-01

One of the key questions regarding intracellular diffusion is how the environment affects molecular mobility. Mostly, intracellular diffusion has been described as hindered, and the physical reasons for this behavior are: immobile barriers, molecular crowding, and binding interactions with immobile or mobile molecules. Using results from multi-photon fluorescence correlation spectroscopy, we describe how immobile barriers and crowding agents affect translational mobility. To study the hindrance produced by immobile barriers, we used sol-gels (silica nanostructures) that consist of a continuous solid phase and aqueous phase in which fluorescently tagged molecules diffuse. In the case of molecular crowding, translational mobility was assessed in increasing concentrations of 500 kDa dextran solutions. Diffusion of fluorescent tracers in both sol-gels and dextran solutions shows clear evidence of anomalous subdiffusion. In addition, data from the autocorrelation function were analyzed using the maximum entropy method as adapted to fluorescence correlation spectroscopy data and compared with the standard model that incorporates anomalous diffusion. The maximum entropy method revealed evidence of different diffusion mechanisms that had not been revealed using the anomalous diffusion model. These mechanisms likely correspond to nanostructuring in crowded environments and to the relative dimensions of the crowding agent with respect to the tracer molecule. Analysis with the maximum entropy method also revealed information about the degree of heterogeneity in the environment as reported by the behavior of diffusive molecules. PMID:17040979

Two-photon time-lapse microscopy of BODIPY-cholesterol reveals anomalous sterol diffusion in chinese hamster ovary cells

PubMed Central

2012-01-01

Background Cholesterol is an important membrane component, but our knowledge about its transport in cells is sparse. Previous imaging studies using dehydroergosterol (DHE), an intrinsically fluorescent sterol from yeast, have established that vesicular and non-vesicular transport modes contribute to sterol trafficking from the plasma membrane. Significant photobleaching, however, limits the possibilities for in-depth analysis of sterol dynamics using DHE. Co-trafficking studies with DHE and the recently introduced fluorescent cholesterol analog BODIPY-cholesterol (BChol) suggested that the latter probe has utility for prolonged live-cell imaging of sterol transport. Results We found that BChol is very photostable under two-photon (2P)-excitation allowing the acquisition of several hundred frames without significant photobleaching. Therefore, long-term tracking and diffusion measurements are possible. Two-photon temporal image correlation spectroscopy (2P-TICS) provided evidence for spatially heterogeneous diffusion constants of BChol varying over two orders of magnitude from the cell interior towards the plasma membrane, where D ~ 1.3 μm2/s. Number and brightness (N&B) analysis together with stochastic simulations suggest that transient partitioning of BChol into convoluted membranes slows local sterol diffusion. We observed sterol endocytosis as well as fusion and fission of sterol-containing endocytic vesicles. The mobility of endocytic vesicles, as studied by particle tracking, is well described by a model for anomalous subdiffusion on short time scales with an anomalous exponent α ~ 0.63 and an anomalous diffusion constant of Dα = 1.95 x 10-3 μm2/sα. On a longer time scale (t > ~5 s), a transition to superdiffusion consistent with slow directed transport with an average velocity of v ~ 6 x 10-3 μm/s was observed. We present an analytical model that bridges the two regimes and fit this model to vesicle trajectories from control cells and cells with disrupted microtubule or actin filaments. Both treatments reduced the anomalous diffusion constant and the velocity by ~40-50%. Conclusions The mobility of sterol-containing vesicles on the short time scale could reflect dynamic rearrangements of the cytoskeleton, while directed transport of sterol vesicles occurs likely along both, microtubules and actin filaments. Spatially varying anomalous diffusion could contribute to fine-tuning and local regulation of intracellular sterol transport. PMID:23078907

A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.

2016-10-01

Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the perspective of computational accuracy and efficiency.

Fractional motion model for characterization of anomalous diffusion from NMR signals.

PubMed

Fan, Yang; Gao, Jia-Hong

2015-07-01

Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

Fractional motion model for characterization of anomalous diffusion from NMR signals

NASA Astrophysics Data System (ADS)

Fan, Yang; Gao, Jia-Hong

2015-07-01

Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

Tissue microstructure features derived from anomalous diffusion measurements in magnetic resonance imaging.

PubMed

Yu, Qiang; Reutens, David; O'Brien, Kieran; Vegh, Viktor

2017-02-01

Tissue microstructure features, namely axon radius and volume fraction, provide important information on the function of white matter pathways. These parameters vary on the scale much smaller than imaging voxels (microscale) yet influence the magnetic resonance imaging diffusion signal at the image voxel scale (macroscale) in an anomalous manner. Researchers have already mapped anomalous diffusion parameters from magnetic resonance imaging data, but macroscopic variations have not been related to microscale influences. With the aid of a tissue model, we aimed to connect anomalous diffusion parameters to axon radius and volume fraction using diffusion-weighted magnetic resonance imaging measurements. An ex vivo human brain experiment was performed to directly validate axon radius and volume fraction measurements in the human brain. These findings were validated using electron microscopy. Additionally, we performed an in vivo study on nine healthy participants to map axon radius and volume fraction along different regions of the corpus callosum projecting into various cortical areas identified using tractography. We found a clear relationship between anomalous diffusion parameters and axon radius and volume fraction. We were also able to map accurately the trend in axon radius along the corpus callosum, and in vivo findings resembled the low-high-low-high behaviour in axon radius demonstrated previously. Axon radius and volume fraction measurements can potentially be used in brain connectivity studies and to understand the implications of white matter structure in brain diseases and disorders. Hum Brain Mapp 38:1068-1081, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Numerical Test of the Additivity Principle in Anomalous Transport

NASA Astrophysics Data System (ADS)

Tamaki, Shuji

2017-10-01

The additivity principle (AP) is one of the remarkable predictions that systematically generates all information on current fluctuations once the value of average current in the linear response regime is input. However, conditions to justify the AP are still ambiguous. We hence consider three tractable models, and discuss possible conditions. The models include the harmonic chain (HC), momentum exchange (ME) model, and momentum flip (MF) model, which respectively show ballistic, anomalous, and diffusive transport. We compare the heat current cumulants predicted by the AP with exact numerical data obtained for these models. The HC does not show the AP, whereas the MF model satisfies it, as expected, since the AP was originally proposed for diffusive systems. Surprisingly, the ME model also shows the AP. The ME model is known to show the anomalous transport similar to that shown in nonlinear systems such as the Fermi-Pasta-Ulam model. Our finding indicates that general nonlinear systems may satisfy the AP. Possible conditions for satisfying the AP are discussed.

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels.

PubMed

Li, Baowen; Wang, Jiao; Wang, Lei; Zhang, Gang

2005-03-01

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.

Onset of anomalous diffusion from local motion rules

NASA Astrophysics Data System (ADS)

de Nigris, Sarah; Carletti, Timoteo; Lambiotte, Renaud

2017-02-01

Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation in animals and also in human mobility. One way to create such regimes are Lévy flights, where the walkers are allowed to perform jumps, the "flights," that can eventually be very long as their length distribution is asymptotically power-law distributed. In our work, we present a model in which walkers are allowed to perform, on a one-dimensional lattice, "cascades" of n unitary steps instead of one jump of a randomly generated length, as in the Lévy case, where n is drawn from a cascade distribution pn. We show that this local mechanism may give rise to superdiffusion or normal diffusion when pn is distributed as a power law. We also introduce waiting times that are power-law distributed as well and therefore the probability distribution scaling is steered by the two local distributions power-law exponents. As a perspective, our approach may engender a possible generalization of anomalous diffusion in context where distances are difficult to define, as in the case of complex networks, and also provide an interesting model for diffusion in temporal networks.

Nonlinear ELM simulations based on a nonideal peeling–ballooning model using the BOUT++ code

DOE PAGES

Xu, X. Q.; Dudson, B. D.; Snyder, P. B.; ...

2011-09-23

A minimum set of equations based on the peeling–ballooning (P–B) model with nonideal physics effects (diamagnetic drift, E × B drift, resistivity and anomalous electron viscosity) is found to simulate pedestal collapse when using the BOUT++ simulation code, developed in part from the original fluid edge code BOUT. Linear simulations of P–B modes find good agreement in growth rate and mode structure with ELITE calculations. The influence of the E × B drift, diamagnetic drift, resistivity, anomalous electron viscosity, ion viscosity and parallel thermal diffusivity on P–B modes is being studied; we find that (1) the diamagnetic drift and Emore » × B drift stabilize the P–B mode in a manner consistent with theoretical expectations; (2) resistivity destabilizes the P–B mode, leading to resistive P–B mode; (3) anomalous electron and parallel ion viscosities destabilize the P–B mode, leading to a viscous P–B mode; (4) perpendicular ion viscosity and parallel thermal diffusivity stabilize the P–B mode. With addition of the anomalous electron viscosity under the assumption that the anomalous kinematic electron viscosity is comparable to the anomalous electron perpendicular thermal diffusivity, or the Prandtl number is close to unity, it is found from nonlinear simulations using a realistic high Lundquist number that the pedestal collapse is limited to the edge region and the ELM size is about 5–10% of the pedestal stored energy. Furthermore, this is consistent with many observations of large ELMs. The estimated island size is consistent with the size of fast pedestal pressure collapse. In the stable α-zones of ideal P–B modes, nonlinear simulations of viscous ballooning modes or current-diffusive ballooning mode (CDBM) for ITER H-mode scenarios are presented.« less

Liquid-liquid phase transition and anomalous diffusion in simulated liquid GeO 2

NASA Astrophysics Data System (ADS)

Hoang, Vo Van; Anh, Nguyen Huynh Tuan; Zung, Hoang

2007-03-01

We perform molecular dynamics (MD) simulation of diffusion in liquid GeO 2 at the temperatures ranged from 3000 to 5000 K and densities ranged from 3.65 to 7.90 g/cm 3. Simulations were done in a model containing 3000 particles with the new interatomic potentials for liquid and amorphous GeO 2, which have weak Coulomb interaction and Morse-type short-range interaction. We found a liquid-liquid phase transition in simulated liquid GeO 2 from a tetrahedral to an octahedral network structure upon compression. Moreover, such phase transition accompanied with an anomalous diffusion of particles in liquid GeO 2 that the diffusion constant of both Ge and O particles strongly increases with increasing density (e.g. with increasing pressure) and it shows a maximum at the density around 4.95 g/cm 3. The possible relation between anomalous diffusion of particles and structural phase transition in the system has been discussed.

A new fractional operator of variable order: Application in the description of anomalous diffusion

NASA Astrophysics Data System (ADS)

Yang, Xiao-Jun; Machado, J. A. Tenreiro

2017-09-01

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

Characterizing acid diffusion lengths in chemically amplified resists from measurements of deprotection kinetics

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

Patil, Abhijit A.; Pandey, Yogendra Narayan; Doxastakis, Manolis

2014-10-01

The acid-catalyzed deprotection of glassy poly(4-hydroxystyrene-co-tertbutyl acrylate) films was studied with infrared absorbance spectroscopy and stochastic simulations. Experimental data were interpreted with a simple description of subdiffusive acid transport coupled to second-order acid loss. This model predicts key attributes of observed deprotection rates, such as fast reaction at short times, slow reaction at long times, and a nonlinear dependence on acid loading. Fickian diffusion is approached by increasing the post-exposure bake temperature or adding plasticizing agents to the polymer resin. These findings demonstrate that acid mobility and overall deprotection kinetics are coupled to glassy matrix dynamics. To complement the analysismore » of bulk kinetics, acid diffusion lengths were calculated from the anomalous transport model and compared with nanopattern line widths. The consistent scaling between experiments and simulations suggests that the anomalous diffusion model could be further developed into a predictive lithography tool.« less

Anomalous diffusion in the evolution of soccer championship scores: Real data, mean-field analysis, and an agent-based model

NASA Astrophysics Data System (ADS)

da Silva, Roberto; Vainstein, Mendeli H.; Gonçalves, Sebastián; Paula, Felipe S. F.

2013-08-01

Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva , Comput. Phys. Commun.CPHCBZ0010-465510.1016/j.cpc.2012.10.030 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.

Fractional phenomenology of cosmic ray anomalous diffusion

NASA Astrophysics Data System (ADS)

Uchaikin, V. V.

2013-11-01

We review the evolution of the cosmic ray diffusion concept from the ordinary (Einstein) model of Brownian motion to the fractional models that appeared in the last decade. The mathematical and physical foundations of these models are discussed, as are their consequences, related problems, and prospects for further development.

Comparisons of anomalous and collisional radial transport with a continuum kinetic edge code

NASA Astrophysics Data System (ADS)

Bodi, K.; Krasheninnikov, S.; Cohen, R.; Rognlien, T.

2009-05-01

Modeling of anomalous (turbulence-driven) radial transport in controlled-fusion plasmas is necessary for long-time transport simulations. Here the focus is continuum kinetic edge codes such as the (2-D, 2-V) transport version of TEMPEST, NEO, and the code being developed by the Edge Simulation Laboratory, but the model also has wider application. Our previously developed anomalous diagonal transport matrix model with velocity-dependent convection and diffusion coefficients allows contact with typical fluid transport models (e.g., UEDGE). Results are presented that combine the anomalous transport model and collisional transport owing to ion drift orbits utilizing a Krook collision operator that conserves density and energy. Comparison is made of the relative magnitudes and possible synergistic effects of the two processes for typical tokamak device parameters.

Anomalous Diffusion of Single Particles in Cytoplasm

PubMed Central

Regner, Benjamin M.; Vučinić, Dejan; Domnisoru, Cristina; Bartol, Thomas M.; Hetzer, Martin W.; Tartakovsky, Daniel M.; Sejnowski, Terrence J.

2013-01-01

The crowded intracellular environment poses a formidable challenge to experimental and theoretical analyses of intracellular transport mechanisms. Our measurements of single-particle trajectories in cytoplasm and their random-walk interpretations elucidate two of these mechanisms: molecular diffusion in crowded environments and cytoskeletal transport along microtubules. We employed acousto-optic deflector microscopy to map out the three-dimensional trajectories of microspheres migrating in the cytosolic fraction of a cellular extract. Classical Brownian motion (BM), continuous time random walk, and fractional BM were alternatively used to represent these trajectories. The comparison of the experimental and numerical data demonstrates that cytoskeletal transport along microtubules and diffusion in the cytosolic fraction exhibit anomalous (nonFickian) behavior and posses statistically distinct signatures. Among the three random-walk models used, continuous time random walk provides the best representation of diffusion, whereas microtubular transport is accurately modeled with fractional BM. PMID:23601312

Dynamical transition for a particle in a squared Gaussian potential

NASA Astrophysics Data System (ADS)

Touya, C.; Dean, D. S.

2007-02-01

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by ψ = phi2/2 where phi is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.

Following fluctuating signs: Anomalous active superdiffusion of swimmers in anisotropic media

NASA Astrophysics Data System (ADS)

Toner, John; Löwen, Hartmut; Wensink, Henricus H.

2016-06-01

Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic nematic background. While the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is superdiffusive, with an anomalous scaling proportional to t lnt of the mean-square displacement with time t . This behavior is predicted by an analytical theory that we present here and is corroborated by numerical simulation of active particle diffusion in a simple lattice model for a nematic liquid crystal. It is universal for any collection of self-propelled elements (e.g., bacteria or active rods) moving in a nematic background, provided only that the swimmers are sufficiently dilute that their interactions with each other can be neglected and that they do not perform hairpin turns.

Anomalous Transport of High Energy Cosmic Rays in Galactic Superbubbles

NASA Technical Reports Server (NTRS)

Barghouty, Nasser F.

2014-01-01

High-energy cosmic rays may exhibit anomalous transport as they traverse and are accelerated by a collection of supernovae explosions in a galactic superbubble. Signatures of this anomalous transport can show up in the particles' evolution and their spectra. In a continuous-time-random- walk (CTRW) model assuming standard diffusive shock acceleration theory (DSA) for each shock encounter, and where the superbubble (an OB stars association) is idealized as a heterogeneous region of particle sources and sinks, acceleration and transport in the superbubble can be shown to be sub-diffusive. While the sub-diffusive transport can be attributed to the stochastic nature of the acceleration time according to DSA theory, the spectral break appears to be an artifact of transport in a finite medium. These CTRW simulations point to a new and intriguing phenomenon associated with the statistical nature of collective acceleration of high energy cosmic rays in galactic superbubbles.

Diffusion of rod-like nanoparticles in non-adhesive and adhesive porous polymeric gels

NASA Astrophysics Data System (ADS)

Wang, Jiuling; Yang, Yiwei; Yu, Miaorong; Hu, Guoqing; Gan, Yong; Gao, Huajian; Shi, Xinghua

2018-03-01

It is known that rod-like nanoparticles (NPs) can achieve higher diffusivity than their spherical counterparts in biological porous media such as mucus and tumor interstitial matrix, but the underlying mechanisms still remain elusive. Here, we present a joint experimental and theoretical study to show that the aspect ratio (AR) of NPs and their adhesive interactions with the host medium play key roles in such anomalous diffusion behaviors of nanorods. In an adhesive polymer solution/gel (e.g., mucus), hopping diffusion enables nanorods to achieve higher diffusivity than spherical NPs with diameters equal to the minor axis of the rods, and there exists an optimal AR that leads to maximum diffusivity. In contrast, the diffusivity of nanorods decreases monotonically with increasing AR in a non-adhesive polymer solution/gel (e.g., hydroxyethyl cellulose, HEC). Our theoretical model, which captures all the experimental observations, generalizes the so-called obstruction-scaling model by incorporating the effects of the NPs/matrix interaction via the mean first passage time (MFPT) theory. This work reveals the physical origin of the anomalous diffusion behaviors of rod-like NPs in biological gels and may provide guidelines for a range of applications that involve NPs diffusion in complex porous media.

Solar-wind/magnetospheric dynamos: MHD-scale collective entry of the solar wind energy, momentum and mass into the magnetosphere

NASA Technical Reports Server (NTRS)

Song, Yan; Lysak, Robert L.

1992-01-01

A quasi open MHD (Magnetohydrodynamic) scale anomalous transport controlled boundary layer model is proposed, where the MHD collective behavior of magnetofluids (direct dynamo effect, anomalous viscous interaction and anomalous diffusion of the mass and the magnetic field) plays the main role in the conversion of the Solar Wind (SW) kinetic and magnetic energy into electromagnetic energy in the Magnetosphere (MSp). The so called direct and indirect dynamo effects are based on inductive and purely dissipative energy conversion, respectively. The self organization ability of vector fields in turbulent magnetofluids implies an inductive response of the plasma, which leads to the direct dynamo effect. The direct dynamo effect describes the direct formation of localized field aligned currents and the transverse Alfven waves and provides a source for MHD scale anomalous diffusivity and viscosity. The SW/MSp coupling depends on the dynamo efficiency.

Cosmic ray injection spectrum at the galactic sources

NASA Astrophysics Data System (ADS)

Lagutin, Anatoly; Tyumentsev, Alexander; Volkov, Nikolay

The spectra of cosmic rays measured at Earth are different from their source spectra. A key to understanding this difference, being crucial for solving the problem of cosmic-ray origin, is the determination of how cosmic-ray (CR) particles propagate through the turbulent interstellar medium (ISM). If the medium is a quasi-homogeneous the propagation process can be described by a normal diffusion model. However, during a last few decades many evidences, both from theory and observations, of the existence of multiscale structures in the Galaxy have been found. Filaments, shells, clouds are entities widely spread in the ISM. In such a highly non-homogeneous (fractal-like) ISM the normal diffusion model certainly is not kept valid. Generalization of this model leads to what is known as "anomalous diffusion". The main goal of the report is to retrieve the cosmic ray injection spectrum at the galactic sources in the framework of the anomalous diffusion (AD) model. The anomaly in this model results from large free paths ("Levy flights") of particles between galactic inhomogeneities. In order to evaluate the CR spectrum at the sources, we carried out new calculation of the CR spectra at Earth. AD equation in terms of fractional derivatives have been used to describe CR propagation from the nearby (r≤1 kpc) young (t≤ 1 Myr) and multiple old distant (r > 1 kpc) sources. The assessment of the key model parameters have been based on the results of the particles diffusion in the cosmic and laboratory plasma. We show that in the framework of the anomalous diffusion model the locally observed basic features of the cosmic rays (difference between spectral exponents of proton, He and other nuclei, "knee" problem, positron to electron ratio) can be explained if the injection spectrum at the main galactic sources of cosmic rays has spectral exponent p˜ 2.85. The authors acknowledge support from The Russian Foundation for Basic Research grant No. 14-02-31524.

Asymptotic neutron scattering laws for anomalously diffusing quantum particles

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

Kneller, Gerald R.; Université d’Orléans, Chateau de la Source-Ave. du Parc Floral, 45067 Orléans; Synchrotron-SOLEIL, L’Orme de Merisiers, 91192 Gif-sur-Yvette

2016-07-28

The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝t{sup α}, with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constantmore » can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.« less

Random-walk diffusion and drying of porous materials

NASA Astrophysics Data System (ADS)

Mehrafarin, M.; Faghihi, M.

2001-12-01

Based on random-walk diffusion, a microscopic model for drying is proposed to explain the characteristic features of the drying-rate curve of porous materials. The constant drying-rate period is considered as a normal diffusion process. The transition to the falling-rate regime is attributed to the fractal nature of porous materials which results in crossover to anomalous diffusion.

Diffusion control for a tempered anomalous diffusion system using fractional-order PI controllers.

PubMed

Juan Chen; Zhuang, Bo; Chen, YangQuan; Cui, Baotong

2017-05-09

This paper is concerned with diffusion control problem of a tempered anomalous diffusion system based on fractional-order PI controllers. The contribution of this paper is to introduce fractional-order PI controllers into the tempered anomalous diffusion system for mobile actuators motion and spraying control. For the proposed control force, convergence analysis of the system described by mobile actuator dynamical equations is presented based on Lyapunov stability arguments. Moreover, a new Centroidal Voronoi Tessellation (CVT) algorithm based on fractional-order PI controllers, henceforth called FOPI-based CVT algorithm, is provided together with a modified simulation platform called Fractional-Order Diffusion Mobile Actuator-Sensor 2-Dimension Fractional-Order Proportional Integral (FO-Diff-MAS2D-FOPI). Finally, extensive numerical simulations for the tempered anomalous diffusion process are presented to verify the effectiveness of our proposed fractional-order PI controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Macías-Díaz, Jorge E.; Kofané, Timoléon Crépin

2018-03-01

We investigate analytically and numerically the conditions for wave instabilities in a hyperbolic activator-inhibitor system with species undergoing anomalous superdiffusion. In the present work, anomalous superdiffusion is modeled using the two-dimensional Weyl fractional operator, with derivative orders α ∈ [1,2]. We perform a linear stability analysis and derive the conditions for diffusion-driven wave instabilities. Emphasis is placed on the effect of the superdiffusion exponent α , the diffusion ratio d , and the inertial time τ . As the superdiffusive exponent increases, so does the wave number of the Turing instability. Opposite to the requirement for Turing instability, the activator needs to diffuse sufficiently faster than the inhibitor in order for the wave instability to occur. The critical wave number for wave instability decreases with the superdiffusive exponent and increases with the inertial time. The maximum value of the inertial time for a wave instability to occur in the system is τmax=3.6 . As one of the main results of this work, we conclude that both anomalous diffusion and inertial time influence strongly the conditions for wave instabilities in hyperbolic fractional reaction-diffusion systems. Some numerical simulations are conducted as evidence of the analytical predictions derived in this work.

Anomalous diffusion of brain metabolites evidenced by diffusion-weighted magnetic resonance spectroscopy in vivo

PubMed Central

Marchadour, Charlotte; Brouillet, Emmanuel; Hantraye, Philippe; Lebon, Vincent; Valette, Julien

2012-01-01

Translational displacement of molecules within cells is a key process in cellular biology. Molecular motion potentially depends on many factors, including active transport, cytosol viscosity and molecular crowding, tortuosity resulting from cytoskeleton and organelles, and restriction barriers. However, the relative contribution of these factors to molecular motion in the cytoplasm remains poorly understood. In this work, we designed an original diffusion-weighted magnetic resonance spectroscopy strategy to probe molecular motion at subcellular scales in vivo. This led to the first observation of anomalous diffusion, that is, dependence of the apparent diffusion coefficient (ADC) on the diffusion time, for endogenous intracellular metabolites in the brain. The observed increase of the ADC at short diffusion time yields evidence that metabolite motion is characteristic of hindered random diffusion rather than active transport, for time scales up to the dozen milliseconds. Armed with this knowledge, data modeling based on geometrically constrained diffusion was performed. Results suggest that metabolite diffusion occurs in a low-viscosity cytosol hindered by ∼2-μm structures, which is consistent with known intracellular organization. PMID:22929443

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

Chechkin, A. V.; Gonchar, V. Yu.; Gorenflo, R.; Korabel, N.; Sokolov, I. M.

2008-08-01

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R. Gorenflo, and I. Sokolov [Phys. Rev. E 66, 046129 (2002)] for the description of the processes getting more anomalous in the course of time (decelerating subdiffusion and accelerating superdiffusion). Here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time, which we call, respectively, accelerating subdiffusion and decelerating superdiffusion. For the former process, by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time. For the latter process we demonstrate by a particular example how the power-law truncated Lévy stable distribution evolves in time to the distribution with power-law asymptotics and Gaussian shape in the central part. The special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics.

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.

Variable-order fractional MSD function to describe the evolution of protein lateral diffusion ability in cell membranes

NASA Astrophysics Data System (ADS)

Yin, Deshun; Qu, Pengfei

2018-02-01

Protein lateral diffusion is considered anomalous in the plasma membrane. And this diffusion is related to membrane microstructure. In order to better describe the property of protein lateral diffusion and find out the inner relationship between protein lateral diffusion and membrane microstructure, this article applies variable-order fractional mean square displacement (f-MSD) function for characterizing the anomalous diffusion. It is found that the variable order can reflect the evolution of diffusion ability. The results of numerical simulation demonstrate variable-order f-MSD function can predict the tendency of anomalous diffusion during the process of confined diffusion. It is also noted that protein lateral diffusion ability during the processes of confined and hop diffusion can be split into three parts. In addition, the comparative analyses reveal that the variable order is related to the confinement-domain size and microstructure of compartment boundary too.

Effects of Anomalous Cosmic Rays on the Structure of the Outer Heliosphere

NASA Astrophysics Data System (ADS)

Guo, Xiaocheng; Florinski, Vladimir; Wang, Chi

2018-06-01

Based on Voyager 1 observations, some anomalous cosmic rays (ACRs) may have crossed the heliopause and escaped into the interstellar medium, providing a mechanism of energy transfer between the inner and outer heliosheaths that is not included in conventional magnetohydrodynamics (MHD) models. In this paper, we study the effect of energetic particles’ escape through the heliopause on the size and shape of the heliosphere using a simple model that includes diffusive transport of cosmic rays. We show that the presence of ACRs significantly changes the heliosphere structure, including the location of the heliopause and termination shock. It was found that the heliopause would contract for certain values of the ACR diffusion coefficients when the diffusive particles’ pressure is comparable to the pressure of the plasma background. The difference in Voyager 1 and 2 observations of energetic particles during their respective termination shock crossings is interpreted here as due to the differences in diffusion environments during the different phases of the solar cycle. The shorter period of enhanced ACR intensities upstream of the shock measured by Voyager 2 may have been caused by weaker radial diffusive transport compared with the time of Voyager 1 crossing. We conclude that ACR diffusive effects could be prominent and should be included in MHD models of the heliosphere.

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Ion Thermal Decoupling and Species Separation in Shock-Driven Implosions

DOE PAGES

Rinderknecht, Hans G.; Rosenberg, M. J.; Li, C. K.; ...

2015-01-14

Here, anomalous reduction of the fusion yields by 50% and anomalous scaling of the burn-averaged ion temperatures with the ion-species fraction has been observed for the first time in D 3He-filled shock-driven inertial confinement fusion implosions. Two ion kinetic mechanisms are used to explain the anomalous observations: thermal decoupling of the D and 3He populations and diffusive species separation. The observed insensitivity of ion temperature to a varying deuterium fraction is shown to be a signature of ion thermal decoupling in shock-heated plasmas. The burn-averaged deuterium fraction calculated from the experimental data demonstrates a reduction in the average core deuteriummore » density, as predicted by simulations that use a diffusion model. Accounting for each of these effects in simulations reproduces the observed yield trends.« less

Superdiffusion revisited in view of collisionless reconnection

NASA Astrophysics Data System (ADS)

Treumann, R. A.; Baumjohann, W.

2014-06-01

The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail during reconnection is reexamined making use of the division of particle orbits into waiting orbits and break-outs into ballistic motion lying at the bottom, for instance, of Lévy flights. The rms average displacement in this case increases with time, describing superdiffusion, though faster than classical, is still a weak process, being however strong enough to support fast reconnection. Referring to two kinds of numerical particle-in-cell simulations we determine the anomalous diffusion coefficient, the anomalous collision frequency on which the diffusion process is based, and construct a relation between the diffusion coefficients and the resistive scale. The anomalous collision frequency from electron pseudo-viscosity in reconnection turns out to be of the order of the lower-hybrid frequency with the latter providing a lower limit, thus making similar assumptions physically meaningful. Tentative though not completely justified use of the κ distribution yields κ ≈ 6 in the reconnection diffusion region and, for the anomalous diffusion coefficient, the order of several times Bohm diffusivity.

Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion.

PubMed

Liu, Lin; Cherstvy, Andrey G; Metzler, Ralf

2017-02-16

What are the physical laws of the diffusive search of proteins for their specific binding sites on DNA in the presence of the macromolecular crowding in cells? We performed extensive computer simulations to elucidate the protein target search on DNA. The novel feature is the viscoelastic non-Brownian protein bulk diffusion recently observed experimentally. We examine the influence of the protein-DNA binding affinity and the anomalous diffusion exponent on the target search time. In all cases an optimal search time is found. The relative contribution of intermittent three-dimensional bulk diffusion and one-dimensional sliding of proteins along the DNA is quantified. Our results are discussed in the light of recent single molecule tracking experiments, aiming at a better understanding of the influence of anomalous kinetics of proteins on the facilitated diffusion mechanism.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

Electrostatic coupling between DNA and its counterions modulates the observed translational diffusion coefficients.

PubMed

Stellwagen, Earle; Stellwagen, Nancy C

2015-09-01

Free solution capillary electrophoresis (CE) is a useful technique for measuring the translational diffusion coefficients of charged analytes. The measurements are relatively fast if the polarity of the electric field is reversed to drive the analyte back and forth past the detection window during each run. We have tested the validity of the resulting diffusion coefficients using double-stranded DNA molecules ranging in size from 20 to 960 base pairs as the model system. The diffusion coefficients of small DNAs are equal to values in the literature measured by other techniques. However, the diffusion coefficients of DNA molecules larger than ∼30 base pairs are anomalously high and deviate increasingly from the literature values with increasing DNA molar mass. The anomalously high diffusion coefficients are due to electrostatic coupling between the DNA and its counterions. As a result, the measured diffusion coefficients vary with the diffusion coefficient of the counterion, as well as with cation concentration and electric field strength. These effects can be reduced or eliminated by measuring apparent diffusion coefficients of the DNA at several different electric field strengths and extrapolating the results to zero electric field.

Anomalous plasma diffusion and the magnetopause boundary layer

NASA Technical Reports Server (NTRS)

Treumann, Rudolf A.; Labelle, James; Haerendel, Gerhard; Pottelette, Raymond

1992-01-01

An overview of the current state of anomalous diffusion research at the magnetopause and its role in the formation of the magnetopause boundary layer is presented. Plasma wave measurements in the boundary layer indicate that most of the relevant unstable wave modes contribute negligibly to the diffusion process at the magnetopause under magnetically undisturbed northward IMF conditions. The most promising instability is the lower hybrid drift instability, which may yield diffusion coefficients of the right order if the highest measured wave intensities are assumed. It is concluded that global stationary diffusion due to wave-particle interactions does not take place at the magnetopause. Microscopic wave-particle interaction and anomalous diffusion may contribute to locally break the MD frozen-in conditions and help in transporting large amounts of magnetosheath plasma across the magnetospheric boundary.

Constrained diffusion or immobile fraction on cell surfaces: a new interpretation.

PubMed Central

Feder, T J; Brust-Mascher, I; Slattery, J P; Baird, B; Webb, W W

1996-01-01

Protein lateral mobility in cell membranes is generally measured using fluorescence photobleaching recovery (FPR). Since the development of this technique, the data have been interpreted by assuming free Brownian diffusion of cell surface receptors in two dimensions, an interpretation that requires that a subset of the diffusing species remains immobile. The origin of this so-called immobile fraction remains a mystery. In FPR, the motions of thousands of particles are inherently averaged, inevitably masking the details of individual motions. Recently, tracking of individual cell surface receptors has identified several distinct types of motion (Gross and Webb, 1988; Ghosh and Webb, 1988, 1990, 1994; Kusumi et al. 1993; Qian et al. 1991; Slattery, 1995), thereby calling into question the classical interpretation of FPR data as free Brownian motion of a limited mobile fraction. We have measured the motion of fluorescently labeled immunoglobulin E complexed to high affinity receptors (Fc epsilon RI) on rat basophilic leukemia cells using both single particle tracking and FPR. As in previous studies, our tracking results show that individual receptors may diffuse freely, or may exhibit restricted, time-dependent (anomalous) diffusion. Accordingly, we have analyzed FPR data by a new model to take this varied motion into account, and we show that the immobile fraction may be due to particles moving with the anomalous subdiffusion associated with restricted lateral mobility. Anomalous subdiffusion denotes random molecular motion in which the mean square displacements grow as a power law in time with a fractional positive exponent less than one. These findings call for a new model of cell membrane structure. PMID:8744314

Computational Study of Poloidal Angular Momentum Transport in DIII-D

NASA Astrophysics Data System (ADS)

Pankin, Alexei; Kruger, Scott; Kritz, Arnold; Rafiq, Tariq; Weiland, Jan

2013-10-01

The new Multi-Mode Model, MMM8.1, includes the capability to predict the anomalous poloidal momentum diffusivity [T. Rafiq et al., Phys. Plasmas 20, 032506 (2013)]. It is important to consider the effect of this diffusivity on the poloidal rotation of tokamak plasmas since some experimental observations suggest that neoclassical effects are not always sufficient to explain the observed poloidal rotation [B.A. Grierson et al., Phys. Plasmas 19, 056107 (2012)]. One of the objectives of this research is to determine if the anomalous contribution to the poloidal rotation can be significant in the regions of internal transport barriers (ITBs). In this study, the MMM8.1 model is used to compute the poloidal momentum diffusivity for a range of plasma parameters that correspond to the parameters that occur in DIII-D discharges. The parameters that are considered include the temperature and density gradients, and magnetic shear. The role of anomalous poloidal transport in the possible poloidal spin up in the ITB regions is discussed. Progress in the implementation of poloidal transport equations in the ASTRA transport code is reported and initial predictive simulation results for the poloidal rotation profiles are presented. This research is partially support by the DOE Grants DE-SC0006629 and DE-FG02-92ER54141.

The γ parameter of the stretched-exponential model is influenced by internal gradients: validation in phantoms.

PubMed

Palombo, Marco; Gabrielli, Andrea; De Santis, Silvia; Capuani, Silvia

2012-03-01

In this paper, we investigate the image contrast that characterizes anomalous and non-gaussian diffusion images obtained using the stretched exponential model. This model is based on the introduction of the γ stretched parameter, which quantifies deviation from the mono-exponential decay of diffusion signal as a function of the b-value. To date, the biophysical substrate underpinning the contrast observed in γ maps, in other words, the biophysical interpretation of the γ parameter (or the fractional order derivative in space, β parameter) is still not fully understood, although it has already been applied to investigate both animal models and human brain. Due to the ability of γ maps to reflect additional microstructural information which cannot be obtained using diffusion procedures based on gaussian diffusion, some authors propose this parameter as a measure of diffusion heterogeneity or water compartmentalization in biological tissues. Based on our recent work we suggest here that the coupling between internal and diffusion gradients provide pseudo-superdiffusion effects which are quantified by the stretching exponential parameter γ. This means that the image contrast of Mγ maps reflects local magnetic susceptibility differences (Δχ(m)), thus highlighting better than T(2)(∗) contrast the interface between compartments characterized by Δχ(m). Thanks to this characteristic, Mγ imaging may represent an interesting tool to develop contrast-enhanced MRI for molecular imaging. The spectroscopic and imaging experiments (performed in controlled micro-beads dispersion) that are reported here, strongly suggest internal gradients, and as a consequence Δχ(m), to be an important factor in fully understanding the source of contrast in anomalous diffusion methods that are based on a stretched exponential model analysis of diffusion data obtained at varying gradient strengths g. Copyright © 2012 Elsevier Inc. All rights reserved.

An anomalous subdiffusion model for calcium spark in cardiac myocytes

NASA Astrophysics Data System (ADS)

Tan, Wenchang; Fu, Chaoqi; Fu, Ceji; Xie, Wenjun; Cheng, Heping

2007-10-01

The elementary events of excitation-contraction coupling in heart muscle are Ca2+ sparks, which arise from ryanodine receptors in the sarcoplasmic reticulum (SR). Here, an anomalous subdiffusion model is developed to explore Ca2+ spark formation in cardiac myocytes. Numerical simulations reproduce the brightness, the time course, and spatial size of a typical cardiac Ca2+ spark. It is suggested that the diffusion of Ca2+ spark in the cytoplasm may no longer obey Fickian second law, but the anomalous space subdiffusion. The physical reason is perhaps due to the effects of the electric field of the calcium ions and the viscoelasticity of the cytoplasm and its complex structures.

Fractal analysis of lateral movement in biomembranes.

PubMed

Gmachowski, Lech

2018-04-01

Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.

Implementation of an anomalous radial transport model for continuum kinetic edge codes

NASA Astrophysics Data System (ADS)

Bodi, K.; Krasheninnikov, S. I.; Cohen, R. H.; Rognlien, T. D.

2007-11-01

Radial plasma transport in magnetic fusion devices is often dominated by plasma turbulence compared to neoclassical collisional transport. Continuum kinetic edge codes [such as the (2d,2v) transport version of TEMPEST and also EGK] compute the collisional transport directly, but there is a need to model the anomalous transport from turbulence for long-time transport simulations. Such a model is presented and results are shown for its implementation in the TEMPEST gyrokinetic edge code. The model includes velocity-dependent convection and diffusion coefficients expressed as a Hermite polynominals in velocity. The specification of the Hermite coefficients can be set, e.g., by specifying the ratio of particle and energy transport as in fluid transport codes. The anomalous transport terms preserve the property of no particle flux into unphysical regions of velocity space. TEMPEST simulations are presented showing the separate control of particle and energy anomalous transport, and comparisons are made with neoclassical transport also included.

Infinite densities for Lévy walks.

PubMed

Rebenshtok, A; Denisov, S; Hänggi, P; Barkai, E

2014-12-01

Motion of particles in many systems exhibits a mixture between periods of random diffusive-like events and ballistic-like motion. In many cases, such systems exhibit strong anomalous diffusion, where low-order moments 〈|x(t)|(q)〉 with q below a critical value q(c) exhibit diffusive scaling while for q>q(c) a ballistic scaling emerges. The mixed dynamics constitutes a theoretical challenge since it does not fall into a unique category of motion, e.g., the known diffusion equations and central limit theorems fail to describe both aspects. In this paper we resolve this problem by resorting to the concept of infinite density. Using the widely applicable Lévy walk model, we find a general expression for the corresponding non-normalized density which is fully determined by the particles velocity distribution, the anomalous diffusion exponent α, and the diffusion coefficient K(α). We explain how infinite densities play a central role in the description of dynamics of a large class of physical processes and discuss how they can be evaluated from experimental or numerical data.

Anomalous Impact in Reaction-Diffusion Financial Models

NASA Astrophysics Data System (ADS)

Mastromatteo, I.; Tóth, B.; Bouchaud, J.-P.

2014-12-01

We generalize the reaction-diffusion model A +B → /0 in order to study the impact of an excess of A (or B ) at the reaction front. We provide an exact solution of the model, which shows that the linear response breaks down: the average displacement of the reaction front grows as the square root of the imbalance. We argue that this model provides a highly simplified but generic framework to understand the square-root impact of large orders in financial markets.

Anomalous current in diffusive ferromagnetic Josephson junctions

NASA Astrophysics Data System (ADS)

Silaev, M. A.; Tokatly, I. V.; Bergeret, F. S.

2017-05-01

We demonstrate that in diffusive superconductor/ferromagnet/superconductor (S/F/S) junctions a finite, anomalous Josephson current can flow even at zero phase difference between the S electrodes. The conditions for the observation of this effect are noncoplanar magnetization distribution and a broken magnetization inversion symmetry of the superconducting current. The latter symmetry is intrinsic for the widely used quasiclassical approximation and prevented previous works based on this approximation from obtaining the Josephson anomalous current. We show that this symmetry can be removed by introducing spin-dependent boundary conditions for the quasiclassical equations at the superconducting/ferromagnet interfaces in diffusive systems. Using this recipe, we consider generic multilayer magnetic systems and determine the ideal experimental conditions in order to maximize the anomalous current.

1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport

NASA Astrophysics Data System (ADS)

Li, Yunyun; Liu, Sha; Li, Nianbei; Hänggi, Peter; Li, Baowen

2015-04-01

Transport and the spread of heat in Hamiltonian one dimensional momentum conserving nonlinear systems is commonly thought to proceed anomalously. Notable exceptions, however, do exist of which the coupled rotator model is a prominent case. Therefore, the quest arises to identify the origin of manifest anomalous energy and momentum transport in those low dimensional systems. We develop the theory for both, the statistical densities for momentum- and energy-spread and particularly its momentum-/heat-diffusion behavior, as well as its corresponding momentum/heat transport features. We demonstrate that the second temporal derivative of the mean squared deviation of the momentum spread is proportional to the equilibrium correlation of the total momentum flux. Subtracting the part which corresponds to a ballistic momentum spread relates (via this integrated, subleading momentum flux correlation) to an effective viscosity, or equivalently, to the underlying momentum diffusivity. We next put forward the intriguing hypothesis: normal spread of this so adjusted excess momentum density causes normal energy spread and alike normal heat transport (Fourier Law). Its corollary being that an anomalous, superdiffusive broadening of this adjusted excess momentum density in turn implies an anomalous energy spread and correspondingly anomalous, superdiffusive heat transport. This hypothesis is successfully corroborated within extensive molecular dynamics simulations over large extended time scales. Our numerical validation of the hypothesis involves four distinct archetype classes of nonlinear pair-interaction potentials: (i) a globally bounded pair interaction (the noted coupled rotator model), (ii) unbounded interactions acting at large distances (the coupled rotator model amended with harmonic pair interactions), (iii) the case of a hard point gas with unbounded square-well interactions and (iv) a pair interaction potential being unbounded at short distances while displaying an asymptotic free part (Lennard-Jones model). We compare our findings with recent predictions obtained from nonlinear fluctuating hydrodynamics theory.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Anomalous dielectric relaxation with linear reaction dynamics in space-dependent force fields.

PubMed

Hong, Tao; Tang, Zhengming; Zhu, Huacheng

2016-12-28

The anomalous dielectric relaxation of disordered reaction with linear reaction dynamics is studied via the continuous time random walk model in the presence of space-dependent electric field. Two kinds of modified reaction-subdiffusion equations are derived for different linear reaction processes by the master equation, including the instantaneous annihilation reaction and the noninstantaneous annihilation reaction. If a constant proportion of walkers is added or removed instantaneously at the end of each step, there will be a modified reaction-subdiffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps, there will be a standard linear reaction kinetics term but a fractional order temporal derivative operating on an anomalous diffusion term. The dielectric polarization is analyzed based on the Legendre polynomials and the dielectric properties of both reactions can be expressed by the effective rotational diffusion function and component concentration function, which is similar to the standard reaction-diffusion process. The results show that the effective permittivity can be used to describe the dielectric properties in these reactions if the chemical reaction time is much longer than the relaxation time.

Parsing anomalous versus normal diffusive behavior of bedload sediment particles

USGS Publications Warehouse

Fathel, Siobhan; Furbish, David; Schmeeckle, Mark

2016-01-01

Bedload sediment transport is the basic physical ingredient of river evolution. Formulae exist for estimating transport rates, but the diffusive contribution to the sediment flux, and the associated spreading rate of tracer particles, are not clearly understood. The start-and-stop motions of sediment particles transported as bedload on a streambed mimic aspects of the Einstein–Smoluchowski description of the random-walk motions of Brownian particles. Using this touchstone description, recent work suggests the presence of anomalous diffusion, where the particle spreading rate differs from the linear dependence with time of Brownian behavior. We demonstrate that conventional measures of particle spreading reveal different attributes of bedload particle behavior depending on details of the calculation. When we view particle motions over start-and-stop timescales obtained from high-speed (250 Hz) imaging of coarse-sand particles, high-resolution measurements reveal ballistic-like behavior at the shortest (10−2 s) timescale, followed by apparent anomalous behavior due to correlated random walks in transition to normal diffusion (>10−1 s) – similar to Brownian particle behavior but involving distinctly different physics. However, when treated as a ‘virtual plume’ over this timescale range, particles exhibit inhomogeneous diffusive behavior because both the mean and the variance of particle travel distances increase nonlinearly with increasing travel times, a behavior that is unrelated to anomalous diffusion or to Brownian-like behavior. Our results indicate that care is needed in suggesting anomalous behavior when appealing to conventional measures of diffusion formulated for ideal particle systems.

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

PubMed Central

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-01-01

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. PMID:24209851

Anomalous Diffusion Measured by a Twice-Refocused Spin Echo Pulse Sequence: Analysis Using Fractional Order Calculus

PubMed Central

2011-01-01

Purpose To theoretically develop and experimentally validate a formulism based on a fractional order calculus (FC) diffusion model to characterize anomalous diffusion in brain tissues measured with a twice-refocused spin-echo (TRSE) pulse sequence. Materials and Methods The FC diffusion model is the fractional order generalization of the Bloch-Torrey equation. Using this model, an analytical expression was derived to describe the diffusion-induced signal attenuation in a TRSE pulse sequence. To experimentally validate this expression, a set of diffusion-weighted (DW) images was acquired at 3 Tesla from healthy human brains using a TRSE sequence with twelve b-values ranging from 0 to 2,600 s/mm2. For comparison, DW images were also acquired using a Stejskal-Tanner diffusion gradient in a single-shot spin-echo echo planar sequence. For both datasets, a Levenberg-Marquardt fitting algorithm was used to extract three parameters: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). Using adjusted R-squared values and standard deviations, D, β and μ values and the goodness-of-fit in three specific regions of interest (ROI) in white matter, gray matter, and cerebrospinal fluid were evaluated for each of the two datasets. In addition, spatially resolved parametric maps were assessed qualitatively. Results The analytical expression for the TRSE sequence, derived from the FC diffusion model, accurately characterized the diffusion-induced signal loss in brain tissues at high b-values. In the selected ROIs, the goodness-of-fit and standard deviations for the TRSE dataset were comparable with the results obtained from the Stejskal-Tanner dataset, demonstrating the robustness of the FC model across multiple data acquisition strategies. Qualitatively, the D, β, and μ maps from the TRSE dataset exhibited fewer artifacts, reflecting the improved immunity to eddy currents. Conclusion The diffusion-induced signal attenuation in a TRSE pulse sequence can be described by an FC diffusion model at high b-values. This model performs equally well for data acquired from the human brain tissues with a TRSE pulse sequence or a conventional Stejskal-Tanner sequence. PMID:21509877

Anomalous diffusion measured by a twice-refocused spin echo pulse sequence: analysis using fractional order calculus.

PubMed

Gao, Qing; Srinivasan, Girish; Magin, Richard L; Zhou, Xiaohong Joe

2011-05-01

To theoretically develop and experimentally validate a formulism based on a fractional order calculus (FC) diffusion model to characterize anomalous diffusion in brain tissues measured with a twice-refocused spin-echo (TRSE) pulse sequence. The FC diffusion model is the fractional order generalization of the Bloch-Torrey equation. Using this model, an analytical expression was derived to describe the diffusion-induced signal attenuation in a TRSE pulse sequence. To experimentally validate this expression, a set of diffusion-weighted (DW) images was acquired at 3 Tesla from healthy human brains using a TRSE sequence with twelve b-values ranging from 0 to 2600 s/mm(2). For comparison, DW images were also acquired using a Stejskal-Tanner diffusion gradient in a single-shot spin-echo echo planar sequence. For both datasets, a Levenberg-Marquardt fitting algorithm was used to extract three parameters: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). Using adjusted R-squared values and standard deviations, D, β, and μ values and the goodness-of-fit in three specific regions of interest (ROIs) in white matter, gray matter, and cerebrospinal fluid, respectively, were evaluated for each of the two datasets. In addition, spatially resolved parametric maps were assessed qualitatively. The analytical expression for the TRSE sequence, derived from the FC diffusion model, accurately characterized the diffusion-induced signal loss in brain tissues at high b-values. In the selected ROIs, the goodness-of-fit and standard deviations for the TRSE dataset were comparable with the results obtained from the Stejskal-Tanner dataset, demonstrating the robustness of the FC model across multiple data acquisition strategies. Qualitatively, the D, β, and μ maps from the TRSE dataset exhibited fewer artifacts, reflecting the improved immunity to eddy currents. The diffusion-induced signal attenuation in a TRSE pulse sequence can be described by an FC diffusion model at high b-values. This model performs equally well for data acquired from the human brain tissues with a TRSE pulse sequence or a conventional Stejskal-Tanner sequence. Copyright © 2011 Wiley-Liss, Inc.

A Fractional PDE Approach to Turbulent Mixing; Part II: Numerical Simulation

NASA Astrophysics Data System (ADS)

Samiee, Mehdi; Zayernouri, Mohsen

2016-11-01

We propose a generalizing fractional order transport model of advection-diffusion kind with fractional time- and space-derivatives, governing the evolution of passive scalar turbulence. This approach allows one to incorporate the nonlocal and memory effects in the underlying anomalous diffusion i.e., sub-to-standard diffusion to model the trapping of particles inside the eddied, and super-diffusion associated with the sudden jumps of particles from one coherent region to another. For this nonlocal model, we develop a high order numerical (spectral) method in addition to a fast solver, examined in the context of some canonical problems. PhD student, Department of Mechanical Engineering, & Department Computational Mathematics, Science, and Engineering.

Moving-Boundary Problems Associated with Lyopreservation

NASA Astrophysics Data System (ADS)

Gruber, Christopher Andrew

The work presented in this Dissertation is motivated by research into the preservation of biological specimens by way of vitrification, a technique known as lyopreservation. The operative principle behind lyopreservation is that a glassy material forms as a solution of sugar and water is desiccated. The microstructure of this glass impedes transport within the material, thereby slowing metabolism and effectively halting the aging processes in a biospecimen. This Dissertation is divided into two segments. The first concerns the nature of diffusive transport within a glassy state. Experimental studies suggest that diffusion within a glass is anomalously slow. Scaled Brownian motion (SBM) is proposed as a mathematical model which captures the qualitative features of anomalously slow diffusion while minimizing computational expense. This model is applied to several moving-boundary problems and the results are compared to a more well-established model, fractional anomalous diffusion (FAD). The virtues of SBM are based on the model's relative mathematical simplicity: the governing equation under FAD dynamics involves a fractional derivative operator, which precludes the use of analytical methods in almost all circumstances and also entails great computational expense. In some geometries, SBM allows similarity solutions, though computational methods are generally required. The use of SBM as an approximation to FAD when a system is "nearly classical'' is also explored. The second portion of this Dissertation concerns spin-drying, which is an experimental approach to biopreservation in a laboratory setting. A biospecimen is adhered to a glass wafer and this substrate is covered with sugar solution and rapidly spun on a turntable while water is evaporated from the film surface. The mathematical model for the spin-drying process includes diffusion, viscous fluid flow, and evaporation, among other contributions to the dynamics. Lubrication theory is applied to the model and an expansion in orthogonal polynomials is applied. The resulting system of equations is solved computationally. The influence of various experimental parameters upon the system dynamics is investigated, particularly the role of the spin rate. A convergence study of the solution verifies that the polynomial expansion method yields accurate results.

Dynamic light scattering measurements of mutual diffusion coefficients of water-rich 2-butoxyethanol/water systems

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

Bender, T.M.; Pecora, R.

1988-03-24

The mutual diffusion coefficients of the water-rich region of the 2-butoxyethanol (BE)water system were measured by dynamic light scattering at 10, 25, and 40/sup 0/C. At mole fraction of BE greater than 0.02 (X/sub BE/ greater than or equal to 0.02), the results were in good agreement with the work of T. Kato. Below X/sub BE/ = 0.02 an anomalous diffusion region appeared with particles of apparent hydrodynamic radius of up to 1000 A being observed in agreement with the work of S. Kato et al. Further investigations using BE from different sources did not show the anomalous diffusion regionmore » and indicate that the possible presence of small amounts of contaminants in the BE is the source of this anomalous diffusion data« less

Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion.

PubMed

Jeon, Jae-Hyung; Chechkin, Aleksei V; Metzler, Ralf

2014-08-14

Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is 〈x(2)(t)〉 ≃ 2K(t)t with K(t) ≃ t(α-1) for 0 < α < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.

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.

Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments

NASA Astrophysics Data System (ADS)

Ghosh, Surya K.; Cherstvy, Andrey G.; Grebenkov, Denis S.; Metzler, Ralf

2016-01-01

A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells.

Brownian Motion in a Speckle Light Field: Tunable Anomalous Diffusion and Selective Optical Manipulation

PubMed Central

Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain

2014-01-01

The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical potential associated to a speckle pattern, i.e., a complex interference pattern generated by the scattering of coherent light by a random medium, provides an ideal model system to study such phenomena. Here, we derive a theory for the motion of a Brownian particle in a speckle field and, in particular, we identify its universal characteristic timescale. Based on this theoretical insight, we show how speckle light fields can be used to control the anomalous diffusion of a Brownian particle and to perform some basic optical manipulation tasks such as guiding and sorting. Our results might broaden the perspectives of optical manipulation for real-life applications. PMID:24496461

Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium.

PubMed

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-11-05

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Anomalous fast diffusion in Cu-NiFe nanolaminates.

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

Jankowski, Alan F.

2017-09-01

For this work, the decomposition of the one-dimensional composition wave in Cu-NiFe nanolaminate structures is examined using x-ray diffraction to assess the kinetics of phase decomposition. The anomalously high diffusivity value found for long-term aging at room temperature is attributed to the inherent nanostructure that features paths for short-circuit diffusion in nanolaminates as attributed to interlayer grain boundaries.

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

PubMed

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

2010-08-01

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

Drift turbulence, particle transport, and anomalous dissipation at the reconnecting magnetopause

NASA Astrophysics Data System (ADS)

Le, A.; Daughton, W.; Ohia, O.; Chen, L.-J.; Liu, Y.-H.; Wang, S.; Nystrom, W. D.; Bird, R.

2018-06-01

Using fully kinetic 3D simulations, the reconnection dynamics of asymmetric current sheets are examined at the Earth's magnetopause. The plasma parameters are selected to model MMS magnetopause diffusion region crossings with guide fields of 0.1, 0.4, and 1 of the reconnecting magnetosheath field. In each case, strong drift-wave fluctuations are observed in the lower-hybrid frequency range at the steep density gradient across the magnetospheric separatrix. These fluctuations give rise to cross-field electron particle transport. In addition, this turbulent mixing leads to significantly enhanced electron parallel heating in comparison to 2D simulations. We study three different methods of quantifying the anomalous dissipation produced by the drift fluctuations, based on spatial averaging, temporal averaging, and temporal averaging followed by integrating along magnetic field lines. A comparison of different methods reveals complications in identifying and measuring the anomalous dissipation. Nevertheless, the anomalous dissipation from short wavelength drift fluctuations appears weak for each case, and the reconnection rates observed in 3D are nearly the same as in 2D models. The 3D simulations feature a number of interesting new features that are consistent with recent MMS observations, including cold beams of magnetosheath electrons that penetrate into the hotter magnetospheric inflow, the related observation of decreasing temperature in regions of increasing total density, and an effective turbulent diffusion coefficient that agrees with predictions from quasi-linear theory.

Fractional Progress Toward Understanding the Fractional Diffusion Limit: The Electromagnetic Response of Spatially Correlated Geomaterials

NASA Astrophysics Data System (ADS)

Weiss, C. J.; Beskardes, G. D.; Everett, M. E.

2016-12-01

In this presentation we review the observational evidence for anomalous electromagnetic diffusion in near-surface geophysical exploration and how such evidence is consistent with a detailed, spatially-correlated geologic medium. To date, the inference of multi-scale geologic correlation is drawn from two independent methods of data analysis. The first of which is analogous to seismic move-out, where the arrival time of an electromagnetic pulse is plotted as a function of transmitter/receiver separation. The "anomalous" diffusion is evident by the fractional-order power law behavior of these arrival times, with an exponent value between unity (pure diffusion) and 2 (lossless wave propagation). The second line of evidence comes from spectral analysis of small-scale fluctuations in electromagnetic profile data which cannot be explained in terms of instrument, user or random error. Rather, the power-law behavior of the spectral content of these signals (i.e., power versus wavenumber) and their increments reveals them to lie in a class of signals with correlations over multiple length scales, a class of signals known formally as fractional Brownian motion. Numerical results over simulated geology with correlated electrical texture - representative of, for example, fractures, sedimentary bedding or metamorphic lineation - are consistent with the (albeit limited, but growing) observational data, suggesting a possible mechanism and modeling approach for a more realistic geology. Furthermore, we show how similar simulated results can arise from a modeling approach where geologic texture is economically captured by a modified diffusion equation containing exotic, but manageable, fractional derivatives. These derivatives arise physically from the generalized convolutional form for the electromagnetic constitutive laws and thus have merit beyond mere mathematical convenience. In short, we are zeroing in on the anomalous, fractional diffusion limit from two converging directions: a zooming down of the macroscopic (fractional derivative) view; and, a heuristic homogenization of the atomistic (brute force discretization) view.

How molecular motors work in the crowded environment of living cells: coexistence and efficiency of normal and anomalous transport.

PubMed

Goychuk, Igor; Kharchenko, Vasyl O; Metzler, Ralf

2014-01-01

Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included.

How Molecular Motors Work in the Crowded Environment of Living Cells: Coexistence and Efficiency of Normal and Anomalous Transport

PubMed Central

Goychuk, Igor; Kharchenko, Vasyl O.; Metzler, Ralf

2014-01-01

Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included. PMID:24626511

Noah, Joseph and Convex Hulls

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Chau, Y.; Chapman, S. C.

2010-12-01

The idea of describing animal movement by mathematical models based on diffusion and Brownian motion has a long heritage. It has thus been natural to account for those aspects of motion that depart from the Brownian by the use of models incorporating long memory & subdiffusion (“the Joseph effect”) and/or heavy tails & superdiffusion (“the Noah effect”). My own interest in this problem was originally from a geoscience perspective, and was triggered by the need to model time series in space physics where both effects coincide. Subsequently I have been involved in animal foraging studies [e.g. Edwards et al, Nature, 2007]. I will describe some recent work [Watkins et al, PRE, 2009] which studies how fixed-timestep and variable-timestep formulations of anomalous diffusion are related in the presence of heavy tails and long range memory (stable processes versus the CTRW). Quantities for which different scaling relations are predicted between the two approaches are of particular interest, to aid testability. I will also present some of work in progress on the convex hull of anomalously diffusing walkers, inspired by its possible relevance to the idea of home range in biology, and by Randon-Furling et al’s recent analytical results in the Brownian case [PRL, 2009].

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.

Molecular dynamics simulations of propane in slit shaped silica nano-pores: direct comparison with quasielastic neutron scattering experiments.

PubMed

Gautam, Siddharth; Le, Thu; Striolo, Alberto; Cole, David

2017-12-13

Molecular motion under confinement has important implications for a variety of applications including gas recovery and catalysis. Propane confined in mesoporous silica aerogel as studied using quasielastic neutron scattering (QENS) showed anomalous pressure dependence in its diffusion coefficient (J. Phys. Chem. C, 2015, 119, 18188). Molecular dynamics (MD) simulations are often employed to complement the information obtained from QENS experiments. Here, we report an MD simulation study to probe the anomalous pressure dependence of propane diffusion in silica aerogel. Comparison is attempted based on the self-diffusion coefficients and on the time scales of the decay of the simulated intermediate scattering functions. While the self-diffusion coefficients obtained from the simulated mean squared displacement profiles do not exhibit the anomalous pressure dependence observed in the experiments, the time scales of the decay of the intermediate scattering functions calculated from the simulation data match the corresponding quantities obtained in the QENS experiment and thus confirm the anomalous pressure dependence of the diffusion coefficient. The origin of the anomaly in pressure dependence lies in the presence of an adsorbed layer of propane molecules that seems to dominate the confined propane dynamics at low pressure, thereby lowering the diffusion coefficient. Further, time scales for rotational motion obtained from the simulations explain the absence of rotational contribution to the QENS spectra in the experiments. In particular, the rotational motion of the simulated propane molecules is found to exhibit large angular jumps at lower pressure. The present MD simulation work thus reveals important new insights into the origin of anomalous pressure dependence of propane diffusivity in silica mesopores and supplements the information obtained experimentally by QENS data.

Thin film growth by 3D multi-particle diffusion limited aggregation model: Anomalous roughening and fractal analysis

NASA Astrophysics Data System (ADS)

Nasehnejad, Maryam; Nabiyouni, G.; Gholipour Shahraki, Mehran

2018-03-01

In this study a 3D multi-particle diffusion limited aggregation method is employed to simulate growth of rough surfaces with fractal behavior in electrodeposition process. A deposition model is used in which the radial motion of the particles with probability P, competes with random motions with probability 1 - P. Thin films growth is simulated for different values of probability P (related to the electric field) and thickness of the layer(related to the number of deposited particles). The influence of these parameters on morphology, kinetic of roughening and the fractal dimension of the simulated surfaces has been investigated. The results show that the surface roughness increases with increasing the deposition time and scaling exponents exhibit a complex behavior which is called as anomalous scaling. It seems that in electrodeposition process, radial motion of the particles toward the growing seeds may be an important mechanism leading to anomalous scaling. The results also indicate that the larger values of probability P, results in smoother topography with more densely packed structure. We have suggested a dynamic scaling ansatz for interface width has a function of deposition time, scan length and probability. Two different methods are employed to evaluate the fractal dimension of the simulated surfaces which are "cube counting" and "roughness" methods. The results of both methods show that by increasing the probability P or decreasing the deposition time, the fractal dimension of the simulated surfaces is increased. All gained values for fractal dimensions are close to 2.5 in the diffusion limited aggregation model.

Origin of resistivity in reconnection

NASA Astrophysics Data System (ADS)

Treumann, Rudolf A.

2001-06-01

Resistivity is believed to play an important role in reconnection leading to the distinction between resistive and collisionless reconnection. The former is treated in the Sweet-Parker model of long current sheets, and the Petschek model of a small resistive region. Both models in spite of their different dynamics attribute to the violation of the frozen-in condition in their diffusion regions due to the action of resistivity. In collisionless reconnection there is little consensus about the processes breaking the frozen-in condition. The question is whether anomalous processes generate sufficient resistivity or whether other processes free the particles from slavery by the magnetic field. In the present paper we review processes that may cause anomalous resistivity in collisionless current sheets. Our general conclusion is that in space plasma boundaries accessible to in situ spacecraft, wave levels have always been found to be high enough to explain the existence of large enough local diffusivity for igniting local reconnection. However, other processes might take place as well. Non-resistive reconnection can be caused by inertia or diamagnetism.

Growing surfaces with anomalous diffusion: Results for the fractal Kardar-Parisi-Zhang equation

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2003-09-01

In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. It is shown that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, the self-consistent expansion (SCE) is used to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the fractal KPZ equation is suggested and the upper critical dimension of this model is discussed.

Anomalous current diffusion and improved confinement in the HT-6M tohamak

NASA Astrophysics Data System (ADS)

Gao, X.; Li, J. G.; Wan, Y. X.; Huo, Y. P.; Guo, W. K.; Fan, S. P.; Yu, C. X.; Luo, J. R.; Yin, F. X.; Meng, Y. D.; Zheng, L.; Yin, F.; Lin, B. L.; Zhang, S. Y.; Wang, S. Y.; Lu, H. J.; Liu, S. X.; Tong, X. D.; Ding, L. C.; Wu, Z. Y.; Yin, X. J.; Guo, Q. L.; Gong, X. Z.; Wu, X. C.; Zhao, J. Y.; Xi, J. S.

1994-10-01

Current diffusion was studied during edge ohmic heating (EOH) experiments in the HT-6M tokamak. The EOH power system makes the plasma current linearly ramp up from an initial steady state ( Ip=55kA) to a second steady state ( Ip=60kA) at a fast ramp rate of 12 MA/s. A stable discharge of an improved confinement was observed experimentally in the HT-6M tokamak after the plasma current was ramped to rise rapidly to a second steady state. The plasma current is ramped up much faster than both the classical skin time and neoclassical skin time. Fast current ramp up increases the anomalous current diffusion. The measured values of {β P+l i}/{2} and the soft X-ray sawtooth inversion radius imply the anomalous current penetration. The mechanism of anomalous penetration and improved confinement is discussed.

Dual control of flow field heterogeneity and immobile porosity on non-Fickian transport in Berea sandstone

NASA Astrophysics Data System (ADS)

Gjetvaj, Filip; Russian, Anna; Gouze, Philippe; Dentz, Marco

2015-10-01

Both flow field heterogeneity and mass transfer between mobile and immobile domains have been studied separately for explaining observed anomalous transport. Here we investigate non-Fickian transport using high-resolution 3-D X-ray microtomographic images of Berea sandstone containing microporous cement with pore size below the setup resolution. Transport is computed for a set of representative elementary volumes and results from advection and diffusion in the resolved macroporosity (mobile domain) and diffusion in the microporous phase (immobile domain) where the effective diffusion coefficient is calculated from the measured local porosity using a phenomenological model that includes a porosity threshold (ϕθ) below which diffusion is null and the exponent n that characterizes tortuosity-porosity power-law relationship. We show that both flow field heterogeneity and microporosity trigger anomalous transport. Breakthrough curve (BTC) tailing is positively correlated to microporosity volume and mobile-immobile interface area. The sensitivity analysis showed that the BTC tailing increases with the value of ϕθ, due to the increase of the diffusion path tortuosity until the volume of the microporosity becomes negligible. Furthermore, increasing the value of n leads to an increase in the standard deviation of the distribution of effective diffusion coefficients, which in turn results in an increase of the BTC tailing. Finally, we propose a continuous time random walk upscaled model where the transition time is the sum of independently distributed random variables characterized by specific distributions. It allows modeling a 1-D equivalent macroscopic transport honoring both the control of the flow field heterogeneity and the multirate mass transfer between mobile and immobile domains.

Computational modeling of diffusion in the cerebellum.

PubMed

Marinov, Toma M; Santamaria, Fidel

2014-01-01

Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance. © 2014 Elsevier Inc. All rights reserved.

Nonlinear simulations of peeling-ballooning modes with anomalous electron viscosity and their role in edge localized mode crashes

DOE PAGES

Xu, X. Q.; Dudson, B.; Snyder, P. B.; ...

2010-10-22

A minimum set of equations based on the peeling-ballooning (P-B) model with nonideal physics effects (diamagnetic drift, E×B drift, resistivity, and anomalous electron viscosity) is found to simulate pedestal collapse when using the new BOUT++ simulation code, developed in part from the original fluid edge code BOUT. Nonlinear simulations of P-B modes demonstrate that the P-B modes trigger magnetic reconnection, which leads to the pedestal collapse. With the addition of a model of the anomalous electron viscosity under the assumption that the electron viscosity is comparable to the anomalous electron thermal diffusivity, it is found from simulations using a realisticmore » high-Lundquist number that the pedestal collapse is limited to the edge region and the edge localized mode (ELM) size is about 5–10% of the pedestal stored energy. Furthermore, this is consistent with many observations of large ELMs.« less

Levitation effect: Distinguishing anomalous from linear regime of guests sorbed in zeolites through the decay of intermediate scattering function and wavevector dependence of self-diffusivity.

PubMed

Ghorai, Pradip Kr; Yashonath, S

2005-03-10

Previous work investigating the dependence of self-diffusivity, D, on the size of the guest diffusing within the porous solid such as zeolite has reported the existence of an anomalous maximum in the diffusion coefficient (J. Phys. Chem. 1994, 98, 6368). Two distinct regimes of dependence of D on sigma(gg), diameter of the guest were reported. D proportional to 1/sigma(gg)2, often referred to as linear regime (LR), is found when sigma(gg) is smaller than sigma(v), the diameter of the void. A maximum in D has been observed when sigma(gg) is comparable to sigma(v) and this regime is referred to as anomalous regime (AR). Here we report the intermediate scattering function for a particle from LR and AR in zeolite faujasite. A particle from LR exhibits a biexponential decay while a particle from AR exhibits a single-exponential decay at small k. Variation with k of the full width at half-maximum of the self-part of the dynamic structure factor is nonmonotonic for a particle in the linear regime. In contrast, this variation is monotonic for a particle in the anomalous regime. These results can be understood in terms of the existence of energetic barrier at the bottleneck, the 12-ring window, in the path of diffusion. They provide additional signatures for the linear regime and anomalous regimes and therefore for levitation effect (LE).

Quantitative model of price diffusion and market friction based on trading as a mechanistic random process.

PubMed

Daniels, Marcus G; Farmer, J Doyne; Gillemot, László; Iori, Giulia; Smith, Eric

2003-03-14

We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.

Quantitative Model of Price Diffusion and Market Friction Based on Trading as a Mechanistic Random Process

NASA Astrophysics Data System (ADS)

Daniels, Marcus G.; Farmer, J. Doyne; Gillemot, László; Iori, Giulia; Smith, Eric

2003-03-01

We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.

Lévy/Anomalous Diffusion as a Mean-Field Theory for 3D Cloud Effects in Shortwave Radiative Transfer: Empirical Support, New Analytical Formulation, and Impact on Atmospheric Absorption

NASA Astrophysics Data System (ADS)

Buldyrev, S.; Davis, A.; Marshak, A.; Stanley, H. E.

2001-12-01

Two-stream radiation transport models, as used in all current GCM parameterization schemes, are mathematically equivalent to ``standard'' diffusion theory where the physical picture is a slow propagation of the diffuse radiation by Gaussian random walks. The space/time spread (technically, the Green function) of this diffusion process is described exactly by a Gaussian distribution; from the statistical physics viewpoint, this follows from the convergence of the sum of many (rescaled) steps between scattering events with a finite variance. This Gaussian picture follows directly from first principles (the radiative transfer equation) under the assumptions of horizontal uniformity and large optical depth, i.e., there is a homogeneous plane-parallel cloud somewhere in the column. The first-order effect of 3D variability of cloudiness, the main source of scattering, is to perturb the distribution of single steps between scatterings which, modulo the ``1-g'' rescaling, can be assumed effectively isotropic. The most natural generalization of the Gaussian distribution is the 1-parameter family of symmetric Lévy-stable distributions because the sum of many zero-mean random variables with infinite variance, but finite moments of order q < α (0 < α < 2), converge to them. It has been shown on heuristic grounds that for these Lévy-based random walks the typical number of scatterings is now (1-g)τ α for transmitted light. The appearance of a non-rational exponent is why this is referred to as ``anomalous'' diffusion. Note that standard/Gaussian diffusion is retrieved in the limit α = 2-. Lévy transport theory has been successfully used in the statistical physics literature to investigate a wide variety of systems with strongly nonlinear dynamics; these applications range from random advection in turbulent fluids to the erratic behavior of financial time-series and, most recently, self-regulating ecological systems. We will briefly survey the state-of-the-art observations that offer compelling empirical support for the Lévy/anomalous diffusion model in atmospheric radiation: (1) high-resolution spectroscopy of differential absorption in the O2 A-band from ground; (2) temporal transient records of lightning strokes transmitted through clouds to a sensitive detector in space; and (3) the Gamma-distributions of optical depths derived from Landsat cloud scenes at 30-m resolution. We will then introduce a rigorous analytical formulation of Lévy/anomalous transport through finite media based on fractional derivatives and Sonin calculus. A remarkable result from this new theoretical development is an extremal property of the α = 1+ case (divergent mean-free-path), as is observed in the cloudy atmosphere. Finally, we will discuss the implications of anomalous transport theory for bulk 3D effects on the current enhanced absorption problem as well as its role as the basis of a next-generation GCM radiation parameterization.

Fractional Brownian motion with a reflecting wall

NASA Astrophysics Data System (ADS)

Wada, Alexander H. O.; Vojta, Thomas

2018-02-01

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior ˜tα , the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α >1 , the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α <1 , in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular, for applications that are dominated by rare events.

Continuous time anomalous diffusion in a composite medium.

PubMed

Stickler, B A; Schachinger, E

2011-08-01

The one-dimensional continuous time anomalous diffusion in composite media consisting of a finite number of layers in immediate contact is investigated. The diffusion process itself is described with the help of two probability density functions (PDFs), one of which is an arbitrary jump-length PDF, and the other is a long-tailed waiting-time PDF characterized by the waiting-time index β∈(0,1). The former is assumed to be a function of the space coordinate x and the time coordinate t while the latter is a function of x and the time interval. For such an environment a very general form of the diffusion equation is derived which describes the continuous time anomalous diffusion in a composite medium. This result is then specialized to two particular forms of the jump-length PDF, namely the continuous time Lévy flight PDF and the continuous time truncated Lévy flight PDF. In both cases the PDFs are characterized by the Lévy index α∈(0,2) which is regarded to be a function of x and t. It is possible to demonstrate that for particular choices of the indices α and β other equations for anomalous diffusion, well known from the literature, follow immediately. This demonstrates the very general applicability of the derivation and of the resulting fractional differential equation discussed here.

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

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

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalousmore » diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.« less

Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models

NASA Astrophysics Data System (ADS)

Kimura, Kenji; Higuchi, Saburo

2017-11-01

We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1, 2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.

Comb model for the anomalous diffusion with dual-phase-lag constitutive relation

NASA Astrophysics Data System (ADS)

Liu, Lin; Zheng, Liancun; Fan, Yu; Chen, Yanping; Liu, Fawang

2018-10-01

As a development of the Fick's model, the dual-phase-lag constitutive relationship with macroscopic and microscopic relaxation characteristics is introduced to describe the anomalous diffusion in comb model. The Dirac delta function in the formulated governing equation represents the special spatial structure of comb model that the horizontal current only exists on the x axis. Solutions are obtained by analytical method with Laplace transform and Fourier transform. The dependence of concentration field and mean square displacement on different parameters are presented and discussed. Results show that the macroscopic and microscopic relaxation parameters have opposite effects on the particle distribution and mean square displacement. Furthermore, four significant results with constant 1/2 are concluded, namely the product of the particle number and the mean square displacement on the x axis equals to 1/2, the exponent of mean square displacement is 1/2 at the special case τq= τP, an asymptotic form of mean square displacement (MSD∼t1/2 as t→0, ∞) is obtained as well at the short time behavior and the long time behavior.

Modelling nematode movement using time-fractional dynamics.

PubMed

Hapca, Simona; Crawford, John W; MacMillan, Keith; Wilson, Mike J; Young, Iain M

2007-09-07

We use a correlated random walk model in two dimensions to simulate the movement of the slug parasitic nematode Phasmarhabditis hermaphrodita in homogeneous environments. The model incorporates the observed statistical distributions of turning angle and speed derived from time-lapse studies of individual nematode trails. We identify strong temporal correlations between the turning angles and speed that preclude the case of a simple random walk in which successive steps are independent. These correlated random walks are appropriately modelled using an anomalous diffusion model, more precisely using a fractional sub-diffusion model for which the associated stochastic process is characterised by strong memory effects in the probability density function.

Anomalous dimension in a two-species reaction-diffusion system

NASA Astrophysics Data System (ADS)

Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

2018-01-01

We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

Anomalous diffusion on the Hanoi networks

NASA Astrophysics Data System (ADS)

Boettcher, S.; Gonçalves, B.

2008-11-01

Diffusion is modeled on the recently proposed Hanoi networks by studying the mean-square displacement of random walks with time, langr2rang~t2/dw. It is found that diffusion —the quintessential mode of transport throughout Nature— proceeds faster than ordinary, in one case with an exact, anomalous exponent dw=2- log2(phi)=1.30576... . It is an instance of a physical exponent containing the "golden ratio"\\phi=(1+\\sqrt{5})/2 that is intimately related to Fibonacci sequences and since Euclid's time has been found to be fundamental throughout geometry, architecture, art, and Nature itself. It originates from a singular renormalization group fixed point with a subtle boundary layer, for whose resolution phi is the main protagonist. The origin of this rare singularity is easily understood in terms of the physics of the process. Yet, the connection between network geometry and the emergence of phi in this context remains elusive. These results provide an accurate test of recently proposed universal scaling forms for first passage times.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Spectral Definition of the Characteristic Times for Anomalous Diffusion in a Potential

NASA Astrophysics Data System (ADS)

Kalmykov, Yuri P.; Coffey, William T.; Titov, Serguey V.

Characteristic times of the noninertial fractional diffusion of a particle in a potential are defined in terms of three time constants, viz., the integral, effective, and longest relaxation times. These times are described using the eigenvalues of the corresponding Fokker-Planck operator for the normal diffusion. Knowledge of them is sufficient to accurately predict the anomalous relaxation behavior for all time scales of interest. As a particular example, we consider the subdiffusion of a planar rotor in a double-well potential.

Self-crowding of AMPA receptors in the excitatory postsynaptic density can effectuate anomalous receptor sub-diffusion.

PubMed

Gupta, Rahul

2018-02-01

AMPA receptors (AMPARs) and their associations with auxiliary transmembrane proteins are bulky structures with large steric-exclusion volumes. Hence, self-crowding of AMPARs, depending on the local density, may affect their lateral diffusion in the postsynaptic membrane as well as in the highly crowded postsynaptic density (PSD) at excitatory synapses. Earlier theoretical studies considered only the roles of transmembrane obstacles and the AMPAR-binding submembranous scaffold proteins in shaping receptor diffusion within PSD. Using lattice model of diffusion, the present study investigates the additional impacts of self-crowding on the anomalousity and effective diffusion coefficient (Deff) of AMPAR diffusion. A recursive algorithm for avoiding false self-blocking during diffusion simulation is also proposed. The findings suggest that high density of AMPARs in the obstacle-free membrane itself engenders strongly anomalous diffusion and severe decline in Deff. Adding transmembrane obstacles to the membrane accentuates the anomalousity arising from self-crowding due to the reduced free diffusion space. Contrarily, enhanced AMPAR-scaffold binding, either through increase in binding strength or scaffold density or both, ameliorates the anomalousity resulting from self-crowding. However, binding has differential impacts on Deff depending on the receptor density. Increase in binding causes consistent decrease in Deff for low and moderate receptor density. For high density, binding increases Deff as long as it reduces anomalousity associated with intense self-crowding. Given a sufficiently strong binding condition when diffusion acquires normal behavior, further increase in binding causes decrease in Deff. Supporting earlier experimental observations are mentioned and implications of present findings to the experimental observations on AMPAR diffusion are also drawn.

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Anomalous diffusion of single metal atoms on a graphene oxide support

DOE PAGES

Furnival, Tom; Leary, Rowan K.; Tyo, Eric C.; ...

2017-04-21

Recent studies of single-atom catalysts open up the prospect of designing exceptionally active and environmentally efficient chemical processes. The stability and durability of such catalysts is governed by the strength with which the atoms are bound to their support and their diffusive behaviour. Here we use aberration-corrected STEM to image the diffusion of single copper adatoms on graphene oxide. As a result, we discover that individual atoms exhibit anomalous diffusion as a result of spatial and energetic disorder inherent in the support, and interpret the origins of this behaviour to develop a physical picture for the surface diffusion of singlemore » metal atoms.« less

Anomalous diffusion and long-range correlations in the score evolution of the game of cricket

NASA Astrophysics Data System (ADS)

Ribeiro, Haroldo V.; Mukherjee, Satyam; Zeng, Xiao Han T.

2012-08-01

We investigate the time evolution of the scores of the second most popular sport in the world: the game of cricket. By analyzing, event by event, the scores of more than 2000 matches, we point out that the score dynamics is an anomalous diffusive process. Our analysis reveals that the variance of the process is described by a power-law dependence with a superdiffusive exponent, that the scores are statistically self-similar following a universal Gaussian distribution, and that there are long-range correlations in the score evolution. We employ a generalized Langevin equation with a power-law correlated noise that describes all the empirical findings very well. These observations suggest that competition among agents may be a mechanism leading to anomalous diffusion and long-range correlation.

Fractional Brownian motion with a reflecting wall.

PubMed

Wada, Alexander H O; Vojta, Thomas

2018-02-01

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior 〈x^{2}〉∼t^{α}, the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α>1, the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α<1, in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular, for applications that are dominated by rare events.

Anomalous transport in turbulent plasmas and continuous time random walks

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

Balescu, R.

1995-05-01

The possibility of a model of anomalous transport problems in a turbulent plasma by a purely stochastic process is investigated. The theory of continuous time random walks (CTRW`s) is briefly reviewed. It is shown that a particular class, called the standard long tail CTRW`s is of special interest for the description of subdiffusive transport. Its evolution is described by a non-Markovian diffusion equation that is constructed in such a way as to yield exact values for all the moments of the density profile. The concept of a CTRW model is compared to an exact solution of a simple test problem:more » transport of charged particles in a fluctuating magnetic field in the limit of infinite perpendicular correlation length. Although the well-known behavior of the mean square displacement proportional to {ital t}{sup 1/2} is easily recovered, the exact density profile cannot be modeled by a CTRW. 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.« less

Anomalous Surface Diffusion of Protons on Lipid Membranes

PubMed Central

Wolf, Maarten G.; Grubmüller, Helmut; Groenhof, Gerrit

2014-01-01

The cellular energy machinery depends on the presence and properties of protons at or in the vicinity of lipid membranes. To asses the energetics and mobility of a proton near a membrane, we simulated an excess proton near a solvated DMPC bilayer at 323 K, using a recently developed method to include the Grotthuss proton shuttling mechanism in classical molecular dynamics simulations. We obtained a proton surface affinity of −13.0 ± 0.5 kJ mol−1. The proton interacted strongly with both lipid headgroup and linker carbonyl oxygens. Furthermore, the surface diffusion of the proton was anomalous, with a subdiffusive regime over the first few nanoseconds, followed by a superdiffusive regime. The time- and distance dependence of the proton surface diffusion coefficient within these regimes may also resolve discrepancies between previously reported diffusion coefficients. Our simulations show that the proton anomalous surface diffusion originates from restricted diffusion in two different surface-bound states, interrupted by the occasional bulk-mediated long-range surface diffusion. Although only a DMPC membrane was considered in this work, we speculate that the restrictive character of the on-surface diffusion is highly sensitive to the specific membrane conditions, which can alter the relative contributions of the surface and bulk pathways to the overall diffusion process. Finally, we discuss the implications of our findings for the energy machinery. PMID:24988343

Anomalous surface diffusion of protons on lipid membranes.

PubMed

Wolf, Maarten G; Grubmüller, Helmut; Groenhof, Gerrit

2014-07-01

The cellular energy machinery depends on the presence and properties of protons at or in the vicinity of lipid membranes. To asses the energetics and mobility of a proton near a membrane, we simulated an excess proton near a solvated DMPC bilayer at 323 K, using a recently developed method to include the Grotthuss proton shuttling mechanism in classical molecular dynamics simulations. We obtained a proton surface affinity of -13.0 ± 0.5 kJ mol(-1). The proton interacted strongly with both lipid headgroup and linker carbonyl oxygens. Furthermore, the surface diffusion of the proton was anomalous, with a subdiffusive regime over the first few nanoseconds, followed by a superdiffusive regime. The time- and distance dependence of the proton surface diffusion coefficient within these regimes may also resolve discrepancies between previously reported diffusion coefficients. Our simulations show that the proton anomalous surface diffusion originates from restricted diffusion in two different surface-bound states, interrupted by the occasional bulk-mediated long-range surface diffusion. Although only a DMPC membrane was considered in this work, we speculate that the restrictive character of the on-surface diffusion is highly sensitive to the specific membrane conditions, which can alter the relative contributions of the surface and bulk pathways to the overall diffusion process. Finally, we discuss the implications of our findings for the energy machinery. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Communication: Probing anomalous diffusion in frequency space

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

Stachura, Sławomir; Synchrotron Soleil, L’Orme de Merisiers, 91192 Gif-sur-Yvette; Kneller, Gerald R., E-mail: gerald.kneller@cnrs-orleans.fr

Anomalous diffusion processes are usually detected by analyzing the time-dependent mean square displacement of the diffusing particles. The latter evolves asymptotically as W(t) ∼ 2D{sub α}t{sup α}, where D{sub α} is the fractional diffusion constant and 0 < α < 2. In this article we show that both D{sub α} and α can also be extracted from the low-frequency Fourier spectrum of the corresponding velocity autocorrelation function. This offers a simple method for the interpretation of quasielastic neutron scattering spectra from complex (bio)molecular systems, in which subdiffusive transport is frequently encountered. The approach is illustrated and validated by analyzing molecularmore » dynamics simulations of molecular diffusion in a lipid POPC bilayer.« less

A nonlinear Fokker-Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

NASA Astrophysics Data System (ADS)

Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.

2018-07-01

We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.

TEMPEST simulations of the plasma transport in a single-null tokamak geometry

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Bodi, K.; Cohen, R. H.; Krasheninnikov, S.; Rognlien, T. D.

2010-06-01

We present edge kinetic ion transport simulations of tokamak plasmas in magnetic divertor geometry using the fully nonlinear (full-f) continuum code TEMPEST. Besides neoclassical transport, a term for divergence of anomalous kinetic radial flux is added to mock up the effect of turbulent transport. To study the relative roles of neoclassical and anomalous transport, TEMPEST simulations were carried out for plasma transport and flow dynamics in a single-null tokamak geometry, including the pedestal region that extends across the separatrix into the scrape-off layer and private flux region. A series of TEMPEST simulations were conducted to investigate the transition of midplane pedestal heat flux and flow from the neoclassical to the turbulent limit and the transition of divertor heat flux and flow from the kinetic to the fluid regime via an anomalous transport scan and a density scan. The TEMPEST simulation results demonstrate that turbulent transport (as modelled by large diffusion) plays a similar role to collisional decorrelation of particle orbits and that the large turbulent transport (large diffusion) leads to an apparent Maxwellianization of the particle distribution. We also show the transition of parallel heat flux and flow at the entrance to the divertor plates from the fluid to the kinetic regime. For an absorbing divertor plate boundary condition, a non-half-Maxwellian is found due to the balance between upstream radial anomalous transport and energetic ion endloss.

Self-crowding of AMPA receptors in the excitatory postsynaptic density can effectuate anomalous receptor sub-diffusion

PubMed Central

Gupta, Rahul

2018-01-01

AMPA receptors (AMPARs) and their associations with auxiliary transmembrane proteins are bulky structures with large steric-exclusion volumes. Hence, self-crowding of AMPARs, depending on the local density, may affect their lateral diffusion in the postsynaptic membrane as well as in the highly crowded postsynaptic density (PSD) at excitatory synapses. Earlier theoretical studies considered only the roles of transmembrane obstacles and the AMPAR-binding submembranous scaffold proteins in shaping receptor diffusion within PSD. Using lattice model of diffusion, the present study investigates the additional impacts of self-crowding on the anomalousity and effective diffusion coefficient (Deff) of AMPAR diffusion. A recursive algorithm for avoiding false self-blocking during diffusion simulation is also proposed. The findings suggest that high density of AMPARs in the obstacle-free membrane itself engenders strongly anomalous diffusion and severe decline in Deff. Adding transmembrane obstacles to the membrane accentuates the anomalousity arising from self-crowding due to the reduced free diffusion space. Contrarily, enhanced AMPAR-scaffold binding, either through increase in binding strength or scaffold density or both, ameliorates the anomalousity resulting from self-crowding. However, binding has differential impacts on Deff depending on the receptor density. Increase in binding causes consistent decrease in Deff for low and moderate receptor density. For high density, binding increases Deff as long as it reduces anomalousity associated with intense self-crowding. Given a sufficiently strong binding condition when diffusion acquires normal behavior, further increase in binding causes decrease in Deff. Supporting earlier experimental observations are mentioned and implications of present findings to the experimental observations on AMPAR diffusion are also drawn. PMID:29444074

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

de Miguel, E.; Rull, L.F.; Gubbins, K.E.

Using molecular-dynamics computer simulation, we study the dynamical behavior of the isotropic and nematic phases of highly anisotropic molecular fluids. The interactions are modeled by means of the Gay-Berne potential with anisotropy parameters {kappa}=3 and {kappa}{prime}=5. The linear-velocity autocorrelation function shows no evidence of a negative region in the isotropic phase, even at the higher densities considered. The self-diffusion coefficient parallel to the molecular axis shows an anomalous increase with density as the system enters the nematic region. This enhancement in parallel diffusion is also observed in the isotropic side of the transition as a precursor effect. The molecular reorientationmore » is discussed in the light of different theoretical models. The Debye diffusion model appears to explain the reorientational mechanism in the nematic phase. None of the models gives a satisfactory account of the reorientation process in the isotropic phase.« less

Molecular dynamics computer simulation of permeation in solids

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

Pohl, P.I.; Heffelfinger, G.S.; Fisler, D.K.

1997-12-31

In this work the authors simulate permeation of gases and cations in solid models using molecular mechanics and a dual control volume grand canonical molecular dynamics technique. The molecular sieving nature of microporous zeolites are discussed and compared with that for amorphous silica made by sol-gel methods. One mesoporous and one microporous membrane model are tested with Lennard-Jones gases corresponding to He, H{sub 2}, Ar and CH{sub 4}. The mesoporous membrane model clearly follows a Knudsen diffusion mechanism, while the microporous model having a hard-sphere cutoff pore diameter of {approximately}3.4 {angstrom} demonstrates molecular sieving of the methane ({sigma} = 3.8more » {angstrom}) but anomalous behavior for Ar ({sigma} = 3.4 {angstrom}). Preliminary results of Ca{sup +} diffusion in calcite and He/H{sub 2} diffusion in polyisobutylene are also presented.« less

Anomalous diffusion of water molecules at grain boundaries in ice Ih.

PubMed

Moreira, Pedro Augusto Franco Pinheiro; Veiga, Roberto Gomes de Aguiar; Ribeiro, Ingrid de Almeida; Freitas, Rodrigo; Helfferich, Julian; de Koning, Maurice

2018-05-23

Using ab initio and classical molecular dynamics simulations, we study pre-melting phenomena in pristine coincident-site-lattice grain boundaries (GBs) in proton-disordered hexagonal ice Ih at temperatures just below the melting point Tm. Concerning pre-melt-layer thicknesses, the results are consistent with the available experimental estimates for low-disorder impurity-free GBs. With regard to molecular mobility, the simulations provide a key new insight: the translational motion of the water molecules is found to be subdiffusive for time scales from ∼10 ns up to at least 0.1 μs. Moreover, the fact that the anomalous diffusion occurs even at temperatures just below Tm where the bulk supercooled liquid still diffuses normally suggests that it is related to the confinement of the GB pre-melt layers by the surrounding crystalline environment. Furthermore, we show that this behavior can be characterized by continuous-time random walk models in which the waiting-time distributions decay according to power-laws that are very similar to those describing dynamics in glass-forming systems.

Parsimonious Continuous Time Random Walk Models and Kurtosis for Diffusion in Magnetic Resonance of Biological Tissue

NASA Astrophysics Data System (ADS)

Ingo, Carson; Sui, Yi; Chen, Yufen; Parrish, Todd; Webb, Andrew; Ronen, Itamar

2015-03-01

In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.

Variable order fractional Fokker-Planck equations derived from Continuous Time Random Walks

NASA Astrophysics Data System (ADS)

Straka, Peter

2018-08-01

Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent β(x) ∈(0 , 1) varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix varies throughout a cell. Scaling limits of CTRWs are known to have probability distributions which solve fractional Fokker-Planck type equations (FFPE). This correspondence between stochastic processes and FFPE solutions has many useful extensions e.g. to nonlinear particle interactions and reactions, but has not yet been sufficiently developed for FFPEs of the "variable order" type with non-constant β(x) . In this article, variable order FFPEs (VOFFPE) are derived from scaling limits of CTRWs. The key mathematical tool is the 1-1 correspondence of a CTRW scaling limit to a bivariate Langevin process, which tracks the cumulative sum of jumps in one component and the cumulative sum of waiting times in the other. The spatially varying anomalous exponent is modelled by spatially varying β(x) -stable Lévy noise in the waiting time component. The VOFFPE displays a spatially heterogeneous temporal scaling behaviour, with generalized diffusivity and drift coefficients whose units are length2/timeβ(x) resp. length/timeβ(x). A global change of the time scale results in a spatially varying change in diffusivity and drift. A consequence of the mathematical derivation of a VOFFPE from CTRW limits in this article is that a solution of a VOFFPE can be approximated via Monte Carlo simulations. Based on such simulations, we are able to confirm that the VOFFPE is consistent under a change of the global time scale.

Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model.

PubMed

Dean, David S; Iorio, Antonio; Marinari, Enzo; Oshanin, Gleb

2016-09-01

The Sinai model of a tracer diffusing in a quenched Brownian potential is a much-studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian bridge on a finite interval (0,L) and then periodically repeated over the whole real line and study the power spectrum S(f) of the diffusive process x(t) in such a potential. We show that for most of realizations of x(t) in a given realization of the potential, the low-frequency behavior is S(f)∼A/f^{2}, i.e., the same as for standard Brownian motion, and the amplitude A is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of A of arbitrary, negative, or positive order k and demonstrate that they exhibit a multifractal dependence on k and a rather unusual dependence on the temperature and on the periodicity L, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of A has a log-normal left tail and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process x(t).

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

NASA Astrophysics Data System (ADS)

Lai, King C.; Liu, Da-Jiang; Evans, James W.

2017-12-01

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal (100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN˜ N-β with β =3 /2 . However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N <9 ; (ii) slow nucleation-mediated diffusion with small β <1 for "perfect" sizes N = Np= L2 or L (L +1 ) , for L =3 ,4 , ... having unique ground-state shapes, for moderate sizes 9 ≤N ≤O (102) ; the same also applies for N =Np+3 , Np+ 4 , ... (iii) facile diffusion but with large β >2 for N =Np+1 and Np+2 also for moderate sizes 9 ≤N ≤O (102) ; (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲β <3 /2 , reflecting the quasifacetted structure of clusters, for larger N =O (102) to N =O (103) ; (v) classic scaling with β =3 /2 for very large N =O (103) and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where we show that diffusivity cycles quasiperiodically from the slowest branch for Np+3 (not Np) to the fastest branch for Np+1 . Behavior is quantified by kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground-state and low-lying excited state cluster configurations, and also of kink populations.

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

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

Lai, King C.; Liu, Da -Jiang; Evans, James W.

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal(100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN ~ N -β with β = 3/2. However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N < 9; (ii) slow nucleation-mediated diffusion with small β < 1 for “perfect” sizes N = N p = L 2 or L(L+1), for L = 3, 4,… having unique ground state shapes, for moderate sizes 9 ≤ N ≤ O(10 2); the samemore » also applies for N = N p +3, N p + 4,… (iii) facile diffusion but with large β > 2 for N = Np + 1 and N p + 2 also for moderate sizes 9 ≤ N ≤ O(10 2); (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲ β < 3/2, reflecting the quasi-facetted structure of clusters, for larger N = O(10 2) to N = O(10 3); and (v) classic scaling with β = 3/2 for very large N = O(103) and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where show that diffusivity cycles quasi-periodically from the slowest branch for N p + 3 (not Np) to the fastest branch for Np + 1. Behavior is quantified by Kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back-correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground state and low-lying excited state cluster configurations, and also of kink populations.« less

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

DOE PAGES

Lai, King C.; Liu, Da -Jiang; Evans, James W.

2017-12-05

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal(100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN ~ N -β with β = 3/2. However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N < 9; (ii) slow nucleation-mediated diffusion with small β < 1 for “perfect” sizes N = N p = L 2 or L(L+1), for L = 3, 4,… having unique ground state shapes, for moderate sizes 9 ≤ N ≤ O(10 2); the samemore » also applies for N = N p +3, N p + 4,… (iii) facile diffusion but with large β > 2 for N = Np + 1 and N p + 2 also for moderate sizes 9 ≤ N ≤ O(10 2); (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲ β < 3/2, reflecting the quasi-facetted structure of clusters, for larger N = O(10 2) to N = O(10 3); and (v) classic scaling with β = 3/2 for very large N = O(103) and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where show that diffusivity cycles quasi-periodically from the slowest branch for N p + 3 (not Np) to the fastest branch for Np + 1. Behavior is quantified by Kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back-correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground state and low-lying excited state cluster configurations, and also of kink populations.« less

Lévy/Anomalous Diffusion as a Mean-Field Theory for 3D Cloud Effects in SW-RT: Empirical Support, New Analytical Formulation, and Impact on Atmospheric Absorption

NASA Astrophysics Data System (ADS)

Pfeilsticker, K.; Davis, A.; Marshak, A.; Suszcynsky, D. M.; Buldryrev, S.; Barker, H.

2001-12-01

2-stream RT models, as used in all current GCMs, are mathematically equivalent to standard diffusion theory where the physical picture is a slow propagation of the diffuse radiation by Gaussian random walks. In other words, after the conventional van de Hulst rescaling by 1/(1-g) in R3 and also by (1-g) in t, solar photons follow convoluted fractal trajectories in the atmosphere. For instance, we know that transmitted light is typically scattered about (1-g)τ 2 times while reflected light is scattered on average about τ times, where τ is the optical depth of the column. The space/time spread of this diffusion process is described exactly by a Gaussian distribution; from the statistical physics viewpoint, this follows from the convergence of the sum of many (rescaled) steps between scattering events with a finite variance. This Gaussian picture follows from directly from first principles (the RT equation) under the assumptions of horizontal uniformity and large optical depth, i.e., there is a homogeneous plane-parallel cloud somewhere in the column. The first-order effect of 3D variability of cloudiness, the main source of scattering, is to perturb the distribution of single steps between scatterings which, modulo the '1-g' rescaling, can be assumed effectively isotropic. The most natural generalization of the Gaussian distribution is the 1-parameter family of symmetric Lévy-stable distributions because the sum of many zero-mean random variables with infinite variance, but finite moments of order q < α (0 < α < 2), converge to them. It has been shown on heuristic grounds that for these Lévy-based random walks the typical number of scatterings is now (1-g)τ α for transmitted light. The appearance of a non-rational exponent is why this is referred to as anomalous diffusion. Note that standard/Gaussian diffusion is retrieved in the limit α = 2-. Lévy transport theory has been successfully used in the statistical physics to investigate a wide variety of systems with strongly nonlinear dynamics; these applications range from random advection in turbulent fluids to the erratic behavior of financial time-series and, most recently, self-regulating ecological systems. We will briefly survey the state-of-the-art observations that offer compelling empirical support for the Lévy/anomalous diffusion model in atmospheric radiation: (1) high-resolution spectroscopy of differential absorption in the O2 A-band from ground; (2) temporal transient records of lightning strokes transmitted through clouds to a sensitive detector in space; and (3) the Gamma-distributions of optical depths derived from Landsat cloud scenes at 30-m resolution. We will then introduce a rigorous analytical formulation of anomalous transport through finite media based on fractional derivatives and Sonin calculus. A remarkable result from this new theoretical development is an extremal property of the α = 1+ case (divergent mean-free-path), as is observed in the cloudy atmosphere. Finally, we will discuss the implications of anomalous transport theory for bulk 3D effects on the current enhanced absorption problem as well as its role as the basis of a next-generation GCM RT parameterization.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Anomalous cross-B field transport and spokes in HiPIMS plasma

NASA Astrophysics Data System (ADS)

Hecimovic, Ante; Maszl, Christian; Schulz-von der Gathen, Volker; von Keudell, Achim

2016-09-01

The rotation of localised ionisation zones, i.e. spokes, in magnetron discharge is investigated as a function of discharge current, ranging from 10 mA (current density 0.5 mA cm-2) to 140 A (7 A cm-2) . The presence of spokes throughout the complete discharge current range indicates that the spokes are an intrinsic property of a magnetron sputtering plasma discharge. Up to discharge currents of several amperes, the spokes rotate in a retrograde ExB direction and beyond the spokes rotate in a ExB direction. In this contribution we present experimental evidence that anomalous diffusion is triggered by the appearance of spokes rotating in the ExB direction. The Hall parameter ωceτc , product of the electron cyclotron frequency and the classical collision time, reduces from Bohm diffusion values (16 and higher) down to the value of 3 as spokes appear, indicating anomalous cross-B field transport. The ion diffusion coefficients calculated from a sideways image of the spoke is six times higher than Bohm diffusion coefficients, which is consistent with the reduction of the Hall parameter.

Scale-invariant Green-Kubo relation for time-averaged diffusivity

NASA Astrophysics Data System (ADS)

Meyer, Philipp; Barkai, Eli; Kantz, Holger

2017-12-01

In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function. The time-averaged mean-squared displacement is given by 〈δ2¯〉 ˜2 DνtβΔν -β , where t is the total measurement time and Δ is the lag time. Here ν is the anomalous diffusion exponent obtained from ensemble-averaged measurements 〈x2〉 ˜tν , while β ≥-1 marks the growth or decline of the kinetic energy 〈v2〉 ˜tβ . Thus, we establish a connection between exponents that can be read off the asymptotic properties of the velocity correlation function and similarly for the transport constant Dν. We demonstrate our results with nonstationary scale-invariant stochastic and deterministic models, thereby highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average. If the averaged kinetic energy is finite, β =0 , the time scaling of 〈δ2¯〉 and 〈x2〉 are identical; however, the time-averaged transport coefficient Dν is not identical to the corresponding ensemble-averaged diffusion constant.

Anomalous diffusion due to hindering by mobile obstacles undergoing Brownian motion or Orstein-Ulhenbeck processes.

PubMed

Berry, Hugues; Chaté, Hugues

2014-02-01

In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report "anomalous diffusion," where mean-squared displacements scale as a power law of time with exponent α<1 (subdiffusion). While the detailed mechanisms causing such behaviors are not always elucidated, movement hindrance by obstacles is often invoked. However, our understanding of how hindered diffusion leads to subdiffusion is based on diffusion amidst randomly located immobile obstacles. Here, we have used Monte Carlo simulations to investigate transient subdiffusion due to mobile obstacles with various modes of mobility. Our simulations confirm that the anomalous regimes rapidly disappear when the obstacles move by Brownian motion. By contrast, mobile obstacles with more confined displacements, e.g., Orstein-Ulhenbeck motion, are shown to preserve subdiffusive regimes. The mean-squared displacement of tracked protein displays convincing power laws with anomalous exponent α that varies with the density of Orstein-Ulhenbeck (OU) obstacles or the relaxation time scale of the OU process. In particular, some of the values we observed are significantly below the universal value predicted for immobile obstacles in two dimensions. Therefore, our results show that subdiffusion due to mobile obstacles with OU type of motion may account for the large variation range exhibited by experimental measurements in living cells and may explain that some experimental estimates are below the universal value predicted for immobile obstacles.

Kinetic studies of divertor heat fluxes in Alcator C-Mod

NASA Astrophysics Data System (ADS)

Pankin, A. Y.; Bateman, G.; Kritz, A. H.; Rafiq, T.; Park, G. Y.; Chang, C. S.; Brunner, D.; Hughes, J. W.; Labombard, B.; Terry, J.

2010-11-01

The kinetic XGC0 code [C.S. Chang et al, Phys. Plasmas 11 (2004) 2649] is used to model the H- mode pedestal and SOL regions in Alcator C-Mod discharges. The self-consistent simulations in this study include kinetic neoclassical physics and anomalous transport models along with the ExB flow shear effects. The heat fluxes on the divertor plates are computed and the fluxes to the outer plate are compared with experimental observations. The dynamics of the radial electric field near the separatrix and in the SOL region are computed with the XGC0 code, and the effect of the anomalous transport on the heat fluxes in the SOL region is investigated. In particular, the particle and thermal diffusivities obtained in the analysis mode are compared with predictions from the theory-based anomalous transport models such as MMM95 [G. Bateman et al, Phys. Plasmas 5 (1998) 1793] and DRIBM [T. Rafiq et al, to appear in Phys. Plasmas (2010)]. It is found that there is a notable pinch effect in the inner separatrix region. Possible physical mechanisms for the particle and thermal pinches are discussed.

Probing the type of anomalous diffusion with single-particle tracking.

PubMed

Ernst, Dominique; Köhler, Jürgen; Weiss, Matthias

2014-05-07

Many reactions in complex fluids, e.g. signaling cascades in the cytoplasm of living cells, are governed by a diffusion-driven encounter of reactants. Yet, diffusion in complex fluids often exhibits an anomalous characteristic ('subdiffusion'). Since different types of subdiffusion have distinct effects on timing and equilibria of chemical reactions, a thorough determination of the reactants' type of random walk is key to a quantitative understanding of reactions in complex fluids. Here we introduce a straightforward and simple approach for determining the type of subdiffusion from single-particle tracking data. Unlike previous approaches, our method also is sensitive to transient subdiffusion phenomena, e.g. obstructed diffusion below the percolation threshold. We validate our strategy with data from experiment and simulation.

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Macromolecule diffusion and confinement in prokaryotic cells.

PubMed

Mika, Jacek T; Poolman, Bert

2011-02-01

We review recent observations on the mobility of macromolecules and their spatial organization in live bacterial cells. We outline the major fluorescence microscopy-based methods to determine the mobility and thus the diffusion coefficients (D) of molecules, which is not trivial in small cells. The extremely high macromolecule crowding of prokaryotes is used to rationalize the reported lower diffusion coefficients as compared to eukaryotes, and we speculate on the nature of the barriers for diffusion observed for proteins (and mRNAs) in vivo. Building on in vitro experiments and modeling studies, we evaluate the size dependence of diffusion coefficients for macromolecules in vivo, in case of both water-soluble and integral membrane proteins. We comment on the possibilities of anomalous diffusion and provide examples where the macromolecule mobility may be limiting biological processes. Copyright © 2010 Elsevier Ltd. All rights reserved.

Tomographic imaging of non-local media based on space-fractional diffusion models

NASA Astrophysics Data System (ADS)

Buonocore, Salvatore; Semperlotti, Fabio

2018-06-01

We investigate a generalized tomographic imaging framework applicable to a class of inhomogeneous media characterized by non-local diffusive energy transport. Under these conditions, the transport mechanism is well described by fractional-order continuum models capable of capturing anomalous diffusion that would otherwise remain undetected when using traditional integer-order models. Although the underlying idea of the proposed framework is applicable to any transport mechanism, the case of fractional heat conduction is presented as a specific example to illustrate the methodology. By using numerical simulations, we show how complex inhomogeneous media involving non-local transport can be successfully imaged if fractional order models are used. In particular, results will show that by properly recognizing and accounting for the fractional character of the host medium not only allows achieving increased resolution but, in case of strong and spatially distributed non-locality, it represents the only viable approach to achieve a successful reconstruction.

Lifetime of Major Histocompatibility Complex Class-I Membrane Clusters Is Controlled by the Actin Cytoskeleton

PubMed Central

Lavi, Yael; Gov, Nir; Edidin, Michael; Gheber, Levi A.

2012-01-01

Lateral heterogeneity of cell membranes has been demonstrated in numerous studies showing anomalous diffusion of membrane proteins; it has been explained by models and experiments suggesting dynamic barriers to free diffusion, that temporarily confine membrane proteins into microscopic patches. This picture, however, comes short of explaining a steady-state patchy distribution of proteins, in face of the transient opening of the barriers. In our previous work we directly imaged persistent clusters of MHC-I, a type I transmembrane protein, and proposed a model of a dynamic equilibrium between proteins newly delivered to the cell surface by vesicle traffic, temporary confinement by dynamic barriers to lateral diffusion, and dispersion of the clusters by diffusion over the dynamic barriers. Our model predicted that the clusters are dynamic, appearing when an exocytic vesicle fuses with the plasma membrane and dispersing with a typical lifetime that depends on lateral diffusion and the dynamics of barriers. In a subsequent work, we showed this to be the case. Here we test another prediction of the model, and show that changing the stability of actin barriers to lateral diffusion changes cluster lifetimes. We also develop a model for the distribution of cluster lifetimes, consistent with the function of barriers to lateral diffusion in maintaining MHC-I clusters. PMID:22500754

TEMPEST Simulations of the Plasma Transport in a Single-Null Tokamak Geometry

DOE PAGES

X. Q. Xu; Bodi, K.; Cohen, R. H.; ...

2010-05-28

We present edge kinetic ion transport simulations of tokamak plasmas in magnetic divertor geometry using the fully nonlinear (full-f) continuum code TEMPEST. Besides neoclassical transport, a term for divergence of anomalous kinetic radial flux is added to mock up the effect of turbulent transport. In order to study the relative roles of neoclassical and anomalous transport, TEMPEST simulations were carried out for plasma transport and flow dynamics in a single-null tokamak geometry, including the pedestal region that extends across the separatrix into the scrape-off layer and private flux region. In a series of TEMPEST simulations were conducted to investigate themore » transition of midplane pedestal heat flux and flow from the neoclassical to the turbulent limit and the transition of divertor heat flux and flow from the kinetic to the fluid regime via an anomalous transport scan and a density scan. The TEMPEST simulation results demonstrate that turbulent transport (as modelled by large diffusion) plays a similar role to collisional decorrelation of particle orbits and that the large turbulent transport (large diffusion) leads to an apparent Maxwellianization of the particle distribution. Moreover, we show the transition of parallel heat flux and flow at the entrance to the divertor plates from the fluid to the kinetic regime. For an absorbing divertor plate boundary condition, a non-half-Maxwellian is found due to the balance between upstream radial anomalous transport and energetic ion endloss.« less

TEMPEST Simulations of the Plasma Transport in a Single-Null Tokamak Geometry

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

X. Q. Xu; Bodi, K.; Cohen, R. H.

We present edge kinetic ion transport simulations of tokamak plasmas in magnetic divertor geometry using the fully nonlinear (full-f) continuum code TEMPEST. Besides neoclassical transport, a term for divergence of anomalous kinetic radial flux is added to mock up the effect of turbulent transport. In order to study the relative roles of neoclassical and anomalous transport, TEMPEST simulations were carried out for plasma transport and flow dynamics in a single-null tokamak geometry, including the pedestal region that extends across the separatrix into the scrape-off layer and private flux region. In a series of TEMPEST simulations were conducted to investigate themore » transition of midplane pedestal heat flux and flow from the neoclassical to the turbulent limit and the transition of divertor heat flux and flow from the kinetic to the fluid regime via an anomalous transport scan and a density scan. The TEMPEST simulation results demonstrate that turbulent transport (as modelled by large diffusion) plays a similar role to collisional decorrelation of particle orbits and that the large turbulent transport (large diffusion) leads to an apparent Maxwellianization of the particle distribution. Moreover, we show the transition of parallel heat flux and flow at the entrance to the divertor plates from the fluid to the kinetic regime. For an absorbing divertor plate boundary condition, a non-half-Maxwellian is found due to the balance between upstream radial anomalous transport and energetic ion endloss.« less

Anomalous transport in the H-mode pedestal of Alcator C-Mod discharges

NASA Astrophysics Data System (ADS)

Pankin, A. Y.; Hughes, J. W.; Greenwald, M. J.; Kritz, A. H.; Rafiq, T.

2017-02-01

Anomalous transport in the H-mode pedestal region of five Alcator C-Mod discharges, representing a collisionality scan is analyzed. The understanding of anomalous transport in the pedestal region is important for the development of a comprehensive model for the H-mode pedestal slope. In this research, a possible role of the drift resistive inertial ballooning modes (Rafiq et al 2010 Phys. Plasmas 17 082511) in the edge of Alcator C-Mod discharges is analyzed. The stability analysis, carried out using the TRANSP code, indicates that the DRIBM modes are strongly unstable in Alcator C-Mod discharges with large electron collisionality. An improved interpretive analysis of H-mode pedestal experimental data is carried out utilizing the additive flux minimization technique (Pankin et al 2013 Phys. Plasmas 20 102501) together with the guiding-center neoclassical kinetic XGC0 code. The neoclassical and neutral physics are simulated in the XGC0 code and the anomalous fluxes are computed using the additive flux minimization technique. The anomalous fluxes are reconstructed and compared with each other for the collisionality scan Alcator C-Mod discharges. It is found that the electron thermal anomalous diffusivities at the pedestal top increase with the electron collisionality. This dependence can also point to the drift resistive inertial ballooning modes as the modes that drive the anomalous transport in the plasma edge of highly collisional discharges.

In Vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules

NASA Astrophysics Data System (ADS)

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

2011-01-01

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

3D time-domain airborne EM modeling for an arbitrarily anisotropic earth

NASA Astrophysics Data System (ADS)

Yin, Changchun; Qi, Yanfu; Liu, Yunhe

2016-08-01

Time-domain airborne EM data is currently interpreted based on an isotropic model. Sometimes, it can be problematic when working in the region with distinct dipping stratifications. In this paper, we simulate the 3D time-domain airborne EM responses over an arbitrarily anisotropic earth with topography by edge-based finite-element method. Tetrahedral meshes are used to describe the abnormal bodies with complicated shapes. We further adopt the Backward Euler scheme to discretize the time-domain diffusion equation for electric field, obtaining an unconditionally stable linear equations system. We verify the accuracy of our 3D algorithm by comparing with 1D solutions for an anisotropic half-space. Then, we switch attentions to effects of anisotropic media on the strengths and the diffusion patterns of time-domain airborne EM responses. For numerical experiments, we adopt three typical anisotropic models: 1) an anisotropic anomalous body embedded in an isotropic half-space; 2) an isotropic anomalous body embedded in an anisotropic half-space; 3) an anisotropic half-space with topography. The modeling results show that the electric anisotropy of the subsurface media has big effects on both the strengths and the distribution patterns of time-domain airborne EM responses; this effect needs to be taken into account when interpreting ATEM data in areas with distinct anisotropy.

Fractional and fractal dynamics approach to anomalous diffusion in porous media: application to landslide behavior

NASA Astrophysics Data System (ADS)

Martelloni, Gianluca; Bagnoli, Franco

2016-04-01

In the past three decades, fractional and fractal calculus (that is, calculus of derivatives and integral of any arbitrary real or complex order) appeared to be an important tool for its applications in many fields of science and engineering. This theory allows to face, analytically and/or numerically, fractional differential equations and fractional partial differential equations. In particular, one of the several applications deals with anomalous diffusion processes. The latter phenomena can be clearly described from the statistical viewpoint. Indeed, in various complex systems, the diffusion processes usually no longer follow Gaussian statistics, and thus Fick's second law fails to describe the related transport behavior. In particular, one observes deviations from the linear time dependence of the mean squared displacement ⟨x2(t)⟩ ∝ t, (1) which is characteristic of Brownian motion, i.e., a direct consequence of the central limit theorem and the Markovian nature of the underlying stochastic process [1-17]. Instead, anomalous diffusion is found in a wide diversity of systems and its feature is the non-linear growth of the mean squared displacement over time. Especially the power-law pattern, with exponent γ different from 1 ⟨ ⟩ x2(t) ∝ tγ, (2) characterizes many systems [18, 19], but a variety of other rules, such as a logarithmic time dependence, exist [20]. The anomalous diffusion, as expressed in Eq. (2) is connected with the breakdown of the central limit theorem, caused by either broad distributions or long-range correlations, e.g., the extreme statistics and the power law distributions, typical of the self-organized criticality [42, 43]. Instead, anomalous diffusion rests on the validity of the Levy-Gnedenko generalized central limit theorem [21-23]. Particularly, broad spatial jumps or waiting time distributions lead to non-Gaussian distribution and non-Markovian time evolution of the system. Anomalous diffusion has been known since Richardson's treatise on turbulent diffusion in 1926 [24] and today, the list of system displaying anomalous dynamical behavior is quite extensive. We only report some examples: charge carrier transport in amorphous semiconductors [25], porous systems [26], reptation dynamics in polymeric systems [27, 28], transport on fractal geometries [29], the long-time dynamics of DNA sequences [30]. In this scenario, the fractional calculus is used to generalized the Fokker-Planck linear equation -∂P (x,t)=D ∇2P (x,t), ∂t (3) where P (x,t) is the density of probability in the space x=[x1, x2, x3] and time t, while D >0 is the diffusion coefficient. Such processes are characterized by Eq. (1). An example of Eq. (3) generalization is ∂∂tP (x,t)=D∇ αP β(x,t) - ∞ < α ≤ 2 β > - 1 , (4) where the fractional based-derivatives Laplacian Σ(∂α/∂xα)i, (i = 1, 2, 3), of non-linear term Pβ(x,t) is taken into account [31]. Another generalized form is represented by equation ∂∂tδδP(x,t)=D ∇ αP(x,t) δ > 0 α ≤ 2 , (5) that considers also the fractional time-derivative [32]. These fractional-described processes exhibit a power law patters as expressed by Eq. (2). This general introduction introduces the presented work, whose aim is to develop a theoretical model in order to forecast the triggering and propagation of landslides, using the techniques of fractional calculus. The latter is suitable for modeling the water infiltration (i.e., the pore water pressure diffusion in the soil) and the dynamical processes in the fractal media [33]. Alternatively the fractal representation of temporal and spatial derivative (the fractal order only appears in the denominator of the derivative) is considered and the results are compared to the fractional one. The prediction of landslides and the discovering of the triggering mechanism, is one of the challenging problems in earth science. Landslides can be triggered by different factors but in most cases the trigger is an intense or long rain that percolates into the soil causing an increasing of the pore water pressure. In literature two type of models exist for attempting to forecast the landslides triggering: statistical or empirical modeling based on rainfall thresholds derived from the analysis of temporal series of daily rain [34] and geotechnical modeling, i.e., slope stability models that take into account water infiltration by rainfall considering classical Richardson equations [35-39]. Regarding the propagation of landslides, the models follow Eulerian (e.g., finite element methods, [40]) or Lagrangian approach (e.g., particle or molecular dynamics methods [41-46]). In a preliminary work [44], the possibility of the integration between fractional-based infiltration modeling and molecular dynamics approach, to model both the triggering and propagation, has been investigated in order to characterize the granular material varying the order of fractional derivative taking into account the equation -∂δ ∂2θ(z,t) ∂tδθ(z,t)=D ∂z2 , (6) where θ(z,t) represents the water content depending on time t and soil depth z [47], while the parameter δ, with 0.5 ≤ δ < 1, represents the fractional derivative order to consider anomalous sub-diffusion [48]; when δ = 1 we have classical derivative, i.e., normal diffusion, and when δ > 1 super-diffusion [32]. To sum up, in [44], a three-dimensional model is developed, the water content is expressed in term of pore pressure (interpreted as a scalar field acting on the particles), whose increasing induces the shear strength reduction. The latter is taking into account by means of Mohr-Coulomb criterion that represents a failure criterion based on limit equilibrium theory [49, 50]. Moreover, the fluctuations depending on positions, in term of pore pressure, are also considered. Concerning the interaction between particles, a Lennard-Jones potential is taking into account and other active forces as gravity, dynamic friction and viscosity are also considered. For the updating of positions, the Verlet algorithm is used [51]. The outcome of simulations are quite satisfactory and, although the model proposed in [44] is still quite schematic, the results encourage the investigations in this direction as this types of modeling can represent a new method to simulate landslides triggered by rainfall. Particularly, the results are consistent with the behavior of real landslides, e.g., it is possible to apply the method of the inverse surface displacement velocity for predicting the failure time (Fukuzono method [52]). An interesting behavior emerges from the dynamic and statistical points of view. In the simulations emerging phenomena such as detachments, fractures and arching are observed. Finally, in the simulated system, a transition of the mean energy increment distribution from Gaussian to power law, varying the value of some parameters (i.e., viscosity coefficient) is observed or, fixed all parameters, the same behavior can be observed in the time, during single simulation, due to the stick and slip phases. As mentioned, considering that our understanding of the triggering mechanisms is limited and alternative approaches based on interconnected elements are meaningful to reproduce transition from slowly moving mass to catastrophic mass release, we are motivated to investigate mathematical methods, as fractional calculus, for the comprehension of non-linearity of the infiltration phenomena and particle-based approach to achieve a realistic description of the behavior of granular materials. References [1] A. Einstein, in: R. Furth (Ed.), Investigations on the theory of the Brownian movement, Dover, New York, 1956. [2] N. Wax (Ed.), Selected Papers on Noise and Stochastic Processes, Dover, New York, 1954. [3] H.S. Carslaw, J.C. Jaegher, Conduction of Heat in Solids, Clarendon Press, Oxford, 1959. [4] E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, 1967. [5] P. Levy, Processus stochastiques et mouvement Brownien, Gauthier-Villars, Paris, 1965. [6] R. Becker, Theorie der Warme, Heidelberger Taschenbucher, Vol. 10, Springer, Berlin, 1966; Theory of Heat, Springer, Berlin, 1967. [7] S.R. de Groot, P. Mazur, Non-equilibrium Thermodynamics, North-Holland, Amsterdam, 1969. [8] J.L. Doob, Stochastic Processes, Wiley, New York, 1953. [9] J. Crank, The Mathematics of Diffusion, Clarendon Press, Oxford, 1970. [10] D.R. Cox, H.D. Miller, The Theory of Stochastic Processes, Methuen, London, 1965. [11] R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysis, Vols. I and II, Clarendon Press, Oxford, 1975. [12] L.D. Landau, E.M. Lifschitz, Statistische Physik, Akademie, Leipzig, 1989; Statistical Physics, Pergamon, Oxford, 1980. [13] N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1981. [14] H. Risken, The Fokker-Planck Equation, Springer, Berlin, 1989. [15] W.T. Coffey, Yu.P. Kalmykov, J.T. Waldron, The Langevin Equation, World Scientific, Singapore, 1996. [16] B.D. Hughes, Random Walks and Random Environments, Vol. 1: Random Walks, Oxford University Press, Oxford, 1995. [17] G.H. Weiss, R.J. Rubin, Adv. Chem. Phys. 52 (1983) 363. [18] A. Blumen, J. Klafter, G. Zumofen, in: I. Zschokke (Ed.), Optical Spectroscopy of Glasses, Reidel, Dordrecht, 1986. [19] G.M. Zaslavsky, S. Benkadda, Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas, Springer, Berlin, 1998. [20] R. Metzler, J. Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics Reports 339 (2000) 1-77. [21] P. Levy, Calcul des Probabilites, Gauthier-Villars, Paris, 1925. [22] P. Levy, Theorie de l'addition des variables Aleatoires, Gauthier-Villars, Paris, 1954. [23] B.V. Gnedenko, A.N. Kolmogorov, Limit Distributions for Sums of Random Variables, Addison-Wesley, Reading, MA, 1954. [24] L.F. Richardson, Atmospheric diffusion shown on a distance-neighbour graph, Proc. R. Soc.Lond. A 110, 709-737, 1926. [25] H. Scher, E.W. Montroll, Phys. Rev. B 12 (1975) 2455. [26] J. P. Bouchaud, A. Georges, Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications, Physics reports, 195(4-5), 127293, 1990. [27] P.-G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, 1979. [28] M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Clarendon Press, Oxford, 1986. [29] M. Porto, A. Bunde, S. Havlin, H.E. Roman, Phys. Rev. E 56 (2), 1997. [30] P. Allegrini, M. Buiatti, P. Grigolini, B. J. West, Non-Gaussian statistics of anomalous diffusion: The DNA sequences of prokaryotes, Physical Review E 58(3), 1998. [31] M. Bologna, C. Tsallis, P. Grigolini, Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions, Physical Review E, 62(2), 2000. [32] W. Chen, H. Sun, X. Zhang, D. Korosak, Anomalous diffusion modeling by fractal and fractional derivatives, Computers and Mathematics with Applications, 59, 1754-1758, 2010. [33] V.E. Tarasov, Fractional Hydrodynamic Equations for Fractal Media, Annals of Physics, 318(2), 286-307, 2005. [34] G. Martelloni, S. Segoni, R. Fanti, F. Catani, Rainfall thresholds for the forecasting of landslide occurrence at regional scale. Landslides Journal, 9(4), 485-495, 2012. [35] M.G. Anderson, S. Howes, Development and application of a combined soil water-slope stability model, Q. J. Eng. Geol. London, 18: 225-236, 1985. [36] R.M. Iverson, Landslide triggering by rain infiltration, Water Resources Research 36(7): 1897-1910, 2000. [37] N. Lu, J. Godt, Infinite slope stability under steady unsaturated seepage conditions, Water Resources Research, Vol. 44, W11404, doi:10.1029/2008WR006976, 2008. [38] W. Wu, R.C. Sidle, A Distributed Slope Stability Model for Steep Forested Basins, Water Resour. Res., 31(8), 2097-2110, doi:10.1029/95WR01136, 1995. [39] G.B. Crosta, P. Frattini, Distributed modelling of shallow landslides triggered by intense rainfall, Natural Hazards and System Sciences 3: 81-93, 2003. [40] A. Patra, A. Bauer, C. Nichita, E. Pitman, M. Sheridan, M. Bursik, et al., Parallel adaptive numerical simulation of dry avalanches over natural terrain, J Volcanol Geotherm Res, 1-21, 2005. [41] E. Massaro, G. Martelloni, F. Bagnoli, Particle based method for shallow landslides: modeling sliding surface lubrification by rainfall, CMSIM International Journal of Nonlinear Scienze ISSN 2241-0503, 147-158, 2011. [42] G. Martelloni, E. Massaro, F. Bagnoli, A computational toy model for shallow landslides: Molecular Dynamics approach, Communications in Nonlinear Science and Numerical Simulation, 18(9), 2479-2492, 2013. [43] G. Martelloni, E. Massaro, F. Bagnoli, Computational modelling for landslide: molecular dynamic 2D application to shallow and deep landslides, In: EGU General Assembly 2012, Vienna (AT), Vol. 14, EGU2012-12219. [44] G. Martelloni, F. Bagnoli, Particle-based models for hydrologically triggered deep seated landslides, In: EGU General Assembly 2013, Vienna (AT), Vol. 15, EGU2013-10599-1. [45] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 819, 47-65, 1979. [46] G. Martelloni, F. Bagnoli, Infiltration effects on a two-dimensional molecular dynamics model of landslides. In NHAZ (Natural Hazards)), special issue in "Modeling in landslide research: advanced methods", 2014. [47] Y. Pachepsky, D. Timlin, W. Rawls, Generalized Richards' equation to simulate water transport in unsaturated soils, Journal of Hidrology 272: 3-13, 2003. [48] G. Drazer, D.H. Zanette, Experimental evidence of power-law trapping-time distributions in porous media, Physical Review E, 60(5), 1999. [49] C.A. Coulomb, Essai sur une application des regles des maximis et minimis a quelques problemes de statique relatifs, a la architecture. Mem. Acad. Roy. Div. Sav., 7: 343-387, 1776. [50] K. Terzaghi, Theoretical soil mechanics. New York: Wiley, 1943. [51] L. Verlet, Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Physycal Review, 159: 98, 1967. [52] T. Fukuzono, A new method for predicting the failure time of a slope. Proc. 4th Int. Conf. Field Workshop Landslides, 145-150. Tokyo: Jpn. Landslide Soc., 1985.

Continuous-time random-walk model for anomalous diffusion in expanding media

NASA Astrophysics Data System (ADS)

Le Vot, F.; Abad, E.; Yuste, S. B.

2017-09-01

Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium. From this hierarchy, the full time evolution of the second-order moment is obtained for some specific types of expansion. In the case of an exponential expansion, exact recurrence relations for the Laplace-transformed moments are obtained, whence the long-time behavior of moments of arbitrary order is subsequently inferred. Our analytical and numerical results for both Lévy flights and subdiffusive CTRWs confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions. In the case of Lévy flights, we quantify this effect by means of the so-called "Lévy horizon."

Continuous-time random-walk model for anomalous diffusion in expanding media.

PubMed

Le Vot, F; Abad, E; Yuste, S B

2017-09-01

Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium. From this hierarchy, the full time evolution of the second-order moment is obtained for some specific types of expansion. In the case of an exponential expansion, exact recurrence relations for the Laplace-transformed moments are obtained, whence the long-time behavior of moments of arbitrary order is subsequently inferred. Our analytical and numerical results for both Lévy flights and subdiffusive CTRWs confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions. In the case of Lévy flights, we quantify this effect by means of the so-called "Lévy horizon."

Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

PubMed

Yuste, S Bravo; Borrego, R; Abad, E

2010-02-01

We consider various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry. The motion of particles is described by a fractional diffusion equation. Their mean-square displacement is given by r(2) proportional, variant t(gamma)(00 , the emergence of such series in the long-time domain is a specific feature of subdiffusion problems. We present a method to regularize such series, and, in some cases, validate the procedure by using alternative techniques (Laplace transform method and numerical simulations). In the normal diffusion case, we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single (the main) decay mode in the long-time regime. In remarkable contrast, long-time memory of the initial condition is present in the subdiffusive case as the spatial part Psi1(r) describing the long-time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem, the weight being dependent on the initial condition. Interestingly, Psi1(r) turns out to be independent of the anomalous diffusion exponent gamma .

Towards elucidation of the drug release mechanism from compressed hydrophilic matrices made of cellulose ethers. III. Critical use of thermodynamic parameters of activation for modeling the water penetration and drug release processes.

PubMed

Ferrero, Carmen; Massuelle, Danielle; Jeannerat, Damien; Doelker, Eric

2013-09-10

The two main purposes of this work were: (i) to critically consider the use of thermodynamic parameters of activation for elucidating the drug release mechanism from hydroxypropyl methylcellulose (HPMC) matrices, and (ii) to examine the effect of neutral (pH 6) and acidic (pH 2) media on the release mechanism. For this, caffeine was chosen as model drug and various processes were investigated for the effect of temperature and pH: caffeine diffusion in solution and HPMC gels, and drug release from and water penetration into the HPMC tablets. Generally, the kinetics of the processes was not significantly affected by pH. As for the temperature dependence, the activation energy (E(a)) values calculated from caffeine diffusivities were in the range of Fickian transport (20-40 kJ mol⁻¹). Regarding caffeine release from HPMC matrices, fitting the profiles using the Korsmeyer-Peppas model would indicate anomalous transport. However, the low apparent E(a) values obtained were not compatible with a swelling-controlled mechanism and can be assigned to the dimensional change of the system during drug release. Unexpectedly, negative apparent E(a) values were calculated for the water uptake process, which can be ascribed to the exothermic dissolution of water into the initially dry HPMC, the expansion of the matrix and the polymer dissolution. Taking these contributions into account, the true E(a) would fall into the range valid for Fickian diffusion. Consequently, a relaxation-controlled release mechanism can be dismissed. The apparent anomalous drug release from HPMC matrices results from a coupled Fickian diffusion-erosion mechanism, both at pH 6 and 2. Copyright © 2013 Elsevier B.V. All rights reserved.

Anomalous Diffusion Reports on the Interaction of Misfolded Proteins with the Quality Control Machinery in the Endoplasmic Reticulum

PubMed Central

Malchus, Nina; Weiss, Matthias

2010-01-01

A multitude of transmembrane proteins enters the endoplasmic reticulum (ER) as unfolded polypeptide chains. During their folding process, they interact repetitively with the ER's quality control machinery. Here, we have used fluorescence correlation spectroscopy to probe these interactions for a prototypical transmembrane protein, VSVG ts045, in vivo. While both folded and unfolded VSVG ts045 showed anomalous diffusion, the unfolded protein had a significantly stronger anomaly. This difference subsided when unfolded VSVG ts045 was in a complex with its chaperone calnexin, or when a mutant form of VSVG ts045 with only one glycan was used. Our experimental data and accompanying simulations suggest that the folding sensor of the quality control (UGT1) oligomerizes unfolded VSVG ts045, leading to a more anomalous/obstructed diffusion. In contrast, calnexin dissolves the oligomers, rendering unfolded VSVG ts045 more mobile, and hence prevents poisoning of the ER. PMID:20713018

Anomalous cation diffusion in salt-doped confined bilayer ice.

PubMed

Qiu, Hu; Xue, Minmin; Shen, Chun; Guo, Wanlin

2018-05-17

The diffusive dynamics of aqueous electrolyte solutions in nanoconfined spaces has attracted considerable attention due to their potential applications in desalination, biosensors and supercapacitors. Here we show by molecular dynamics simulations that lithium and sodium ions diffuse at a rate at least an order of magnitude higher than that of water molecules when the ions are trapped in an ice bilayer confined between two parallel plates. This novel picture is in sharp contrast to the prevailing view that the diffusion rate of ions is comparable to or even lower than that of water in both bulk and confined solutions. The predicted high ion mobility stems from frequent lateral hopping of ions along the coordination sites inside the hydrogen-bonding network connecting the two water layers of the ice bilayer. This anomalous diffusion should provide new insights into the physics of confined aqueous electrolytes.

Steady state and dynamical structure of a cosmic-ray-modified termination shock

NASA Technical Reports Server (NTRS)

Donohue, D. J.; Zank, G. P.

1993-01-01

A hydrodynamic model is developed for the structure of a cosmic-ray-modified termination shock. The model is based on the two-fluid equations of diffuse shock acceleration (Drury and Volk, 1981). Both the steady state structure of the shock and its interaction with outer heliospheric disturbances are considered. Under the assumption that the solar wind is decelerated by diffusing interstellar cosmic rates, it is shown that the natural state of the termination shock is a gradual deceleration and compression, followed by a discontinuous jump to a downstream state which is dominated by the pressure contribution of the cosmic rays. A representative model is calculated for the steady state which incorporates both interstellar cosmic ray mediation and diffusively accelerated anomalous ions through a proposed thermal leakage mechanism. The interaction of large-scale disturbances with the equilibrium termination shock model is shown to result in some unusual downstream structure, including transmitted shocks and cosmic-ray-modified contact discontinuities. The structure observed may be connected to the 2-kHz outer heliospheric radio emission (Cairns et al., 1992a, b). The time-dependent simulations also demonstrate that interaction with solar wind compressible turbulence (e.g., traveling interplanetary shocks, etc.) could induce the termination shock to continually fluctuate between cosmic-ray-dominated and gas-dynamic states. This fluctuation may represent a partial explanation of the galactic cosmic ray modulation effect and illustrates that the Pioneer and Voyager satellites will encounter an evolving shock whose structure and dynamic properties are strongly influence by the mediation of interstellar and anomalous cosmic rays.

Steady state and dynamical structure of a cosmic-ray-modified termination shock

NASA Astrophysics Data System (ADS)

Donohue, D. J.; Zank, G. P.

1993-11-01

A hydrodynamic model is developed for the structure of a cosmic-ray-modified termination shock. The model is based on the two-fluid equations of diffuse shock acceleration (Drury and Volk, 1981). Both the steady state structure of the shock and its interaction with outer heliospheric disturbances are considered. Under the assumption that the solar wind is decelerated by diffusing interstellar cosmic rates, it is shown that the natural state of the termination shock is a gradual deceleration and compression, followed by a discontinuous jump to a downstream state which is dominated by the pressure contribution of the cosmic rays. A representative model is calculated for the steady state which incorporates both interstellar cosmic ray mediation and diffusively accelerated anomalous ions through a proposed thermal leakage mechanism. The interaction of large-scale disturbances with the equilibrium termination shock model is shown to result in some unusual downstream structure, including transmitted shocks and cosmic-ray-modified contact discontinuities. The structure observed may be connected to the 2-kHz outer heliospheric radio emission (Cairns et al., 1992a, b). The time-dependent simulations also demonstrate that interaction with solar wind compressible turbulence (e.g., traveling interplanetary shocks, etc.) could induce the termination shock to continually fluctuate between cosmic-ray-dominated and gas-dynamic states. This fluctuation may represent a partial explanation of the galactic cosmic ray modulation effect and illustrates that the Pioneer and Voyager satellites will encounter an evolving shock whose structure and dynamic properties are strongly influence by the mediation of interstellar and anomalous cosmic rays.

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.

Diffusion of a Concentrated Lattice Gas in a Regular Comb Structure

NASA Astrophysics Data System (ADS)

Garcia, Paul; Wentworth, Christopher

2008-10-01

Understanding diffusion in constrained geometries is of interest in a variety of contexts as varied as mass transport in disordered solids, such as a percolation cluster, or intercellular transport of water molecules in biological tissue. In this investigation we explore diffusion in a very simple constrained geometry: a comb-like structure involving a one-dimensional backbone of lattice sites with regularly spaced teeth of fixed length. The model considered assumes a fixed concentration of diffusing particles can hop to nearest-neighbor sites only, and they do not interact with each other except that double occupancy is not allowed. The system is simulated using a Monte Carlo simulation procedure. The mean-square displacement of a tagged particle is calculated from the simulation as a function of time. The simulation shows normal diffusive behavior after a period of anomalous diffusion that increases as the tooth size increases.

The exit-time problem for a Markov jump process

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

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Anomalous Diffusion of Water in Lamellar Membranes Formed by Pluronic Polymers

NASA Astrophysics Data System (ADS)

Zhang, Zhe; Ohl, Michael; Han, Youngkyu; Smith, Gregory; Do, Changwoo; Biology; Soft-Matter Division, Oak Ridge National Laboratory Team; Julich CenterNeutron Science Team

Water diffusion is playing an important role in polymer systems. We calculated the water diffusion coefficient at different layers along z-direction which is perpendicular to the lamellar membrane formed by Pluronic block copolymers (L62: (EO6-PO34-EO6)) with the molecular dynamics simulation trajectories. Water molecules at bulk layers are following the normal diffusion, while that at hydration layers formed by polyethylene oxide (PEO) and hydrophobic layers formed by polypropylene oxide (PPO) are following anomalous diffusion. We find that although the subdiffusive regimes at PEO layers and PPO layers are the same, which is the fractional Brownian motion, however, the dynamics are different, i.e. diffusion at the PEO layers is much faster than that at the PPO layers, and meanwhile it exhibits a normal diffusive approximation within a short time period which is governed by the localized free self-diffusion, but becomes subdiffusive after t >8 ps, which is governed by the viscoelastic medium. The Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy; and Zhe Zhang gratefully acknowledges financial support from Julich Center for Neutron Science.

Anomalous transport regimes and asymptotic concentration distributions in the presence of advection and diffusion on a comb structure

NASA Astrophysics Data System (ADS)

Dvoretskaya, Olga A.; Kondratenko, Peter S.

2009-04-01

We study the transport of impurity particles on a comb structure in the presence of advection. The main body concentration and asymptotic concentration distributions are obtained. Seven different transport regimes occur on the comb structure with finite teeth: classical diffusion, advection, quasidiffusion, subdiffusion, slow classical diffusion, and two kinds of slow advection. Quasidiffusion deserves special attention. It is characterized by a linear growth of the mean-square displacement. However, quasidiffusion is an anomalous transport regime. We established that a change in transport regimes in time leads to a change in regimes in space. Concentration tails have a cascade structure, namely, consisting of several parts.

Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Meshwork

NASA Astrophysics Data System (ADS)

Sadegh, Sanaz; Higgins, Jenny L.; Mannion, Patrick C.; Tamkun, Michael M.; Krapf, Diego

2017-01-01

A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized because of experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data confirm that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar meshwork. These results present a hierarchical nanoscale picture of the plasma membrane.

The Dissolution of an Interfween Miscible Liquids

NASA Technical Reports Server (NTRS)

Vlad, D.H.; Maher, J.V.

1999-01-01

The disappearance of the surface tension of the interface of a binary mixture, measured using the dynamic surface light scattering technique, is slower for a binary mixture of higher density contrast. A comparison with a naive diffusion model, expected to provide a lower limit for the speed of dissolution in the absence of gravity shows that the interfacial surface tension disappears much slower than even by diffusion with the effect becoming much more pronounced when density contrast between the liquid phases is increased. Thus, the factor most likely to be responsible for this anomalously slow dissolution is gravity. A mechanism could be based on the competition between diffusive relaxation and sedimentation at the dissolving interface.

Glasslike Membrane Protein Diffusion in a Crowded Membrane.

PubMed

Munguira, Ignacio; Casuso, Ignacio; Takahashi, Hirohide; Rico, Felix; Miyagi, Atsushi; Chami, Mohamed; Scheuring, Simon

2016-02-23

Many functions of the plasma membrane depend critically on its structure and dynamics. Observation of anomalous diffusion in vivo and in vitro using fluorescence microscopy and single particle tracking has advanced our concept of the membrane from a homogeneous fluid bilayer with freely diffusing proteins to a highly organized crowded and clustered mosaic of lipids and proteins. Unfortunately, anomalous diffusion could not be related to local molecular details given the lack of direct and unlabeled molecular observation capabilities. Here, we use high-speed atomic force microscopy and a novel analysis methodology to analyze the pore forming protein lysenin in a highly crowded environment and document coexistence of several diffusion regimes within one membrane. We show the formation of local glassy phases, where proteins are trapped in neighbor-formed cages for time scales up to 10 s, which had not been previously experimentally reported for biological membranes. Furthermore, around solid-like patches and immobile molecules a slower glass phase is detected leading to protein trapping and creating a perimeter of decreased membrane diffusion.

Dynamics of comb-of-comb-network polymers in random layered flows

NASA Astrophysics Data System (ADS)

Katyal, Divya; Kant, Rama

2016-12-01

We analyze the dynamics of comb-of-comb-network polymers in the presence of external random flows. The dynamics of such structures is evaluated through relevant physical quantities, viz., average square displacement (ASD) and the velocity autocorrelation function (VACF). We focus on comparing the dynamics of the comb-of-comb network with the linear polymer. The present work displays an anomalous diffusive behavior of this flexible network in the random layered flows. The effect of the polymer topology on the dynamics is analyzed by varying the number of generations and branch lengths in these networks. In addition, we investigate the influence of external flow on the dynamics by varying flow parameters, like the flow exponent α and flow strength Wα. Our analysis highlights two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The anomalous long-time dynamics is governed by the temporal exponent ν of ASD, viz., ν =2 -α /2 . Compared to a linear polymer, the comb-of-comb network shows a shorter crossover time (from the subdiffusive to superdiffusive regime) but a reduced magnitude of ASD. Our theory displays an anomalous VACF in the random layered flows that scales as t-α /2. We show that the network with greater total mass moves faster.

Identifying mechanisms for superdiffusive dynamics in cell trajectories

NASA Astrophysics Data System (ADS)

Passucci, Giuseppe; Brasch, Megan; Henderson, James; Manning, M. Lisa

Self-propelled particle (SPP) models have been used to explore features of active matter such as motility-induced phase separation, jamming, and flocking, and are often used to model biological cells. However, many cells exhibit super-diffusive trajectories, where displacements scale faster than t 1 / 2 in all directions, and these are not captured by traditional SPP models. We extract cell trajectories from image stacks of mouse fibroblast cells moving on 2D substrates and find super-diffusive mean-squared displacements in all directions across varying densities. Two SPP model modifications have been proposed to capture super-diffusive dynamics: Levy walks and heterogeneous motility parameters. In mouse fibroblast cells displacement probability distributions collapse when time is rescaled by a power greater than 1/2, which is consistent with Levy walks. We show that a simple SPP model with heterogeneous rotational noise can also generate a similar collapse. Furthermore, a close examination of statistics extracted directly from cell trajectories is consistent with a heterogeneous mobility SPP model and inconsistent with a Levy walk model. Our work demonstrates that a simple set of analyses can distinguish between mechanisms for anomalous diffusion in active matter.

Lévy walks

NASA Astrophysics Data System (ADS)

Zaburdaev, V.; Denisov, S.; Klafter, J.

2015-04-01

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévy-walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.

Modeling meiotic chromosome pairing: nuclear envelope attachment, telomere-led active random motion, and anomalous diffusion

PubMed Central

Marshall, Wallace F.; Fung, Jennifer C.

2016-01-01

The recognition and pairing of homologous chromosomes during meiosis is a complex physical and molecular process involving a combination of polymer dynamics and molecular recognition events. Two highly conserved features of meiotic chromosome behavior are the attachment of telomeres to the nuclear envelope and the active random motion of telomeres driven by their interaction with cytoskeletal motor proteins. Both of these features have been proposed to facilitate the process of homolog pairing, but exactly what role these features play in meiosis remains poorly understood. Here we investigate the roles of active motion and nuclear envelope tethering using a Brownian dynamics simulation in which meiotic chromosomes are represented by a Rouse polymer model subjected to tethering and active forces at the telomeres. We find that tethering telomeres to the nuclear envelope slows down pairing relative to the rates achieved by un-attached chromosomes, but that randomly-directed active forces applied to the telomeres speeds up pairing dramatically in a manner that depends on the statistical properties of the telomere force fluctuations. The increased rate of initial pairing cannot be explained by stretching out of the chromosome conformation but instead seems to correlate with anomalous diffusion of sub-telomeric regions. PMID:27046097

Modeling meiotic chromosome pairing: nuclear envelope attachment, telomere-led active random motion, and anomalous diffusion

NASA Astrophysics Data System (ADS)

Marshall, Wallace F.; Fung, Jennifer C.

2016-04-01

The recognition and pairing of homologous chromosomes during meiosis is a complex physical and molecular process involving a combination of polymer dynamics and molecular recognition events. Two highly conserved features of meiotic chromosome behavior are the attachment of telomeres to the nuclear envelope and the active random motion of telomeres driven by their interaction with cytoskeletal motor proteins. Both of these features have been proposed to facilitate the process of homolog pairing, but exactly what role these features play in meiosis remains poorly understood. Here we investigate the roles of active motion and nuclear envelope tethering using a Brownian dynamics simulation in which meiotic chromosomes are represented by a Rouse polymer model subjected to tethering and active forces at the telomeres. We find that tethering telomeres to the nuclear envelope slows down pairing relative to the rates achieved by unattached chromosomes, but that randomly directed active forces applied to the telomeres speed up pairing dramatically in a manner that depends on the statistical properties of the telomere force fluctuations. The increased rate of initial pairing cannot be explained by stretching out of the chromosome conformation but instead seems to correlate with anomalous diffusion of sub-telomeric regions.

Monte Carlo investigation of anomalous transport in presence of a discontinuity and of an advection field

NASA Astrophysics Data System (ADS)

Marseguerra, M.; Zoia, A.

2007-04-01

Anomalous diffusion has recently turned out to be almost ubiquitous in transport problems. When the physical properties of the medium where the transport process takes place are stationary and constant at each spatial location, anomalous transport has been successfully analysed within the Continuous Time Random Walk (CTRW) model. In this paper, within a Monte Carlo approach to CTRW, we focus on the particle transport through two regions characterized by different physical properties, in presence of an external driving action constituted by an additional advective field, modelled within both the Galilei invariant and Galilei variant schemes. Particular attention is paid to the interplay between the distributions of space and time across the discontinuity. The resident concentration and the flux of the particles are finally evaluated and it is shown that at the interface between the two regions the flux is continuous as required by mass conservation, while the concentration may reveal a neat discontinuity. This result could open the route to the Monte Carlo investigation of the effectiveness of a physical discontinuity acting as a filter on particle concentration.

Anomalous waterlike behavior in spherically-symmetric water models optimized with the relative entropy.

PubMed

Chaimovich, Aviel; Shell, M Scott

2009-03-28

Recent efforts have attempted to understand many of liquid water's anomalous properties in terms of effective spherically-symmetric pairwise molecular interactions entailing two characteristic length scales (so-called "core-softened" potentials). In this work, we examine the extent to which such simple descriptions of water are representative of the true underlying interactions by extracting coarse-grained potential functions that are optimized to reproduce the behavior of an all-atom model. To perform this optimization, we use a novel procedure based upon minimizing the relative entropy, a quantity that measures the extent to which a coarse-grained configurational ensemble overlaps with a reference all-atom one. We show that the optimized spherically-symmetric water models exhibit notable variations with the state conditions at which they were optimized, reflecting in particular the shifting accessibility of networked hydrogen bonding interactions. Moreover, we find that water's density and diffusivity anomalies are only reproduced when the effective coarse-grained potentials are allowed to vary with state. Our results therefore suggest that no state-independent spherically-symmetric potential can fully capture the interactions responsible for water's unique behavior; rather, the particular way in which the effective interactions vary with temperature and density contributes significantly to anomalous properties.

Microtomography-based Inter-Granular Network for the simulation of radionuclide diffusion and sorption in a granitic rock

NASA Astrophysics Data System (ADS)

Iraola, Aitor; Trinchero, Paolo; Voutilainen, Mikko; Gylling, Björn; Selroos, Jan-Olof; Molinero, Jorge; Svensson, Urban; Bosbach, Dirk; Deissmann, Guido

2017-12-01

Field investigation studies, conducted in the context of safety analyses of deep geological repositories for nuclear waste, have pointed out that in fractured crystalline rocks sorbing radionuclides can diffuse surprisingly long distances deep into the intact rock matrix; i.e. much longer distances than those predicted by reactive transport models based on a homogeneous description of the properties of the rock matrix. Here, we focus on cesium diffusion and use detailed micro characterisation data, based on micro computed tomography, along with a grain-scale Inter-Granular Network model, to offer a plausible explanation for the anomalously long cesium penetration profiles observed in these in-situ experiments. The sparse distribution of chemically reactive grains (i.e. grains belonging to sorbing mineral phases) is shown to have a strong control on the diffusive patterns of sorbing radionuclides. The computed penetration profiles of cesium agree well with an analytical model based on two parallel diffusive pathways. This agreement, along with visual inspection of the spatial distribution of cesium concentration, indicates that for sorbing radionuclides the medium indeed behaves as a composite system, with most of the mass being retained close to the injection boundary and a non-negligible part diffusing faster along preferential diffusive pathways.

Lévy flight with absorption: A model for diffusing diffusivity with long tails

NASA Astrophysics Data System (ADS)

Jain, Rohit; Sebastian, K. L.

2017-03-01

We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016), 10.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., ∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., πe(D ) ˜e-D /D0 . In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., πe(D ) ˜D-1 -α with 0 <α <1 . We find that in the short time limit, the width of displacement distribution is proportional to √{T }, implying that the diffusion is Fickian. But for long times, the width is proportional to T1 /2 α which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2 α which preserves its shape at all times.

The effects of bound state motion on macromolecular diffusion

NASA Astrophysics Data System (ADS)

Hough, Loren; Stefferson, Michael; Norris, Samantha; Maguire, Laura; Vernerey, Franck; Betterton, Meredith

The diffusion of macromolecules is modified in crowded environments by both inert obstacles and interaction sites. Molecules are generally slowed in their movement inducing transient anomalous subdiffusion. Obstacles also modify the kinetics and equilibrium behavior of interaction between mobile proteins. In some biophysical contexts, bound molecules can still experience mobility, for example transcription factors sliding along DNA, membrane proteins with some entry and diffusion within lipid domains, or proteins that can enter into non-membrane bound compartments such as the nucleolus. We used lattice and continuum models to study the diffusive behavior of tracer particles which bind to obstacles and can diffuse within them. We show that binding significantly alters the motion of tracers. The type and degree of motion while bound is a key determinant of the tracer mobility. Our work has implications for protein-protein movement and interactions within living cells, including those involving intrinsically disordered proteins.

SPECTRAL EVOLUTION OF ANOMALOUS COSMIC RAYS AT VOYAGER 1 BEYOND THE TERMINATION SHOCK

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

Senanayake, U. K.; Florinski, V.; Cummings, A. C.

When the Voyager 1 spacecraft crossed the termination shock (TS) on 2004 December 16, the energy spectra of anomalous cosmic rays (ACRs) could not have been produced by steady-state diffusive shock acceleration. However, over the next few years, in the declining phase of the solar cycle, the spectra began to evolve into the expected power-law profile. Observations at the shock led to a broad range of alternative theories for ACR acceleration. In spite of that, in this work we show that the observations could be explained by assuming ACRs are accelerated at the TS. In this paper, we propose thatmore » the solar cycle had an important effect on the unrolling of the spectra in the heliosheath. To investigate the spectral evolution of ACRs, a magnetohydrodynamic background model with stationary solar-wind inner boundary conditions was used to model the transport of helium and oxygen ions. We used a backward-in-time stochastic integration technique where phase-space trajectories are integrated until the so-called “injection energy” is reached. Our simulation results were compared with Voyager 1 observations using three different diffusion models. It is shown that the spectral evolution of ACRs in the heliosheath at Voyager 1 could be explained by an increase in the source strength and an enhancement in diffusion as a result of a decrease of the turbulent correlation length in the declining phase of the solar cycle. At the same time, drift effects seem to have had a smaller effect on the evolution of the spectra.« less

Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles

NASA Astrophysics Data System (ADS)

Stefferson, Michael W.; Norris, Samantha L.; Vernerey, Franck J.; Betterton, Meredith D.; E Hough, Loren

2017-08-01

Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.

Modelling and simulation techniques for membrane biology.

PubMed

Burrage, Kevin; Hancock, John; Leier, André; Nicolau, Dan V

2007-07-01

One of the most important aspects of Computational Cell Biology is the understanding of the complicated dynamical processes that take place on plasma membranes. These processes are often so complicated that purely temporal models cannot always adequately capture the dynamics. On the other hand, spatial models can have large computational overheads. In this article, we review some of these issues with respect to chemistry, membrane microdomains and anomalous diffusion and discuss how to select appropriate modelling and simulation paradigms based on some or all the following aspects: discrete, continuous, stochastic, delayed and complex spatial processes.

Modeling methanol transfer in the mesoporous catalyst for the methanol-to-olefins reaction by the time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The solutions of the time-fractional diffusion equation for the short and long times are obtained via an application of the asymptotic Green's functions. The derived solutions are applied to analysis of the methanol mass transfer through H-ZSM-5/alumina catalyst grain. It is demonstrated that the methanol transport in the catalysts pores may be described by the obtained solutions in a fairly good manner. The measured fractional exponent is equal to 1.20 ± 0.02 and reveals the super-diffusive regime of the methanol mass transfer. The presence of the anomalous transport may be caused by geometrical restrictions and the adsorption process on the internal surface of the catalyst grain's pores.

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.

Fractional Brownian motion run with a multi-scaling clock mimics diffusion of spherical colloids in microstructural fluids.

PubMed

Park, Moongyu; Cushman, John Howard; O'Malley, Dan

2014-09-30

The collective molecular reorientations within a nematic liquid crystal fluid bathing a spherical colloid cause the colloid to diffuse anomalously on a short time scale (i.e., as a non-Brownian particle). The deformations and fluctuations of long-range orientational order in the liquid crystal profoundly influence the transient diffusive regimes. Here we show that an anisotropic fractional Brownian process run with a nonlinear multiscaling clock effectively mimics this collective and transient phenomenon. This novel process has memory, Gaussian increments, and a multiscale mean square displacement that can be chosen independently from the fractal dimension of a particle trajectory. The process is capable of modeling multiscale sub-, super-, or classical diffusion. The finite-size Lyapunov exponents for this multiscaling process are defined for future analysis of related mixing processes.

Diffusion of knowledge and globalization in the web of twentieth century science

NASA Astrophysics Data System (ADS)

Naumis, G. G.; Phillips, J. C.

2012-08-01

Scientific communication is an essential part of modern science: whereas Archimedes worked alone, Newton (correspondence with Hooke, 1676) acknowledged that “If I have seen a little further, it is by standing on the shoulders of Giants.” How is scientific communication reflected in the patterns of citations in scientific papers? How have these patterns changed in the 20th century, as both means of communication and individual transportation changed rapidly, compared to the earlier post-Newton 18th and 19th centuries? Here we discuss a diffusive model for scientific communications, based on a unique 2009 scientometric study of 25 million papers and 600 million citations that encapsulates the epistemology of modern science. The diffusive model predicts and explains, using no adjustable parameters, a surprisingly universal internal structure in the development of scientific research, which is essentially constant across the natural sciences, but which because of globalization changed qualitatively around 1960. Globalization corresponds physically to anomalous diffusion, which has been observed near the molecular glass transition, and can enhance molecular diffusion by factors as large as 100.

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.

Computed versus measured ion velocity distribution functions in a Hall effect thruster

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

Garrigues, L.; CNRS, LAPLACE, F-31062 Toulouse; Mazouffre, S.

2012-06-01

We compare time-averaged and time-varying measured and computed ion velocity distribution functions in a Hall effect thruster for typical operating conditions. The ion properties are measured by means of laser induced fluorescence spectroscopy. Simulations of the plasma properties are performed with a two-dimensional hybrid model. In the electron fluid description of the hybrid model, the anomalous transport responsible for the electron diffusion across the magnetic field barrier is deduced from the experimental profile of the time-averaged electric field. The use of a steady state anomalous mobility profile allows the hybrid model to capture some properties like the time-averaged ion meanmore » velocity. Yet, the model fails at reproducing the time evolution of the ion velocity. This fact reveals a complex underlying physics that necessitates to account for the electron dynamics over a short time-scale. This study also shows the necessity for electron temperature measurements. Moreover, the strength of the self-magnetic field due to the rotating Hall current is found negligible.« less

Experimental tests of truncated diffusion in fault damage zones

NASA Astrophysics Data System (ADS)

Suzuki, Anna; Hashida, Toshiyuki; Li, Kewen; Horne, Roland N.

2016-11-01

Fault zones affect the flow paths of fluids in groundwater aquifers and geological reservoirs. Fault-related fracture damage decreases to background levels with increasing distance from the fault core according to a power law. This study investigated mass transport in such a fault-related structure using nonlocal models. A column flow experiment is conducted to create a permeability distribution that varies with distance from a main conduit. The experimental tracer response curve is preasymptotic and implies subdiffusive transport, which is slower than the normal Fickian diffusion. If the surrounding area is a finite domain, an upper truncated behavior in tracer response (i.e., exponential decline at late times) is observed. The tempered anomalous diffusion (TAD) model captures the transition from subdiffusive to Fickian transport, which is characterized by a smooth transition from power-law to an exponential decline in the late-time breakthrough curves.

Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion.

PubMed

Zhao, Yi; Cao, Xiangyu; Gao, Jun; Liu, Xiao; Li, Sijia

2016-05-16

We demonstrate a simple reconfigurable metasurface with multiple functions. Anisotropic tiles are investigated and manufactured as fundamental elements. Then, the tiles are combined in a certain sequence to construct a metasurface. Each of the tiles can be adjusted independently which is like a jigsaw puzzle and the whole metasurface can achieve diverse functions by different layouts. For demonstration purposes, we realize polarization conversion, anomalous reflection and diffusion by a jigsaw puzzle metasurface with 6 × 6 pieces of anisotropic tile. Simulated and measured results prove that our method offers a simple and effective strategy for metasurface design.

Anomalously Fast Diffusion of Targeted Carbon Nanotubes in Cellular Spheroids.

PubMed

Wang, Yichun; Bahng, Joong Hwan; Che, Quantong; Han, Jishu; Kotov, Nicholas A

2015-08-25

Understanding transport of carbon nanotubes (CNTs) and other nanocarriers within tissues is essential for biomedical imaging and drug delivery using these carriers. Compared to traditional cell cultures in animal studies, three-dimensional tissue replicas approach the complexity of the actual organs and enable high temporal and spatial resolution of the carrier permeation. We investigated diffusional transport of CNTs in highly uniform spheroids of hepatocellular carcinoma and found that apparent diffusion coefficients of CNTs in these tissue replicas are anomalously high and comparable to diffusion rates of similarly charged molecules with molecular weights 10000× lower. Moreover, diffusivity of CNTs in tissues is enhanced after functionalization with transforming growth factor β1. This unexpected trend contradicts predictions of the Stokes-Einstein equation and previously obtained empirical dependences of diffusivity on molecular mass for permeants in gas, liquid, solid or gel. It is attributed to the planar diffusion (gliding) of CNTs along cellular membranes reducing effective dimensionality of diffusional space. These findings indicate that nanotubes and potentially similar nanostructures are capable of fast and deep permeation into the tissue, which is often difficult to realize with anticancer agents.

Shock Wave Dynamics in Weakly Ionized Plasmas

NASA Technical Reports Server (NTRS)

Johnson, Joseph A., III

1999-01-01

An investigation of the dynamics of shock waves in weakly ionized argon plasmas has been performed using a pressure ruptured shock tube. The velocity of the shock is observed to increase when the shock traverses the plasma. The observed increases cannot be accounted for by thermal effects alone. Possible mechanisms that could explain the anomalous behavior include a vibrational/translational relaxation in the nonequilibrium plasma, electron diffusion across the shock front resulting from high electron mobility, and the propagation of ion-acoustic waves generated at the shock front. Using a turbulence model based on reduced kinetic theory, analysis of the observed results suggest a role for turbulence in anomalous shock dynamics in weakly ionized media and plasma-induced hypersonic drag reduction.

Waterlike anomalies in a two-dimensional core-softened potential

NASA Astrophysics Data System (ADS)

Bordin, José Rafael; Barbosa, Marcia C.

2018-02-01

We investigate the structural, thermodynamic, and dynamic behavior of a two-dimensional (2D) core-corona system using Langevin dynamics simulations. The particles are modeled by employing a core-softened potential which exhibits waterlike anomalies in three dimensions. In previous studies in a quasi-2D system a new region in the pressure versus temperature phase diagram of structural anomalies was observed. Here we show that for the two-dimensional case two regions in the pressure versus temperature phase diagram with structural, density, and diffusion anomalies are observed. Our findings indicate that, while the anomalous region at lower densities is due the competition between the two length scales in the potential at higher densities, the anomalous region is related to the reentrance of the melting line.

Anomalous behaviors during infiltration into heterogeneous porous media

NASA Astrophysics Data System (ADS)

Aarão Reis, F. D. A.; Bolster, D.; Voller, V. R.

2018-03-01

Flow and transport in heterogeneous porous media often exhibit anomalous behavior. A physical analog example is the uni-directional infiltration of a viscous liquid into a horizontal oriented Hele-Shaw cell containing through thickness flow obstacles; a system designed to mimic a gravel/sand medium with impervious inclusions. When there are no obstacles present or the obstacles form a multi-repeating pattern, the change of the length of infiltration F with time t tends to follow a Fickian like scaling, F ∼t1/2 . In the presence of obstacle fields laid out as Sierpinski carpet fractals, infiltration is anomalous, i.e., F ∼ tn, n ≠ 1/2. Here, we study infiltration into such Hele-Shaw cells. First we investigate infiltration into a square cell containing one fractal carpet and make the observation that it is possible to generate both sub (n < 1/2) and super (n > 1/2) diffusive behaviors within identical heterogeneity configurations. We show that this can be explained in terms of a scaling analysis developed from results of random-walk simulations in fractal obstacles; a result indicating that the nature of the domain boundary controls the exponent n of the resulting anomalous transport. Further, we investigate infiltration into a rectangular cell containing several repeats of a given Sierpinski carpet. At very early times, before the liquid encounters any obstacles, the infiltration is Fickian. When the liquid encounters the first (smallest scale) obstacle the infiltration sharply transitions to sub-diffusive. Subsequently, around the time where the liquid has sampled all of the heterogeneity length scales in the system, there is a rapid transition back to Fickian behavior. An explanation for this second transition is obtained by developing a simplified infiltration model based on the definition of a representative averaged hydraulic conductivity.

Anomalous diffusion due to the non-Markovian process of the dust particle velocity in complex plasmas

NASA Astrophysics Data System (ADS)

Ghannad, Z.; Hakimi Pajouh, H.

2017-12-01

In this work, the motion of a dust particle under the influence of the random force due to dust charge fluctuations is considered as a non-Markovian stochastic process. Memory effects in the velocity process of the dust particle are studied. A model is developed based on the fractional Langevin equation for the motion of the dust grain. The fluctuation-dissipation theorem for the dust grain is derived from this equation. The mean-square displacement and the velocity autocorrelation function of the dust particle are obtained in terms of the Mittag-Leffler functions. Their asymptotic behavior and the dust particle temperature due to charge fluctuations are studied in the long-time limit. As an interesting result, it is found that the presence of memory effects in the velocity process of the dust particle as a non-Markovian process can cause an anomalous diffusion in dusty plasmas. In this case, the velocity autocorrelation function of the dust particle has a power-law decay like t - α - 2, where the exponent α take values 0 < α < 1.

The Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Fractal

NASA Astrophysics Data System (ADS)

Sadegh, Sanaz; Higgin, Jenny; Mannion, Patrick; Tamkun, Michael; Krapf, Diego

A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized due to experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data show that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar fractal. These results present a hierarchical nanoscale picture of the plasma membrane and demonstrate direct interactions between the actin cortex and the cell surface.

MESOSCOPIC MODELING OF STOCHASTIC REACTION-DIFFUSION KINETICS IN THE SUBDIFFUSIVE REGIME

PubMed Central

BLANC, EMILIE; ENGBLOM, STEFAN; HELLANDER, ANDREAS; LÖTSTEDT, PER

2017-01-01

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model of subdiffusion into an accurate and consistent reaction-subdiffusion computational framework. Two different possible models of chemical reaction are revealed and some basic dynamic properties are derived. In certain cases those mesoscopic models have a direct interpretation at the macroscopic level as fractional partial differential equations in a bounded time interval. Through analysis and numerical experiments we estimate the macroscopic effects of reactions under subdiffusive mixing. The models display properties observed also in experiments: for a short time interval the behavior of the diffusion and the reaction is ordinary, in an intermediate interval the behavior is anomalous, and at long times the behavior is ordinary again. PMID:29046618

Anomalous diffusion in neutral evolution of model proteins.

PubMed

Nelson, Erik D; Grishin, Nick V

2015-06-01

Protein evolution is frequently explored using minimalist polymer models, however, little attention has been given to the problem of structural drift, or diffusion. Here, we study neutral evolution of small protein motifs using an off-lattice heteropolymer model in which individual monomers interact as low-resolution amino acids. In contrast to most earlier models, both the length and folded structure of the polymers are permitted to change. To describe structural change, we compute the mean-square distance (MSD) between monomers in homologous folds separated by n neutral mutations. We find that structural change is episodic, and, averaged over lineages (for example, those extending from a single sequence), exhibits a power-law dependence on n. We show that this exponent depends on the alignment method used, and we analyze the distribution of waiting times between neutral mutations. The latter are more disperse than for models required to maintain a specific fold, but exhibit a similar power-law tail.

Anomalous diffusion in neutral evolution of model proteins

NASA Astrophysics Data System (ADS)

Nelson, Erik D.; Grishin, Nick V.

2015-06-01

Protein evolution is frequently explored using minimalist polymer models, however, little attention has been given to the problem of structural drift, or diffusion. Here, we study neutral evolution of small protein motifs using an off-lattice heteropolymer model in which individual monomers interact as low-resolution amino acids. In contrast to most earlier models, both the length and folded structure of the polymers are permitted to change. To describe structural change, we compute the mean-square distance (MSD) between monomers in homologous folds separated by n neutral mutations. We find that structural change is episodic, and, averaged over lineages (for example, those extending from a single sequence), exhibits a power-law dependence on n . We show that this exponent depends on the alignment method used, and we analyze the distribution of waiting times between neutral mutations. The latter are more disperse than for models required to maintain a specific fold, but exhibit a similar power-law tail.

Temporal correlation functions of concentration fluctuations: an anomalous case.

PubMed

Lubelski, Ariel; Klafter, Joseph

2008-10-09

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

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.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

Persistent random walk of cells involving anomalous effects and random death

NASA Astrophysics Data System (ADS)

Fedotov, Sergei; Tan, Abby; Zubarev, Andrey

2015-04-01

The purpose of this paper is to implement a random death process into a persistent random walk model which produces sub-ballistic superdiffusion (Lévy walk). We develop a stochastic two-velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction. It is assumed that the switching rate is a decreasing function of residence (running) time. This assumption leads to the power law for the velocity switching time distribution. This describes the anomalous persistence of cell motility: the longer the cell moves in one direction, the smaller the switching probability to another direction becomes. We derive master equations for the cell densities with the generalized switching terms involving the tempered fractional material derivatives. We show that the random death of cells has an important implication for the transport process through tempering of the superdiffusive process. In the long-time limit we write stationary master equations in terms of exponentially truncated fractional derivatives in which the rate of death plays the role of tempering of a Lévy jump distribution. We find the upper and lower bounds for the stationary profiles corresponding to the ballistic transport and diffusion with the death-rate-dependent diffusion coefficient. Monte Carlo simulations confirm these bounds.

Coherent structure diffusivity in the edge region of Reversed Field Pinch experiments

NASA Astrophysics Data System (ADS)

Spolaore, M.; Antoni, V.; Spada, E.; Bergsåker, H.; Cavazzana, R.; Drake, J. R.; Martines, E.; Regnoli, G.; Serianni, G.; Vianello, N.

2005-01-01

Coherent structures emerging from the background turbulence have been detected by electrostatic measurements in the edge region of two Reversed Field Pinch experiments, RFX (Padua) and Extrap-T2R (Stockholm). Measurements have been performed by arrays of Langmuir probes which allowed simultaneous measurements of temperature, potential and density to be carried out. These structures have been interpreted as a dynamic balance of dipolar and monopolar vortices, whose relative population are found to depend on the local mean E × B flow shear. The contribution to the anomalous transport of these structures has been investigated and it has been found that the corresponding diffusion coeffcient accounts up to 50% of the total diffusivity. The experimental findings indicate that the diffusion coeffcient associated to the coherent structures depends on the relative population of the two types of vortices and is minimum when the two populations are equal. An interpretative model is proposed to explain this feature.

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Mechanisms of the Diffusion of Nonpolar Substances in a Hydrophilic Ionic Liquid

NASA Astrophysics Data System (ADS)

Atamas', N. A.

2018-01-01

The structural-dynamic features of ionic liquid-nonpolar substance systems are studied by means of molecular dynamics using Frenkel's fundamental theory of a liquid and the phonon theory of the thermodynamics of a liquid, in combination with the DL_POLY_4.05 software package. Argon, methane, and benzene molecules serve as the dissolved substances. Model concepts are proposed and analyzed to describe the diffusion of molecules of a dissolved substance in an ionic liquid. It is shown that an increase in the mass of the molecules of a dissolved nonpolar substance correlates with their mobility in a hydrophilic ionic liquid (IL). This determines the diffusion of the components of dmim+/Cl- IL solutions and is responsible for the anomalous behavior of the solubility of nonpolar substances in them.

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-02-01

Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.

Logarithmic violation of scaling in anisotropic kinematic dynamo model

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2016-01-01

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t')/k⊥d-1 +ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to the distinguished direction. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: instead of power-like corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L.

Improved estimation of anomalous diffusion exponents in single-particle tracking experiments

NASA Astrophysics Data System (ADS)

Kepten, Eldad; Bronshtein, Irena; Garini, Yuval

2013-05-01

The mean square displacement is a central tool in the analysis of single-particle tracking experiments, shedding light on various biophysical phenomena. Frequently, parameters are extracted by performing time averages on single-particle trajectories followed by ensemble averaging. This procedure, however, suffers from two systematic errors when applied to particles that perform anomalous diffusion. The first is significant at short-time lags and is induced by measurement errors. The second arises from the natural heterogeneity in biophysical systems. We show how to estimate and correct these two errors and improve the estimation of the anomalous parameters for the whole particle distribution. As a consequence, we manage to characterize ensembles of heterogeneous particles even for rather short and noisy measurements where regular time-averaged mean square displacement analysis fails. We apply this method to both simulations and in vivo measurements of telomere diffusion in 3T3 mouse embryonic fibroblast cells. The motion of telomeres is found to be subdiffusive with an average exponent constant in time. Individual telomere exponents are normally distributed around the average exponent. The proposed methodology has the potential to improve experimental accuracy while maintaining lower experimental costs and complexity.

Anomalous increase of diffuse CO_{2} emission from Brava (Cape Verde): evidence of volcanic unrest or increase gas release from a stationary magma body?

NASA Astrophysics Data System (ADS)

García-Merino, Marta; García-Hernández, Rubén; Montrond, Eurico; Dionis, Samara; Fernandes, Paulo; Silva, Sonia V.; Alfama, Vera; Cabral, Jeremías; Pereira, Jose M.; Padrón, Eleazar; Pérez, Nemesio M.

2017-04-01

Brava (67 km2) is the southwestern most and the smallest inhabited island of the Cape Verde archipelago. It is located 18 km west of Fogo Island and rises 976 m from the sea level. Brava has not any documented historical eruptions, but its Holocene volcanism and relatively high seismic activity clearly indicate that it is an active volcanic island. Since there have been no historic eruptions in Brava, volcanic hazard awareness among the population and the authorities is very low; therefore, its volcano monitoring program is scarce. With the aim of helping to provide a multidisciplinary monitoring program for the volcanic surveillance of the island, diffuse CO2 emission surveys have been carried out since 2010; approximately every 2 years. Soil CO2 efflux measurements are periodically performed at ˜ 275 observation sites all over the island and after taking into consideration their accessibility and the island volcano-structural characteristics. At each sampling site, soil CO2 efflux measurement was performed by means of a portable NDIR sensor according to the accumulation chamber method. To quantify the total diffuse CO2 emission from Brava volcanic system, soil CO2 efflux maps were constructed using sequential Gaussian simulations (sGs). An increase trend of diffuse CO2 emission rate from 42 to 681 t d-1at Brava was observed; just one year prior the 2014-2015 Fogo eruption and almost three years before the anomalous seismic activity recorded on August 2016 with more than 1000 seismic events registered by the INMG on August 1st, 2016 (Bruno Faria, personal communication). Due to this anomalous seismic activity, a diffuse CO2 emission survey at Brava was performed from August 2 to 10, 2016, and the estimated degassing rate yield a value about 72 t d-1; typical background values. An additional survey was carried out from October 22 to November 6, 2016. For this last survey, the estimated diffuse CO2 emission from Brava showed the highest observed value with a degassing rate about 1.700 t d-1. These observed changes on diffuse CO2 emission are geochemical evidences which seem to support a volcanic unrest for the recent anomalous seismic activity registered at Brava.

Physiological Environment Induces Quick Response – Slow Exhaustion Reactions

PubMed Central

Hiroi, Noriko; Lu, James; Iba, Keisuke; Tabira, Akito; Yamashita, Shuji; Okada, Yasunori; Flamm, Christoph; Oka, Kotaro; Köhler, Gottfried; Funahashi, Akira

2011-01-01

In vivo environments are highly crowded and inhomogeneous, which may affect reaction processes in cells. In this study we examined the effects of intracellular crowding and an inhomogeneity on the behavior of in vivo reactions by calculating the spectral dimension (ds), which can be translated into the reaction rate function. We compared estimates of anomaly parameters obtained from fluorescence correlation spectroscopy (FCS) data with fractal dimensions derived from transmission electron microscopy (TEM) image analysis. FCS analysis indicated that the anomalous property was linked to physiological structure. Subsequent TEM analysis provided an in vivo illustration; soluble molecules likely percolate between intracellular clusters, which are constructed in a self-organizing manner. We estimated a cytoplasmic spectral dimension ds to be 1.39 ± 0.084. This result suggests that in vivo reactions initially run faster than the same reactions in a homogeneous space; this conclusion is consistent with the anomalous character indicated by FCS analysis. We further showed that these results were compatible with our Monte-Carlo simulation in which the anomalous behavior of mobile molecules correlates with the intracellular environment, leading to description as a percolation cluster, as demonstrated using TEM analysis. We confirmed by the simulation that the above-mentioned in vivo like properties are different from those of homogeneously concentrated environments. Additionally, simulation results indicated that crowding level of an environment might affect diffusion rate of reactant. Such knowledge of the spatial information enables us to construct realistic models for in vivo diffusion and reaction systems. PMID:21960972

What is the alternative to the Alexander-Orbach relation?

NASA Astrophysics Data System (ADS)

Sokolov, Igor M.

2016-03-01

The Alexander-Orbach (AO) relation d w = 2d f /d s connecting the fractal dimension of a random walk’s (RW) trajectory d w or the exponent of anomalous diffusion α = 2/d w on a fractal structure with the fractal and spectral dimension of the structure itself plays a key role in discussion of dynamical properties of complex systems including living cells and single biomolecules. This relation however does not hold universally and breaks down for some structures like diffusion limited aggregates and Eden trees. We show that the alternative to the AO relation is the explicit dependence of the coefficient of the anomalous diffusion on the system’s size, i.e. the absence of its thermodynamical limit. The prerequisite for its breakdown is the dependence of the local structure of possible steps of the RW on the system’s size. The discussion is illustrated by the examples of diffusion on a Koch curve (AO-conform) and on a Cantor dust (violating AO relation).

Electronic shot noise in fractal conductors.

PubMed

Groth, C W; Tworzydło, J; Beenakker, C W J

2008-05-02

By solving a master equation in the Sierpiński lattice and in a planar random-resistor network, we determine the scaling with size L of the shot noise power P due to elastic scattering in a fractal conductor. We find a power-law scaling P proportional, variantL;{d_{f}-2-alpha}, with an exponent depending on the fractal dimension d_{f} and the anomalous diffusion exponent alpha. This is the same scaling as the time-averaged current I[over ], which implies that the Fano factor F=P/2eI[over ] is scale-independent. We obtain a value of F=1/3 for anomalous diffusion that is the same as for normal diffusion, even if there is no smallest length scale below which the normal diffusion equation holds. The fact that F remains fixed at 1/3 as one crosses the percolation threshold in a random-resistor network may explain recent measurements of a doping-independent Fano factor in a graphene flake.

A Scientific Approach to the Investigation on Anomalous Atmospheric Light Phenomena

NASA Astrophysics Data System (ADS)

Teodorani, M.

2011-12-01

Anomalous atmospheric light phenomena tend to occur recurrently in several places of our planet. Statistical studies show that a phenomenon's real recurrence area can be identified only after pondering reported cases on the population number and on the diffusion of communication media. The main scientific results that have been obtained so far after explorative instrumented missions have been carried out are presented, including the empirical models that have been set up in order to describe the observed reality. Subsequently, a focused theorization is discussed in order to attack the physical problem concerning the structure and the dynamics of "light balls" and the enigma related to the central force that maintains them in spherical shape. Finally, several important issues are discussed regarding methodology, strategy, tactics and interdisciplinary approaches.

Regimes of stability and scaling relations for the removal time in the asteroid belt: a simple kinetic model and numerical tests

NASA Astrophysics Data System (ADS)

Cubrovic, Mihailo

2005-02-01

We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws) between the removal time (the time for an asteroid to experience a qualitative change of dynamical behavior and enter a wide chaotic zone) and the Lyapunov time. The correlations are shown to arise in two different regimes, characterized by exponential and power-law scalings. We also show how is the so-called “stable chaos” (exponential regime) related to anomalous diffusion. Finally, we check our results numerically and discuss their possible applications in analyzing the motion of particular asteroids.

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells.

PubMed

Longeville, Stéphane; Stingaciu, Laura-Roxana

2017-09-05

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement by neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells ([Formula: see text]330 g.L -1 ) corresponds to an optimum for oxygen transport for individuals under strong activity.

Molecular Dynamics Simulation of Salt Diffusion in Polyelectrolyte Assemblies.

PubMed

Zhang, Ran; Duan, Xiaozheng; Ding, Mingming; Shi, Tongfei

2018-06-05

The diffusion of salt ions and charged probe molecules in polyelectrolyte assemblies is often assumed to follow a theoretical hopping model, in which the diffusing ion is hopping between charged sites of chains based on electroneutrality. However, experimental verification of diffusing pathway at such microscales is difficult, and the corresponding molecular mechanisms remain elusive. In this study, we perform all-atom molecular dynamics (MD) simulations of salt diffusion in polyelectrolyte (PE) assembly of poly (sodium 4-styrenesulfonate) (PSS) and poly (diallyldimethylammonium chloride) (PDAC). Besides the ion hopping mode, the diffusing trajectories are found presenting common features of a jump process, i.e., subjecting to PE relaxation, water pockets in the structure open and close, thus the ion can move from one pocket to another. Anomalous subdiffusion of ions and water is observed due to the trapping scenarios in these water pockets. The jump events are much rarer compared with ion hopping but significantly increases salt diffusion with increasing temperature. Our result strongly indicates that salt diffusion in hydrated PDAC/PSS is a combined process of ion hopping and jump motion. This provides new molecular explanation for the coupling of salt motion with chain motion and the nonlinear increase of salt diffusion at glass transition temperature.

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells

DOE PAGES

Longeville, Stéphane; Stingaciu, Laura-Roxana

2017-09-05

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement bymore » neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells (≃330 g.L -1) corresponds to an optimum for oxygen transport for individuals under strong activity.« less

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells

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

Longeville, Stéphane; Stingaciu, Laura-Roxana

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement bymore » neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells (≃330 g.L -1) corresponds to an optimum for oxygen transport for individuals under strong activity.« less

Langevin equation with fluctuating diffusivity: A two-state model

NASA Astrophysics Data System (ADS)

Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji

2016-07-01

Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

Weak Ergodicity Breaking of Receptor Motion in Living Cells Stemming from Random Diffusivity

NASA Astrophysics Data System (ADS)

Manzo, Carlo; Torreno-Pina, Juan A.; Massignan, Pietro; Lapeyre, Gerald J.; Lewenstein, Maciej; Garcia Parajo, Maria F.

2015-01-01

Molecular transport in living systems regulates numerous processes underlying biological function. Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive motion been associated with nonergodic behavior. These findings have stimulated new questions for their implications in statistical mechanics and cell biology. Is nonergodicity a common strategy shared by living systems? Which physical mechanisms generate it? What are its implications for biological function? Here, we use single-particle tracking to demonstrate that the motion of dendritic cell-specific intercellular adhesion molecule 3-grabbing nonintegrin (DC-SIGN), a receptor with unique pathogen-recognition capabilities, reveals nonergodic subdiffusion on living-cell membranes In contrast to previous studies, this behavior is incompatible with transient immobilization, and, therefore, it cannot be interpreted according to continuous-time random-walk theory. We show that the receptor undergoes changes of diffusivity, consistent with the current view of the cell membrane as a highly dynamic and diverse environment. Simulations based on a model of an ordinary random walk in complex media quantitatively reproduce all our observations, pointing toward diffusion heterogeneity as the cause of DC-SIGN behavior. By studying different receptor mutants, we further correlate receptor motion to its molecular structure, thus establishing a strong link between nonergodicity and biological function. These results underscore the role of disorder in cell membranes and its connection with function regulation. Because of its generality, our approach offers a framework to interpret anomalous transport in other complex media where dynamic heterogeneity might play a major role, such as those found, e.g., in soft condensed matter, geology, and ecology.

Coupled Protein Diffusion and Folding in the Cell

PubMed Central

Guo, Minghao; Gelman, Hannah; Gruebele, Martin

2014-01-01

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control's diffusion coefficient, PGK's diffusion coefficient is a non-monotonic function of temperature, signaling ‘sticking’ of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates. PMID:25436502

Coupled protein diffusion and folding in the cell.

PubMed

Guo, Minghao; Gelman, Hannah; Gruebele, Martin

2014-01-01

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control's diffusion coefficient, PGK's diffusion coefficient is a non-monotonic function of temperature, signaling 'sticking' of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates.

Spin transport study in a Rashba spin-orbit coupling system

PubMed Central

Mei, Fuhong; Zhang, Shan; Tang, Ning; Duan, Junxi; Xu, Fujun; Chen, Yonghai; Ge, Weikun; Shen, Bo

2014-01-01

One of the most important topics in spintronics is spin transport. In this work, spin transport properties of two-dimensional electron gas in AlxGa1-xN/GaN heterostructure were studied by helicity-dependent photocurrent measurements at room temperature. Spin-related photocurrent was detected under normal incidence of a circularly polarized laser with a Gaussian distribution. On one hand, spin polarized electrons excited by the laser generate a diffusive spin polarization current, which leads to a vortex charge current as a result of anomalous circular photogalvanic effect. On the other hand, photo-induced spin polarized electrons driven by a longitudinal electric field give rise to a transverse current via anomalous Hall Effect. Both of these effects originated from the Rashba spin-orbit coupling. By analyzing spin-related photocurrent varied with laser position, the contributions of the two effects were differentiated and the ratio of the spin diffusion coefficient to photo-induced anomalous spin Hall mobility Ds/μs = 0.08 V was extracted at room temperature. PMID:24504193

Turbulence-induced anomalous electron diffusion in the plume of the VASIMR VX-200

NASA Astrophysics Data System (ADS)

Olsen, Christopher; Ballenger, Maxwell; Squire, Jared; Longmier, Benjamin; Carter, Mark; Glover, Tim

2012-10-01

The separation of electrons from magnetic nozzles is critical to the function of the VASIMR engine and is of general importance to the field of electric propulsion. Separation of electrons by means of anomalous cross field diffusion is considered. Plume measurements using spectral analysis of custom high frequency probes characterizes the nature of oscillating electric fields in the expanding magnetic nozzle. The oscillating electric field results in frequency dependent density variations that can lead to anomalously high transport in the absence of collisions mimicking collisional transport. The spatial structure of the fluctuating fields is consistent with turbulence caused by separation of energetic (> 100 eV) non-magnetized ions and low energy magnetized electrons via the modified two-stream instability (MTSI) and generalized lower hybrid drift instability (GLHDI). Electric fields as high as 300 V/m are observed at frequencies up to an order of magnitude above the lower hybrid frequency. The electric field fluctuations dissipate with increasing axial distance consistent with changes in ion flux streamlines as plasma detachment occurs.

Anomalous Dynamics of a Lipid Recognition Protein on a Membrane Surface

PubMed Central

Yamamoto, Eiji; Kalli, Antreas C.; Akimoto, Takuma; Yasuoka, Kenji; Sansom, Mark S. P.

2015-01-01

Pleckstrin homology (PH) domains are lipid-binding modules present in peripheral membrane proteins which interact with phosphatidyl-inositol phosphates (PIPs) in cell membranes. We use multiscale molecular dynamics simulations to characterize the localization and anomalous dynamics of the DAPP1 PH domain on the surface of a PIP-containing lipid bilayer. Both translational and rotational diffusion of the PH domain on the lipid membrane surface exhibit transient subdiffusion, with an exponent α ≈ 0.5 for times of less than 10 ns. In addition to a PIP3 molecule at the canonical binding site of the PH domain, we observe additional PIP molecules in contact with the protein. Fluctuations in the number of PIPs associated with the PH domain exhibit 1/f noise. We suggest that the anomalous diffusion and long-term correlated interaction of the PH domain with the membrane may contribute to an enhanced probability of encounter with target complexes on cell membrane surfaces. PMID:26657413

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

NASA Astrophysics Data System (ADS)

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

2011-03-01

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

A simple model of the effect of ocean ventilation on ocean heat uptake

NASA Astrophysics Data System (ADS)

Nadiga, Balu; Urban, Nathan

2017-11-01

Transport of water from the surface mixed layer into the ocean interior is achieved, in large part, by the process of ventilation-a process associated with outcropping isopycnals. Starting from such a configuration of outcropping isopycnals, we derive a simple model of the effect of ventilation on ocean uptake of anomalous radiative forcing. This model can be seen as an improvement of the popular anomaly-diffusing class of energy balance models (AD-EBM) that are routinely employed to analyze and emulate the warming response of both observed and simulated Earth system. We demonstrate that neither multi-layer, nor continuous-diffusion AD-EBM variants can properly represent both surface-warming and the vertical distribution of ocean heat uptake. The new model overcomes this deficiency. The simplicity of the models notwithstanding, the analysis presented and the necessity of the modification is indicative of the role played by processes related to the down-welling branch of global ocean circulation in shaping the vertical distribution of ocean heat uptake.

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

Gaggero, Daniele; Urbano, Alfredo; Valli, Mauro

We compute the γ-ray and neutrino diffuse emission of the Galaxy on the basis of a recently proposed phenomenological model characterized by radially dependent cosmic-ray (CR) transport properties. We show how this model, designed to reproduce both Fermi-LAT γ-ray data and local CR observables, naturally reproduces the anomalous TeV diffuse emission observed by Milagro in the inner Galactic plane. Above 100 TeV our picture predicts a neutrino flux that is about five (two) times larger than the neutrino flux computed with conventional models in the Galactic Center region (full-sky). Explaining in that way up to ∼25% of the flux measuredmore » by IceCube, we reproduce the full-sky IceCube spectrum adding an extra-Galactic component derived from the muonic neutrinos flux in the northern hemisphere. We also present precise predictions for the Galactic plane region where the flux is dominated by the Galactic emission.« less

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

Li, Renzhong; Sun, Gang; Xu, Limei, E-mail: limei.xu@pku.edu.cn

A group of materials including water and silicon exhibit many anomalous behaviors, e.g., density anomaly and diffusivity anomaly (increase upon compression). These materials are hypothesized to have a liquid-liquid phase transition (LLPT) and the critical fluctuation in the vicinity of the liquid-liquid critical point is considered as the origin of different anomalies. Liquid gallium was also reported to have a LLPT, yet whether it shows similar water-like anomalies is not yet studied. Using molecular dynamics simulations on a modified embedded-atom model, we study the thermodynamic, dynamic, and structural properties of liquid gallium as well as its LLPT. We find that,more » similar to water-like materials predicted to have the LLPT, gallium also shows different anomalous behaviors (e.g., density anomaly, diffusivity anomaly, and structural anomaly). We also find that its thermodynamic and structural response functions are continuous and show maxima in the supercritical region, the loci of which asymptotically approach to the other and merge to the Widom line. These phenomena are consistent with the supercritical phenomenon in a category of materials with a liquid-liquid critical point, which could be common features in most materials with a LLPT.« less

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.

Normal and anomalous diffusion in fluctuations of dust concentration nearby emission source

NASA Astrophysics Data System (ADS)

Szczurek, Andrzej; Maciejewska, Monika; Wyłomańska, Agnieszka; Sikora, Grzegorz; Balcerek, Michał; Teuerle, Marek

2018-02-01

Particulate matter (PM) is an important component of air. Nowadays, major attention is payed to fine dust. It has considerable environmental impact, including adverse effect on human health. One of important issues regarding PM is the temporal variation of its concentration. The variation contains information about factors influencing this quantity in time. The work focuses on the character of PM concentration dynamics indoors, in the vicinity of emission source. The objective was to recognize between the homogeneous or heterogeneous dynamics. The goal was achieved by detecting normal and anomalous diffusion in fluctuations of PM concentration. For this purpose we used anomalous diffusion exponent, β which was derived from Mean Square Displacement (MSD) analysis. The information about PM concentration dynamics may be used to design sampling strategy, which serves to attain representative information about PM behavior in time. The data analyzed in this work was collected from single-point PM concentration monitoring in the vicinity of seven emission sources in industrial environment. In majority of cases we observed heterogeneous character of PM concentration dynamics. It confirms the complexity of interactions between the emission sources and indoor environment. This result also votes against simplistic approach to PM concentration measurement indoors, namely their occasional character, short measurement periods and long term averaging.

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

NASA Astrophysics Data System (ADS)

Liu, Jian; Li, Baohe; Chen, Xiaosong

2018-02-01

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

Generalized Langevin equation with a three parameter Mittag-Leffler noise

NASA Astrophysics Data System (ADS)

Sandev, Trifce; Tomovski, Živorad; Dubbeldam, Johan L. A.

2011-10-01

The relaxation functions for a given generalized Langevin equation in the presence of a three parameter Mittag-Leffler noise are studied analytically. The results are represented by three parameter Mittag-Leffler functions. Exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the Laplace transform method. The asymptotic behavior of the particle in the short and long time limits are found by using the Tauberian theorems. It is shown that for large times the particle motion is subdiffusive for β-1<αδ<β, and superdiffusive for β<αδ. Many previously obtained results are recovered. Due to the many parameters contained in the noise term, the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media.

Is the acceleration of anomalous cosmic rays affected by the geometry of the termination shock?

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

Senanayake, U. K.; Florinski, V., E-mail: uks0001@uah.edu, E-mail: vaf0001@uah.edu

2013-12-01

Historically, anomalous cosmic rays (ACRs) were thought to be accelerated at the solar-wind termination shock (TS) by the diffusive shock acceleration process. When Voyager 1 crossed the TS in 2004, the measured ACR spectra did not match the theoretical prediction of a continuous power law, and the source of the high-energy ACRs was not observed. When the Voyager 2 crossed the TS in 2007, it produced similar results. Several possible explanations have since appeared in the literature, but we follow the suggestion that ACRs are still accelerated at the shock, only away from the Voyager crossing points. To investigate thismore » hypothesis closer, we study ACR acceleration using a three-dimensional, non-spherical model of the heliosphere that is axisymmetric with respect to the interstellar flow direction. We then compare the results with those obtained for a spherical TS. A semi-analytic model of the plasma and magnetic field backgrounds is developed to permit an investigation over a wide range of parameters under controlled conditions. The model is applied to helium ACRs, whose phase-space trajectories are stochastically integrated backward in time until a pre-specified, low-energy boundary, taken to be 0.5 MeV n{sup –1} (the so-called injection energy), is reached. Our results show that ACR acceleration is quite efficient on the heliotail-facing part of the TS. For small values of the perpendicular diffusion coefficient, our model yields a positive intensity gradient between the TS and about midway through the heliosheath, in agreement with the Voyager observations.« less

Theory and simulation of time-fractional fluid diffusion in porous media

NASA Astrophysics Data System (ADS)

Carcione, José M.; Sanchez-Sesma, Francisco J.; Luzón, Francisco; Perez Gavilán, Juan J.

2013-08-01

We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 < ν < 2 replaces the first-order time derivative in the classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald-Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’.

The Impacts of Dry Dynamic Cores on Asymmetric Hurricane Intensification

NASA Technical Reports Server (NTRS)

Guimond, Stephen R.; Reisner, Jon M.; Marras, Simone; Giraldo, Francis X.

2016-01-01

The fundamental pathways for tropical cyclone (TC) intensification are explored by considering axisymmetric and asymmetric impulsive thermal perturbations to balanced, TC-like vortices using the dynamic cores of three different nonlinear numerical models. Attempts at reproducing the results of previous work, which used the community WRF Model, revealed a discrepancy with the impacts of purely asymmetric thermal forcing. The current study finds that thermal asymmetries can have an important, largely positive role on the vortex intensification, whereas other studies find that asymmetric impacts are negligible. Analysis of the spectral energetics of each numerical model indicates that the vortex response to asymmetric thermal perturbations is significantly damped in WRF relative to the other models. Spectral kinetic energy budgets show that this anomalous damping is primarily due to the increased removal of kinetic energy from the vertical divergence of the vertical pressure flux, which is related to the flux of inertia-gravity wave energy. The increased kinetic energy in the other two models is shown to originate around the scales of the heating and propagate upscale with time from nonlinear effects. For very large thermal amplitudes (50 K), the anomalous removal of kinetic energy due to inertia-gravity wave activity is much smaller, resulting in good agreement between models. The results of this paper indicate that the numerical treatment of small-scale processes that project strongly onto inertia-gravity wave energy can lead to significant differences in asymmetric TC intensification. Sensitivity tests with different time integration schemes suggest that diffusion entering into the implicit solution procedure is partly responsible for the anomalous damping of energy.

The origin of anomalous transport in porous media - is it possible to make a priori predictions?

NASA Astrophysics Data System (ADS)

Bijeljic, Branko; Blunt, Martin

2013-04-01

Despite the range of significant applications of flow and solute transport in porous rock, including contaminant migration in subsurface hydrology, geological storage of carbon-dioxide and tracer studies and miscible displacement in oil recovery, even the qualitative behavior in the subsurface is uncertain. The non-Fickian nature of dispersive processes in heterogeneous porous media has been demonstrated experimentally from pore to field scales. However, the exact relationship between structure, velocity field and transport has not been fully understood. Advances in X ray imaging techniques made it possible to accurately describe structure of the pore space, helping predict flow and anomalous transport behaviour using direct simulation. This is demonstrated by simulating solute transport through 3D images of rock samples, with resolutions of a few microns, representing geological media of increasing pore-scale complexity: a sandpack, a sandstone, and a carbonate. A novel methodology is developed that predicts solute transport at the pore scale by using probability density functions of displacement (propagators) and probability density function of transit time between the image voxels, and relates it to probability density function of normalized local velocity. A key advantage is that full information on velocity and solute concentration is retained in the models. The methodology includes solving for Stokes flow by Open Foam, solving for advective transport by the novel streamline simulation method, and superimposing diffusive transport diffusion by the random walk method. It is shown how computed propagators for beadpack, sandstone and carbonate depend on the spread in the velocity distribution. A narrow velocity distribution in the beadpack leads to the least anomalous behaviour where the propagators rapidly become Gaussian; the wider velocity distribution in the sandstone gives rise to a small immobile concentration peak, and a large secondary mobile peak moving at approximately the average flow speed; in the carbonate with the widest velocity distribution the stagnant concentration peak is persistent, while the emergence of a smaller secondary mobile peak is observed, leading to a highly anomalous behavior. This defines different generic nature of non-Fickian transport in the three media and quantifies the effect of pore structure on transport. Moreover, the propagators obtained by the model are in a very good agreement with the propagators measured on beadpack, Bentheimer sandstone and Portland carbonate cores in nuclear magnetic resonance experiments. These findings demonstrate that it is possible to make a priori predictions of anomalous transport in porous media. The importance of these findings for transport in complex carbonate rock micro-CT images is discussed, classifying them in terms of degree of anomalous transport that can have an impact at the field scale. Extensions to reactive transport will be discussed.

Effect of double layers on magnetosphere-ionosphere coupling

NASA Technical Reports Server (NTRS)

Lysak, Robert L.; Hudson, Mary K.

1987-01-01

The dynamic aspects of auroral current structures are reviewed with emphasis on consequences for models of microscopic turbulence (MT). A number of models of MT are introduced into a large-scale model of Alfven wave propagation to determine the effect of various models on the overall structure of auroral currents. The effect of a double layer (DL) electric field which scales with the plasma temperature and the Debye length is compared with the effect of anomalous resistivity due to electrostatic ion cyclotron turbulence in which the electric field scales with the magnetic field strength. It is shown that the DL model is less diffusive than the resistive model, indicating the possibility of narrow intense current structures.

Analysis of Molecular Diffusion by First-Passage Time Variance Identifies the Size of Confinement Zones

PubMed Central

Rajani, Vishaal; Carrero, Gustavo; Golan, David E.; de Vries, Gerda; Cairo, Christopher W.

2011-01-01

The diffusion of receptors within the two-dimensional environment of the plasma membrane is a complex process. Although certain components diffuse according to a random walk model (Brownian diffusion), an overwhelming body of work has found that membrane diffusion is nonideal (anomalous diffusion). One of the most powerful methods for studying membrane diffusion is single particle tracking (SPT), which records the trajectory of a label attached to a membrane component of interest. One of the outstanding problems in SPT is the analysis of data to identify the presence of heterogeneity. We have adapted a first-passage time (FPT) algorithm, originally developed for the interpretation of animal movement, for the analysis of SPT data. We discuss the general application of the FPT analysis to molecular diffusion, and use simulations to test the method against data containing known regions of confinement. We conclude that FPT can be used to identify the presence and size of confinement within trajectories of the receptor LFA-1, and these results are consistent with previous reports on the size of LFA-1 clusters. The analysis of trajectory data for cell surface receptors by FPT provides a robust method to determine the presence and size of confined regions of diffusion. PMID:21402028

Persistent mobility edges and anomalous quantum diffusion in order-disorder separated quantum films

NASA Astrophysics Data System (ADS)

Zhong, Jianxin; Stocks, G. Malcolm

2007-01-01

A concept of order-disorder separated quantum films is proposed for the design of ultrathin quantum films of a few atomic layers thick with unconventional transport properties. The concept is demonstrated through studying an atomic bilayer comprised of an ordered layer and a disordered layer. Without the disordered layer or the ordered layer, the system is a conducting two-dimensional (2D) crystal or an insulating disordered 2D electron system. Without the order-disorder phase separation, a disordered bilayer is insulating under large disorder. In an order-disorder separated atomic bilayer, however, we show that the system behaves remarkably different from conventional ordered or disordered electron systems, exhibiting metal-insulator transitions with persistent mobility edges and superdiffusive anomalous quantum diffusion.

Anomalous Galactic Cosmic Rays in the Framework of AMS-02

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

Khiali, Behrouz; Haino, Sadakazu; Feng, Jie, E-mail: behrouz.khiali@cern.ch

2017-02-01

The cosmic-ray (CR) energy spectra of protons and helium nuclei, which are the most abundant components of cosmic radiation, exhibit a remarkable hardening at energies above 100 GeV/nucleon. Recent data from AMS-02 confirm this feature with a higher significance. These data challenge the current models of CR acceleration in Galactic sources and propagation in the Galaxy. Here, we explain the observed break in the spectra of protons and helium nuclei in light of recent advances in CR diffusion theories in turbulent astrophysical sources as being a result of a transition between different CR diffusion regimes. We reconstruct the observed CRmore » spectra using the fact that a transition from normal diffusion to superdiffusion changes the efficiency of particle acceleration and causes the change in the spectral index. We find that calculated proton and helium spectra match the data very well.« less

Effect of Greenhouse Gases Dissolved in Seawater

PubMed Central

Matsunaga, Shigeki

2015-01-01

A molecular dynamics simulation has been performed on the greenhouse gases carbon dioxide and methane dissolved in a sodium chloride aqueous solution, as a simple model of seawater. A carbon dioxide molecule is also treated as a hydrogen carbonate ion. The structure, coordination number, diffusion coefficient, shear viscosity, specific heat, and thermal conductivity of the solutions have been discussed. The anomalous behaviors of these properties, especially the negative pressure dependence of thermal conductivity, have been observed in the higher-pressure region. PMID:26729101

Effect of Greenhouse Gases Dissolved in Seawater.

PubMed

Matsunaga, Shigeki

2015-12-30

A molecular dynamics simulation has been performed on the greenhouse gases carbon dioxide and methane dissolved in a sodium chloride aqueous solution, as a simple model of seawater. A carbon dioxide molecule is also treated as a hydrogen carbonate ion. The structure, coordination number, diffusion coefficient, shear viscosity, specific heat, and thermal conductivity of the solutions have been discussed. The anomalous behaviors of these properties, especially the negative pressure dependence of thermal conductivity, have been observed in the higher-pressure region.

Anomalous law of cooling

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

Lapas, Luciano C., E-mail: luciano.lapas@unila.edu.br; Ferreira, Rogelma M. S., E-mail: rogelma.maria@gmail.com; Rubí, J. Miguel, E-mail: mrubi@ub.edu

2015-03-14

We analyze the temperature relaxation phenomena of systems in contact with a thermal reservoir that undergoes a non-Markovian diffusion process. From a generalized Langevin equation, we show that the temperature is governed by a law of cooling of the Newton’s law type in which the relaxation time depends on the velocity autocorrelation and is then characterized by the memory function. The analysis of the temperature decay reveals the existence of an anomalous cooling in which the temperature may oscillate. Despite this anomalous behavior, we show that the variation of entropy remains always positive in accordance with the second law ofmore » thermodynamics.« less

Nonlinear subdiffusive fractional equations and the aggregation phenomenon.

PubMed

Fedotov, Sergei

2013-09-01

In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on the mean density of particles. We derive a set of nonlinear subdiffusive fractional master equations and consider their diffusion approximations. We show that these equations describe the transition from an intermediate subdiffusive regime to asymptotically normal advection-diffusion transport regime. This transition is governed by nonlinear tempering parameter that generalizes the standard linear tempering. We illustrate the general results through the use of the examples from cell and population biology. We find that a nonuniform anomalous exponent has a strong influence on the aggregation phenomenon.

Is the Eagle Nebula powered by a hidden supernova remnant ?

NASA Astrophysics Data System (ADS)

Boulanger, Francois

2008-10-01

Spitzer observations of the Eagle nebula (M16) reveal the presence of a large (8 pc diameter) shell of dust heated to anomalously high temperatures. Modeling of dust excitation shows that the shell emission cannot be powered by the cluster UV radiation but that it can be accounted for by collisionally heated dust in a young (a few 1000 yrs) supernova remnant. We have re-analyzed deep Chandra observations that show diffuse emission consistent with this hypothesis, but also with galactic ridge emission. We propose a 50 ksec XMM observation to probe the spatial extent of the diffuse X-ray emission beyond the Spitzer shell. Absence of emission outside of this shell will strongly support the supernova remnant interpretation

Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation.

PubMed

Anta, Juan A; Mora-Seró, Iván; Dittrich, Thomas; Bisquert, Juan

2008-08-14

We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.

A Huygens principle for diffusion and anomalous diffusion in spatially extended systems

PubMed Central

Gottwald, Georg A.; Melbourne, Ian

2013-01-01

We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions. PMID:23653481

Direct in situ observations of single Fe atom catalytic processes and anomalous diffusion at graphene edges

PubMed Central

Zhao, Jiong; Deng, Qingming; Avdoshenko, Stanislav M.; Fu, Lei; Eckert, Jürgen; Rümmeli, Mark H.

2014-01-01

Single-atom catalysts are of great interest because of their high efficiency. In the case of chemically deposited sp2 carbon, the implementation of a single transition metal atom for growth can provide crucial insight into the formation mechanisms of graphene and carbon nanotubes. This knowledge is particularly important if we are to overcome fabrication difficulties in these materials and fully take advantage of their distinct band structures and physical properties. In this work, we present atomically resolved transmission EM in situ investigations of single Fe atoms at graphene edges. Our in situ observations show individual iron atoms diffusing along an edge either removing or adding carbon atoms (viz., catalytic action). The experimental observations of the catalytic behavior of a single Fe atom are in excellent agreement with supporting theoretical studies. In addition, the kinetics of Fe atoms at graphene edges are shown to exhibit anomalous diffusion, which again, is in agreement with our theoretical investigations. PMID:25331874

Anomalous Price Impact and the Critical Nature of Liquidity in Financial Markets

NASA Astrophysics Data System (ADS)

Tóth, B.; Lempérière, Y.; Deremble, C.; de Lataillade, J.; Kockelkoren, J.; Bouchaud, J.-P.

2011-10-01

We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V shaped and vanishes around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are, to a first approximation, diffusive. This naturally accounts for two striking stylized facts: First, large metaorders have to be fragmented in order to be digested by the liquidity funnel, which leads to a long memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of the linear response and a diverging impact of small orders, explaining the “square-root” impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.

Additivity Principle in High-Dimensional Deterministic Systems

NASA Astrophysics Data System (ADS)

Saito, Keiji; Dhar, Abhishek

2011-12-01

The additivity principle (AP), conjectured by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.180601], is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high dimensional. Surprisingly, even in the anomalous regime the CGF is also well fitted by the AP. Lower-dimensional systems are also studied and the importance of three dimensionality for the validity is stressed.

In Silico Determination of Gas Permeabilities by Non-Equilibrium Molecular Dynamics: CO2 and He through PIM-1

PubMed Central

Frentrup, Hendrik; Hart, Kyle E.; Colina, Coray M.; Müller, Erich A.

2015-01-01

We study the permeation dynamics of helium and carbon dioxide through an atomistically detailed model of a polymer of intrinsic microporosity, PIM-1, via non-equilibrium molecular dynamics (NEMD) simulations. This work presents the first explicit molecular modeling of gas permeation through a high free-volume polymer sample, and it demonstrates how permeability and solubility can be obtained coherently from a single simulation. Solubilities in particular can be obtained to a very high degree of confidence and within experimental inaccuracies. Furthermore, the simulations make it possible to obtain very specific information on the diffusion dynamics of penetrant molecules and yield detailed maps of gas occupancy, which are akin to a digital tomographic scan of the polymer network. In addition to determining permeability and solubility directly from NEMD simulations, the results shed light on the permeation mechanism of the penetrant gases, suggesting that the relative openness of the microporous topology promotes the anomalous diffusion of penetrant gases, which entails a deviation from the pore hopping mechanism usually observed in gas diffusion in polymers. PMID:25764366

Direct Acceleration of Pickup Ions at The Solar Wind Termination Shock: The Production of Anomalous Cosmic Rays

NASA Technical Reports Server (NTRS)

Ellison, Donald C.; Jones, Frank C.; Baring, Matthew G.

1998-01-01

We have modeled the injection and acceleration of pickup ions at the solar wind termination shock and investigated the parameters needed to produce the observed Anomalous Cosmic Ray (ACR) fluxes. A non-linear Monte Carlo technique was employed, which in effect solves the Boltzmann equation and is not restricted to near-isotropic particle distribution functions. This technique models the injection of thermal and pickup ions, the acceleration of these ions, and the determination of the shock structure under the influence of the accelerated ions. The essential effects of injection are treated in a mostly self-consistent manner, including effects from shock obliquity, cross- field diffusion, and pitch-angle scattering. Using recent determinations of pickup ion densities, we are able to match the absolute flux of hydrogen in the ACRs by assuming that pickup ion scattering mean free paths, at the termination shock, are much less than an AU and that modestly strong cross-field diffusion occurs. Simultaneously, we match the flux ratios He(+)/H(+) or O(+)/H(+) to within a factor approx. 5. If the conditions of strong scattering apply, no pre-termination-shock injection phase is required and the injection and acceleration of pickup ions at the termination shock is totally analogous to the injection and acceleration of ions at highly oblique interplanetary shocks recently observed by the Ulysses spacecraft. The fact that ACR fluxes can be modeled with standard shock assumptions suggests that the much-discussed "injection problem" for highly oblique shocks stems from incomplete (either mathematical or computer) modeling of these shocks rather than from any actual difficulty shocks may have in injecting and accelerating thermal or quasi-thermal particles.

A model of return intervals between earthquake events

NASA Astrophysics Data System (ADS)

Zhou, Yu; Chechkin, Aleksei; Sokolov, Igor M.; Kantz, Holger

2016-06-01

Application of the diffusion entropy analysis and the standard deviation analysis to the time sequence of the southern California earthquake events from 1976 to 2002 uncovered scaling behavior typical for anomalous diffusion. However, the origin of such behavior is still under debate. Some studies attribute the scaling behavior to the correlations in the return intervals, or waiting times, between aftershocks or mainshocks. To elucidate a nature of the scaling, we applied specific reshulffling techniques to eliminate correlations between different types of events and then examined how it affects the scaling behavior. We demonstrate that the origin of the scaling behavior observed is the interplay between mainshock waiting time distribution and the structure of clusters of aftershocks, but not correlations in waiting times between the mainshocks and aftershocks themselves. Our findings are corroborated by numerical simulations of a simple model showing a very similar behavior. The mainshocks are modeled by a renewal process with a power-law waiting time distribution between events, and aftershocks follow a nonhomogeneous Poisson process with the rate governed by Omori's law.

Ion acceleration in a plasma focus

NASA Technical Reports Server (NTRS)

Gary, S. P.

1974-01-01

The electric and magnetic fields associated with anomalous diffusion to the axis of a linear plasma discharge are used to compute representative ion trajectories. Substantial axial acceleration of the ions is demonstrated.

Topological Weyl superconductor to diffusive thermal Hall metal crossover in the B phase of UPt3

NASA Astrophysics Data System (ADS)

Goswami, Pallab; Nevidomskyy, Andriy H.

2015-12-01

The recent phase-sensitive measurements in the superconducting B phase of UPt3 provide strong evidence for the triplet, chiral kz(kx±i ky) 2 pairing symmetries, which endow the Cooper pairs with orbital angular momentum projections Lz=±2 along the c axis. In the absence of disorder such pairing can support both line and point nodes, and both types of nodal quasiparticles exhibit nontrivial topology in the momentum space. The point nodes, located at the intersections of the closed Fermi surfaces with the c axis, act as the double monopoles and the antimonopoles of the Berry curvature, and generalize the notion of Weyl quasiparticles. Consequently, the B phase should support an anomalous thermal Hall effect, the polar Kerr effect, in addition to the protected Fermi arcs on the (1 ,0 ,0 ) and the (0 ,1 ,0 ) surfaces. The line node at the Fermi surface equator acts as a vortex loop in the momentum space and gives rise to the zero-energy, dispersionless Andreev bound states on the (0 ,0 ,1 ) surface. At the transition from the B phase to the A phase, the time-reversal symmetry is restored, and only the line node survives inside the A phase. As both line and double-Weyl point nodes possess linearly vanishing density of states, we show that weak disorder acts as a marginally relevant perturbation. Consequently, an infinitesimal amount of disorder destroys the ballistic quasiparticle pole, while giving rise to a diffusive phase with a finite density of states at the zero energy. The resulting diffusive phase exhibits T -linear specific heat, and an anomalous thermal Hall effect. We predict that the low-temperature thermodynamic and transport properties display a crossover between a ballistic thermal Hall semimetal and a diffusive thermal Hall metal. By contrast, the diffusive phase obtained from a time-reversal-invariant pairing exhibits only the T -linear specific heat without any anomalous thermal Hall effect.

Fractional Diffusion Analysis of the Electromagnetic Field In Fractured Media Part II: 2.5-D Approach

NASA Astrophysics Data System (ADS)

Ge, J.; Everett, M. E.; Weiss, C. J.

2012-12-01

A 2.5D finite difference (FD) frequency-domain modeling algorithm based on the theory of fractional diffusion of electromagnetic (EM) fields generated by a loop source lying above a fractured geological medium is addressed in this paper. The presence of fractures in the subsurface, usually containing highly conductive pore fluids, gives rise to spatially hierarchical flow paths of induced EM eddy currents. The diffusion of EM eddy currents in such formations is anomalous, generalizing the classical Gaussian process described by the conventional Maxwell equations. Based on the continuous time random walk (CTRW) theory, the diffusion of EM eddy currents in a rough medium is governed by the fractional Maxwell equations. Here, we model the EM response of a 2D subsurface containing fractured zones, with a 3D loop source, which results the so-called 2.5D model geometry. The governing equation in the frequency domain is converted using Fourier transform into k domain along the strike direction (along which the model conductivity doesn't vary). The resulting equation system is solved by the multifrontal massively parallel solver (MUMPS). The data obtained is then converted back to spatial domain and the time domain. We find excellent agreement between the FD and analytic solutions for a rough halfspace model. Then FD solutions are calculated for a 2D fault zone model with variable conductivity and roughness. We compare the results with responses from several classical models and explore the relationship between the roughness and the spatial density of the fracture distribution.

Non-universal tracer diffusion in crowded media of non-inert obstacles.

PubMed

Ghosh, Surya K; Cherstvy, Andrey G; Metzler, Ralf

2015-01-21

We study the diffusion of a tracer particle, which moves in continuum space between a lattice of excluded volume, immobile non-inert obstacles. In particular, we analyse how the strength of the tracer-obstacle interactions and the volume occupancy of the crowders alter the diffusive motion of the tracer. From the details of partitioning of the tracer diffusion modes between trapping states when bound to obstacles and bulk diffusion, we examine the degree of localisation of the tracer in the lattice of crowders. We study the properties of the tracer diffusion in terms of the ensemble and time averaged mean squared displacements, the trapping time distributions, the amplitude variation of the time averaged mean squared displacements, and the non-Gaussianity parameter of the diffusing tracer. We conclude that tracer-obstacle adsorption and binding triggers a transient anomalous diffusion. From a very narrow spread of recorded individual time averaged trajectories we exclude continuous type random walk processes as the underlying physical model of the tracer diffusion in our system. For moderate tracer-crowder attraction the motion is found to be fully ergodic, while at stronger attraction strength a transient disparity between ensemble and time averaged mean squared displacements occurs. We also put our results into perspective with findings from experimental single-particle tracking and simulations of the diffusion of tagged tracers in dense crowded suspensions. Our results have implications for the diffusion, transport, and spreading of chemical components in highly crowded environments inside living cells and other structured liquids.

Flying over decades

NASA Astrophysics Data System (ADS)

Hoeller, Judith; Issler, Mena; Imamoglu, Atac

Levy flights haven been extensively used in the past three decades to describe non-Brownian motion of particles. In this presentation I give an overview on how Levy flights have been used across several disciplines, ranging from biology to finance to physics. In our publication we describe how a single electron spin 'flies' when captured in quantum dot using the central spin model. At last I motivate the use of Levy flights for the description of anomalous diffusion in modern experiments, concretely to describe the lifetimes of quasi-particles in Josephson junctions. Finished PhD at ETH in Spring 2015.

A unified multicomponent stress-diffusion model of drug release from non-biodegradable polymeric matrix tablets.

PubMed

Salehi, Ali; Zhao, Jin; Cabelka, Tim D; Larson, Ronald G

2016-02-28

We propose a new transport model of drug release from hydrophilic polymeric matrices, based on Stefan-Maxwell flux laws for multicomponent transport. Polymer stress is incorporated in the total mixing free energy, which contributes directly to the diffusion driving force while leading to time-dependent boundary conditions at the tablet interface. Given that hydrated matrix tablets are dense multicomponent systems, extended Stefan-Maxwell (ESM) flux laws are adopted to ensure consistency with the Onsager reciprocity principle and the Gibbs-Duhem thermodynamic constraint. The ESM flux law for any given component takes into account the friction exerted by all other species and is invariant with respect to reference velocity, thus satisfying Galilean translational invariance. Our model demonstrates that penetrant-induced plasticization of polymer chains partially or even entirely offsets the steady decline of chemical potential gradients at the tablet-medium interface that drive drug release. Utilizing a Flory-Huggins thermodynamic model, a modified form of the upper convected Maxwell constitutive equation for polymer stress and a Fujita-type dependence of mutual diffusivities on composition, depending on parameters, Fickian, anomalous or case II drug transport arises naturally from the model, which are characterized by quasi-power-law release profiles with exponents ranging from 0.5 to 1, respectively. A necessary requirement for non-Fickian release in our model is that the matrix stress relaxation time is comparable to the time scale for water diffusion. Mutual diffusivities and their composition dependence are the most decisive factors in controlling drug release characteristics in our model. Regression of the experimental polymer dissolution and drug release profiles in a system of Theophylline/cellulose (K15M) demonstrate that API-water mutual diffusivity in the presence of excipient cannot generally be taken as a constant. Copyright © 2016 Elsevier B.V. All rights reserved.

Fractional calculus applied to the analysis of spectral electrical conductivity of clay-water system.

PubMed

Korosak, Dean; Cvikl, Bruno; Kramer, Janja; Jecl, Renata; Prapotnik, Anita

2007-06-16

The analysis of the low-frequency conductivity spectra of the clay-water mixtures is presented. The frequency dependence of the conductivity is shown to follow the power-law with the exponent n=0.67 before reaching the frequency-independent part. When scaled with the value of the frequency-independent part of the spectrum the conductivity spectra for samples at different water content values are shown to fit to a single master curve. It is argued that the observed conductivity dispersion is a consequence of the anomalously diffusing ions in the clay-water system. The fractional Langevin equation is then used to describe the stochastic dynamics of the single ion. The results indicate that the experimentally observed dielectric properties originate in anomalous ion transport in clay-water system characterized with time-dependent diffusion coefficient.

Bounded fractional diffusion in geological media: Definition and Lagrangian approximation

NASA Astrophysics Data System (ADS)

Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang

2016-11-01

Spatiotemporal fractional-derivative models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and nonzero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing nonzero-value spatial-nonlocal boundary conditions with directional superdiffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eulerian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the nonlocal and nonsymmetric fractional diffusion. For a nonzero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite domains to those with any size and boundary conditions.

Inferring nonlinear mantle rheology from the shape of the Hawaiian swell.

PubMed

Asaadi, N; Ribe, N M; Sobouti, F

2011-05-26

The convective circulation generated within the Earth's mantle by buoyancy forces of thermal and compositional origin is intimately controlled by the rheology of the rocks that compose it. These can deform either by the diffusion of point defects (diffusion creep, with a linear relationship between strain rate and stress) or by the movement of intracrystalline dislocations (nonlinear dislocation creep). However, there is still no reliable map showing where in the mantle each of these mechanisms is dominant, and so it is important to identify regions where the operative mechanism can be inferred directly from surface geophysical observations. Here we identify a new observable quantity--the rate of downstream decay of the anomalous seafloor topography (swell) produced by a mantle plume--which depends only on the value of the exponent in the strain rate versus stress relationship that defines the difference between diffusion and dislocation creep. Comparison of the Hawaiian swell topography with the predictions of a simple fluid mechanical model shows that the swell shape is poorly explained by diffusion creep, and requires a dislocation creep rheology. The rheology predicted by the model is reasonably consistent with laboratory deformation data for both olivine and clinopyroxene, suggesting that the source of Hawaiian lavas could contain either or both of these components.

Studies of multi-ion-fluid yield anomaly in shock-driven implosions

NASA Astrophysics Data System (ADS)

Rinderknecht, H. G.; Rosenberg, M. J.; Li, C. K.; Zylstra, A. B.; Sio, H.; Gatu Johnson, M.; Frenje, J. A.; Séguin, F. H.; Petrasso, R. D.; Amendt, P. A.; Bellei, C.; Wilks, S. C.; Zimmerman, G.; Hoffman, N. M.; Kagan, G.; Molvig, K.; Glebov, V. Yu.; Stoeckl, C.; Marshall, F. J.; Seka, W.; Delettrez, J. A.; Sangster, T. C.; Betti, R.; Goncharov, V. N.; Meyerhofer, D. D.

2014-10-01

A. NIKROO, GA - Anomalously reduced yields relative to hydrodynamically calculated values have been observed for mixtures of D:3He compared to pure D2 gas-filled implosions in a series of shock-driven implosions at OMEGA. An extensive suite of measurements including temporal and spatial measurements of both the DD- and D3He-fusion reactions were obtained to identify the origin and physics behind this anomalous yield reduction. Measured spectral linewidths of fusion products suggest that the D ions are not thermalized to 3He during the burn, contributing to the reduced yield. The hypothesis that ion-species separation due to diffusive processes contributes to the observed yield reduction is explored using hydrodynamic simulations incorporating ion diffusion. Recent observations by Rosenberg et al. of a yield reduction with increased ion-ion mean free path do not explain the observed anomalous yield trend. Future work that will directly probe species separation with high-precision relative fusion reaction rate measurements between DD-neutrons and D3He-protons using the DualPTD instrument is discussed. This work was supported in part by the U.S. DOE, NLUF, LLE, and LLNL.

Diffusion of water and sodium counter-ions in nanopores of a β-lactoglobulin crystal: a molecular dynamics study

NASA Astrophysics Data System (ADS)

Malek, Kourosh; Odijk, Theo; Coppens, Marc-Olivier

2005-07-01

The dynamics of water and sodium counter-ions (Na+) in a C2221 orthorhombic β-lactoglobulin crystal is investigated by means of 5 ns molecular dynamics simulations. The effect of the fluctuation of the protein atoms on the motion of water and sodium ions is studied by comparing simulations in a rigid and in a flexible lattice. The electrostatic interactions of sodium ions with the positively charged LYS residues inside the crystal channels significantly influence the ionic motion. According to our results, water molecules close to the protein surface undergo an anomalous diffusive motion. On the other hand, the motion of water molecules further away from the protein surface is normal diffusive. Protein fluctuations affect the diffusion constant of water, which increases from 0.646 ± 0.108 to 0.887 ± 0.41 nm2 ns-1, when protein fluctuations are taken into account. The pore size (0.63-1.05 nm) and the water diffusivities are in good agreement with previous experimental results. The dynamics of sodium ions is disordered. LYS residues inside the pore are the main obstacles to the motion of sodium ions. However, the simulation time is still too short for providing a precise description of anomalous diffusion of sodium ions. The results are not only of interest for studying ion and water transport through biological nanopores, but may also elucidate water-protein and ion-protein interactions in protein crystals.

Interfacial Stresses and the Anomalous Character of Thermoelastic-Deformation Curves of a Cu-Al-Ni Shape-Memory Alloy

NASA Astrophysics Data System (ADS)

Malygin, G. A.; Nikolaev, V. I.; Pulnev, S. A.; Chikiryaka, A. V.

2017-12-01

Thermoelastic-deformation curves of a single-crystalline Cu-13.5 wt % Al-4.0 wt % Ni shapememory (SM) alloy have been studied. Cyclic temperature variation in a 300-450 K interval revealed an anomalous character of thermoelastic hysteresis loops with regions of accelerated straining at both heating and cooling stages. The observed phenomenon can be used for increasing the response speed of SM-alloy based drive and sensor devices. Analysis of this phenomenon in the framework of the theory of diffuse martensitic transformations showed that the anomalous character of thermoelastic hysteresis loops may be related to the influence of interfacial stresses on the dynamics of martensitic transformations in these SM alloys.

Recent off-axis volcanism in the eastern Gulf of Aden: Implications for plume-ridge interaction

NASA Astrophysics Data System (ADS)

Leroy, Sylvie; d'Acremont, Elia; Tiberi, Christel; Basuyau, Clémence; Autin, Julia; Lucazeau, Francis; Sloan, Heather

2010-04-01

Evidence of anomalous volcanism is readily observed in the Gulf of Aden, although, much of this oceanic basin remains as yet unmapped. In this paper, we investigate the possible connection of the Afar hotspot with a major off-axis volcanic structure and its interpretation as a consequence of a the anomalous presence of melt by integrating several data sets, both published and unpublished, from the Encens-Sheba cruise, the Aden New Century (ANC) cruise and several other onshore and marine surveys. These include bathymetric, gravity, magnetic, magneto-telluric data, and rock samples. Based upon these observations, interpretations were made of seafloor morphology, gravity and magnetic models, seafloor age, geochemical analyses and tectonic setting. We discuss the possible existence of a regional melting anomaly in the Gulf of Aden area and of the probability of its connection to the Afar plume. Several models that might explain the anomalous volcanism are taken into account, such as a local melting anomaly unrelated to the Afar plume, an anomalously large volume of melt associated with seafloor spreading, and interaction of the ridge with the Afar plume. A local melting anomaly and atypical seafloor spreading prove inconsistent with our observations. Two previously proposed models of plume-ridge interactions are examined: the diffuse plume dispersion called pancaked flow and channelized along-axis flow. We conclude that the configuration and structure of this young ocean basin may have the effect of channeling material away from the Afar plume along the Aden and Sheba Ridges to produce the off-axis volcanism observed on the ridge flanks. This interpretation implies that the influence of the Afar hotspot may extend much farther eastwards into the Gulf of Aden than previously believed. The segmentation of the Gulf of Aden and the configuration of the Aden-Sheba system may provide a potential opportunity to study channeled flow of solid plume mantle from the plume along a segmented ridge and nearby continental margins.

Non-equilibrium dynamics in disordered materials: Ab initio molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Ohmura, Satoshi; Nagaya, Kiyonobu; Shimojo, Fuyuki; Yao, Makoto

2015-08-01

The dynamic properties of liquid B2O3 under pressure and highly-charged bromophenol molecule are studied by using molecular dynamics (MD) simulations based on density functional theory (DFT). Diffusion properties of covalent liquids under high pressure are very interesting in the sense that they show unexpected pressure dependence. It is found from our simulation that the magnitude relation of diffusion coefficients for boron and oxygen in liquid B2O3 shows the anomalous pressure dependence. The simulation clarified the microscopic origin of the anomalous diffusion properties. Our simulation also reveals the dissociation mechanism in the coulomb explosion of the highly-charged bromophenol molecule. When the charge state n is 6, hydrogen atom in the hydroxyl group dissociates at times shorter than 20 fs while all hydrogen atoms dissociate when n is 8. After the hydrogen dissociation, the carbon ring breaks at about 100 fs. There is also a difference on the mechanism of the ring breaking depending on charge states, in which the ring breaks with expanding (n = 6) or shrink (n = 8).

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

Ohmura, Satoshi; Nagaya, Kiyonobu; Yao, Makoto

The dynamic properties of liquid B{sub 2}O{sub 3} under pressure and highly-charged bromophenol molecule are studied by using molecular dynamics (MD) simulations based on density functional theory (DFT). Diffusion properties of covalent liquids under high pressure are very interesting in the sense that they show unexpected pressure dependence. It is found from our simulation that the magnitude relation of diffusion coefficients for boron and oxygen in liquid B{sub 2}O{sub 3} shows the anomalous pressure dependence. The simulation clarified the microscopic origin of the anomalous diffusion properties. Our simulation also reveals the dissociation mechanism in the coulomb explosion of the highly-chargedmore » bromophenol molecule. When the charge state n is 6, hydrogen atom in the hydroxyl group dissociates at times shorter than 20 fs while all hydrogen atoms dissociate when n is 8. After the hydrogen dissociation, the carbon ring breaks at about 100 fs. There is also a difference on the mechanism of the ring breaking depending on charge states, in which the ring breaks with expanding (n = 6) or shrink (n = 8)« less

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.

MO-G-BRF-07: Anomalously Fast Diffusion of Carbon Nanotubes Carriers in 3D Tissue Model

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

Wang, Y; Bahng, J; Kotov, N

Purpose: We aim to investigate and understand diffusion process of carbon nanotubes (CNTs) and other nanoscale particles in tissue and organs. Methods: In this research, we utilized a 3D model tissue of hepatocellular carcinoma (HCC)cultured in inverted colloidal crystal (ICC) scaffolds to compare the diffusivity of CNTs with small molecules such as Rhodamine and FITC in vitro, and further investigated the transportation of CNTs with and without targeting ligand, TGFβ1. The real-time permeation profiles of CNTs in HCC tissue model with high temporal and spatial resolution was demonstrated by using standard confocal microscopy. Quantitative analysis of the diffusion process inmore » 3D was carried out using luminescence intensity in a series of Z-stack images obtained for different time points of the diffusion process after initial addition of CNTs or small molecules to the cell culture and the image data was analyzed by software ImageJ and Mathematica. Results: CNTs display diffusion rate in model tissues substantially faster than small molecules of the similar charge such as FITC, and the diffusion rate of CNTs are significantly enhanced with targeting ligand, TGFβ1. Conclusion: In terms of the advantages of in-vitro model, we were able to have access to measuring the rate of CNT penetration at designed conditions with variable parameters. And the findings by using this model, changed our understanding about advantages of CNTs as nanoscale drug carriers and provides design principles for making new drug carriers for both treatment and diagnostics. Additionally the fast diffusion opens the discussion of the best possible drug carriers to reach deep parts of cancerous tissues, which is often a prerequisite for successful cancer treatment. This work was supported by the Center for Photonic and Multiscale Nanomaterials funded by National Science Foundation Materials Research Science and Engineering Center program DMR 1120923. The work was also partially supported by NSF grant ECS-0601345; EFRI-BSBA 0938019; CBET 0933384; CBET 0932823; CBET 1036672, AFOSR MURI 444286-P061716 and NIH 1R21CA121841-01A2.« less

Normal versus anomalous self-diffusion in two-dimensional fluids: memory function approach and generalized asymptotic Einstein relation.

PubMed

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-07

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

NASA Astrophysics Data System (ADS)

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-01

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Normal and Anomalous Diffusion: An Analytical Study Based on Quantum Collision Dynamics and Boltzmann Transport Theory.

PubMed

Mahakrishnan, Sathiya; Chakraborty, Subrata; Vijay, Amrendra

2016-09-15

Diffusion, an emergent nonequilibrium transport phenomenon, is a nontrivial manifestation of the correlation between the microscopic dynamics of individual molecules and their statistical behavior observed in experiments. We present a thorough investigation of this viewpoint using the mathematical tools of quantum scattering, within the framework of Boltzmann transport theory. In particular, we ask: (a) How and when does a normal diffusive transport become anomalous? (b) What physical attribute of the system is conceptually useful to faithfully rationalize large variations in the coefficient of normal diffusion, observed particularly within the dynamical environment of biological cells? To characterize the diffusive transport, we introduce, analogous to continuous phase transitions, the curvature of the mean square displacement as an order parameter and use the notion of quantum scattering length, which measures the effective interactions between the diffusing molecules and the surrounding, to define a tuning variable, η. We show that the curvature signature conveniently differentiates the normal diffusion regime from the superdiffusion and subdiffusion regimes and the critical point, η = ηc, unambiguously determines the coefficient of normal diffusion. To solve the Boltzmann equation analytically, we use a quantum mechanical expression for the scattering amplitude in the Boltzmann collision term and obtain a general expression for the effective linear collision operator, useful for a variety of transport studies. We also demonstrate that the scattering length is a useful dynamical characteristic to rationalize experimental observations on diffusive transport in complex systems. We assess the numerical accuracy of the present work with representative experimental results on diffusion processes in biological systems. Furthermore, we advance the idea of temperature-dependent effective voltage (of the order of 1 μV or less in a biological environment, for example) as a dynamical cause of the perpetual molecular movement, which eventually manifests as an ordered motion, called the diffusion.

Combined effects of drift waves and neoclassical transport on density profiles in tokamaks

NASA Astrophysics Data System (ADS)

Houlberg, W. A.; Strand, P.

2005-10-01

The relative importance of neoclassical and anomalous particle transport depends on the charge number of the species being studied. The detailed particle balance including the EDWM [1] drift wave model for anomalous transport that includes ITG, TEM and in some cases ETG modes, and the neoclassical model NCLASS [2], are illustrated by simulations with the DEA particle transport code. DEA models the evolution of all ion species, and can be run in a mode to evaluate dynamic responses to perturbations or to conditions far from equilibrium by perturbing the profiles from the experimental measurements. The perturbations allow the fluxes to be decomposed into diffusive and convective (pinch) terms. The different scaling with charge number between drift wave and neoclassical models favors a stronger component of neoclassical transport for higher Z impurities through the effective pinch term. Although trace impurities illustrate a simple Ficks Law form, the main ions as well as higher concentrations of intrinsic impurities exhibit non-linear responses to the density gradients as well as off-diagonal gradient dependencies, leading to a more complicated response for the particle fluxes.[1] H. Nordman, et al., Plasma Phys. Control. Fusion 47 (2005) L11. [2] W.A. Houlberg, et al., Phys. Plasmas 4 (1997) 3230.

A new parameter-free soft-core potential for silica and its application to simulation of silica anomalies

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

Izvekov, Sergei, E-mail: sergiy.izvyekov.civ@mail.mil; Rice, Betsy M.

2015-12-28

A core-softening of the effective interaction between oxygen atoms in water and silica systems and its role in developing anomalous thermodynamic, transport, and structural properties have been extensively debated. For silica, the progress with addressing these issues has been hampered by a lack of effective interaction models with explicit core-softening. In this work, we present an extension of a two-body soft-core interatomic force field for silica recently reported by us [S. Izvekov and B. M. Rice, J. Chem. Phys. 136(13), 134508 (2012)] to include three-body forces. Similar to two-body interaction terms, the three-body terms are derived using parameter-free force-matching ofmore » the interactions from ab initio MD simulations of liquid silica. The derived shape of the O–Si–O three-body potential term affirms the existence of repulsion softening between oxygen atoms at short separations. The new model shows a good performance in simulating liquid, amorphous, and crystalline silica. By comparing the soft-core model and a similar model with the soft-core suppressed, we demonstrate that the topology reorganization within the local tetrahedral network and the O–O core-softening are two competitive mechanisms responsible for anomalous thermodynamic and kinetic behaviors observed in liquid and amorphous silica. The studied anomalies include the temperature of density maximum locus and anomalous diffusivity in liquid silica, and irreversible densification of amorphous silica. We show that the O–O core-softened interaction enhances the observed anomalies primarily through two mechanisms: facilitating the defect driven structural rearrangements of the silica tetrahedral network and modifying the tetrahedral ordering induced interactions toward multiple characteristic scales, the feature which underlies the thermodynamic anomalies.« less

Comparison of liquid-state anomalies in Stillinger-Weber models of water, silicon, and germanium

NASA Astrophysics Data System (ADS)

Dhabal, Debdas; Chakravarty, Charusita; Molinero, Valeria; Kashyap, Hemant K.

2016-12-01

We use molecular dynamics simulations to compare and contrast the liquid-state anomalies in the Stillinger-Weber models of monatomic water (mW), silicon (Si), and germanium (Ge) over a fairly wide range of temperatures and densities. The relationships between structure, entropy, and mobility, as well as the extent of the regions of anomalous behavior, are discussed as a function of the degree of tetrahedrality. We map out the cascade of density, structural, pair entropy, excess entropy, viscosity, and diffusivity anomalies for these three liquids. Among the three liquids studied here, only mW displays anomalies in the thermal conductivity, and this anomaly is evident only at very low temperatures. Diffusivity and viscosity, on the other hand, show pronounced anomalous regions for the three liquids. The temperature of maximum density of the three liquids shows re-entrant behavior consistent with either singularity-free or liquid-liquid critical point scenarios proposed to explain thermodynamic anomalies. The order-map, which shows the evolution of translational versus tetrahedral order in liquids, is different for Ge than for Si and mW. We find that although the monatomic water reproduces several thermodynamic and dynamic properties of rigid-body water models (e.g., SPC/E, TIP4P/2005), its sequence of anomalies follows, the same as Si and Ge, the silica-like hierarchy: the region of dynamic (diffusivity and viscosity) anomalies encloses the region of structural anomalies, which in turn encloses the region of density anomaly. The hierarchy of the anomalies based on excess entropy and Rosenfeld scaling, on the other hand, reverses the order of the structural and dynamic anomalies, i.e., predicts that the three Stillinger-Weber liquids follow a water-like hierarchy of anomalies. We investigate the scaling of diffusivity, viscosity, and thermal conductivity with the excess entropy of the liquid and find that for dynamical properties that present anomalies there is no universal scaling of the reduced property with excess entropy for the whole range of temperatures and densities. Instead, Rosenfeld's scaling holds for all the three liquids at high densities and high temperatures, although deviations from simple exponential dependence are observed for diffusivity and viscosity at lower temperatures and intermediate densities. The slope of the scaling of transport properties obtained for Ge is comparable to that obtained for simple liquids, suggesting that this low tetrahedrality liquid, although it stabilizes a diamond crystal, is already close to simple liquid behavior for certain properties.

Comparison of liquid-state anomalies in Stillinger-Weber models of water, silicon, and germanium.

PubMed

Dhabal, Debdas; Chakravarty, Charusita; Molinero, Valeria; Kashyap, Hemant K

2016-12-07

We use molecular dynamics simulations to compare and contrast the liquid-state anomalies in the Stillinger-Weber models of monatomic water (mW), silicon (Si), and germanium (Ge) over a fairly wide range of temperatures and densities. The relationships between structure, entropy, and mobility, as well as the extent of the regions of anomalous behavior, are discussed as a function of the degree of tetrahedrality. We map out the cascade of density, structural, pair entropy, excess entropy, viscosity, and diffusivity anomalies for these three liquids. Among the three liquids studied here, only mW displays anomalies in the thermal conductivity, and this anomaly is evident only at very low temperatures. Diffusivity and viscosity, on the other hand, show pronounced anomalous regions for the three liquids. The temperature of maximum density of the three liquids shows re-entrant behavior consistent with either singularity-free or liquid-liquid critical point scenarios proposed to explain thermodynamic anomalies. The order-map, which shows the evolution of translational versus tetrahedral order in liquids, is different for Ge than for Si and mW. We find that although the monatomic water reproduces several thermodynamic and dynamic properties of rigid-body water models (e.g., SPC/E, TIP4P/2005), its sequence of anomalies follows, the same as Si and Ge, the silica-like hierarchy: the region of dynamic (diffusivity and viscosity) anomalies encloses the region of structural anomalies, which in turn encloses the region of density anomaly. The hierarchy of the anomalies based on excess entropy and Rosenfeld scaling, on the other hand, reverses the order of the structural and dynamic anomalies, i.e., predicts that the three Stillinger-Weber liquids follow a water-like hierarchy of anomalies. We investigate the scaling of diffusivity, viscosity, and thermal conductivity with the excess entropy of the liquid and find that for dynamical properties that present anomalies there is no universal scaling of the reduced property with excess entropy for the whole range of temperatures and densities. Instead, Rosenfeld's scaling holds for all the three liquids at high densities and high temperatures, although deviations from simple exponential dependence are observed for diffusivity and viscosity at lower temperatures and intermediate densities. The slope of the scaling of transport properties obtained for Ge is comparable to that obtained for simple liquids, suggesting that this low tetrahedrality liquid, although it stabilizes a diamond crystal, is already close to simple liquid behavior for certain properties.

Correlation properties of interstellar dust: Diffuse interstellar bands

NASA Technical Reports Server (NTRS)

Somerville, W. B.

1989-01-01

Results are presented from a research program in which an attempt was made to establish the physical nature of the interstellar grains, and the carriers of the diffuse interstellar bands, by comparing relations between different observed properties; the properties used include the extinction in the optical and ultraviolet (including wavelength 2200 and the far-UV rise), cloud density, atomic depletions, and strengths of the diffuse bands. Observations and also data from literature were used, selecting particularly sight-lines where some observed property was found to have anomalous behavior.

Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

NASA Astrophysics Data System (ADS)

Khorrami, Mohammad; Shariati, Ahmad; Aghamohammadi, Amir; Fatollahi, Amir H.

2012-01-01

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.

Bounded fractional diffusion in geological media: Definition and Lagrangian approximation

USGS Publications Warehouse

Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang

2016-01-01

Spatiotemporal Fractional-Derivative Models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and non-zero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing non-zero-value spatial-nonlocal boundary conditions with directional super-diffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eularian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the non-local and non-symmetric fractional diffusion. For a non-zero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite do mains to those with any size and boundary conditions.

Analysis of structure of hyperfine poly(3-hydroxybutyrate) fibers (PHB) for controlled drug delivery

NASA Astrophysics Data System (ADS)

Olkhov, A. A.; Kosenko, R. Yu; Markin, V. S.; Zykova, A. K.; Pantyukhov, P. V.; Karpova, S. G.; Iordanskii, A. L.

2017-12-01

Hyperfine fibers based on biodegradable poly (3-hydroxybutyrate) with encapsulated drug substance (dipyridamol) were obtained by using electrospinning method. Addition of dipyridamol has a significant effect on geometrical shape and structure of microfibers as well as total porosity of fibrous material. Observation of fibers using scanning electron microscopy (SEM) method showed that without or at lower dipyridamol content (<3%) fibers consisted of interleaved ellipsoid and cylindrical fragments. At higher dipyridamol content (3-5%) anomalous ellipsoid structures did not practically form, and fiber’s shape became cylindrical. The totality of morphological and structural characteristics determined the rate of dipyridamol diffusive transports. The simplified model of drug desorption from fibrous matrix was presented. In current work it was showed that the rate-limiting stage of transport was the diffusion of dipyridamol in the bulk of cylindrical fibers.

Strange kinetics of bulk-mediated diffusion on lipid bilayers

PubMed Central

Campagnola, Grace; Nepal, Kanti; Peersen, Olve B.

2016-01-01

Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide rich complexities. In particular, bulk-mediated diffusion occurs when molecules are transiently released from the surface to perform three-dimensional excursions into the liquid bulk. This phenomenon bears the dichotomy where a molecule always return to the surface but the mean jump length is infinite. Such behavior is associated with a breakdown of the central limit theorem and weak ergodicity breaking. Here, we use single-particle tracking to study the statistics of bulk-mediated diffusion on a supported lipid bilayer. We find that the time-averaged mean square displacement (MSD) of individual trajectories, the archetypal measure in diffusion processes, does not converge to the ensemble MSD but it remains a random variable, even in the long observation-time limit. The distribution of time averages is shown to agree with a Lévy flight model. Our results also unravel intriguing anomalies in the statistics of displacements. The time averaged MSD is shown to depend on experimental time and investigations of fractional moments show a scaling 〈|r(t)|q〉 ∼ tqv(q) with non-linear exponents, i.e. v(q) ≠ const. This type of behavior is termed strong anomalous diffusion and is rare among experimental observations. PMID:27095275

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

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

Metzler, Ralf

2014-01-14

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

Effect of attractive interactions on the water-like anomalies of a core-softened model potential.

PubMed

Pant, Shashank; Gera, Tarun; Choudhury, Niharendu

2013-12-28

It is now well established that water-like anomalies can be reproduced by a spherically symmetric potential with two length scales, popularly known as core-softened potential. In the present study we aim to investigate the effect of attractive interactions among the particles in a model fluid interacting with core-softened potential on the existence and location of various water-like anomalies in the temperature-pressure plane. We employ extensive molecular dynamic simulations to study anomalous nature of various order parameters and properties under isothermal compression. Order map analyses have also been done for all the potentials. We observe that all the systems with varying depth of attractive wells show structural, dynamic, and thermodynamic anomalies. As many of the previous studies involving model water and a class of core softened potentials have concluded that the structural anomaly region encloses the diffusion anomaly region, which in turn, encloses the density anomaly region, the same pattern has also been observed in the present study for the systems with less depth of attractive well. For the systems with deeper attractive well, we observe that the diffusion anomaly region shifts toward higher densities and is not always enclosed by the structural anomaly region. Also, density anomaly region is not completely enclosed by diffusion anomaly region in this case.

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.

Expression, purification, crystallization and preliminary X-ray crystallographic analysis of a resuscitation-promoting factor from Mycobacterium tuberculosis

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

Ruggiero, Alessia; Tizzano, Barbara; Geerlof, Arie

2007-10-01

The first crystallization of a resuscitation-promoting factor has been performed. Multiwavelength anomalous dispersion experiments have been carried out to obtain experimental phases using data at 2.9 Å resolution from a selenomethionine derivative. The resuscitation-promoting factor RpfB, the most complex of the five resuscitation-promoting factors produced by M. tuberculosis, is devoted to bacterial reactivation from the dormant state. RpfB consists of 362 residues predicted to form five domains. An RpfB fragment containing the protein catalytic domain and a G5 domain has been successfully crystallized using vapour-diffusion methods. This is the first crystallographic study of a resuscitation-promoting factor. Crystals of this proteinmore » belong to space group I422, with unit-cell parameters a = 97.63, b = 97.63, c = 114.87 Å. Diffraction data have also been collected from a selenomethionine derivative at 2.9 Å resolution. Model building using the phases derived from the multiwavelength anomalous dispersion experiment is in progress.« less

Transport behaviors of locally fractional coupled Brownian motors with fluctuating interactions

NASA Astrophysics Data System (ADS)

Wang, Huiqi; Ni, Feixiang; Lin, Lifeng; Lv, Wangyong; Zhu, Hongqiang

2018-09-01

In some complex viscoelastic mediums, it is ubiquitous that absorbing and desorbing surrounding Brownian particles randomly occur in coupled systems. The conventional method is to model a variable-mass system driven by both multiplicative and additive noises. In this paper, an improved mathematical model is created based on generalized Langevin equations (GLE) to characterize the random interaction with locally fluctuating number of coupled particles in the elastically coupled factional Brownian motors (FBM). By the numerical simulations, the effect of fluctuating interactions on collective transport behaviors is investigated, and some abnormal phenomena, such as cooperative behaviors, stochastic resonance (SR) and anomalous transport, are observed in the regime of sub-diffusion.

Final Technical Report

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

Alexander Pigarov

2012-06-05

This is the final report for the Research Grant DE-FG02-08ER54989 'Edge Plasma Simulations in NSTX and CTF: Synergy of Lithium Coating, Non-Diffusive Anomalous Transport and Drifts'. The UCSD group including: A.Yu. Pigarov (PI), S.I. Krasheninnikov and R.D. Smirnov, was working on modeling of the impact of lithium coatings on edge plasma parameters in NSTX with the multi-species multi-fluid code UEDGE. The work was conducted in the following main areas: (i) improvements of UEDGE model for plasma-lithium interactions, (ii) understanding the physics of low-recycling divertor regime in NSTX caused by lithium pumping, (iii) study of synergistic effects with lithium coatings andmore » non-diffusive ballooning-like cross-field transport, (iv) simulation of experimental multi-diagnostic data on edge plasma with lithium pumping in NSTX via self-consistent modeling of D-Li-C plasma with UEDGE, and (v) working-gas balance analysis. The accomplishments in these areas are given in the corresponding subsections in Section 2. Publications and presentations made under the Grant are listed in Section 3.« less

An improved oxygen diffusion model to explain the effect of low-temperature baking on high field losses in niobium superconducting cavities

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

Ciovati, Gianluigi

Radio-frequency (RF) superconducting cavities made of high purity niobium are widely used to accelerate charged particle beams in particle accelerators. The major limitation to achieve RF field values approaching the theoretical limit for niobium is represented by ''anomalous'' losses which degrade the quality factor of the cavities starting at peak surface magnetic fields of about 100 mT, in absence of field emission. These high field losses are often referred to as ''Q-drop''. It has been observed that the Q-drop is drastically reduced by baking the cavities at 120 C for about 48 h under ultrahigh vacuum. An improved oxygen diffusionmore » model for the niobium-oxide system is proposed to explain the benefit of the low-temperature baking on the Q-drop in niobium superconducting rf cavities. The model shows that baking at 120 C for 48 h allows oxygen to diffuse away from the surface, and therefore increasing the lower critical field towards the value for pure niobium.« less

Anomalous transport in fracture networks: field scale experiments and modelling

NASA Astrophysics Data System (ADS)

Kang, P. K.; Le Borgne, T.; Bour, O.; Dentz, M.; Juanes, R.

2012-12-01

Anomalous transport is widely observed in different settings and scales of transport through porous and fractured geologic media. A common signature of anomalous transport is the late-time power law tailing in breakthrough curves (BTCs) during tracer tests. Various conceptual models of anomalous transport have been proposed, including multirate mass transfer, continuous time random walk, and stream tube models. Since different conceptual models can produce equally good fits to a single BTC, tracer test interpretation has been plagued with ambiguity. Here, we propose to resolve such ambiguity by analyzing BTCs obtained from both convergent and push-pull flow configurations at two different fracture planes. We conducted field tracer tests in a fractured granite formation close to Ploemeur, France. We observe that BTC tailing depends on the flow configuration and the injection fracture. Specifically the tailing disappears under push-pull geometry, and when we injected at a fracture with high flux (Figure 1). This indicates that for this fractured granite, BTC tailing is controlled by heterogeneous advection and not by matrix diffusion. To explain the change in tailing behavior for different flow configurations, we employ a simple lattice network model with heterogeneous conductivity distribution. The model assigns random conductivities to the fractures and solves the Darcy equation for an incompressible fluid, enforcing mass conservation at fracture intersections. The mass conservation constraint yields a correlated random flow through the fracture system. We investigate whether BTC tailing can be explained by the spatial distribution of preferential flow paths and stagnation zones, which is controlled by the conductivity variance and correlation length. By combining the results from the field tests and numerical modeling, we show that the reversibility of spreading is a key mechanism that needs to be captured. We also demonstrate the dominant role of the injection fracture on the tailing behavior: where we inject makes the difference in the tailing. Blue line is a BTC with injection into a slow velocity zone under convergent flow configuration. The late-time tailing observed for the convergent test diminished for push-pull experiment performed in the same zone(red line). Black line is a BTC with injection into a high velocity zone under convergent flow configuration. Insets: illustration of convergent and push-pull tracer tests using a double packer system.

Upscaling anomalous reactive kinetics (A+B-->C) from pore scale Lagrangian velocity analysis

NASA Astrophysics Data System (ADS)

De Anna, P.; Tartakovsky, A. M.; Le Borgne, T.; Dentz, M.

2011-12-01

Natural flow fields in porous media display a complex spatio-temporal organization due to heterogeneous geological structures at different scales. This multiscale disorder implies anomalous dispersion, mixing and reaction kinetics (Berkowitz et al. RG 2006, Tartakovsky PRE 2010). Here, we focus on the upscaling of anomalous kinetics arising from pore scale, non Gaussian and correlated, velocity distributions. We consider reactive front simulations, where a component A displaces a component B that saturates initially the porous domain. The reactive component C is produced at the dispersive front located at interface between the A and B domains. The simulations are performed with the SPH method. As the mixing zone grows, the total mass of C produced increases with time. The scaling of this evolution with time is different from that which would be obtained from the homogeneous advection dispersion reaction equation. This anomalous kinetics property is related to spatial structure of the reactive mixture, and its evolution with time under the combined action of advective and diffusive processes. We discuss the different scaling regimes arising depending on the dominant process that governs mixing. In order to upscale these processes, we analyze the Lagrangian velocity properties, which are characterized by the non Gaussian distributions and long range temporal correlation. The main origin of these properties is the existence of very low velocity regions where solute particles can remain trapped for a long time. Another source of strong correlation is the channeling of flow in localized high velocity regions, which created finger-like structures in the concentration field. We show the spatial Markovian, and temporal non Markovian, nature of the Lagrangian velocity field. Therefore, an upscaled model can be defined as a correlated Continuous Time Random Walk (Le Borgne et al. PRL 2008). A key feature of this model is the definition of a transition probability density for Lagrangian velocities across a characteristic correlation distance. We quantify this transition probability density from pore scale simulations and use it in the effective stochastic model. In this framework, we investigate the ability of this effective model to represent correctly dispersion and mixing.

A self-organized criticality model for ion temperature gradient mode driven turbulence in confined plasma

NASA Astrophysics Data System (ADS)

Isliker, H.; Pisokas, Th.; Strintzi, D.; Vlahos, L.

2010-08-01

A new self-organized criticality (SOC) model is introduced in the form of a cellular automaton (CA) for ion temperature gradient (ITG) mode driven turbulence in fusion plasmas. Main characteristics of the model are that it is constructed in terms of the actual physical variable, the ion temperature, and that the temporal evolution of the CA, which necessarily is in the form of rules, mimics actual physical processes as they are considered to be active in the system, i.e., a heating process and a local diffusive process that sets on if a threshold in the normalized ITG R /LT is exceeded. The model reaches the SOC state and yields ion temperature profiles of exponential shape, which exhibit very high stiffness, in that they basically are independent of the loading pattern applied. This implies that there is anomalous heat transport present in the system, despite the fact that diffusion at the local level is imposed to be of a normal kind. The distributions of the heat fluxes in the system and of the heat out-fluxes are of power-law shape. The basic properties of the model are in good qualitative agreement with experimental results.

Spin diffusion in disordered organic semiconductors

NASA Astrophysics Data System (ADS)

Li, Ling; Gao, Nan; Lu, Nianduan; Liu, Ming; Bässler, Heinz

2015-12-01

An analytical theory for spin diffusion in disordered organic semiconductors is derived. It is based on percolation theory and variable range hopping in a disordered energy landscape with a Gaussian density of states. It describes universally the dependence of the spin diffusion on temperature, carrier density, material disorder, magnetic field, and electric field at the arbitrary magnitude of the Hubbard energy of charge pairs. It is found that, compared to the spin transport carried by carriers hopping, the spin exchange will hinder the spin diffusion process at low carrier density, even under the condition of a weak electric field. Importantly, under the influence of a bias voltage, anomalous spreading of the spin packet will lead to an abnormal temperature dependence of the spin diffusion coefficient and diffusion length. This explains the recent experimental data for spin diffusion length observed in Alq3.

Diffusion of aqueous solutions of ionic, zwitterionic, and polar solutes

NASA Astrophysics Data System (ADS)

Teng, Xiaojing; Huang, Qi; Dharmawardhana, Chamila Chathuranga; Ichiye, Toshiko

2018-06-01

The properties of aqueous solutions of ionic, zwitterionic, and polar solutes are of interest to many fields. For instance, one of the many anomalous properties of aqueous solutions is the behavior of water diffusion in different monovalent salt solutions. In addition, solutes can affect the stabilities of macromolecules such as proteins in aqueous solution. Here, the diffusivities of aqueous solutions of sodium chloride, potassium chloride, tri-methylamine oxide (TMAO), urea, and TMAO-urea are examined in molecular dynamics simulations. The decrease in the diffusivity of water with the concentration of simple ions and urea can be described by a simple model in which the water molecules hydrogen bonded to the solutes are considered to diffuse at the same rate as the solutes, while the remainder of the water molecules are considered to be bulk and diffuse at almost the same rate as pure water. On the other hand, the decrease in the diffusivity of water with the concentration of TMAO is apparently affected by a decrease in the diffusion rate of the bulk water molecules in addition to the decrease due to the water molecules hydrogen bonded to TMAO. In other words, TMAO enhances the viscosity of water, while urea barely affects it. Overall, this separation of water molecules into those that are hydrogen bonded to solute and those that are bulk can provide a useful means of understanding the short- and long-range effects of solutes on water.

The Skylab barium plasma injection experiments. II - Evidence for a double layer

NASA Technical Reports Server (NTRS)

Wescott, E. M.; Stenbaek-Nielsen, H. C.; Hallinan, T. J.; Davis, T. N.; Peek, H. M.

1976-01-01

Television observations of a barium-plasma flux tube extending from near 4500 km to near 10,000 km during a magnetic substorm and dawn-sector auroral display indicated several interesting anomalous events. Beyond 5500 km, there was a rapid increase in brightness accompanied by flux-tube splitting and diffusion, leaving behind a truncated single flux tube. From the orientation of the flux tube compared with theoretical field models, the presence of a substantial field-aligned current sheet is deduced. A suggested explanation of these phenomena is given in terms of a plasma potential double layer.

Some notes on hydrogen-related point defects and their role in the isotope exchange and electrical conductivity in olivine

NASA Astrophysics Data System (ADS)

Karato, Shun-ichiro

2015-11-01

Nominally anhydrous minerals such as olivine dissolve hydrogen in a variety of forms including free (or interstitial) proton (Hrad) and two protons trapped at the M-site ((2 H)M×). The strength of chemical bonding between protons and the surrounding atoms are different among different species, and consequently protons belonging to different species likely have different mobility (diffusion coefficients). I discuss the role of diffusion of protons in different species in the isotope exchange and hydrogen-assisted electrical conductivity adding a few notes to the previous work by Karato (2013) including a new way to test the model. I conclude that in the case of isotope exchange, the interaction among these species is strong because diffusion is heterogeneous, whereas there is no strong interaction among different species in electrical conduction where diffusion is homogeneous (in an infinite crystal). Consequently, the slowest diffusing species controls the rate of isotope exchange, whereas the fastest diffusing species controls electrical conductivity leading to a different temperature dependence of activation energy and anisotropy. This model explains the differences in the activation energy and anisotropy between isotope diffusion and electrical conductivity, and predicts that the mechanism of electrical conductivity changes with temperature providing an explanation for most of the discrepancies among different experimental observations at different temperatures except for those by Poe et al. (2010) who reported anomalously high water content dependence and highly anisotropic activation energy. When the results obtained at high temperatures are used, most of the geophysically observed high and highly anisotropic electrical conductivity in the asthenosphere can be explained without invoking partial melting.

Reversible island nucleation and growth with anomalous diffusion

NASA Astrophysics Data System (ADS)

Sabbar, Ehsan H.; Amar, Jacques G.

2017-10-01

Motivated by recent experiments on submonolayer organic film growth with anomalous diffusion, a general rate-equation (RE) theory of submonolayer island nucleation and growth was developed (Amar and Semaan, 2016) [23], which takes into account the critical island-size i, island fractal dimension df, substrate dimension d, and diffusion exponent μ, and good agreement with simulations was found for the case of irreversible growth corresponding to a critical island-size i = 1 with d = 2 . However, since many experiments correspond to a critical island-size larger than 1, it is of interest to determine if the RE predictions also hold in the case of reversible island nucleation with anomalous diffusion. Here we present the results of simulations of submonolayer growth with i = 2 (d = 2) which were carried out for both the case of superdiffusion (μ > 1) and subdiffusion (μ < 1) as well as for both ramified islands (df ≃ 2) and point-islands (df = ∞) . In the case of superdiffusion, corresponding to 'hot' freshly deposited monomers, excellent agreement is obtained with the predictions of the generalized RE theory for the exponents χ(μ) and χ1(μ) which describe the dependence of the island and monomer densities at fixed coverage on deposition rate F. In addition, the exponents do not depend on whether or not monomers remain superdiffusive or are thermalized (e.g. undergo regular diffusion) after detaching from a dimer. However, we also find that, as was previously found in the case of irreversible growth, the exponent χ only approaches its asymptotic value logarithmically with increasing 1/F. This result has important implications for the interpretation of experiments. Good agreement with the RE theory is also found in the case of subdiffusion for point-islands. However, in the case of ramified islands with subdiffusion and i = 2 , the exponents are significantly higher than predicted due to the fact that monomer capture dominates in the nucleation regime. A modified RE theory which takes this into account is presented, and excellent agreement is found with our simulations.

Diffusive and subdiffusive dynamics of indoor microclimate: a time series modeling.

PubMed

Maciejewska, Monika; Szczurek, Andrzej; Sikora, Grzegorz; Wyłomańska, Agnieszka

2012-09-01

The indoor microclimate is an issue in modern society, where people spend about 90% of their time indoors. Temperature and relative humidity are commonly used for its evaluation. In this context, the two parameters are usually considered as behaving in the same manner, just inversely correlated. This opinion comes from observation of the deterministic components of temperature and humidity time series. We focus on the dynamics and the dependency structure of the time series of these parameters, without deterministic components. Here we apply the mean square displacement, the autoregressive integrated moving average (ARIMA), and the methodology for studying anomalous diffusion. The analyzed data originated from five monitoring locations inside a modern office building, covering a period of nearly one week. It was found that the temperature data exhibited a transition between diffusive and subdiffusive behavior, when the building occupancy pattern changed from the weekday to the weekend pattern. At the same time the relative humidity consistently showed diffusive character. Also the structures of the dependencies of the temperature and humidity data sets were different, as shown by the different structures of the ARIMA models which were found appropriate. In the space domain, the dynamics and dependency structure of the particular parameter were preserved. This work proposes an approach to describe the very complex conditions of indoor air and it contributes to the improvement of the representative character of microclimate monitoring.

On the role of adhesion in single-file dynamics

NASA Astrophysics Data System (ADS)

Fouad, Ahmed M.; Noel, John A.

2017-08-01

For a one-dimensional interacting system of Brownian particles with hard-core interactions (a single-file model), we study the effect of adhesion on both the collective diffusion (diffusion of the entire system with respect to its center of mass) and the tracer diffusion (diffusion of the individual tagged particles). For the case with no adhesion, all properties of these particle systems that are independent of particle labeling (symmetric in all particle coordinates and velocities) are identical to those of non-interacting particles (Lebowitz and Percus, 1967). We clarify this last fact twice. First, we derive our analytical predictions that show that the probability-density functions of single-file (ρsf) and ordinary (ρord) diffusion are identical, ρsf =ρord, predicting a nonanomalous (ordinary) behavior for the collective single-file diffusion, where the average second moment with respect to the center of mass, < x(t) 2 > , is calculated from ρ for both diffusion processes. Second, for single-file diffusion, we show, both analytically and through large-scale simulations, that < x(t) 2 > grows linearly with time, confirming the nonanomalous behavior. This nonanomalous collective behavior comes in contrast to the well-known anomalous sub-diffusion behavior of the individual tagged particles (Harris, 1965). We introduce adhesion to single-file dynamics as a second inter-particle interaction rule and, interestingly, we show that adding adhesion does reduce the magnitudes of both < x(t) 2 > and the mean square displacement per particle Δx2; but the diffusion behavior remains intact independent of adhesion in both cases. Moreover, we study the dependence of both the collective diffusion constant D and the tracer diffusion constant DT on the adhesion coefficient α.

Anomalous transport of charged dust grains in a magnetized collisional plasma: A molecular dynamics study

NASA Astrophysics Data System (ADS)

Bezbaruah, Pratikshya; Das, Nilakshi

2018-05-01

Anomalous diffusion of charged dust grains immersed in a plasma in the presence of strong ion-neutral collision, flowing ions, and a magnetic field has been observed. Molecular Dynamics simulation confirms the deviation from normal diffusion in an ensemble of dust grains probed in laboratory plasma chambers. Collisional effects are significant in governing the nature of diffusion. In order to have a clear idea on the transport of particles in a real experimental situation, the contribution of streaming ions and the magnetic field along with collision is considered through the relevant interaction potential. The nonlinear evolution of Mean Square Displacement is an indication of the modification in particle trajectories due to several effects as mentioned above. It is found that strong collision and ion flow significantly affect the interparticle interaction potential in the presence of the magnetic field and lead to the appearance of the asymmetric type of Debye Hückel (D H) potential. Due to the combined effect of the magnetic field, ion flow, and collision, dusty plasma exhibits a completely novel behavior. The coupling parameter Γ enhances the asymmetric D H type potential arising due to ion flow, and this may drive the system to a disordered state.

Membrane Orientation and Lateral Diffusion of BODIPY-Cholesterol as a Function of Probe Structure

PubMed Central

Solanko, Lukasz M.; Honigmann, Alf; Midtiby, Henrik Skov; Lund, Frederik W.; Brewer, Jonathan R.; Dekaris, Vjekoslav; Bittman, Robert; Eggeling, Christian; Wüstner, Daniel

2013-01-01

Cholesterol tagged with the BODIPY fluorophore via the central difluoroboron moiety of the dye (B-Chol) is a promising probe for studying intracellular cholesterol dynamics. We synthesized a new BODIPY-cholesterol probe (B-P-Chol) with the fluorophore attached via one of its pyrrole rings to carbon-24 of cholesterol (B-P-Chol). Using two-photon fluorescence polarimetry in giant unilamellar vesicles and in the plasma membrane (PM) of living intact and actin-disrupted cells, we show that the BODIPY-groups in B-Chol and B-P-Chol are oriented perpendicular and almost parallel to the bilayer normal, respectively. B-Chol is in all three membrane systems much stronger oriented than B-P-Chol. Interestingly, we found that the lateral diffusion in the PM was two times slower for B-Chol than for B-P-Chol, although we found no difference in lateral diffusion in model membranes. Stimulated emission depletion microscopy, performed for the first time, to our knowledge, with fluorescent sterols, revealed that the difference in lateral diffusion of the BODIPY-cholesterol probes was not caused by anomalous subdiffusion, because diffusion of both analogs in the PM was free but not hindered. Our combined measurements show that the position and orientation of the BODIPY moiety in cholesterol analogs have a severe influence on lateral diffusion specifically in the PM of living cells. PMID:24209853

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.

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

Anchoring effect on first passage process in Taiwan financial market

NASA Astrophysics Data System (ADS)

Liu, Hsing; Liao, Chi-Yo; Ko, Jing-Yuan; Lih, Jiann-Shing

2017-07-01

Empirical analysis of the price fluctuations of financial markets has received extensive attention because a substantial amount of financial market data has been collected and because of advances in data-mining techniques. Price fluctuation trends can help investors to make informed trading decisions, but such decisions may also be affected by a psychological factors-the anchoring effect. This study explores the intraday price time series of Taiwan futures, and applies diffusion model and quantitative methods to analyze the relationship between the anchoring effect and price fluctuations during first passage process. Our results indicate that power-law scaling and anomalous diffusion for stock price fluctuations are related to the anchoring effect. Moreover, microscopic price fluctuations before switching point in first passage process correspond with long-term price fluctuations of Taiwan's stock market. We find that microscopic trends could provide useful information for understanding macroscopic trends in stock markets.

An alternative theoretical model for an anomalous hollow beam.

PubMed

Cai, Yangjian; Wang, Zhaoying; Lin, Qiang

2008-09-15

An alternative and convenient theoretical model is proposed to describe a flexible anomalous hollow beam of elliptical symmetry with an elliptical solid core, which was observed in experiment recently (Phys. Rev. Lett, 94 (2005) 134802). In this model, the electric field of anomalous hollow beam is expressed as a finite sum of elliptical Gaussian modes. Flattopped beams, dark hollow beams and Gaussian beams are special cases of our model. Analytical propagation formulae for coherent and partially coherent anomalous hollow beams passing through astigmatic ABCD optical systems are derived. Some numerical examples are calculated to show the propagation and focusing properties of coherent and partially coherent anomalous hollow beams.

NMR signals within the generalized Langevin model for fractional Brownian motion

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-03-01

The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

Solvable continuous-time random walk model of the motion of tracer particles through porous media.

PubMed

Fouxon, Itzhak; Holzner, Markus

2016-08-01

We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.

Areas of Weakly Anomalous to Anomalous Surface Temperature in Chaffee County, Colorado, as Identified from ASTER Thermal Data

DOE Data Explorer

Khalid Hussein

2012-02-01

Note: This "Weakly Anomalous to Anomalous Surface Temperature" dataset differs from the "Anomalous Surface Temperature" dataset for this county (another remotely sensed CIRES product) by showing areas of modeled temperatures between 1o and 2o above the mean, as opposed to the greater than 2o temperatures contained in the "Anomalous Surface Temperature" dataset. This layer contains areas of anomalous surface temperature in Chaffee County identified from ASTER thermal data and spatial based insolation model. The temperature is calculated using the Emissivity Normalization Algorithm that separate temperature from emissivity. The incoming solar radiation was calculated using spatial based insolation model developed by Fu and Rich (1999). Then the temperature due to solar radiation was calculated using emissivity derived from ASTER data. The residual temperature, i.e. temperature due to solar radiation subtracted from ASTER temperature was used to identify thermally anomalous areas. Areas that had temperature greater than 2o were considered ASTER modeled very warm surface exposures (thermal anomalies). Note: 'o' is used in this description to represent lowercase sigma.

Areas of Weakly Anomalous to Anomalous Surface Temperature in Garfield County, Colorado, as Identified from ASTER Thermal Data

DOE Data Explorer

Khalid Hussein

2012-02-01

Note: This "Weakly Anomalous to Anomalous Surface Temperature" dataset differs from the "Anomalous Surface Temperature" dataset for this county (another remotely sensed CIRES product) by showing areas of modeled temperatures between 1o and 2o above the mean, as opposed to the greater than 2o temperatures contained in the "Anomalous Surface Temperature" dataset. This layer contains areas of anomalous surface temperature in Garfield County identified from ASTER thermal data and spatial based insolation model. The temperature is calculated using the Emissivity Normalization Algorithm that separate temperature from emissivity. The incoming solar radiation was calculated using spatial based insolation model developed by Fu and Rich (1999). Then the temperature due to solar radiation was calculated using emissivity derived from ASTER data. The residual temperature, i.e. temperature due to solar radiation subtracted from ASTER temperature was used to identify thermally anomalous areas. Areas that had temperature between 1o and 2o were considered ASTER modeled warm surface exposures (thermal anomalies) Note: 'o' is used in this description to represent lowercase sigma.

Areas of Weakly Anomalous to Anomalous Surface Temperature in Routt County, Colorado, as Identified from ASTER Thermal Data

DOE Data Explorer

Khalid Hussein

2012-02-01

Note: This "Weakly Anomalous to Anomalous Surface Temperature" dataset differs from the "Anomalous Surface Temperature" dataset for this county (another remotely sensed CIRES product) by showing areas of modeled temperatures between 1o and 2o above the mean, as opposed to the greater than 2o temperatures contained in the "Anomalous Surface Temperature" dataset. This layer contains areas of anomalous surface temperature in Routt County identified from ASTER thermal data and spatial based insolation model. The temperature is calculated using the Emissivity Normalization Algorithm that separate temperature from emissivity. The incoming solar radiation was calculated using spatial based insolation model developed by Fu and Rich (1999). Then the temperature due to solar radiation was calculated using emissivity derived from ASTER data. The residual temperature, i.e. temperature due to solar radiation subtracted from ASTER temperature was used to identify thermally anomalous areas. Areas that had temperature between 1o and 2o were considered ASTER modeled warm surface exposures (thermal anomalies). Note: 'o' is used in this description to represent lowercase sigma.

Areas of Weakly Anomalous to Anomalous Surface Temperature in Dolores County, Colorado, as Identified from ASTER Thermal Data

DOE Data Explorer

Khalid Hussein

2012-02-01

Note: This "Weakly Anomalous to Anomalous Surface Temperature" dataset differs from the "Anomalous Surface Temperature" dataset for this county (another remotely sensed CIRES product) by showing areas of modeled temperatures between 1o and 2o above the mean, as opposed to the greater than 2o temperatures contained in the "Anomalous Surface Temperature" dataset. This layer contains areas of anomalous surface temperature in Dolores County identified from ASTER thermal data and spatial based insolation model. The temperature is calculated using the Emissivity Normalization Algorithm that separate temperature from emissivity. The incoming solar radiation was calculated using spatial based insolation model developed by Fu and Rich (1999). Then the temperature due to solar radiation was calculated using emissivity derived from ASTER data. The residual temperature, i.e. temperature due to solar radiation subtracted from ASTER temperature was used to identify thermally anomalous areas. Areas that had temperature greater than 2o were considered ASTER modeled very warm surface exposures (thermal anomalies) Note: 'o' is used in this description to represent lowercase sigma.

Areas of Weakly Anomalous to Anomalous Surface Temperature in Archuleta County, Colorado, as Identified from ASTER Thermal Data

DOE Data Explorer

Khalid Hussein

2012-02-01

Note: This "Weakly Anomalous to Anomalous Surface Temperature" dataset differs from the "Anomalous Surface Temperature" dataset for this county (another remotely sensed CIRES product) by showing areas of modeled temperatures between 1o and 2o above the mean, as opposed to the greater than 2o temperatures contained in the "Anomalous Surface Temperature" dataset. This layer contains areas of anomalous surface temperature in Archuleta County identified from ASTER thermal data and spatial based insolation model. The temperature is calculated using the Emissivity Normalization Algorithm that separate temperature from emissivity. The incoming solar radiation was calculated using spatial based insolation model developed by Fu and Rich (1999). Then the temperature due to solar radiation was calculated using emissivity derived from ASTER data. The residual temperature, i.e. temperature due to solar radiation subtracted from ASTER temperature was used to identify thermally anomalous areas. Areas that had temperature between 1o and 2o were considered ASTER modeled warm surface exposures (thermal anomalies). Note: 'o' is used in this description to represent lowercase sigma.

Fluorescence fluctuation analysis of BACE1-GFP fusion protein in cultured HEK293 cells

NASA Astrophysics Data System (ADS)

Gardeen, Spencer; Johnson, Joseph L.; Heikal, Ahmed A.

2016-10-01

Beta-site APP cleaving enzyme 1 (BACE1) is a type I transmembrane aspartyl protease. In the amyloidogenic pathway, BACE1 provides β-secretase activity that cleaves the amyloid precursor protein (APP) that leads to amyloid beta (Aβ) peptides. The aggregation of these Aβ will ultimately results in amyloid plaque formation, a hallmark of Alzheimer's disease (AD). Amyloid aggregation leads to progressive memory impairment and neural loss. Recent detergent protein extraction studies suggest that the untreated BACE1 protein forms a dimer that has significantly higher catalytic activity than its monomeric counterpart. Here, we examine the dimerization hypothesis of BACE1 in cultured HEK293 cells using fluorescence correlation spectroscopy (FCS). Cells were transfected with a BACE1-EGFP fusion protein construct and imaged using confocal and DIC microscopy to monitor labeled BACE1 localization and distribution within the cell. Our one-photon fluorescence fluctuation autocorrelation of BACE1- EGFP on the plasma membrane of HEK cells is modeled using two diffusing species on the plasma membrane with estimated diffusion coefficients of 1.39 x 10-7 cm2/sec and 2.8 x 10-8 cm2/sec under resting conditions and STA-200 inhibition, respectively. Anomalous diffusion model also provided adequate description of the observed autocorrelation function of BACE1- EGFP on the plasma membrane with an estimate exponent (α) of 0.8 and 0.5 for resting and STA-200 treated cells, respectively. The corresponding hydrodynamic radius of this transmembrane fusion protein was estimated using the measured diffusion coefficients assuming both Stokes-Einstein and Saffman-Delbruck models. Our results suggest a complex diffusion pattern of BACE1-EGFP on the plasma membrane of HEK cells with the possibility for dimer formation, especially under STA-200 inhibition.

Broken symmetry and critical transport properties of random metals

PubMed Central

Phillips, J. C.

1997-01-01

Recent experimental data on the conductivity σ+(T), T → 0, on the metallic side of the metal–insulator transition in ideally random (neutron transmutation-doped) 70Ge:Ga have shown that σ+(0) ∝ (N − Nc)μ with μ = ½, confirming earlier ultra-low-temperature results for Si:P. This value is inconsistent with theoretical predictions based on diffusive classical scaling models, but it can be understood by a quantum-directed percolative filamentary amplitude model in which electronic basis states exist which have a well-defined momentum parallel but not normal to the applied electric field. The model, which is based on a new kind of broken symmetry, also explains the anomalous sign reversal of the derivative of the temperature dependence in the critical regime. PMID:11038579

A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements

NASA Astrophysics Data System (ADS)

Qin, Shanlin; Liu, Fawang; Turner, Ian W.

2018-03-01

The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.

On the source of the dust extinction in type Ia supernovae and the discovery of anomalously strong Na I absorption

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

Phillips, M. M.; Morrell, Nidia; Hsiao, E. Y.

High-dispersion observations of the Na I D λλ5890, 5896 and K I λλ7665, 7699 interstellar lines, and the diffuse interstellar band at 5780 Å in the spectra of 32 Type Ia supernovae are used as an independent means of probing dust extinction. We show that the dust extinction of the objects where the diffuse interstellar band at 5780 Å is detected is consistent with the visual extinction derived from the supernova colors. This strongly suggests that the dust producing the extinction is predominantly located in the interstellar medium of the host galaxies and not in circumstellar material associated with themore » progenitor system. One quarter of the supernovae display anomalously large Na I column densities in comparison to the amount of dust extinction derived from their colors. Remarkably, all of the cases of unusually strong Na I D absorption correspond to 'Blueshifted' profiles in the classification scheme of Sternberg et al. This coincidence suggests that outflowing circumstellar gas is responsible for at least some of the cases of anomalously large Na I column densities. Two supernovae with unusually strong Na I D absorption showed essentially normal K I column densities for the dust extinction implied by their colors, but this does not appear to be a universal characteristic. Overall, we find the most accurate predictor of individual supernova extinction to be the equivalent width of the diffuse interstellar band at 5780 Å, and provide an empirical relation for its use. Finally, we identify ways of producing significant enhancements of the Na abundance of circumstellar material in both the single-degenerate and double-degenerate scenarios for the progenitor system.« less

Diffusion in randomly perturbed dissipative dynamics

NASA Astrophysics Data System (ADS)

Rodrigues, Christian S.; Chechkin, Aleksei V.; de Moura, Alessandro P. S.; Grebogi, Celso; Klages, Rainer

2014-11-01

Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no longer invariant and there is the possibility of transport among them. Here we introduce a basic theoretical setting which enables us to study this hopping process from the perspective of anomalous transport using the concept of a random dynamical system with holes. We apply it to a simple model by investigating the role of hyperbolicity for the transport among basins. We show numerically that our system exhibits non-Gaussian position distributions, power-law escape times, and subdiffusion. Our simulation results are reproduced consistently from stochastic continuous time random walk theory.

Multicomponent Gas Diffusion and an Appropriate Momentum Boundary Condition

NASA Technical Reports Server (NTRS)

Noever, David A.

1994-01-01

Multicomponent gas diffusion is reviewed with particular emphasis on gas flows near solid boundaries-the so-called Kramers-Kistemaker effect. The aim is to derive an appropriate momentum boundary condition which governs many gaseous species diffusing together. The many species' generalization of the traditional single gas condition, either as slip or stick (no-slip), is not obvious, particularly for technologically important cases of lower gas pressures and very dissimilar molecular weight gases. No convincing theoretical case exists for why two gases should interact with solid boundaries equally but in opposite flow directions, such that the total gas flow exactly vanishes. ln this way, the multicomponent no-slip boundary requires careful treatment The approaches discussed here generally adopt a microscopic model for gas-solid contact. The method has the advantage that the mathematics remain tractable and hence experimentally testable. Two new proposals are put forward, the first building in some molecular collision physics, the second drawing on a detailed view of surface diffusion which does not unphysically extrapolate bulk gas properties to govern the adsorbed molecules. The outcome is a better accounting of previously anomalous experiments. Models predict novel slip conditions appearing even for the case of equal molecular weight components. These approaches become particularly significant in view of a conceptual contradiction found to arise in previous derivations of the appropriate boundary conditions. The analogous case of three gases, one of which is uniformly distributed and hence non-diffusing, presents a further refinement which gives unexpected flow reversals near solid boundaries. This case is investigated alone and for aggregating gas species near their condensation point. In addition to predicting new physics, this investigation carries practical implications for controlling vapor diffusion in the growth of crystals used in medical diagnosis (e.g. mercuric iodide) and semiconductors.

Maximum Path Information and Fokker Planck Equation

NASA Astrophysics Data System (ADS)

Li, Wei; Wang A., Q.; LeMehaute, A.

2008-04-01

We present a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons & Fractals 23 (2005) 1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy [J. Stat. Phys. 52 (1988) 479] and the time t.

ERO modeling and sensitivity analysis of locally enhanced beryllium erosion by magnetically connected antennas

NASA Astrophysics Data System (ADS)

Lasa, A.; Borodin, D.; Canik, J. M.; Klepper, C. C.; Groth, M.; Kirschner, A.; Airila, M. I.; Borodkina, I.; Ding, R.; Contributors, JET

2018-01-01

Experiments at JET showed locally enhanced, asymmetric beryllium (Be) erosion at outer wall limiters when magnetically connected ICRH antennas were in operation. A first modeling effort using the 3D erosion and scrape-off layer impurity transport modeling code ERO reproduced qualitatively the experimental outcome. However, local plasma parameters—in particular when 3D distributions are of interest—can be difficult to determine from available diagnostics and so erosion / impurity transport modeling input relies on output from other codes and simplified models, increasing uncertainties in the outcome. In the present contribution, we introduce and evaluate the impact of improved models and parameters with largest uncertainties of processes that impact impurity production and transport across the scrape-off layer, when simulated in ERO: (i) the magnetic geometry has been revised, for affecting the separatrix position (located 50-60 mm away from limiter surface) and thus the background plasma profiles; (ii) connection lengths between components, which lead to shadowing of ion fluxes, are also affected by the magnetic configuration; (iii) anomalous transport of ionized impurities, defined by the perpendicular diffusion coefficient, has been revisited; (iv) erosion yields that account for energy and angular distributions of background plasma ions under the present enhanced sheath potential and oblique magnetic field, have been introduced; (v) the effect of additional erosion sources, such as charge-exchange neutral fluxes, which are dominant in recessed areas like antennas, has been evaluated; (vi) chemically assisted release of Be in molecular form has been included. Sensitivity analysis highlights a qualitative effect (i.e. change in emission patterns) of magnetic shadowing, anomalous diffusion, and inclusion of neutral fluxes and molecular release of Be. The separatrix location, and energy and angular distribution of background plasma fluxes impact erosion quantitatively. ERO simulations that include all features described above match experimentally measured Be I (457.3 nm) and Be II (467.4 nm) signals, and erosion increases with varying ICRH antenna’s RF power. However, this increase in erosion is only partially captured by ERO’s emission measurements, as most contributions from plasma wetted surfaces fall outside the volume observed by sightlines. ).

Tracer particles in two-dimensional elastic networks diffuse logarithmically slow

NASA Astrophysics Data System (ADS)

Lizana, Ludvig; Ambjörnsson, Tobias; Lomholt, Michael A.

2017-01-01

Several experiments on tagged molecules or particles in living systems suggest that they move anomalously slow—their mean squared displacement (MSD) increase slower than linearly with time. Leading models aimed at understanding these experiments predict that the MSD grows as a power law with a growth exponent that is smaller than unity. However, in some experiments the growth is so slow (fitted exponent  ˜0.1-0.2) that they hint towards other mechanisms at play. In this paper, we theoretically demonstrate how in-plane collective modes excited by thermal fluctuations in a two dimensional membrane lead to logarithmic time dependence for the the tracer particle’s MSD.

Anomalous neuronal responses to fluctuated inputs

NASA Astrophysics Data System (ADS)

Hosaka, Ryosuke; Sakai, Yutaka

2015-10-01

The irregular firing of a cortical neuron is thought to result from a highly fluctuating drive that is generated by the balance of excitatory and inhibitory synaptic inputs. A previous study reported anomalous responses of the Hodgkin-Huxley neuron to the fluctuated inputs where an irregularity of spike trains is inversely proportional to an input irregularity. In the current study, we investigated the origin of these anomalous responses with the Hindmarsh-Rose neuron model, map-based models, and a simple mixture of interspike interval distributions. First, we specified the parameter regions for the bifurcations in the Hindmarsh-Rose model, and we confirmed that the model reproduced the anomalous responses in the dynamics of the saddle-node and subcritical Hopf bifurcations. For both bifurcations, the Hindmarsh-Rose model shows bistability in the resting state and the repetitive firing state, which indicated that the bistability was the origin of the anomalous input-output relationship. Similarly, the map-based model that contained bistability reproduced the anomalous responses, while the model without bistability did not. These results were supported by additional findings that the anomalous responses were reproduced by mimicking the bistable firing with a mixture of two different interspike interval distributions. Decorrelation of spike trains is important for neural information processing. For such spike train decorrelation, irregular firing is key. Our results indicated that irregular firing can emerge from fluctuating drives, even weak ones, under conditions involving bistability. The anomalous responses, therefore, contribute to efficient processing in the brain.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

Anomalous sound absorption in the Voronoi liquid

NASA Astrophysics Data System (ADS)

Farago, Jean; Ruscher, CéLine; Semenov, Alexandr; Baschnagel, Joerg

The physics of simple fluids in the hydrodynamic limit, and notably the connection between the proper microscopic scales and the macroscopic hydrodynamical description are nowadays well understood. In particular, the three peak shape of the dynamical structure factor S (k , ω) is a universal feature, as well as the k-dependence of the peak position ( k), and width k2 , the latter accounting for the sound attenuation rate. In this talk, I will present a theoretical model of monodisperse fluid, whose interactions are defined via the Voronoi tessellations of the configurations (called the Voronoi liquid and first studied in), which displays at low temperatures a marked violation of the universal features of S (k , ω) with sound attenuation rate only k . This anomalous behaviour, which apparently violates the basic symmetries of the liquid state, is traced back to the existence of a timescale which is both (1) short enough for the viscoelastic features of the liquid to impact the relaxational dynamics and (2) long enough for the momentum diffusion to be substantially slower than the sound propagation on that characteristic time.

Anomalous White Matter Morphology in Adults Who Stutter

ERIC Educational Resources Information Center

Cieslak, Matthew; Ingham, Rojer J.; Ingham, Janis C.; Grafton, Scott T.

2015-01-01

Aims: Developmental stuttering is now generally considered to arise from genetic determinants interacting with neurologic function. Changes within speech-motor white matter (WM) connections may also be implicated. These connections can now be studied in great detail by high-angular-resolution diffusion magnetic resonance imaging. Therefore,…

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

Garcia, Andres

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems canmore » be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use Langevin Molecular Dynamics (MD) simulations to assess these parameters.« less

Membrane orientation and lateral diffusion of BODIPY-cholesterol as a function of probe structure.

PubMed

Solanko, Lukasz M; Honigmann, Alf; Midtiby, Henrik Skov; Lund, Frederik W; Brewer, Jonathan R; Dekaris, Vjekoslav; Bittman, Robert; Eggeling, Christian; Wüstner, Daniel

2013-11-05

Cholesterol tagged with the BODIPY fluorophore via the central difluoroboron moiety of the dye (B-Chol) is a promising probe for studying intracellular cholesterol dynamics. We synthesized a new BODIPY-cholesterol probe (B-P-Chol) with the fluorophore attached via one of its pyrrole rings to carbon-24 of cholesterol (B-P-Chol). Using two-photon fluorescence polarimetry in giant unilamellar vesicles and in the plasma membrane (PM) of living intact and actin-disrupted cells, we show that the BODIPY-groups in B-Chol and B-P-Chol are oriented perpendicular and almost parallel to the bilayer normal, respectively. B-Chol is in all three membrane systems much stronger oriented than B-P-Chol. Interestingly, we found that the lateral diffusion in the PM was two times slower for B-Chol than for B-P-Chol, although we found no difference in lateral diffusion in model membranes. Stimulated emission depletion microscopy, performed for the first time, to our knowledge, with fluorescent sterols, revealed that the difference in lateral diffusion of the BODIPY-cholesterol probes was not caused by anomalous subdiffusion, because diffusion of both analogs in the PM was free but not hindered. Our combined measurements show that the position and orientation of the BODIPY moiety in cholesterol analogs have a severe influence on lateral diffusion specifically in the PM of living cells. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

The Shape of Protein Crowders is a Major Determinant of Protein Diffusion

PubMed Central

Balbo, Jessica; Mereghetti, Paolo; Herten, Dirk-Peter; Wade, Rebecca C.

2013-01-01

As a model for understanding how molecular crowding influences diffusion and transport of proteins in cellular environments, we combined experimental and theoretical approaches to study the diffusion of proteins in highly concentrated protein solutions. Bovine serum albumin and γ-Globulin were chosen as molecular crowders and as tracers. These two proteins are representatives of the main types of plasma protein and have different shapes and sizes. Solutions consisting of one or both proteins were studied. The self-diffusion coefficients of the fluorescently labeled tracer proteins were measured by means of fluorescence correlation spectroscopy at a total protein concentration of up to 400 g/L. γ-Globulin is found to have a stronger influence as a crowder on the tracer self-diffusion coefficient than Bovine serum albumin. Brownian dynamics simulations show that the excluded volume and the shape of the crowding protein have a significantly stronger influence on translational and rotational diffusion coefficients, as well as transient oligomerization, than hydrodynamic or direct interactions. Anomalous subdiffusion, which is not observed at the experimental fluorescence correlation spectroscopy timescales (>100 μs), appears only at very short timescales (<1 μs) in the simulations due to steric effects of the proteins. We envision that the combined experimental and computational approach employed here can be developed to unravel the different biophysical contributions to protein motion and interaction in cellular environments by systematically varying protein properties such as molecular weight, size, shape, and electrostatic interactions. PMID:23561534

Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders

DOE PAGES

Erikson, William W.; Coker, Eric N.

2016-11-10

It has long been observed that oxidation processes in metals tend to follow a parabolic rate law associated with the growth of a surface oxide layer. Here we observe that for certain titanium powders, the expected parabolic law (∝t 1/2) is recovered, yet for others, the exponent differs significantly. One explanation for this non-parabolic, anomalous diffusion arises from fractal geometry. Theoretical considerations indicate that the time response of diffusion-limited processes in an object closely follow a power-law in time (t n) with n=(E–D)/2, where E is the object's Euclidean dimension and D is its boundary's Hausdorff dimension. Non-integer, (fractal) valuesmore » of D will result in n≠1/2. Finite element simulations of several canonical fractal objects were performed to verify the application of this theory; the results matched the theory well. Two different types of titanium powder were tested in isothermal thermogravimetric tests under dilute oxygen. Time-dependent mass uptake data were fit with power-law forms and the associated exponents were used to determine an equivalent fractal dimension. One Ti powder type has an implied surface dimension of ca. 2.3 to 2.5, suggesting fractal geometry may be operative. Finally, the other has a dimension near 2.0, indicating it behaves like traditional material.« less

Single Molecule Fluorescence Measurements of Complex Systems

NASA Astrophysics Data System (ADS)

Sadegh, Sanaz

Single molecule methods are powerful tools for investigating the properties of complex systems that are generally concealed by ensemble measurements. Here we use single molecule fluorescent measurements to study two different complex systems: 1/ƒ noise in quantum dots and diffusion of the membrane proteins in live cells. The power spectrum of quantum dot (QD) fluorescence exhibits 1/ƒ beta noise, related to the intermittency of these nanosystems. As in other systems exhibiting 1/ƒ noise, this power spectrum is not integrable at low frequencies, which appears to imply infinite total power. We report measurements of individual QDs that address this long-standing paradox. We find that the level of 1/ƒbeta noise for QDs decays with the observation time. We show that the traditional description of the power spectrum with a single exponent is incomplete and three additional critical exponents characterize the dependence on experimental time. A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized due to experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data show that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar fractal.

Diffusion in Jammed Particle Packs.

PubMed

Bolintineanu, Dan S; Grest, Gary S; Lechman, Jeremy B; Silbert, Leonardo E

2015-08-21

Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions ϕ in the vicinity of the jamming transition at ϕ(c). Various diffusion properties are computed over several orders of magnitude in both time and packing pressure. Two well-separated regimes of normal "Fickian" diffusion, where the mean squared displacement is linear in time, are observed. The first corresponds to diffusion inside individual spheres, while the latter is the long-time bulk diffusion. The intermediate anomalous diffusion regime and the long-time value of the diffusion coefficient are both shown to be controlled by particle contacts, which in turn depend on proximity to ϕ(c). The time required to recover normal diffusion t* scales as (ϕ-ϕ(c))(-0.5) and the long-time diffusivity D(∞)∼(ϕ-ϕ(c))0.5, or D(∞)∼1/t*. It is shown that the distribution of mean first passage times associated with the escape of random walkers between neighboring particles controls both t* and D(∞) in the limit ϕ→ϕ(c).

Signals of New Physics in the Underlying Event

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

Harnik, Roni; /Stanford U., ITP /SLAC; Wizansky, Tommer

2010-06-11

LHC searches for new physics focus on combinations of hard physics objects. In this work we propose a qualitatively different soft signal for new physics at the LHC - the 'anomalous underlying event'. Every hard LHC event will be accompanied by a soft underlying event due to QCD and pile-up effects. Though it is often used for QCD and monte carlo studies, here we propose the incorporation of an underlying event analysis in some searches for new physics. An excess of anomalous underlying events may be a smoking-gun signal for particular new physics scenarios such as 'quirks' or 'hidden valleys'more » in which large amounts of energy may be emitted by a large multiplicity of soft particles. We discuss possible search strategies for such soft diffuse signals in the tracking system and calorimetry of the LHC experiments. We present a detailed study of the calorimetric signal in a concrete example, a simple quirk model motivated by folded supersymmetry. In these models the production and radiative decay of highly excited quirk bound states leads to an 'antenna pattern' of soft unclustered energy. Using a dedicated simulation of a toy detector and a 'CMB-like' multipole analysis we compare the signal to the expected backgrounds.« less

Some Basic Concepts of Wave-Particle Interactions in Collisionless Plasmas

NASA Technical Reports Server (NTRS)

Lakhina, Gurbax S.; Tsurutani, Bruce T.

1997-01-01

The physical concepts of wave-particle interactions in a collisionless plasma are developed from first principles. Using the Lorentz force, starting with the concepts of gyromotion, particle mirroring and the loss-cone, normal and anomalous cyclotron resonant interactions, pitch-angle scattering, and cross-field diffusion are developed.

Ion distribution effects of turbulence on a kinetic auroral arc model

NASA Technical Reports Server (NTRS)

Cornwall, J. M.; Chiu, Y. T.

1982-01-01

An inverted-V auroral arc structure plasma-kinetic model is extended to phenomenologically include the effects of electrostatic turbulence, with k-parallel/k-perpendicular being much less than unity. It is shown that, unless plasma sheet ions are very much more energetic than the electrons, anomalous resistivity is not a large contributor to parallel electrostatic potential drops, since the support of the observed potential drop requires a greater dissipation of energy than can be provided by the plasma sheet. Wave turbulence can, however, be present, with the ion cyclotron turbulence levels suggested by the ion resonance broadening saturation mechanism of Dum and Dupree (1970) being comparable to those observed on auroral field lines. The diffusion coefficient and net growth rate are much smaller than estimates based solely on local plasma properties.

Computational Study of Anomalous Transport in High Beta DIII-D Discharges with ITBs

NASA Astrophysics Data System (ADS)

Pankin, Alexei; Garofalo, Andrea; Grierson, Brian; Kritz, Arnold; Rafiq, Tariq

2015-11-01

The advanced tokamak scenarios require a large bootstrap current fraction and high β. These large values are often outside the range that occurs in ``conventional'' tokamak discharges. The GLF23, TGLF, and MMM transport models have been previously validated for discharges with parameters associated with ``conventional'' tokamak discharges. It has been demonstrated that the TGLF model under-predicts anomalous transport in high β DIII-D discharges [A.M. Garofalo et al. 2015 TTF Workshop]. In this research, the validity of MMM7.1 model [T. Rafiq et al. Phys. Plasmas 20 032506 (2013)] is tested for high β DIII-D discharges with low and high torque. In addition, the sensitivity of the anomalous transport to β is examined. It is shown that the MMM7.1 model over-predicts the anomalous transport in the DIII-D discharge 154406. In particular, a significant level of anomalous transport is found just outside the internal transport barrier. Differences in the anomalous transport predicted using TGLF and MMM7.1 are reviewed. Mechanisms for quenching of anomalous transport in the ITB regions of high-beta discharges are investigated. This research is supported by US Department of Energy.

Anomalous symmetry breaking in classical two-dimensional diffusion of coherent atoms

NASA Astrophysics Data System (ADS)

Pugatch, Rami; Bhattacharyya, Dipankar; Amir, Ariel; Sagi, Yoav; Davidson, Nir

2014-03-01

The electromagnetically induced transparency (EIT) spectrum of atoms diffusing in and out of a narrow beam is measured and shown to manifest the two-dimensional δ-function anomaly in a classical setting. In the limit of small-area beams, the EIT line shape is independent of power, and equal to the renormalized local density of states of a free particle Hamiltonian. The measured spectra for different powers and beam sizes collapses to a single universal curve with a characteristic logarithmic Van Hove singularity close to resonance.

Anomalous Diffusion of Particles Dispersed in Xanthan Solutions Subjected to Shear Flow

NASA Astrophysics Data System (ADS)

Takikawa, Yoshinori; Yasuta, Muneharu; Fujii, Shuji; Orihara, Hiroshi; Tanaka, Yoshimi; Nishinari, Katsuyoshi

2018-05-01

Xanthan gum exhibits viscoelastic and shear-thinning properties. We investigate the Brownian motion of particles dispersed in xanthan gum solutions that are subjected to simple shear flow. The mean square displacements (MSDs) are obtained in both the flow and vorticity directions. In the absence of shear flow, subdiffusion is observed, MSD ∝ tα with α < 1, where t is time. In the presence of shear flow, however, the exponent α becomes larger together with the MSD itself in both the flow and vorticity directions. We show that the diffusion is enhanced by Taylor dispersion in the flow direction, whereas in the vorticity direction it is enhanced by nonthermal self-diffusion.

Reactions and Transport: Diffusion, Inertia, and Subdiffusion

NASA Astrophysics Data System (ADS)

Méndez, Vicenç; Fedotov, Sergei; Horsthemke, Werner

Particles, such as molecules, atoms, or ions, and individuals, such as cells or animals, move in space driven by various forces or cues. In particular, particles or individuals can move randomly, undergo velocity jump processes or spatial jump processes [333]. The steps of the random walk can be independent or correlated, unbiased or biased. The probability density function (PDF) for the jump length can decay rapidly or exhibit a heavy tail. Similarly, the PDF for the waiting time between successive jumps can decay rapidly or exhibit a heavy tail. We will discuss these various possibilities in detail in Chap. 3. Below we provide an introduction to three transport processes: standard diffusion, transport with inertia, and anomalous diffusion.

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

NASA Astrophysics Data System (ADS)

Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

2016-05-01

Diffusion in one dimensional rugged energy landscape (REL) is predicted to be pathologically different (from any higher dimension) with a much larger chance of encountering broken ergodicity [D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479, 620 (2012)]. However, no quantitative study of this difference has been reported, despite the prevalence of multidimensional physical models in the literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at an intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (˜5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement (MSD) is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d = ∞) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

PubMed

Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

2016-05-21

Diffusion in one dimensional rugged energy landscape (REL) is predicted to be pathologically different (from any higher dimension) with a much larger chance of encountering broken ergodicity [D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479, 620 (2012)]. However, no quantitative study of this difference has been reported, despite the prevalence of multidimensional physical models in the literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at an intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (∼5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement (MSD) is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d = ∞) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.

PubMed

Chen, Duan

2017-11-01

In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems

NASA Astrophysics Data System (ADS)

Kim, Seonghak; Yan, Baisheng

2018-06-01

We study some non-parabolic diffusion problems in one space dimension, where the diffusion flux exhibits forward and backward nature of the Perona–Malik, Höllig or non-Fourier type. Classical weak solutions to such problems are constructed in a way to capture some expected and unexpected properties, including anomalous asymptotic behaviors and energy dissipation or allocation. Specific properties of solutions will depend on the type of the diffusion flux, but the primary method of our study relies on reformulating diffusion equations involved as an inhomogeneous partial differential inclusion and on constructing solutions from the differential inclusion by a combination of the convex integration and Baire’s category methods. In doing so, we introduce the appropriate notion of subsolutions of the partial differential inclusion and their transition gauge, which plays a pivotal role in dealing with some specific features of the constructed weak solutions.

Neoclassical diffusion at low L-shel

NASA Astrophysics Data System (ADS)

Cunningham, G.; Ripoll, J. F.; Loridan, V.; Schulz, M.

2017-12-01

At very low L-shell, the lifetime of MeV electrons is dominated by pitch-angle scattering due to Coulomb collisions with background neutrals and ions. Walt's evaluation of this lifetime explained Van Allen's observations of the decay of the radiation belts in the early 1960's, for L<1.25 but Imhof et al showed that the apparent lifetime of >500 keV electrons for L=[1.15,1.21] was much greater than predicted by Walt's model when the decay was observed over 3 years rather than just a few months. Imhof et al argued that inward radial diffusion from larger L would be a source of electrons at low L, thus increasing the apparent lifetimes that were observed, but did not speculate on the cause of such diffusion across L. Newkirk and Walt estimated the radial diffusion coefficient that would be needed to explain the apparent lifetimes observed by Imhof et al. The radial diffusion coefficients they inferred dropped sharply as L increased, contrasting with the radial diffusion coefficients that had been recently developed by Falthammar [1965], which increase as a power law in L. Newkirk and Walt noted Falthammar's speculation that pitch-angle diffusion caused by Coulomb scattering, when coupled to drift-shell splitting associated with non-dipolar terms in the near-Earth geomagnetic field, might be the physical basis for the radial diffusion, but they did not attempt to quantify this effect. Roederer et al demonstrated that Coulomb scattering plus drift-shell splitting could explain the Newkirk and Walt results but they did not perform an exhaustive study. In the field of magnetically confined fusion, the movement of charged particles to different drift-shells caused by the combination of collisions and drift-shell splitting is labeled `neoclassical' diffusion. By contrast, `anomalous' diffusion results from pitch-angle diffusion caused by wave turbulence combined with drift-shell splitting, an effect recently studied by O'Brien in the outer radiation belt. We have constructed a comprehensive model of neoclassical diffusion at low L as a function of pitch-angle, energy and L-shell, and find that we quantitatively reproduce the results in Newkirk and Walt and Imhof et al, conclusively demonstrating that neoclassical diffusion is an important effect for energetic electrons in the deep inner belt.

Anomalous stress diffusion, Omori's law and Continuous Time Random Walk in the 2010 Efpalion aftershock sequence (Corinth rift, Greece)

NASA Astrophysics Data System (ADS)

Michas, Georgios; Vallianatos, Filippos; Karakostas, Vassilios; Papadimitriou, Eleftheria; Sammonds, Peter

2014-05-01

Efpalion aftershock sequence occurred in January 2010, when an M=5.5 earthquake was followed four days later by another strong event (M=5.4) and numerous aftershocks (Karakostas et al., 2012). This activity interrupted a 15 years period of low to moderate earthquake occurrence in Corinth rift, where the last major event was the 1995 Aigion earthquake (M=6.2). Coulomb stress analysis performed in previous studies (Karakostas et al., 2012; Sokos et al., 2012; Ganas et al., 2013) indicated that the second major event and most of the aftershocks were triggered due to stress transfer. The aftershocks production rate decays as a power-law with time according to the modified Omori law (Utsu et al., 1995) with an exponent larger than one for the first four days, while after the occurrence of the second strong event the exponent turns to unity. We consider the earthquake sequence as a point process in time and space and study its spatiotemporal evolution considering a Continuous Time Random Walk (CTRW) model with a joint probability density function of inter-event times and jumps between the successive earthquakes (Metzler and Klafter, 2000). Jump length distribution exhibits finite variance, whereas inter-event times scale as a q-generalized gamma distribution (Michas et al., 2013) with a long power-law tail. These properties are indicative of a subdiffusive process in terms of CTRW. Additionally, the mean square displacement of aftershocks is constant with time after the occurrence of the first event, while it changes to a power-law with exponent close to 0.15 after the second major event, illustrating a slow diffusive process. During the first four days aftershocks cluster around the epicentral area of the second major event, while after that and taking as a reference the second event, the aftershock zone is migrating slowly with time to the west near the epicentral area of the first event. This process is much slower from what would be expected from normal diffusion, a result that is in accordance to earthquake triggering in global scale (Huc and Main, 2003) and aftershocks diffusion in California (Helmstetter et al., 2003). While other mechanisms may be plausible, the results indicate that anomalous stress transfer due to the occurrence of the two major events control the migration of the aftershock activity, activating different fault segments and having strong implications for the seismic hazard of the area. Acknowledgments. G. Michas wishes to acknowledge the partial financial support from the Greek State Scholarships Foundation (IKY). This work has been accomplished in the framework of the postgraduate program and co-funded through the action "Program for scholarships provision I.K.Y. through the procedure of personal evaluation for the 2011-2012 academic year" from resources of the educational program "Education and Life Learning" of the European Social Register and NSRF 2007- 2013. References Ganas, A., Chousianitis, K., Batsi, E., Kolligri, M., Agalos, A., Chouliaras, G., Makropoulos, K. (2013). The January 2010 Efpalion earthquakes (Gulf of Corinth, central Greece): Earthquake interactions and blind normal faulting. J. of Seism., 17(2), 465-484. Helmstetter, A., Ouillon, G., Sornette, D. (2003). Are aftershocks of large California earthquakes diffusing? J. of Geophys. Res. B, 108(10), 2483. Huc, M., Main, I. G. (2003). Anomalous stress diffusion in earthquake triggering: Correlation length, time dependence, and directionality. J. of Geophys. Res. B, 108(7), 2324. Karakostas, V., Karagianni, E., Paradisopoulou, P. (2012). Space-time analysis, faulting and triggering of the 2010 earthquake doublet in western Corinth gulf. Nat.Haz., 63(2), 1181-1202. Metzler, R., Klafter, J. (2000). The random walk's guide to anomalous diffusion: a fractional dynamics approach. Physics Reports, 339, 1-77. Michas, G., Vallianatos, F., Sammonds, P. (2013). Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece). Nonlin. Processes Geophys., 20, 713-724. Sokos, E., Zahradník, J., Kiratzi, A., Janský, J., Gallovič, F., Novotny, O., Kostelecký, J., Serpetsidaki, A., Tselentis, G.-A. (2012). The January 2010 Efpalio earthquake sequence in the western Corinth gulf (Greece). Tectonophysics, 530-531, 299-309. Utsu, T., Y. Ogata, Matsu'ura R. S. (1995). The centenary of the Omori formula for a decay law of aftershock activity. J. Phys. Earth, 43, 1- 33.

Polymer translocation through a nanopore: a showcase of anomalous diffusion.

PubMed

Milchev, A; Dubbeldam, Johan L A; Rostiashvili, Vakhtang G; Vilgis, Thomas A

2009-04-01

We investigate the translocation dynamics of a polymer chain threaded through a membrane nanopore by a chemical potential gradient that acts on the chain segments inside the pore. By means of diverse methods (scaling theory, fractional calculus, and Monte Carlo and molecular dynamics simulations), we demonstrate that the relevant dynamic variable, the transported number of polymer segments, s(t), displays an anomalous diffusive behavior, both with and without an external driving force being present. We show that in the absence of drag force the time tau, needed for a macromolecule of length N to thread from the cis into the trans side of a cell membrane, scales as tauN(2/alpha) with the chain length. The anomalous dynamics of the translocation process is governed by a universal exponent alpha= 2/(2nu + 2 - gamma(1)), which contains the basic universal exponents of polymer physics, nu (the Flory exponent) and gamma(1) (the surface entropic exponent). A closed analytic expression for the probability to find s translocated segments at time t in terms of chain length N and applied drag force f is derived from the fractional Fokker-Planck equation, and shown to provide analytic results for the time variation of the statistical moments and . It turns out that the average translocation time scales as tau proportional, f(-1)N(2/alpha-1). These results are tested and found to be in perfect agreement with extensive Monte Carlo and molecular dynamics computer simulations.

Magnetic field diffusion and dissipation in reversed-field plasmas

NASA Technical Reports Server (NTRS)

Drake, J. F.; Gladd, N. T.; Huba, J. D.

1981-01-01

A diffusion equation is derived which describes the evolution of a magnetic field in a plasma of arbitrary beta and resistivity. The equation is valid for a one-dimensional slab geometry, assumes the plasma remains in quasi-equilibrium throughout its evolution and does not include thermal transport. Scaling laws governing the rate of change of the magnetic energy, particle drift energy, and magnetic flux are calculated. It is found that the magnetic free energy can be substantially larger than the particle drift energy and can be an important energy reservoir in driving plasma instabilities (e.g., the lower-hybrid-drift instability). In addition, the effect of a spatially varying resistivity on the evolution of a reversed-field plasma is studied. The resistivity model used is based upon the anomalous transport properties associated with the nonlocal mode structure of the lower-hybrid-drift instability. The relevance of this research to laboratory plasmas (e.g., theta pinches, reversed-field theta pinches) and space plasmas (e.g., the earth's magnetotail) is discussed.

Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi-Ulam model

NASA Astrophysics Data System (ADS)

Livorati, André L. P.; Palmero, Matheus S.; Díaz-I, Gabriel; Dettmann, Carl P.; Caldas, Iberê L.; Leonel, Edson D.

2018-02-01

We study the dynamics of an ensemble of non interacting particles constrained by two infinitely heavy walls, where one of them is moving periodically in time, while the other is fixed. The system presents mixed dynamics, where the accessible region for the particle to diffuse chaotically is bordered by an invariant spanning curve. Statistical analysis for the root mean square velocity, considering high and low velocity ensembles, leads the dynamics to the same steady state plateau for long times. A transport investigation of the dynamics via escape basins reveals that depending of the initial velocity ensemble, the decay rates of the survival probability present different shapes and bumps, in a mix of exponential, power law and stretched exponential decays. After an analysis of step-size averages, we found that the stable manifolds play the role of a preferential path for faster escape, being responsible for the bumps and different shapes of the survival probability.

Areas of Weakly Anomalous to Anomalous Surface Temperature in Alamosa and Saguache Counties, Colorado, as Identified from ASTER Thermal Data

DOE Data Explorer

Khalid Hussein

2012-02-01

This "Weakly Anomalous to Anomalous Surface Temperature" dataset differs from the "Anomalous Surface Temperature" dataset for this county (another remotely sensed CIRES product) by showing areas of modeled temperatures between 1o and 2o above the mean, as opposed to the greater than 2o temperatures contained in the "Anomalous Surface Temperature" dataset. Note: 'o' is used in this description to represent lowercase sigma

Kubo conductivity of a strongly magnetized two-dimensional plasma.

NASA Technical Reports Server (NTRS)

Montgomery, D.; Tappert, F.

1971-01-01

The Kubo formula is used to evaluate the bulk electrical conductivity of a two-dimensional guiding-center plasma in a strong dc magnetic field. The particles interact only electrostatically. An ?anomalous' electrical conductivity is derived for this system, which parallels a recent result of Taylor and McNamara for the coefficient of spatial diffusion.

Behind the Mpemba paradox

PubMed Central

Sun, Chang Qing

2015-01-01

Mpemba paradox results from hydrogen-bond anomalous relaxation. Heating stretches the O:H nonbond and shortens the H‒O bond via Coulomb coupling; cooling reverses this process to emit heat at a rate depending on its initial storage. Skin ultra-low mass density raises the thermal diffusivity and favors outward heat flow from the liquid. PMID:27227000

Chromosomal locus tracking with proper accounting of static and dynamic errors

PubMed Central

Backlund, Mikael P.; Joyner, Ryan; Moerner, W. E.

2015-01-01

The mean-squared displacement (MSD) and velocity autocorrelation (VAC) of tracked single particles or molecules are ubiquitous metrics for extracting parameters that describe the object’s motion, but they are both corrupted by experimental errors that hinder the quantitative extraction of underlying parameters. For the simple case of pure Brownian motion, the effects of localization error due to photon statistics (“static error”) and motion blur due to finite exposure time (“dynamic error”) on the MSD and VAC are already routinely treated. However, particles moving through complex environments such as cells, nuclei, or polymers often exhibit anomalous diffusion, for which the effects of these errors are less often sufficiently treated. We present data from tracked chromosomal loci in yeast that demonstrate the necessity of properly accounting for both static and dynamic error in the context of an anomalous diffusion that is consistent with a fractional Brownian motion (FBM). We compare these data to analytical forms of the expected values of the MSD and VAC for a general FBM in the presence of these errors. PMID:26172745

Turbulent resistivity, diffusion and heating

NASA Technical Reports Server (NTRS)

Fried, B. D.; Kennel, C. F.; Mackenzie, K.; Coroniti, F. V.; Kindel, J. M.; Stenzel, R.; Taylor, R. J.; White, R.; Wong, A. Y.; Bernstein, W.

1971-01-01

Experimental and theoretical studies are reported on ion acoustic and ion cyclotron turbulence and their roles in anomalous resistivity, viscosity, diffusion and heating and in the structure of collisionless electrostatic shocks. Resistance due to ion acoustic turbulence has been observed in experiments with a streaming cesium plasma in which electron current, potential rise due to turbulent resistivity, spectrum of unstable ion acoustic waves, and associated electron heating were all measured directly. Kinetic theory calculations for an expanding, unstable plasma, give results in agreement with the experiment. In a strong magnetic field, with T sub e/T sub i approximately 1 and current densities typical for present Tokomaks, the plasma is stable to ion acoustic but unstable to current driven electrostatic ion cyclotron waves. Relevant characteristics of these waves are calculated and it is shown that for ion, beta greater than m sub e/m sub i, the electromagnetic ion cyclotron wave has a lower instability threshold than the electrostatic one. However, when ion acoustic turbulence is present experiments with double plasma devices show rapid anomalous heating of an ion beam streaming through a plasma.

Nature of self-diffusion in two-dimensional fluids

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

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

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

Cleaver, G.B.; Faraggi, A.E.

The realistic free fermionic models have had an intriguing success in explaining different properties of the observed particle spectrum. In this paper the authors discuss in some detail the anomalous U(1) symmetry which exists in these models. They study the properties of the anomalous U(1) in both the more realistic NAHE-based free fermionic models and those in a general NAHE class. Appearance of an anomalous U(1) in the more realistic NAHE models is shown to be an effect of reduction of world-sheet supersymmetry from (2,2) to (2,0). They show, however, that in more general (2,1) and (2,0) models, all U(1)more » can remain anomaly-free under certain conditions. Several phenomenological issues related to the anomalous U(1) are discussed. In particular, they note that in some examples the anomalous U(1) arises from the breaking E{sub 6} {yields} SO(10) {times} U(1){sub A}, resulting in U(1){sub A} being family universal.« less

Passive scalars: Mixing, diffusion, and intermittency in helical and nonhelical rotating turbulence

NASA Astrophysics Data System (ADS)

Imazio, P. Rodriguez; Mininni, P. D.

2017-03-01

We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions, and effective transport coefficients of passive scalars in turbulent rotating helical and nonhelical flows. We show that helicity affects the inertial range scaling of the velocity and of the passive scalar when rotation is present, with a spectral law consistent with ˜k⊥-1.4 for the passive scalar variance spectrum. This scaling law is consistent with a phenomenological argument [P. Rodriguez Imazio and P. D. Mininni, Phys. Rev. E 83, 066309 (2011), 10.1103/PhysRevE.83.066309] for rotating nonhelical flows, which follows directly from Kolmogorov-Obukhov scaling and states that if energy follows a E (k ) ˜k-n law, then the passive scalar variance follows a law V (k ) ˜k-nθ with nθ=(5 -n ) /2 . With the second-order scaling exponent obtained from this law, and using the Kraichnan model, we obtain anomalous scaling exponents for the passive scalar that are in good agreement with the numerical results. Multifractal intermittency models are also considered. Intermittency of the passive scalar is stronger than in the nonhelical rotating case, a result that is also confirmed by stronger non-Gaussian tails in the probability density functions of field increments. Finally, Fick's law is used to compute the effective diffusion coefficients in the directions parallel and perpendicular to rotation. Calculations indicate that horizontal diffusion decreases in the presence of helicity in rotating flows, while vertical diffusion increases. A simple mean field argument explains this behavior in terms of the amplitude of velocity fluctuations.

Fractionation of lithium isotopes in magmatic systems as a natural consequence of cooling

NASA Astrophysics Data System (ADS)

Gallagher, Kerry; Elliott, Tim

2009-02-01

High-temperature, diffusive fractionation has been invoked to account for striking Li isotopic variability recently observed within individual phenocrysts and xenolith minerals. It has been argued that chemical potential gradients required to drive such diffusion arise from changes in Li partitioning between coexisting phases during cooling. If so, Li isotopic zoning should be a common occurrence but the role of temperature-dependent partition coefficients in generating Li isotopic variability remains to be tested in a quantitative manner. Here we consider a basic scenario of a phenocryst in a cooling lava, using simple parameterisations of the temperature dependence of Li partitioning and diffusivity in clinopyroxene. Our model initially produces an asymmetric isotope profile across the crystal with a δ7Li minimum that remains close to the edge of a crystal. Such a distinctive shape mimics Li isotopic profiles documented in some olivine and clinopyroxene phenocrysts, which have isotopically normal cores but anomalously light rims. The temperature dependence of both the diffusivity and the partition coefficient of Li are key factors in generating this form of diffusion profile. Continued diffusion leads to an inversion in the sense of isotopic change between core and rim and results in the whole phenocryst attaining markedly light isotopic values. Our calculations show that significant Li isotopic zoning can occur as a natural consequence of cooling magmatic systems. Crystals that have experienced more complex thermal histories (e.g. re-entrained cumulates versus true phenocrysts) will therefore exhibit contrasting isotopic profiles and, as such, these data may be useful for tracing sub-volcanic processes.

ERTS-1 anomalous dark patches

NASA Technical Reports Server (NTRS)

Strong, A. E. (Principal Investigator)

1973-01-01

The author has identified the following significant results. Through combined use of imagery from ERTS-1 and NOAA-2 satellites was found that when the sun elevation exceeds 55 degrees, the ERTS-1 imagery is subject to considerable contamination by sunlight even though the actual specular point is nearly 300 nautical miles from nadir. Based on sea surface wave slope information, a wind speed of 10 knots will theoretically provide approximately 0.5 percent incident solar reflectance under observed ERTS multispectral scanner detectors. This reflectance nearly doubles under the influence of a 20 knot wind. The most pronounced effect occurs in areas of calm water where anomalous dark patches are observed. Calm water at distances from the specular point found in ERTS scenes will reflect no solar energy to the multispectral scanner, making these regions stand out as dark areas in all bands in an ocean scene otherwise comprosed by a general diffuse sunlight from rougher ocean surfaces. Anomalous dark patches in the outer parts of the glitter zones may explain the unusual appearance of some scenes.

Anomalous transport from holography: part II

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2017-03-01

This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous U(1)_V× U(1)_A Maxwell theory in Schwarzschild-AdS_5 spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the presence of a static spatially inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative B^2-correction to the diffusion constant. We also find modifications to the chiral magnetic wave nonlinear in B. In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second.

Directed Vertical Diffusion of Photovoltaic Active Layer Components into Porous ZnO-Based Cathode Buffer Layers.

PubMed

Kang, Jia-Jhen; Yang, Tsung-Yu; Lan, Yi-Kang; Wu, Wei-Ru; Su, Chun-Jen; Weng, Shih-Chang; Yamada, Norifumi L; Su, An-Chung; Jeng, U-Ser

2018-04-01

Cathode buffer layers (CBLs) can effectively further the efficiency of polymer solar cells (PSCs), after optimization of the active layer. Hidden between the active layer and cathode of the inverted PSC device configuration is the critical yet often unattended vertical diffusion of the active layer components across CBL. Here, a novel methodology of contrast variation with neutron and anomalous X-ray reflectivity to map the multicomponent depth compositions of inverted PSCs, covering from the active layer surface down to the bottom of the ZnO-based CBL, is developed. Uniquely revealed for a high-performance model PSC are the often overlooked porosity distributions of the ZnO-based CBL and the differential diffusions of the polymer PTB7-Th and fullerene derivative PC 71 BM of the active layer into the CBL. Interface modification of the ZnO-based CBL with fullerene derivative PCBEOH for size-selective nanochannels can selectively improve the diffusion of PC 71 BM more than that of the polymer. The deeper penetration of PC 71 BM establishes a gradient distribution of fullerene derivatives over the ZnO/PCBE-OH CBL, resulting in markedly improved electron mobility and device efficiency of the inverted PSC. The result suggests a new CBL design concept of progressive matching of the conduction bands. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Rotation driven translational diffusion of polyatomic ions in water: A novel mechanism for breakdown of Stokes-Einstein relation

NASA Astrophysics Data System (ADS)

Banerjee, Puja; Yashonath, Subramanian; Bagchi, Biman

2017-04-01

While most of the existing theoretical and simulation studies have focused on simple, spherical, halide and alkali ions, many chemically, biologically, and industrially relevant electrolytes involve complex non-spherical polyatomic ions like nitrate, chlorate, and sulfate to name only a few. Interestingly, some polyatomic ions in spite of being larger in size show anomalously high diffusivity and therefore cause a breakdown of the venerable Stokes-Einstein (S-E) relation between the size and diffusivity. Here we report a detailed analysis of the dynamics of anions in aqueous potassium nitrate (KNO3) and aqueous potassium acetate (CH3COOK) solutions. The two ions, nitrate (-NO3) and acetate (CH3-CO2 ), with their similar size show a large difference in diffusivity values. We present evidence that the translational motion of these polyatomic ions is coupled to the rotational motion of the ion. We show that unlike the acetate ion, nitrate ion with a symmetric charge distribution among all periphery oxygen atoms shows a faster rotational motion with large amplitude rotational jumps which enhances its translational motion due to translational-rotational coupling. By creating a family of modified-charge model systems, we have analysed the rotational motion of asymmetric polyatomic ions and the contribution of it to the translational motion. These model systems help clarifying and establishing the relative contribution of rotational motion in enhancing the diffusivity of the nitrate ion over the value predicted by the S-E relation and also over the other polyatomic ions having asymmetric charge distribution like the acetate ion. In the latter case, reduced rotational motion results in lower diffusivity values than those with symmetric charge distribution. We propose translational-rotational coupling as a general mechanism of the breakdown of the S-E relation in the case of polyatomic ions.

Rotation driven translational diffusion of polyatomic ions in water: A novel mechanism for breakdown of Stokes-Einstein relation.

PubMed

Banerjee, Puja; Yashonath, Subramanian; Bagchi, Biman

2017-04-28

While most of the existing theoretical and simulation studies have focused on simple, spherical, halide and alkali ions, many chemically, biologically, and industrially relevant electrolytes involve complex non-spherical polyatomic ions like nitrate, chlorate, and sulfate to name only a few. Interestingly, some polyatomic ions in spite of being larger in size show anomalously high diffusivity and therefore cause a breakdown of the venerable Stokes-Einstein (S-E) relation between the size and diffusivity. Here we report a detailed analysis of the dynamics of anions in aqueous potassium nitrate (KNO 3 ) and aqueous potassium acetate (CH 3 COOK) solutions. The two ions, nitrate (NO3-) and acetate (CH 3 CO2-), with their similar size show a large difference in diffusivity values. We present evidence that the translational motion of these polyatomic ions is coupled to the rotational motion of the ion. We show that unlike the acetate ion, nitrate ion with a symmetric charge distribution among all periphery oxygen atoms shows a faster rotational motion with large amplitude rotational jumps which enhances its translational motion due to translational-rotational coupling. By creating a family of modified-charge model systems, we have analysed the rotational motion of asymmetric polyatomic ions and the contribution of it to the translational motion. These model systems help clarifying and establishing the relative contribution of rotational motion in enhancing the diffusivity of the nitrate ion over the value predicted by the S-E relation and also over the other polyatomic ions having asymmetric charge distribution like the acetate ion. In the latter case, reduced rotational motion results in lower diffusivity values than those with symmetric charge distribution. We propose translational-rotational coupling as a general mechanism of the breakdown of the S-E relation in the case of polyatomic ions.

Formation of amorphous materials

DOEpatents

Johnson, William L.; Schwarz, Ricardo B.

1986-01-01

Metastable amorphous or fine crystalline materials are formed by solid state reactions by diffusion of a metallic component into a solid compound or by diffusion of a gas into an intermetallic compound. The invention can be practiced on layers of metals deposited on an amorphous substrate or by intermixing powders with nucleating seed granules. All that is required is that the diffusion of the first component into the second component be much faster than the self-diffusion of the first component. The method is practiced at a temperature below the temperature at which the amorphous phase transforms into one or more crystalline phases and near or below the temperature at which the ratio of the rate of diffusion of the first component to the rate of self-diffusion is at least 10.sup.4. This anomalous diffusion criteria is found in many binary, tertiary and higher ordered systems of alloys and appears to be found in all alloy systems that form amorphous materials by rapid quenching. The method of the invention can totally convert much larger dimensional materials to amorphous materials in practical periods of several hours or less.

Correlations, soliton modes, and non-Hermitian linear mode transmutation in the one-dimensional noisy Burgers equation.

PubMed

Fogedby, Hans C

2003-08-01

Using the previously developed canonical phase space approach applied to the noisy Burgers equation in one dimension, we discuss in detail the growth morphology in terms of nonlinear soliton modes and superimposed linear modes. We moreover analyze the non-Hermitian character of the linear mode spectrum and the associated dynamical pinning, and mode transmutation from diffusive to propagating behavior induced by the solitons. We discuss the anomalous diffusion of growth modes, switching and pathways, correlations in the multisoliton sector, and in detail the correlations and scaling properties in the two-soliton sector.

Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2015-01-01

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field-theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t') /k⊥d -1 +ξ , where k⊥=|k⊥| and k⊥ is the component of the wave vector, perpendicular to the distinguished direction ("direction of the flow")—the d -dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990), 10.1007/BF02161420]. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: Instead of powerlike corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L . The key point is that the matrices of scaling dimensions of the relevant families of composite operators appear nilpotent and cannot be diagonalized. The detailed proof of this fact is given for the correlation functions of arbitrary order.

Cooper Pair-Like Systems at High Temperature and their Role on Fluctuations Near the Critical Temperature

NASA Astrophysics Data System (ADS)

Ausloos, M.; Dorbolo, S.

A logarithmic behavior is hidden in the linear temperature regime of the electrical resistivity R(T) of some YBCO sample below 2Tc where "pairs" break apart, fluctuations occur and "a gap is opening". An anomalous effect also occurs near 200 K in the normal state Hall coefficient. In a simulation of oxygen diffusion in planar 123 YBCO, an anomalous behavior is found in the oxygen-vacancy motion near such a temperature. We claim that the behavior of the specific heat above and near the critical temperature should be reexamined in order to show the influence and implications of fluctuations and dimensionality on the nature of the phase transition and on the true onset temperature.

Modulation of galactic cosmic rays in solar cycles 22-24: Analysis and physical interpretation

NASA Astrophysics Data System (ADS)

Kalinin, M. S.; Bazilevskaya, G. A.; Krainev, M. B.; Svirzhevskaya, A. K.; Svirzhevsky, N. S.; Starodubtsev, S. A.

2017-09-01

This work represents a physical interpretation of cosmic ray modulation in the 22nd-24th solar cycles, including an interpretation of an unusual behavior of their intensity in the last minimum of the solar activity (2008-2010). In terms of the Parker modulation model, which deals with regularly measured heliospheric characteristics, it is shown that the determining factor of the increased intensity of the galactic cosmic rays in the minimum of the 24th solar cycle is an anomalous reduction of the heliospheric magnetic field strength during this time interval under the additional influence of the solar wind velocity and the tilt angle of the heliospheric current sheet. We have used in the calculations the dependence of the diffusion tensor on the rigidity in the form K ij ∝ R 2-μ with μ = 1.2 in the sector zones of the heliospheric magnetic field and with μ = 0.8 outside the sector zones, which leads to an additional amplification of the diffusion mechanism of cosmic ray modulation. The proposed approach allows us to describe quite satisfactorily the integral intensity of protons with an energy above 0.1 GeV and the energy spectra in the minima of the 22nd-24th solar cycles at the same value of the free parameter. The determining factor of the anomalously high level of the galactic cosmic ray intensity in the minimum of the 24th solar cycle is the significant reduction of the heliospheric magnetic field strength during this time interval. The forecast of the intensity level in the minimum of the 25th solar cycle is provided.

Thermodynamics, Diffusion, and Structure of Liquid NaAlSi3O8 at Elevated Temperature and Pressure from Molecular Dynamics Simulations

NASA Astrophysics Data System (ADS)

Neilson, R.; Spera, F. J.; Ghiorso, M. S.

2014-12-01

Thermodynamic properties of silicate melts at high temperature (T) and pressure (P) are crucial to understanding Earth accretion, magma oceans, petrogenesis, and crustal growth. However, equations of state for silicate liquids at mantle conditions are scarce, due to experimental challenges. Molecular Dynamics (MD) simulations allow investigation of thermodynamic and transport properties of silicate melts at high P and T and enable the correlation of liquid structure with computed properties. Using classical MD, we studied liquid NaAlSi3O8 in the range 0-42 GPa and 3000-5137 K. Density ranged from 2.2 to 3.6 g/cm3, and all simulations were performed in the microcanonical (NEV) ensemble using the potential from Matsui (1998). An equation of state with internal energy E(V,T) was developed using the RT scaling-Vinet formulation (Ghiorso et al., 2009). From thermodynamic relationships, the Grüneisen parameter, isobaric expansivity, isothermal compressibility, heat capacity, and other functions are computed over the P-T range of the MD simulations. Diffusion coefficients (D) range from 1.5×10-9 to 5.9×10-8 m2/s and typically order Na>Al>O>Si at a given state point. Generally, D decreases with P and increases with T except for a low P anomalous region along the 3065 K isotherm. Anomalous diffusion for Al, Si, and O is congruent with laboratory experiments at P<10 GPa (e.g., Shimizu and Kushiro, 1984; Poe et al., 1997; Tinker and Lesher, 2001; Tinker et al., 2003). Activation energy for Na is on the order of -75.3 kJ/mol with activation volume -1.74 cm3/mol. The anomalous peak in diffusivity for Si and O occurs at ~3 GPa, which marks a subtle increase in the average coordination number (CN) for O around O from 9.35 to 10.31. The average CN for O around O generally increases with P, but it systematically drops at 8, 15, and 20 GPa for 3065, 3944, and 5137 K, respectively. The concentrations of AlO5 and SiO5 polyhedra maximize near 16 and 35 GPa, respectively.

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

PubMed Central

Spiechowicz, Jakub; Łuczka, Jerzy; Hänggi, Peter

2016-01-01

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

Time analysis of volcanic activity on Io by means of plasma observations

NASA Technical Reports Server (NTRS)

Mekler, Y.; Eviatar, A.

1980-01-01

A model of Io volcanism in which the probability of activity obeys a binomial distribution is presented. Observed values of the electron density obtained over a 3-year period by ground-based spectroscopy are fitted to such a distribution. The best fit is found for a total number of 15 volcanoes with a probability of individual activity at any time of 0.143. The Pioneer 10 ultraviolet observations are reinterpreted as emissions of sulfur and oxygen ions and are found to be consistent with a plasma much less dense than that observed by the Voyager spacecraft. Late 1978 and the first half of 1979 are shown to be periods of anomalous volcanicity. Rapid variations in electron density are related to enhanced radial diffusion.

Incoherent neutron scattering in acetanilide and three deuterated derivatives

NASA Astrophysics Data System (ADS)

Barthes, Mariette; Almairac, Robert; Sauvajol, Jean-Louis; Moret, Jacques; Currat, Roland; Dianoux, José

1991-03-01

Incoherent-neutron-scattering measurements of the vibrational density of states of acetanilide and three deuterated derivatives are presented. These data allow one to identify an intense maximum, assigned to the N-H out-of-plane bending mode. The data display the specific behavior of the methyl torsional modes: large isotopic shift and strong low-temperature intensity; confirm our previous inelastic-neutron-scattering studies, indicating no obvious anomalies in the range of frequency of the acoustic phonons. In addition, the data show the existence of thermally activated quasielastic scattering above 100 K, assigned to the random diffusive motion of the methyl protons. These results are discussed in the light of recent theoretical models proposed to explain the anomalous optical properties of this crystal.

Chaotic Lagrangian models for turbulent relative dispersion.

PubMed

Lacorata, Guglielmo; Vulpiani, Angelo

2017-04-01

A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.

Chaotic Lagrangian models for turbulent relative dispersion

NASA Astrophysics Data System (ADS)

Lacorata, Guglielmo; Vulpiani, Angelo

2017-04-01

A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.

Nonlinear Analysis of Surface EMG Time Series of Back Muscles

NASA Astrophysics Data System (ADS)

Dolton, Donald C.; Zurcher, Ulrich; Kaufman, Miron; Sung, Paul

2004-10-01

A nonlinear analysis of surface electromyography time series of subjects with and without low back pain is presented. The mean-square displacement and entropy shows anomalous diffusive behavior on intermediate time range 10 ms < t < 1 s. This behavior implies the presence of correlations in the signal. We discuss the shape of the power spectrum of the signal.

DUST IN ACTIVE GALACTIC NUCLEI: ANOMALOUS SILICATE TO OPTICAL EXTINCTION RATIOS?

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

Lyu, Jianwei; Hao, Lei; Li, Aigen, E-mail: haol@shao.ac.cn

Dust plays a central role in the unification theory of active galactic nuclei (AGNs). However, little is known about the nature (e.g., size, composition) of the dust that forms a torus around the AGN. In this Letter, we report a systematic exploration of the optical extinction (A{sub V} ) and the silicate absorption optical depth (Δτ{sub 9.7}) of 110 type 2 AGNs. We derive A{sub V} from the Balmer decrement based on the Sloan Digital Sky Survey data, and Δτ{sub 9.7} from the Spitzer/InfraRed Spectrograph data. We find that with a mean ratio of (A{sub V} /Δτ{sub 9.7}) ≲ 5.5, themore » optical-to-silicate extinction ratios of these AGNs are substantially lower than that of the Galactic diffuse interstellar medium (ISM) for which A{sub V} /Δτ{sub 9.7} ≈ 18.5. We argue that the anomalously low A{sub V} /Δτ{sub 9.7} ratio could be due to the predominance of larger grains in the AGN torus compared to that in the Galactic diffuse ISM.« less

Internal Shocks in the Magnetic Reconnection Jet in Solar Flares: Multiple Fast Shocks Created by the Secondary Tearing Instability

NASA Astrophysics Data System (ADS)

Tanuma, S.; Shibata, K.

2005-07-01

Space solar missions such as Yohkoh and RHESSI observe the hard X- and gamma-ray emission from energetic electrons in impulsive solar flares. Their energization mechanism, however, is unknown. In this Letter, we suggest that the internal shocks are created in the reconnection jet and that they are possible sites of particle acceleration. We examine how magnetic reconnection creates the multiple shocks by performing two-dimensional resistive magnetohydrodynamic simulations. In this Letter, we use a very small grid to resolve the diffusion region. As a result, we find that the current sheet becomes thin due to the tearing instability, and it collapses to a Sweet-Parker sheet. The thin sheet becomes unstable to the secondary tearing instability. Fast reconnection starts by the onset of anomalous resistivity immediately after the secondary tearing instability. During the bursty, time-dependent magnetic reconnection, the secondary tearing instability continues in the diffusion region where the anomalous resistivity is enhanced. As a result, many weak shocks are created in the reconnection jet. This situation produces turbulent reconnection. We suggest that multiple fast shocks are created in the jet and that the energetic electrons can be accelerated by these shocks.

The QUIJOTE experiment

NASA Astrophysics Data System (ADS)

López-Caniego, Marcos

2015-08-01

The QUIJOTE (Q-U-I JOint Tenerife) CMB Experiment is observing the polarization of the Cosmic Microwave Background and other Galactic and extragalactic signals at medium and large angular scales in the frequency range of 10-40 GHz. This experiment will provide valuable information about the polarization properties of synchrotron and anomalous microwave emission at these frequencies. The maps obtained with the multi-frequency instrument (10-20 GHz), in combination with data from other experiments like Planck and the VLA, will be used to clean the diffuse and compact foreground emission at 30 and 40 GHz, the cosmological channels. After three years of effective observations we expect to reach the required sensitivity to detect a primordial gravitational-wave component if the tensor-to-scalar ratio is larger than r = 0.05. At the moment we have completed the Wide Survey with the multi-frequency instrument, covering 20.000 square degrees of the Northern hemisphere. In addition, we have deep integrations of our main calibrators Taurus A, Cassiopea A, Jupiter and of the Perseus molecular complex region, where we have measured the spectrum of the anomalous microwave emission. We also have observed several regions of interest for our science program where we plan to study the compact and diffuse polarized emission.

Levitation effect in zeolites: Quasielastic neutron scattering and molecular dynamics study of pentane isomers in zeolite NaY.

PubMed

Borah, Bhaskar J; Jobic, H; Yashonath, S

2010-04-14

We report the quasielastic neutron scattering (QENS) and molecular dynamics (MD) investigations into diffusion of pentane isomers in zeolite NaY. The molecular cross section perpendicular to the long molecular axis varies for the three isomers while the mass and the isomer-zeolite interaction remains essentially unchanged. Both QENS and MD results show that the branched isomers neopentane and isopentane have higher self-diffusivities as compared with n-pentane at 300 K in NaY zeolite. This result provides direct experimental evidence for the existence of nonmonotonic, anomalous dependence of self-diffusivity on molecular diameter known as the levitation effect. The energetic barrier at the bottleneck derived from MD simulations exists for n-pentane which lies in the linear regime while no such barrier is seen for neopentane which is located clearly in the anomalous regime. Activation energy is in the order E(a)(n-pentane)>E(a)(isopentane)>E(a)(neopentane) consistent with the predictions of the levitation effect. In the liquid phase, it is seen that D(n-pentane)>D(isopentane)>D(neopentane) and E(a)(n-pentane)

Levitation effect in zeolites: Quasielastic neutron scattering and molecular dynamics study of pentane isomers in zeolite NaY

NASA Astrophysics Data System (ADS)

Borah, Bhaskar J.; Jobic, H.; Yashonath, S.

2010-04-01

We report the quasielastic neutron scattering (QENS) and molecular dynamics (MD) investigations into diffusion of pentane isomers in zeolite NaY. The molecular cross section perpendicular to the long molecular axis varies for the three isomers while the mass and the isomer-zeolite interaction remains essentially unchanged. Both QENS and MD results show that the branched isomers neopentane and isopentane have higher self-diffusivities as compared with n-pentane at 300 K in NaY zeolite. This result provides direct experimental evidence for the existence of nonmonotonic, anomalous dependence of self-diffusivity on molecular diameter known as the levitation effect. The energetic barrier at the bottleneck derived from MD simulations exists for n-pentane which lies in the linear regime while no such barrier is seen for neopentane which is located clearly in the anomalous regime. Activation energy is in the order Ea(n-pentane)>Ea(isopentane)>Ea(neopentane) consistent with the predictions of the levitation effect. In the liquid phase, it is seen that D(n-pentane)>D(isopentane)>D(neopentane) and Ea(n-pentane)

Effect of Al-diffusion-induced positive flatband voltage shift on the electrical characteristics of Al-incorporated high-k metal-oxide-semiconductor field-effective transistor

NASA Astrophysics Data System (ADS)

Wang, Wenwu; Akiyama, Koji; Mizubayashi, Wataru; Nabatame, Toshihide; Ota, Hiroyuki; Toriumi, Akira

2009-03-01

We systematically studied what effect Al diffusion from high-k dielectrics had on the flatband voltage (Vfb) of Al-incorporated high-k gate stacks. An anomalous positive shift fin Vfb with the decreasing equivalent oxide thickness (EOT) of high-k gate stacks is reported. As the SiO2 interfacial layer is aggressively thinned in Al-incorporated HfxAl1-xOy gate stacks with a metal-gate electrode, the Vfb first lies on the well known linear Vfb-EOT plot and deviates toward the positive-voltage direction (Vfb roll-up), followed by shifting toward negative voltage (Vfb roll-off). We demonstrated that the Vfb roll-up behavior remarkably decreases the threshold voltage (Vth) of p-type metal-oxide-semiconductor field-effect transistors (p-MOSFETs), and does not cause severe degradation in the characteristics of hole mobility. The Vfb roll-up behavior, which is independent of gate materials but strongly dependent on high-k dielectrics, was ascribed to variations in fixed charges near the SiO2/Si interface, which are caused by Al diffusion from HfxAl1-xOy through SiO2 to the SiO2/Si interface. These results indicate that anomalous positive shift in Vfb, i.e., Vfb roll-up, should be taken into consideration in quantitatively adjusting Vfb in thin EOT regions and that it could be used to further tune Vth in p-MOSFETs.

Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: two-loop approximation.

PubMed

Adzhemyan, L Ts; Antonov, N V; Honkonen, J; Kim, T L

2005-01-01

The field theoretic renormalization group and operator-product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the Navier-Stokes equation, subject to an external random stirring force with the correlation function proportional to delta(t- t')k(4-d-2epsilon). It is shown that the scalar field is intermittent already for small epsilon, its structure functions display anomalous scaling behavior, and the corresponding exponents can be systematically calculated as series in epsilon. The practical calculation is accomplished to order epsilon2 (two-loop approximation), including anisotropic sectors. As for the well-known Kraichnan rapid-change model, the anomalous scaling results from the existence in the model of composite fields (operators) with negative scaling dimensions, identified with the anomalous exponents. Thus the mechanism of the origin of anomalous scaling appears similar for the Gaussian model with zero correlation time and the non-Gaussian model with finite correlation time. It should be emphasized that, in contrast to Gaussian velocity ensembles with finite correlation time, the model and the perturbation theory discussed here are manifestly Galilean covariant. The relevance of these results for real passive advection and comparison with the Gaussian models and experiments are briefly discussed.

Theoretical model for a Faraday anomalous dispersion optical filter

NASA Technical Reports Server (NTRS)

Yin, B.; Shay, T. M.

1991-01-01

A model for the Faraday anomalous dispersion optical filter is presented. The model predicts a bandwidth of 0.6 GHz and a transmission peak of 0.98 for a filter operating on the Cs (D2) line. The model includes hyperfine effects and is valid for arbitrary magnetic fields.

Scaling relation of the anomalous Hall effect in (Ga,Mn)As

NASA Astrophysics Data System (ADS)

Glunk, M.; Daeubler, J.; Schoch, W.; Sauer, R.; Limmer, W.

2009-09-01

We present magnetotransport studies performed on an extended set of (Ga,Mn)As samples at 4.2 K with longitudinal conductivities σxx ranging from the low-conductivity to the high-conductivity regime. The anomalous Hall conductivity σxy(AH) is extracted from the measured longitudinal and Hall resistivities. A transition from σxy(AH)=20Ω-1cm-1 due to the Berry phase effect in the high-conductivity regime to a scaling relation σxy(AH)∝σxx1.6 for low-conductivity samples is observed. This scaling relation is consistent with a recently developed unified theory of the anomalous Hall effect in the framework of the Keldysh formalism. It turns out to be independent of crystallographic orientation, growth conditions, Mn concentration, and strain, and can therefore be considered universal for low-conductivity (Ga,Mn)As. The relation plays a crucial role when deriving values of the hole concentration from magnetotransport measurements in low-conductivity (Ga,Mn)As. In addition, the hole diffusion constants for the high-conductivity samples are determined from the measured longitudinal conductivities.

Chiral anomaly and anomalous finite-size conductivity in graphene

NASA Astrophysics Data System (ADS)

Shen, Shun-Qing; Li, Chang-An; Niu, Qian

2017-09-01

Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two spin degenerate pairs of massless two-dimensional Dirac fermions with different chirality. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of a zigzag nanoribbon and some anomalous transport properties. Here it is proposed that the Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges of Dirac fermions at different valleys can be realized in a confined ribbon of finite width, even in the absence of a magnetic field. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and is inversely proportional to the square of the lateral dimension W, which is different from the finite-size correction inversely proportional to W from the boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and it is measurable experimentally. This finding provides an alternative platform to explore the purely quantum mechanical effect in graphene.

The use of copula functions for predictive analysis of correlations between extreme storm tides

NASA Astrophysics Data System (ADS)

Domino, Krzysztof; Błachowicz, Tomasz; Ciupak, Maurycy

2014-11-01

In this paper we present a method used in quantitative description of weakly predictable hydrological, extreme events at inland sea. Investigations for correlations between variations of individual measuring points, employing combined statistical methods, were carried out. As a main tool for this analysis we used a two-dimensional copula function sensitive for correlated extreme effects. Additionally, a new proposed methodology, based on Detrended Fluctuations Analysis (DFA) and Anomalous Diffusion (AD), was used for the prediction of negative and positive auto-correlations and associated optimum choice of copula functions. As a practical example we analysed maximum storm tides data recorded at five spatially separated places at the Baltic Sea. For the analysis we used Gumbel, Clayton, and Frank copula functions and introduced the reversed Clayton copula. The application of our research model is associated with modelling the risk of high storm tides and possible storm flooding.

Anomalous transport in cellular flows: The role of initial conditions and aging

NASA Astrophysics Data System (ADS)

Pöschke, Patrick; Sokolov, Igor M.; Nepomnyashchy, Alexander A.; Zaks, Michael A.

2016-09-01

We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples of subdiffusive tracer motion) and concentrate on the intermediate time range, in which the tracer motion indeed may show subdiffusion. We perform extensive numerical simulations of the systems under different initial conditions and show that the pure intermediate-time subdiffusion regime is only evident when the particles start at the border between different cells, i.e., at the separatrix, and is less pronounced or absent for other initial conditions. The motion moreover shows quite peculiar aging properties, which are also mirrored in the behavior of the time-averaged mean squared displacement for single trajectories. This kind of behavior is due to the complex motion of tracers trapped inside the cell and is absent in classical models based on continuous-time random walks with no dynamics in the trapped state.

Revealing nonergodic dynamics in living cells from a single particle trajectory

NASA Astrophysics Data System (ADS)

Lanoiselée, Yann; Grebenkov, Denis S.

2016-05-01

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

Growth rate of crystalline ice and the diffusivity of supercooled water from 126 to 262 K

DOE PAGES

Xu, Yuntao; Petrik, Nikolay G.; Smith, R. Scott; ...

2016-12-12

Understanding deeply supercooled water is key to unraveling many of water’s anomalous properties. However, this has proven difficult due to rapid and uncontrolled crystallization. Using a pulsed laser heating technique, we measure the growth rate of crystalline ice, G(T), for 180 K < T < 262 K, i.e. deep within water’s “no man’s land.” The self-diffusion of supercooled liquid water, D(T), is obtained from G(T) using the Wilson-Frenkel model of crystal growth. For T > 237 K, G(T) and D(T) have super-Arrhenius (“fragile”) temperature dependences, but both crossover to Arrhenius (“strong”) behavior with a large activation energy in “no man’smore » land.” The fact that G(T) and D(T) are smoothly varying rules out the hypothesis that liquid water’s properties have a singularity at or near 228 K. However the results are consistent with a previous prediction for D(T) that assumed no thermodynamic transitions occur in “no man’s land.« less

Creating unstable velocity-space distributions with barium injections

NASA Technical Reports Server (NTRS)

Pongratz, M. B.

1983-01-01

Ion velocity-space distributions resulting from barium injections from orbiting spacecraft and shaped charges are discussed. Active experiments confirm that anomalous ionization processes may operate, but photoionization accounts for the production of the bulk of the barium ions. Pitch-angle diffusion and/or velocity-space diffusion may occur, but observations of barium ions moving upwards against gravity suggests that the ions retain a significant enough fraction of their initial perpendicular velocity to provide a mirror force. The barium ion plasmas should have a range of Alfven Mach numbers and plasma betas. Because the initial conditions can be predicted these active experiments should permit testing plasma instability hypotheses.

Reduction of ion thermal diffusivity associated with the transition of the radial electric field in neutral-beam-heated plasmas in the large helical device.

PubMed

Ida, K; Funaba, H; Kado, S; Narihara, K; Tanaka, K; Takeiri, Y; Nakamura, Y; Ohyabu, N; Yamazaki, K; Yokoyama, M; Murakami, S; Ashikawa, N; deVries, P C; Emoto, M; Goto, M; Idei, H; Ikeda, K; Inagaki, S; Inoue, N; Isobe, M; Itoh, K; Kaneko, O; Kawahata, K; Khlopenkov, K; Komori, A; Kubo, S; Kumazawa, R; Liang, Y; Masuzaki, S; Minami, T; Miyazawa, J; Morisaki, T; Morita, S; Mutoh, T; Muto, S; Nagayama, Y; Nakanishi, H; Nishimura, K; Noda, N; Notake, T; Kobuchi, T; Ohdachi, S; Ohkubo, K; Oka, Y; Osakabe, M; Ozaki, T; Pavlichenko, R O; Peterson, B J; Sagara, A; Saito, K; Sakakibara, S; Sakamoto, R; Sanuki, H; Sasao, H; Sasao, M; Sato, K; Sato, M; Seki, T; Shimozuma, T; Shoji, M; Suzuki, H; Sudo, S; Tamura, N; Toi, K; Tokuzawa, T; Torii, Y; Tsumori, K; Yamamoto, T; Yamada, H; Yamada, I; Yamaguchi, S; Yamamoto, S; Yoshimura, Y; Watanabe, K Y; Watari, T; Hamada, Y; Motojima, O; Fujiwara, M

2001-06-04

Recent large helical device experiments revealed that the transition from ion root to electron root occurred for the first time in neutral-beam-heated discharges, where no nonthermal electrons exist. The measured values of the radial electric field were found to be in qualitative agreement with those estimated by neoclassical theory. A clear reduction of ion thermal diffusivity was observed after the mode transition from ion root to electron root as predicted by neoclassical theory when the neoclassical ion loss is more dominant than the anomalous ion loss.

Convection in a colloidal suspension in a closed horizontal cell

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

Smorodin, B. L., E-mail: bsmorodin@yandex.ru; Cherepanov, I. N.

2015-02-15

The experimentally detected [1] oscillatory regimes of convection in a colloidal suspension of nanoparticles with a large anomalous thermal diffusivity in a closed horizontal cell heated from below have been simulated numerically. The concentration inhomogeneity near the vertical cavity boundaries arising from the interaction of thermal-diffusion separation and convective mixing has been proven to serve as a source of oscillatory regimes (traveling waves). The dependence of the Rayleigh number at the boundary of existence of the traveling-wave regime on the aspect ratio of the closed cavity has been established. The spatial characteristics of the emerging traveling waves have been determined.

Memory beyond memory in heart beating, a sign of a healthy physiological condition.

PubMed

Allegrini, P; Grigolini, P; Hamilton, P; Palatella, L; Raffaelli, G

2002-04-01

We describe two types of memory and illustrate each using artificial and actual heartbeat data sets. The first type of memory, yielding anomalous diffusion, implies the inverse power-law nature of the waiting time distribution and the second the correlation among distinct times, and consequently also the occurrence of many pseudoevents, namely, not genuinely random events. Using the method of diffusion entropy analysis, we establish the scaling that would be determined by the real events alone. We prove that the heart beating of healthy patients reveals the existence of many more pseudoevents than in the patients with congestive heart failure.

Diffusion in jammed particle packs

NASA Astrophysics Data System (ADS)

Bolintineanu, Dan S.; Silbert, Leonardo E.; Grest, Gary S.; Lechman, Jeremy B.

2015-03-01

Diffusive transport in jammed particle packs is of interest for a number of applications, as well as being a potential indicator of structural properties near the jamming point. To this end, we report stochastic simulations of equilibrium diffusion through monodisperse sphere packs near the jamming point in the limit of a perfectly insulating surrounding medium. The time dependence of various diffusion properties is resolved over several orders of magnitude. Two time regimes of expected Fickian diffusion are observed, separated by an intermediate regime of anomalous diffusion. This intermediate regime grows as the particle volume fraction approaches the critical jamming transition. The diffusion behavior is fully controlled by the extent of the contacts between neighboring particles, which in turn depend on proximity to the jamming point. In particular, the mean first passage time associated with the escape of random walkers between neighboring particles is shown to control both the time to recover Fickian diffusion and the long time diffusivity. Scaling laws are established that relate these quantities to the difference between the actual and critical jamming volume fractions. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's NNSA under Contract DE- AC04-94AL85000.

Anomalous evolution of Ar metastable density with electron density in high density Ar discharge

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

Park, Min; Chang, Hong-Young; You, Shin-Jae

2011-10-15

Recently, an anomalous evolution of argon metastable density with plasma discharge power (electron density) was reported [A. M. Daltrini, S. A. Moshkalev, T. J. Morgan, R. B. Piejak, and W. G. Graham, Appl. Phys. Lett. 92, 061504 (2008)]. Although the importance of the metastable atom and its density has been reported in a lot of literature, however, a basic physics behind the anomalous evolution of metastable density has not been clearly understood yet. In this study, we investigated a simple global model to elucidate the underlying physics of the anomalous evolution of argon metastable density with the electron density. Onmore » the basis of the proposed simple model, we reproduced the anomalous evolution of the metastable density and disclosed the detailed physics for the anomalous result. Drastic changes of dominant mechanisms for the population and depopulation processes of Ar metastable atoms with electron density, which take place even in relatively low electron density regime, is the clue to understand the result.« less

Searching for the fourth family quarks through anomalous decays

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

Sahin, M.; Sultansoy, S.; Turkoz, S.

2010-09-01

The flavor democracy hypothesis predicts the existence of the fourth standard model family. Because of the high masses of the fourth family quarks, their anomalous decays could be dominant if certain criteria are met. This will drastically change the search strategy at hadron colliders. We show that the fourth standard model family down quarks with masses up to 400-450 GeV can be observed (or excluded) via anomalous decays by Tevatron.

Anomalous behavior of curves of pseudo-elastic deformation of Ni-Fe-Ga-Co alloy crystals as a result of interphase stresses

NASA Astrophysics Data System (ADS)

Malygin, G. A.; Nikolaev, V. I.; Averkin, A. I.; Zograf, A. P.

2016-12-01

The compression diagram of Ni49Fe18Ga27Co6 alloy crystals in the [011] direction was studied until full shape memory strain at various temperatures in the range of 259-340 K. It is found that all load curves are anomalously shaped and contain portions of sharp and gradual decreases in deformation stresses. Simulation of pseudo-elastic stress-strain curves within the theory of diffuse martensitic transitions, describing not only equilibrium of phases, but also the kinetics of the transition between them, shows that elastic interphase stresses during martensitic reactions Ll 2 → 14 M and 14 M → Ll 0 characteristic of this alloy can be responsible for the extraordinary shape of compression diagrams.

Anomalous Nonlocal Resistance and Spin-Charge Conversion Mechanisms in Two-Dimensional Metals

NASA Astrophysics Data System (ADS)

Huang, Chunli; Chong, Y. D.; Cazalilla, Miguel A.

2017-09-01

We uncover two anomalous features in the nonlocal transport behavior of two-dimensional metallic materials with spin-orbit coupling. First, the nonlocal resistance can have negative values and oscillate with distance, even in the absence of a magnetic field. Second, the oscillations of the nonlocal resistance under an applied in-plane magnetic field (the Hanle effect) can be asymmetric under field reversal. Both features are produced by direct magnetoelectric coupling, which is possible in materials with broken inversion symmetry but was not included in previous spin-diffusion theories of nonlocal transport. These effects can be used to identify the relative contributions of different spin-charge conversion mechanisms. They should be observable in adatom-functionalized graphene, and they may provide the reason for discrepancies in recent nonlocal transport experiments on graphene.

Effect of double layers on magnetosphere-ionosphere coupling

NASA Technical Reports Server (NTRS)

Lysak, Robert L.; Hudson, Mary K.

1987-01-01

The Earth's auroral zone contains dynamic processes occurring on scales from the length of an auroral zone field line which characterizes Alfven wave propagation to the scale of microscopic processes which occur over a few Debye lengths. These processes interact in a time-dependent fashion since the current carried by the Alfven waves can excite microscopic turbulence which can in turn provide dissipation of the Alfven wave energy. This review will first describe the dynamic aspects of auroral current structures with emphasis on consequences for models of microscopic turbulence. A number of models of microscopic turbulence will be introduced into a large-scale model of Alfven wave propagation to determine the effect of various models on the overall structure of auroral currents. In particular, the effects of a double layer electric field which scales with the plasma temperature and Debye length is compared with the effect of anomalous resistivity due to electrostatic ion cyclotron turbulence in which the electric field scales with the magnetic field strength. It is found that the double layer model is less diffusive than in the resistive model leading to the possibility of narrow, intense current structures.

A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability

PubMed Central

Kedem, O.; Katchalsky, A.

1961-01-01

A "translation" of the phenomenological permeability coefficients into friction and distribution coefficients amenable to physical interpretation is presented. Expressions are obtained for the solute permeability coefficient ω and the reflection coefficient σ for both non-electrolytic and electrolytic permeants. An analysis of the coefficients is given for loose membranes as well as for dense natural membranes where transport may go through capillaries or by solution in the lipoid parts of the membrane. Water diffusion and filtration and the relation between these and capillary pore radius of the membrane are discussed. For the permeation of ions through the charged membranes equations are developed for the case of zero electrical current in the membrane. The correlation of σ with ω and Lp for electrolytes resembles that for non-electrolytes. In this case ω and σ depend markedly on ion concentration and on the charge density of the membrane. The reflection coefficient may assume negative values indicating anomalous osmosis. An analysis of the phenomena of anomalous osmosis was carried out for the model of Teorell and Meyer and Sievers and the results agree with the experimental data of Loeb and of Grim and Sollner. A set of equations and reference curves are presented for the evaluation of ω and σ in the transport of polyvalent ions through charged membranes. PMID:13752127

Precursory signals of the 2014-15 Fogo eruption (Cape Verde) detected by surface CO2 emission and heat flow observations

NASA Astrophysics Data System (ADS)

Pérez, Nemesio M.; Dionis, Samara; Fernandes, Paulo; Barrancos, José; Rodríguez, Fátima; Bandomo, Zuleyka; Hernández, Pedro A.; Melián, Gladys V.; Silva, Sónia; Padilla, Germán; Padrón, Eleazar; Cabral, Jeremias; Calvo, David; Asensio-Ramos, María; Pereira, José Manuel; Gonçalves, António A.; Barros, Inocencio; Semedo, Helio

2015-04-01

On November 23, 2014 a new eruption occurred at Fogo volcano (Cape Verde) after 19 years of the last eruptive event in 1995. In the case of the 1995 Fogo eruption, a volcano monitoring program for the volcanic surveillance of Fogo did not exist. On the contrary, a simple and multidisciplinary volcano monitoring program was initiated since 2007 to detect early warning signals of a new volcanic unrest such as the 2014-15 Fogo eruption. Diffuse CO2 emission surveys at the summit crater of Pico do Fogo volcano were periodically carried out from May 2007 to October 2014 to provide this multidisciplinary approach and to monitor potential volcanic activity changes. During this 7 year period, CO2 efflux ranged from non detectable (< 1.5 g m-2 d-1) up to relatively high (61.9 kg m-2 d-1) values. The observed average δ13C- CO2 values related to these diffuse CO2 emission surveys ranged from -22.1 to 1.6 ‰, and surface heat flux measurements, following the method of Dawson (1964), showed also a wide range of values from 0.1 to 460 W m-2. Areas with the highest observed CO2 efflux values were also characterized by a relatively high soil temperature and an intense surface hydrothermal alteration, which supports that degassing process is primary controlled by an advective mechanism generated by geothermal gradients (convection). Two periods of anomalous diffuse CO2 emission were observed between February 2009 to February 2010 and March to August 2014, respectively. Rest of surveys showed the lowest variability on diffuse CO2 emission, ranging from 23 to 186 t d-1 (average = 86 t d-1). The first anomalous period was characterized by a sharp increase on diffuse CO2 emission, suggesting the first magma intrusion beneath Pico do Fogo volcano. This observation is also supported by a significant change on the δ13C- CO2 signature from May 2009 (-10.2 ‰) to February 2010 (-6.1‰) of the diffuse CO2 degassing, indicating an enrichment on the magmatic CO2 component. On February 2010, the diffuse CO2 emission rate was 219 ± 36 t d-1 (Dionis et al., 2015). The second anomalous period started on March 2014, eight months before the 2014-15 Fogo eruption onset, and reached a relatively high value of 337 ± 119 t d-1 on August 30, 2014. It was likely caused by rising of magmatic gases from a second magma intrusion which ended on an eruption. Heat flow temporal evolution during the observation period also shows a quasi-continuous increase before the eruption onset, with the maximum observed heat flow (16.4 ± 3.4 MW) on March 2014. These geochemical and geophysical evidences are clearly precursory signals of the 2014-15 Fogo eruption. Dawson, G.B. (1964), N Z J Geol Geophys 7:155-171; Dionis S. et al. (2015), Bull. Volcanol., in press

Evidence for anisotropic polar nanoregions in relaxor Pb(Mg1/3Nb2/3)O3: A neutron study of the elastic constants and anomalous TA phonon damping in PMN

NASA Astrophysics Data System (ADS)

Stock, C.; Gehring, P. M.; Hiraka, H.; Swainson, I.; Xu, Guangyong; Ye, Z.-G.; Luo, H.; Li, J.-F.; Viehland, D.

2012-09-01

We use neutron inelastic scattering to characterize the acoustic phonons in the relaxor Pb(Mg1/3Nb2/3)O3 (PMN) and demonstrate the presence of a highly anisotropic damping mechanism that is directly related to short-range polar correlations. For a large range of temperatures above Tc˜210 K, where dynamic, short-range polar correlations are present, acoustic phonons propagating along [11¯0] and polarized along [110] (TA2 phonons) are overdamped and softened across most of the Brillouin zone. By contrast, acoustic phonons propagating along [100] and polarized along [001] (TA1 phonons) are overdamped and softened for a more limited range of wave vectors q. The anisotropy and temperature dependence of the acoustic phonon energy linewidth Γ are directly correlated with neutron diffuse scattering cross section, indicating that polar nanoregions are the cause of the anomalous behavior. The damping and softening vanish for q→0, i.e., for long-wavelength acoustic phonons near the zone center, which supports the notion that the anomalous damping is a result of the coupling between the relaxational component of the diffuse scattering and the harmonic TA phonons. Therefore, these effects are not due to large changes in the elastic constants with temperature because the elastic constants correspond to the long-wavelength limit. We compare the elastic constants we measure to those from Brillouin scattering experiments and to values reported for pure PbTiO3. We show that while the values of C44 are quite similar, those for C11 and C12 are significantly less in PMN and result in a softening of (C11-C12) over PbTiO3. The elastic constants also show an increased elastic anisotropy [2C44/(C11-C12)] in PMN versus that in PbTiO3. These results are suggestive of an instability to TA2 acoustic fluctuations in PMN and other relaxor ferroelectrics. We discuss our results in the context of the current debate over the “waterfall” effect and show that they are inconsistent with acoustic-optic phonon coupling or other models that invoke the presence of a second, low-energy optic mode.

AN UPDATED MODEL FOR THE ANOMALOUS RESISITIVITY OF LNAPL PLUMES IN SANDY ENVIRONMENTS

EPA Science Inventory

Anomalously low resistivities have been observed at some sites contaminated by light nonaqueous phase liquid (LNAPL) since 1997. The conductive model that has been used to explain this phenomenon was published in 2000. The working hypothesis in the conductive model invokes both p...

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

Complete description of all self-similar models driven by Lévy stable noise

NASA Astrophysics Data System (ADS)

Weron, Aleksander; Burnecki, Krzysztof; Mercik, Szymon; Weron, Karina

2005-01-01

A canonical decomposition of H -self-similar Lévy symmetric α -stable processes is presented. The resulting components completely described by both deterministic kernels and the corresponding stochastic integral with respect to the Lévy symmetric α -stable motion are shown to be related to the dissipative and conservative parts of the dynamics. This result provides stochastic analysis tools for study the anomalous diffusion phenomena in the Langevin equation framework. For example, a simple computer test for testing the origins of self-similarity is implemented for four real empirical time series recorded from different physical systems: an ionic current flow through a single channel in a biological membrane, an energy of solar flares, a seismic electric signal recorded during seismic Earth activity, and foreign exchange rate daily returns.

Anomaly clustering in hyperspectral images

NASA Astrophysics Data System (ADS)

Doster, Timothy J.; Ross, David S.; Messinger, David W.; Basener, William F.

2009-05-01

The topological anomaly detection algorithm (TAD) differs from other anomaly detection algorithms in that it uses a topological/graph-theoretic model for the image background instead of modeling the image with a Gaussian normal distribution. In the construction of the model, TAD produces a hard threshold separating anomalous pixels from background in the image. We build on this feature of TAD by extending the algorithm so that it gives a measure of the number of anomalous objects, rather than the number of anomalous pixels, in a hyperspectral image. This is done by identifying, and integrating, clusters of anomalous pixels via a graph theoretical method combining spatial and spectral information. The method is applied to a cluttered HyMap image and combines small groups of pixels containing like materials, such as those corresponding to rooftops and cars, into individual clusters. This improves visualization and interpretation of objects.

Can I solve my structure by SAD phasing? Anomalous signal in SAD phasing

DOE PAGES

Terwilliger, Thomas C.; Bunkóczi, Gábor; Hung, Li-Wei; ...

2016-03-01

A key challenge in the SAD phasing method is solving a structure when the anomalous signal-to-noise ratio is low. We present a simple theoretical framework for describing measurements of anomalous differences and the resulting useful anomalous correlation and anomalous signal in a SAD experiment. Here, the useful anomalous correlation is defined as the correlation of anomalous differences with ideal anomalous differences from the anomalous substructure. The useful anomalous correlation reflects the accuracy of the data and the absence of minor sites. The useful anomalous correlation also reflects the information available for estimating crystallographic phases once the substructure has been determined.more » In contrast, the anomalous signal (the peak height in a model-phased anomalous difference Fourier at the coordinates of atoms in the anomalous substructure) reflects the information available about each site in the substructure and is related to the ability to find the substructure. A theoretical analysis shows that the expected value of the anomalous signal is the product of the useful anomalous correlation, the square root of the ratio of the number of unique reflections in the data set to the number of sites in the substructure, and a function that decreases with increasing values of the atomic displacement factor for the atoms in the substructure. In conclusion, this means that the ability to find the substructure in a SAD experiment is increased by high data quality and by a high ratio of reflections to sites in the substructure, and is decreased by high atomic displacement factors for the substructure.« less

Can I solve my structure by SAD phasing? Anomalous signal in SAD phasing.

PubMed

Terwilliger, Thomas C; Bunkóczi, Gábor; Hung, Li Wei; Zwart, Peter H; Smith, Janet L; Akey, David L; Adams, Paul D

2016-03-01

A key challenge in the SAD phasing method is solving a structure when the anomalous signal-to-noise ratio is low. A simple theoretical framework for describing measurements of anomalous differences and the resulting useful anomalous correlation and anomalous signal in a SAD experiment is presented. Here, the useful anomalous correlation is defined as the correlation of anomalous differences with ideal anomalous differences from the anomalous substructure. The useful anomalous correlation reflects the accuracy of the data and the absence of minor sites. The useful anomalous correlation also reflects the information available for estimating crystallographic phases once the substructure has been determined. In contrast, the anomalous signal (the peak height in a model-phased anomalous difference Fourier at the coordinates of atoms in the anomalous substructure) reflects the information available about each site in the substructure and is related to the ability to find the substructure. A theoretical analysis shows that the expected value of the anomalous signal is the product of the useful anomalous correlation, the square root of the ratio of the number of unique reflections in the data set to the number of sites in the substructure, and a function that decreases with increasing values of the atomic displacement factor for the atoms in the substructure. This means that the ability to find the substructure in a SAD experiment is increased by high data quality and by a high ratio of reflections to sites in the substructure, and is decreased by high atomic displacement factors for the substructure.

Surface Parameters of Titan Feature Classes From Cassini RADAR Backscatter Measurements

NASA Astrophysics Data System (ADS)

Wye, L. C.; Zebker, H. A.; Lopes, R. M.; Peckyno, R.; Le Gall, A.; Janssen, M. A.

2008-12-01

Multimode microwave measurements collected by the Cassini RADAR instrument during the spacecraft's first four years of operation form a fairly comprehensive set of radar backscatter data over a variety of Titan surface features. We use the real-aperture scatterometry processor to analyze the entire collection of active data, creating a uniformly-calibrated dataset that covers 93% of Titan's surface at a variety of viewing angles. Here, we examine how the measured backscatter response (radar reflectivity as a function of incidence angle) varies with surface feature type, such as dunes, cryovolcanic areas, and anomalous albedo terrain. We identify the feature classes using a combination of maps produced by the RADAR, ISS, and VIMS instruments. We then derive surface descriptors including roughness, dielectric constant, and degree of volume scatter. Radar backscatter on Titan is well-modeled as a superposition of large-scale surface scattering (quasispecular scattering) together with a combination of small-scale surface scattering and subsurface volume scattering (diffuse scattering). The viewing geometry determines which scattering mechanism is strongest. At low incidence angles, quasispecular scatter dominates the radar backscatter return. At higher incidence angles (angles greater than ~30°), diffuse scatter dominates the return. We use a composite model to separate the two scattering regimes; we model the quasispecular term with a combination of two traditional backscatter laws (we consider the Hagfors, Gaussian, and exponential models), following a technique developed by Sultan-Salem and Tyler [1], and we model the diffuse term, which encompasses both diffuse mechanisms, with a simple cosine power law. Using this total composite model, we analyze the backscatter curves of all features classes on Titan for which we have adequate angular coverage. In most cases, we find that the superposition of the Hagfors law with the exponential law best models the quasispecular response. A generalized geometric optics approach permits us to combine the best-fit parameters from each component of the composite model to yield a single value for the surface dielectric constant and RMS slope [1]. In this way, we map the relative variation of composition and wavelength-scale structure across the surface. We also map the variation of radar albedo across the analyzed features, as well as the relative prevalence of the different scattering mechanisms through the measured ratio of diffuse power to quasispecular power. These map products help to constrain how different geological processes might be interacting on a global scale. [1] A. K. Sultan-Salem, G. L. Tyler, JGR 112, 2007.

Anomalous U(1) models in four and five dimensions and their anomaly poles

NASA Astrophysics Data System (ADS)

Armillis, Roberta; Corianò, Claudio; Delle Rose, Luigi; Guzzi, Marco

2009-12-01

We analyze the role played by anomaly poles in an anomalous gauge theory by discussing their signature in the corresponding off-shell effective action. The origin of these contributions, in the most general kinematical case, is elucidated by performing a complete analysis of the anomaly vertex at perturbative level. We use two independent (but equivalent) representations: the Rosenberg representation and the longitudinal/transverse (L/T) parameterization, used in recent studies of g-2 of the muon and in the proof of non-renormalization theorems of the anomaly vertex. The poles extracted from the L/T parameterization do not couple in the infrared for generic anomalous vertices, as in Rosenberg, but we show that they are responsible for the violations of unitarity in the UV region, using a class of pole-dominated amplitudes. We conclude that consistent formulations of anomalous models require necessarily the cancellation of these polar contributions. Establishing the UV significance of these terms provides a natural bridge between the anomalous effective action and its completion by a nonlocal theory. Some additional difficulties with unitarity of the mechanism of inflow in extra dimensional models with an anomalous theory on the brane, due to the presence of anomaly poles, are also pointed out.

Strongly anomalous diffusion in sheared magnetic configurations

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

Vanden Eijnden, E.; Balescu, R.

1996-03-01

The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface {ital x}=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface {ital x}=0. Due to the shear, the diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly non-Gaussian. The reference surface acts likemore » an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of the first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded that the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium. {copyright} {ital 1996 American Institute of Physics.}« less

Gaussian fluctuation of the diffusion exponent of virus capsid in a living cell nucleus

NASA Astrophysics Data System (ADS)

Itto, Yuichi

2018-05-01

In their work [4], Bosse et al. experimentally showed that virus capsid exhibits not only normal diffusion but also anomalous diffusion in nucleus of a living cell. There, it was found that the distribution of fluctuations of the diffusion exponent characterizing them takes the Gaussian form, which is, quite remarkably, the same form for two different types of the virus. This suggests high robustness of such fluctuations. Here, the statistical property of local fluctuations of the diffusion exponent of the virus capsid in the nucleus is studied. A maximum-entropy-principle approach (originally proposed for a different virus in a different cell) is applied for obtaining the fluctuation distribution of the exponent. Largeness of the number of blocks identified with local areas of interchromatin corrals is also examined based on the experimental data. It is shown that the Gaussian distribution of the local fluctuations can be derived, in accordance with the above form. In addition, it is quantified how the fluctuation distribution on a long time scale is different from the Gaussian distribution.

Inhibition of ordinary and diffusive convection in the water condensation zone of the ice giants and implications for their thermal evolution

NASA Astrophysics Data System (ADS)

Friedson, A. James; Gonzales, Erica J.

2017-11-01

We explore the conditions under which ordinary and double-diffusive thermal convection may be inhibited by water condensation in the hydrogen atmospheres of the ice giants and examine the consequences. The saturation of vapor in the condensation layer induces a vertical gradient in the mean molecular weight that stabilizes the layer against convective instability when the abundance of vapor exceeds a critical value. In this instance, the layer temperature gradient can become superadiabatic and heat must be transported vertically by another mechanism. On Uranus and Neptune, water is inferred to be sufficiently abundant for inhibition of ordinary convection to take place in their respective condensation zones. We find that suppression of double-diffusive convection is sensitive to the ratio of the sedimentation time scale of the condensates to the buoyancy period in the condensation layer. In the limit of rapid sedimentation, the layer is found to be stable to diffusive convection. In the opposite limit, diffusive convection can occur. However, if the fluid remains saturated, then layered convection is generally suppressed and the motion is restricted in form to weak, homogeneous, oscillatory turbulence. This form of diffusive convection is a relatively inefficient mechanism for transporting heat, characterized by low Nusselt numbers. When both ordinary and layered convection are suppressed, the condensation zone acts effectively as a thermal insulator, with the heat flux transported across it only slightly greater than the small value that can be supported by radiative diffusion. This may allow a large superadiabatic temperature gradient to develop in the layer over time. Once the layer has formed, however, it is vulnerable to persistent erosion by entrainment of fluid into the overlying convective envelope of the cooling planet, potentially leading to its collapse. We discuss the implications of our results for thermal evolution models of the ice giants, for understanding Uranus' anomalously low intrinsic luminosity, and for inducing episodes of intense convection in the atmospheres of Saturn, Uranus, and Neptune.

Current Driven Instabilities and Anomalous Mobility in Hall-effect Thrusters

NASA Astrophysics Data System (ADS)

Tran, Jonathan; Eckhardt, Daniel; Martin, Robert

2017-10-01

Due to the extreme cost of fully resolving the Debye length and plasma frequency, hybrid plasma simulations utilizing kinetic ions and quasi-steady state fluid electrons have long been the principle workhorse methodology for Hall-effect thruster (HET) modeling. Plasma turbulence and the resulting anomalous electron transport in HETs is a promising candidate for developing predictive models for the observed anomalous transport. In this work, we investigate the implementation of an anomalous electron cross field transport model for hybrid HET simulations such a HPHall. A theory for anomalous transport in HETs and current driven instabilities has been recently studied by Lafleur et al. This work has shown collective electron-wave scattering due to large amplitude azimuthal fluctuations of the electric field. We will further adapt the previous results for related current driven instabilities to electric propulsion relevant mass ratios and conduct a preliminary study of resolving this instability with a modified hybrid (fluid electron and kinetic ion) simulation with the hope of integration with established hybrid HET simulations. This work is supported by the Air Force Office of Scientific Research award FA9950-17RQCOR465.

The Electron Diffusion Region: Forces and Currents

NASA Technical Reports Server (NTRS)

Hesse, Michael

2008-01-01

The dissipation mechanism of magnetic reconnection remains a subject of intense scientific interest. On one hand, one set of recent studies have shown that particle inertia-based processes, which include thermal and bulk inertial effects, provide the reconnection electric field in the diffusion region. On the other hand, a second set of studies emphasizes the role of wave-particle interactions in providing anomalous resistivity in the diffusion region. In this presentation, we present analytical theory results, as well as PIC simulations of guide-field magnetic reconnection. We will show that the thermal electron inertia-based dissipation mechanism, expressed through nongyrotropic electron pressure tensors, remains viable in three dimensions. We will demonstrate the thermal inertia effect through studies of electron distribution functions. Furthermore, we will show that the reconnection electric field provides a transient acceleration on particles traversing the inner reconnection region. This inertia1 effect can be described as a diffusion-like term of the current density, which matches key features of electron distribution functions.

The Electron Diffusion Region: Forces and Currents

NASA Technical Reports Server (NTRS)

Hesse, Michael

2009-01-01

The dissipation mechanism of magnetic reconnection remains a subject of intense scientific interest. On one hand, one set of recent studies have shown that particle inertia-based processes, which include thermal and bulk inertial effects, provide the reconnection electric field in the diffusion region. On the other hand, a second set of studies emphasizes the role of wave-particle interactions in providing anomalous resistivity in the diffusion region. In this presentation, we present analytical theory results, as well as PIC simulations of guide-field magnetic reconnection. We will show that the thermal electron inertia-based dissipation mechanism, expressed through nongyrotropic electron pressure tensors, remains viable in three dimensions. We will demonstrate the thermal inertia effect through studies of electron distribution functions. Furthermore, we will show that the reconnection electric field provides a transient acceleration on particles traversing the inner reconnection region. This inertial effect can be described as a diffusion-like term of the current density, which matches key features of electron distribution functions.

Diffusive shock acceleration - Acceleration rate, magnetic-field direction and the diffusion limit

NASA Technical Reports Server (NTRS)

Jokipii, J. R.

1992-01-01

This paper reviews the concept of diffusive shock acceleration, showing that the acceleration of charged particles at a collisionless shock is a straightforward consequence of the standard cosmic-ray transport equation, provided that one treats the discontinuity at the shock correctly. This is true for arbitrary direction of the upstream magnetic field. Within this framework, it is shown that acceleration at perpendicular or quasi-perpendicular shocks is generally much faster than for parallel shocks. Paradoxically, it follows also that, for a simple scattering law, the acceleration is faster for less scattering or larger mean free path. Obviously, the mean free path can not become too large or the diffusion limit becomes inapplicable. Gradient and curvature drifts caused by the magnetic-field change at the shock play a major role in the acceleration process in most cases. Recent observations of the charge state of the anomalous component are shown to require the faster acceleration at the quasi-perpendicular solar-wind termination shock.

Anomalous thermal diffusivity in underdoped YBa2Cu3O6+x

PubMed Central

Levenson-Falk, Eli M.; Ramshaw, B. J.; Bonn, D. A.; Liang, Ruixing; Hardy, W. N.; Hartnoll, Sean A.; Kapitulnik, Aharon

2017-01-01

The thermal diffusivity in the ab plane of underdoped YBCO crystals is measured by means of a local optical technique in the temperature range of 25–300 K. The phase delay between a point heat source and a set of detection points around it allows for high-resolution measurement of the thermal diffusivity and its in-plane anisotropy. Although the magnitude of the diffusivity may suggest that it originates from phonons, its anisotropy is comparable with reported values of the electrical resistivity anisotropy. Furthermore, the anisotropy drops sharply below the charge order transition, again similar to the electrical resistivity anisotropy. Both of these observations suggest that the thermal diffusivity has pronounced electronic as well as phononic character. At the same time, the small electrical and thermal conductivities at high temperatures imply that neither well-defined electron nor phonon quasiparticles are present in this material. We interpret our results through a strongly interacting incoherent electron–phonon “soup” picture characterized by a diffusion constant D∼vB2τ, where vB is the soup velocity, and scattering of both electrons and phonons saturates a quantum thermal relaxation time τ∼ℏ/kBT. PMID:28484003

Anomalous frequency-dependent ionic conductivity of lesion-laden human-brain tissue

NASA Astrophysics Data System (ADS)

Emin, David; Akhtari, Massoud; Fallah, Aria; Vinters, Harry V.; Mathern, Gary W.

2017-10-01

We study the effect of lesions on our four-electrode measurements of the ionic conductivity of (˜1 cm3) samples of human brain excised from patients undergoing pediatric epilepsy surgery. For most (˜94%) samples, the low-frequency ionic conductivity rises upon increasing the applied frequency. We attributed this behavior to the long-range (˜0.4 mm) diffusion of solvated sodium cations before encountering intrinsic impenetrable blockages such as cell membranes, blood vessels, and cell walls. By contrast, the low-frequency ionic conductivity of some (˜6%) brain-tissue samples falls with increasing applied frequency. We attribute this unusual frequency-dependence to the electric-field induced liberation of sodium cations from traps introduced by the unusually severe pathology observed in samples from these patients. Thus, the anomalous frequency-dependence of the ionic conductivity indicates trap-producing brain lesions.

Single-particle tracking: applications to membrane dynamics.

PubMed

Saxton, M J; Jacobson, K

1997-01-01

Measurements of trajectories of individual proteins or lipids in the plasma membrane of cells show a variety of types of motion. Brownian motion is observed, but many of the particles undergo non-Brownian motion, including directed motion, confined motion, and anomalous diffusion. The variety of motion leads to significant effects on the kinetics of reactions among membrane-bound species and requires a revision of existing views of membrane structure and dynamics.

Biophysical dynamics in disorderly environments.

PubMed

Nelson, David R

2012-01-01

Three areas where time-independent disorder plays a key role in biological dynamics far from equilibrium are reviewed. We first discuss the anomalous localization dynamics that arises when a single species spreads in space and time via diffusion and fluid advection in the presence of frozen heterogeneities in the growth rate. Next we treat the unzipping of double-stranded DNA as a function of force and temperature, a challenge that must be surmounted every time a cell divides. Heterogeneity in the DNA sequence dominates the physics of single-molecule force-extension curves for a broad range of forces upon approaching a sharp unzipping transition. The dynamics of the unzipping fork exhibits anomalous drift and diffusion in a similar range above this transition, with energy barriers that scale as the square root of the genome size. Finally, we describe how activated peptidoglycan strand extension sites, called dislocations in materials science, can mediate the growth of bacterial cell walls. Enzymatically driven circumferential motions of a few dozen of these defects are sufficient to describe the exponential elongation rates observed in experiments on Escherichia coli in a nutrient-rich environment. However, long-range elastic forces transmitted by the peptidoglycan meshwork cause the moving dislocations to interact not only with each other, but also with a disorderly array of frozen, inactivated strand ends.

Osmotic phenomena in application for hyperbaric oxygen treatment.

PubMed

Babchin, A; Levich, E; Melamed M D, Y; Sivashinsky, G

2011-03-01

Hyperbaric oxygen (HBO) treatment defines the medical procedure when the patient inhales pure oxygen at elevated pressure conditions. Many diseases and all injuries are associated with a lack of oxygen in tissues, known as hypoxia. HBO provides an effective method for fast oxygen delivery in medical practice. The exact mechanism of the oxygen transport under HBO conditions is not fully identified. The objective of this article is to extend the colloid and surface science basis for the oxygen transport in HBO conditions beyond the molecular diffusion transport mechanism. At a pressure in the hyperbaric chamber of two atmospheres, the partial pressure of oxygen in the blood plasma increases 10 times. The sharp increase of oxygen concentration in the blood plasma creates a considerable concentration gradient between the oxygen dissolved in the plasma and in the tissue. The concentration gradient of oxygen as a non-electrolyte solute causes an osmotic flow of blood plasma with dissolved oxygen. In other words, the molecular diffusion transport of oxygen is supplemented by the convective diffusion raised due to the osmotic flow, accelerating the oxygen delivery from blood to tissue. A non steady state equation for non-electrolyte osmosis is solved asymptotically. The solution clearly demonstrates two modes of osmotic flow: normal osmosis, directed from lower to higher solute concentrations, and anomalous osmosis, directed from higher to lower solute concentrations. The fast delivery of oxygen from blood to tissue is explained on the basis of the strong molecular interaction between the oxygen and the tissue, causing an influx of oxygen into the tissue by convective diffusion in the anomalous osmosis process. The transport of the second gas, nitrogen, dissolved in the blood plasma, is also taken into the consideration. As the patient does not inhale nitrogen during HBO treatment, but exhales it along with oxygen and carbon dioxide, the concentration of nitrogen in blood plasma drops and the nitrogen concentration gradient becomes directed from blood to tissue. On the assumption of weak interaction between the inert nitrogen and the human tissue, normal osmosis for the nitrogen transport takes place. Thus, the directions of anomalous osmotic flow caused by the oxygen concentration gradient coincide with the directions of normal osmotic flow, caused by the nitrogen concentration gradient. This leads to the conclusion that the presence of nitrogen in the human body promotes the oxygen delivery under HBO conditions, rendering the overall success of the hyperbaric oxygen treatment procedure. 2010 Elsevier B.V. All rights reserved.

Anomalous quartic couplings in W+W- gamma production at e+e- colliders

NASA Astrophysics Data System (ADS)

Leil, G. A.; Stirling, W. J.

1995-04-01

We study the process $e^+e^- \\rightarrow W^+W^- \\gamma$ at high-energy $e^+ e^-$ colliders to investigate the effect of genuine quartic $W^+W^-\\gamma\\gamma$ and $W^+W^- Z\\gamma$ anomalous couplings on the cross section. Deviations from the Standard Model predictions are quantified. We show how bounds on the anomalous couplings can be improved by choosing specific initial state helicity combinations. The dependence of the anomalous contributions on the collider energy is studied.

Bayesian anomaly detection in monitoring data applying relevance vector machine

NASA Astrophysics Data System (ADS)

Saito, Tomoo

2011-04-01

A method for automatically classifying the monitoring data into two categories, normal and anomaly, is developed in order to remove anomalous data included in the enormous amount of monitoring data, applying the relevance vector machine (RVM) to a probabilistic discriminative model with basis functions and their weight parameters whose posterior PDF (probabilistic density function) conditional on the learning data set is given by Bayes' theorem. The proposed framework is applied to actual monitoring data sets containing some anomalous data collected at two buildings in Tokyo, Japan, which shows that the trained models discriminate anomalous data from normal data very clearly, giving high probabilities of being normal to normal data and low probabilities of being normal to anomalous data.

Structural controls on anomalous transport in fractured porous rock

NASA Astrophysics Data System (ADS)

Edery, Yaniv; Geiger, Sebastian; Berkowitz, Brian

2016-07-01

Anomalous transport is ubiquitous in a wide range of disordered systems, notably in fractured porous formations. We quantitatively identify the structural controls on anomalous tracer transport in a model of a real fractured geological formation that was mapped in an outcrop. The transport, determined by a continuum scale mathematical model, is characterized by breakthrough curves (BTCs) that document anomalous (or "non-Fickian") transport, which is accounted for by a power law distribution of local transition times ψ>(t>) within the framework of a continuous time random walk (CTRW). We show that the determination of ψ>(t>) is related to fractures aligned approximately with the macroscopic direction of flow. We establish the dominant role of fracture alignment and assess the statistics of these fractures by determining a concentration-visitation weighted residence time histogram. We then convert the histogram to a probability density function (pdf) that coincides with the CTRW ψ>(t>) and hence anomalous transport. We show that the permeability of the geological formation hosting the fracture network has a limited effect on the anomalous nature of the transport; rather, it is the fractures transverse to the flow direction that play the major role in forming the long BTC tail associated with anomalous transport. This is a remarkable result, given the complexity of the flow field statistics as captured by concentration transitions.

Engineering Weyl Superfluid in Ultracold Fermionic Gases by One-Dimensional Optical Superlattices

NASA Astrophysics Data System (ADS)

Huang, Beibing

2018-01-01

In this paper, we theoretically demonstrate by using one-dimensional superlattices to couple two-dimensional time-reversal-breaking gapped topological superfluid models, an anomalous Weyl superfluid (WS) can be obtained. This new phase features its unique Fermi arc states (FAS) on the surfaces. In the conventional WS, FAS exist only for a part of the line connecting the projections of Weyl points and extending to the border and/or center of surface Brillouin zone. But for the anomalous WS, FAS exist for the whole line. As a proof of principle, we self-consistently at the mean-field level claim the achievement of the anomalous WS in the model with a dichromatic superlattice. In addition, inversion symmetry and band inversion in this model are analyzed to provide the unique features of identifying the anomalous WS experimentally by the momentum-resolved radio-frequency spectroscopy.

Lateral density anomalies and the earth's gravitational field

NASA Technical Reports Server (NTRS)

Lowrey, B. E.

1978-01-01

The interpretation of gravity is valuable for understanding lithospheric plate motion and mantle convection. Postulated models of anomalous mass distributions in the earth and the observed geopotential as expressed in the spherical harmonic expansion are compared. In particular, models of the anomalous density as a function of radius are found which can closely match the average magnitude of the spherical harmonic coefficients of a degree. These models include: (1) a two-component model consisting of an anomalous layer at 200 km depth (below the earth's surface) and at 1500 km depth (2) a two-component model where the upper component is distributed in the region between 1000 and 2800 km depth, and(3) a model with density anomalies which continuously increase with depth more than an order of magnitude.

Classification and Segmentation of Nanoparticle Diffusion Trajectories in Cellular Micro Environments

PubMed Central

Kroll, Alexandra; Haramagatti, Chandrashekara R.; Lipinski, Hans-Gerd; Wiemann, Martin

2017-01-01

Darkfield and confocal laser scanning microscopy both allow for a simultaneous observation of live cells and single nanoparticles. Accordingly, a characterization of nanoparticle uptake and intracellular mobility appears possible within living cells. Single particle tracking allows to measure the size of a diffusing particle close to a cell. However, within the more complex system of a cell’s cytoplasm normal, confined or anomalous diffusion together with directed motion may occur. In this work we present a method to automatically classify and segment single trajectories into their respective motion types. Single trajectories were found to contain more than one motion type. We have trained a random forest with 9 different features. The average error over all motion types for synthetic trajectories was 7.2%. The software was successfully applied to trajectories of positive controls for normal- and constrained diffusion. Trajectories captured by nanoparticle tracking analysis served as positive control for normal diffusion. Nanoparticles inserted into a diblock copolymer membrane was used to generate constrained diffusion. Finally we segmented trajectories of diffusing (nano-)particles in V79 cells captured with both darkfield- and confocal laser scanning microscopy. The software called “TraJClassifier” is freely available as ImageJ/Fiji plugin via https://git.io/v6uz2. PMID:28107406

Surface Andreev Bound States and Odd-Frequency Pairing in Topological Superconductor Junctions

NASA Astrophysics Data System (ADS)

Tanaka, Yukio; Tamura, Shun

2018-04-01

In this review, we summarize the achievement of the physics of surface Andreev bound states (SABS) up to now. The route of this activity has started from the physics of SABS of unconventional superconductors where the pair potential has a sign change on the Fermi surface. It has been established that SABS can be regarded as a topological edge state with topological invariant defined in the bulk Hamiltonian. On the other hand, SABS accompanies odd-frequency pairing like spin-triplet s-wave or spin-singlet p-wave. In a spin-triplet superconductor junction, induced odd-frequency pairing can penetrate into a diffusive normal metal (DN) attached to the superconductor. It causes so called anomalous proximity effect where the local density of states of quasiparticle in DN has a zero energy peak. When bulk pairing symmetry is spin-triplet px-wave, the anomalous proximity effect becomes prominent and the zero bias voltage conductance is always quantized independent of the resistance in DN and interface. Finally, we show that the present anomalous proximity effect is realized in an artificial topological superconducting system, where a nanowire with spin-orbit coupling and Zeeman field is put on the conventional spin-singlet s-wave superconductor.

Modeling of anomalous electron mobility in Hall thrusters

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

Koo, Justin W.; Boyd, Iain D.

Accurate modeling of the anomalous electron mobility is absolutely critical for successful simulation of Hall thrusters. In this work, existing computational models for the anomalous electron mobility are used to simulate the UM/AFRL P5 Hall thruster (a 5 kW laboratory model) in a two-dimensional axisymmetric hybrid particle-in-cell Monte Carlo collision code. Comparison to experimental results indicates that, while these computational models can be tuned to reproduce the correct thrust or discharge current, it is very difficult to match all integrated performance parameters (thrust, power, discharge current, etc.) simultaneously. Furthermore, multiple configurations of these computational models can produce reasonable integrated performancemore » parameters. A semiempirical electron mobility profile is constructed from a combination of internal experimental data and modeling assumptions. This semiempirical electron mobility profile is used in the code and results in more accurate simulation of both the integrated performance parameters and the mean potential profile of the thruster. Results indicate that the anomalous electron mobility, while absolutely necessary in the near-field region, provides a substantially smaller contribution to the total electron mobility in the high Hall current region near the thruster exit plane.« less

Theory and modeling of particles with DNA-mediated interactions

NASA Astrophysics Data System (ADS)

Licata, Nicholas A.

In recent years significant attention has been attracted to proposals which utilize DNA for nanotechnological applications. Potential applications of these ideas range from the programmable self-assembly of colloidal crystals, to biosensors and nanoparticle based drug delivery platforms. In Chapter I we introduce the system, which generically consists of colloidal particles functionalized with specially designed DNA markers. The sequence of bases on the DNA markers determines the particle type. Due to the hybridization between complementary single-stranded DNA, specific, type-dependent interactions can be introduced between particles by choosing the appropriate DNA marker sequences. In Chapter II we develop a statistical mechanical description of the aggregation and melting behavior of particles with DNA-mediated interactions. A quantitative comparison between the theory and experiments is made by calculating the experimentally observed melting profile. In Chapter III a model is proposed to describe the dynamical departure and diffusion of particles which form reversible key-lock connections. The model predicts a crossover from localized to diffusive behavior. The random walk statistics for the particles' in plane diffusion is discussed. The lateral motion is analogous to dispersive transport in disordered semiconductors, ranging from standard diffusion with a renormalized diffusion coefficient to anomalous, subdiffusive behavior. In Chapter IV we propose a method to self-assemble nanoparticle clusters using DNA scaffolds. An optimal concentration ratio is determined for the experimental implementation of our self-assembly proposal. A natural extension is discussed in Chapter V, the programmable self-assembly of nanoparticle clusters where the desired cluster geometry is encoded using DNA-mediated interactions. We determine the probability that the system self-assembles the desired cluster geometry, and discuss the connections to jamming in granular and colloidal systems. In Chapter VI we consider a nanoparticle based drug delivery platform for targeted, cell specific chemotherapy. A key-lock model is proposed to describe the results of in-vitro experiments, and the situation in-vivo is discussed. The cooperative binding, and hence the specificity to cancerous cells, is kinetically limited. The implications for optimizing the design of nanoparticle based drug delivery platforms is discussed. In Chapter VII we present prospects for future research: the connection between DNA-mediated colloidal crystallization and jamming, and the inverse problem in self-assembly.

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

NASA Astrophysics Data System (ADS)

Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.

2018-03-01

The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.

Anomalous and non-Gaussian diffusion in Hertzian spheres

NASA Astrophysics Data System (ADS)

Ouyang, Wenze; Sun, Bin; Sun, Zhiwei; Xu, Shenghua

2018-09-01

By means of molecular dynamics simulations, we study the non-Gaussian diffusion in the fluid of Hertzian spheres. The time dependent non-Gaussian parameter, as an indicator of the dynamic heterogeneity, is increased with the increasing of temperature. When the temperature is high enough, the dynamic heterogeneity becomes very significant, and it seems counterintuitive that the maximum of non-Gaussian parameter and the position of its peak decrease monotonically with the increasing of density. By fitting the curves of self intermediate scattering function, we find that the character relaxation time τα is surprisingly not coupled with the time τmax where the non-Gaussian parameter reaches to a maximum. The intriguing features of non-Gaussian diffusion at high enough temperatures can be associated with the weakly correlated mean-field behavior of Hertzian spheres. Especially the time τmax is nearly inversely proportional to the density at extremely high temperatures.

Diffusive behavior of a greedy traveling salesman.

PubMed

Lipowski, Adam; Lipowska, Dorota

2011-06-01

Using Monte Carlo simulations we examine the diffusive properties of the greedy algorithm in the d-dimensional traveling salesman problem. Our results show that for d=3 and 4 the average squared distance from the origin (r(2)) is proportional to the number of steps t. In the d=2 case such a scaling is modified with some logarithmic corrections, which might suggest that d=2 is the critical dimension of the problem. The distribution of lengths also shows marked differences between d=2 and d>2 versions. A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behavior has recently been reported and interpreted in terms of Lévy flights. Our results suggest that broad and Lévy-like distributions in such systems might appear due to dimension-dependent properties of a search space.

A Falling Corona Model for the Anomalous Behavior of the Broad Emission Lines in NGC 5548

NASA Astrophysics Data System (ADS)

Sun, Mouyuan; Xue, Yongquan; Cai, Zhenyi; Guo, Hengxiao

2018-04-01

NGC 5548 has been intensively monitored by the AGN Space Telescope and Optical Reverberation Mapping collaboration. Approximately after half of the light curves, the correlation between the broad emission lines and the lag-corrected ultraviolet (UV) continua becomes weak. This anomalous behavior is accompanied by an increase of soft X-ray emission. We propose a simple model to understand this anomalous behavior, i.e., the corona might fall down, thereby increasing the covering fraction of the inner disk. Therefore, X-ray and extreme-UV emission suffer from spectral variations. The UV continua variations are driven by both X-ray and extreme-UV variations. Consequently, the spectral variability induced by the falling corona would dilute the correlation between the broad emission lines and the UV continua. Our model can explain many additional observational facts, including the dependence of the anomalous behavior on velocity and ionization energy. We also show that the time lag and correlation between the X-ray and the UV variations change as NGC 5548 displays the anomalous behavior. The time lag is dramatically longer than the expectation from disk reprocessing if the anomalous behavior is properly excluded. During the anomalous state, the time lag approaches the light-travel timescale of disk reprocessing albeit with a much weaker correlation. We speculate that the time lag in the normal state is caused by reprocessing of the broad line region gas. As NGC 5548 enters the abnormal state, the contribution of the broad line region gas is smaller; the time lag reflects disk reprocessing. We also discuss alternative scenarios.

Analysis of drift effects on the tokamak power scrape-off width using SOLPS-ITER

NASA Astrophysics Data System (ADS)

Meier, E. T.; Goldston, R. J.; Kaveeva, E. G.; Makowski, M. A.; Mordijck, S.; Rozhansky, V. A.; Senichenkov, I. Yu; Voskoboynikov, S. P.

2016-12-01

SOLPS-ITER, a comprehensive 2D scrape-off layer modeling package, is used to examine the physical mechanisms that set the scrape-off width ({λq} ) for inter-ELM power exhaust. Guided by Goldston’s heuristic drift (HD) model, which shows remarkable quantitative agreement with experimental data, this research examines drift effects on {λq} in a DIII-D H-mode magnetic equilibrium. As a numerical expedient, a low target recycling coefficient of 0.9 is used in the simulations, resulting in outer target plasma that is sheath limited instead of conduction limited as in the experiment. Scrape-off layer (SOL) particle diffusivity (D SOL) is scanned from 1 to 0.1 m2 s-1. Across this diffusivity range, outer divertor heat flux is dominated by a narrow (˜3-4 mm when mapped to the outer midplane) electron convection channel associated with thermoelectric current through the SOL from outer to inner divertor. An order-unity up-down ion pressure asymmetry allows net ion drift flux across the separatrix, facilitated by an artificial mechanism that mimics the anomalous electron transport required for overall ambipolarity in the HD model. At {{D}\\text{SOL}}=0.1 m2 s-1, the density fall-off length is similar to the electron temperature fall-off length, as predicted by the HD model and as seen experimentally. This research represents a step toward a deeper understanding of the power scrape-off width, and serves as a basis for extending fluid modeling to more experimentally relevant, high-collisionality regimes.

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer.

PubMed

Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

2017-02-01

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized " n -diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter [Formula: see text] introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

PubMed Central

Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

2017-01-01

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized “n-diffusion theory,” which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system. PMID:28344433

Analysis of drift effects on the tokamak power scrape-off width using SOLPS-ITER

DOE PAGES

Meier, E. T.; Goldston, R. J.; Kaveeva, E. G.; ...

2016-11-02

SOLPS-ITER, a comprehensive 2D scrape-off layer modeling package, is used to examine the physical mechanisms that set the scrape-off width (more » $${{\\lambda}_{q}}$$ ) for inter-ELM power exhaust. Guided by Goldston's heuristic drift (HD) model, which shows remarkable quantitative agreement with experimental data, this research examines drift effects on $${{\\lambda}_{q}}$$ in a DIII-D H-mode magnetic equilibrium. As a numerical expedient, a low target recycling coefficient of 0.9 is used in the simulations, resulting in outer target plasma that is sheath limited instead of conduction limited as in the experiment. Scrape-off layer (SOL) particle diffusivity (D SOL) is scanned from 1 to 0.1 m2 s –1. Across this diffusivity range, outer divertor heat flux is dominated by a narrow (~3–4mm when mapped to the outer midplane) electron convection channel associated with thermoelectric current through the SOL from outer to inner divertor. An order-unity up–down ion pressure asymmetry allows net ion drift flux across the separatrix, facilitated by an artificial mechanism that mimics the anomalous electron transport required for overall ambipolarity in the HD model. At $${{D}_{\\text{SOL}}}=0.1$$ m2 s –1, the density fall-off length is similar to the electron temperature fall-off length, as predicted by the HD model and as seen experimentally. Furthermore, this research represents a step toward a deeper understanding of the power scrape-off width, and serves as a basis for extending fluid modeling to more experimentally relevant, high-collisionality regimes.« less

Measurements and modelling of fast-ion redistribution due to resonant MHD instabilities in MAST

NASA Astrophysics Data System (ADS)

Jones, O. M.; Cecconello, M.; McClements, K. G.; Klimek, I.; Akers, R. J.; Boeglin, W. U.; Keeling, D. L.; Meakins, A. J.; Perez, R. V.; Sharapov, S. E.; Turnyanskiy, M.; the MAST Team

2015-12-01

The results of a comprehensive investigation into the effects of toroidicity-induced Alfvén eigenmodes (TAE) and energetic particle modes on the NBI-generated fast-ion population in MAST plasmas are reported. Fast-ion redistribution due to frequency-chirping TAE in the range 50 kHz-100 kHz and frequency-chirping energetic particle modes known as fishbones in the range 20 kHz-50 kHz, is observed. TAE and fishbones are also observed to cause losses of fast ions from the plasma. The spatial and temporal evolution of the fast-ion distribution is determined using a fission chamber, a radially-scanning collimated neutron flux monitor, a fast-ion deuterium alpha spectrometer and a charged fusion product detector. Modelling using the global transport analysis code Transp, with ad hoc anomalous diffusion and fishbone loss models introduced, reproduces the coarsest features of the affected fast-ion distribution in the presence of energetic particle-driven modes. The spectrally and spatially resolved measurements show, however, that these models do not fully capture the effects of chirping modes on the fast-ion distribution.

Visual saliency detection based on modeling the spatial Gaussianity

NASA Astrophysics Data System (ADS)

Ju, Hongbin

2015-04-01

In this paper, a novel salient object detection method based on modeling the spatial anomalies is presented. The proposed framework is inspired by the biological mechanism that human eyes are sensitive to the unusual and anomalous objects among complex background. It is supposed that a natural image can be seen as a combination of some similar or dissimilar basic patches, and there is a direct relationship between its saliency and anomaly. Some patches share high degree of similarity and have a vast number of quantity. They usually make up the background of an image. On the other hand, some patches present strong rarity and specificity. We name these patches "anomalies". Generally, anomalous patch is a reflection of the edge or some special colors and textures in an image, and these pattern cannot be well "explained" by their surroundings. Human eyes show great interests in these anomalous patterns, and will automatically pick out the anomalous parts of an image as the salient regions. To better evaluate the anomaly degree of the basic patches and exploit their nonlinear statistical characteristics, a multivariate Gaussian distribution saliency evaluation model is proposed. In this way, objects with anomalous patterns usually appear as the outliers in the Gaussian distribution, and we identify these anomalous objects as salient ones. Experiments are conducted on the well-known MSRA saliency detection dataset. Compared with other recent developed visual saliency detection methods, our method suggests significant advantages.

Anomalous thermoelectric phenomena in lattice models of multi-Weyl semimetals

NASA Astrophysics Data System (ADS)

Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.

2017-10-01

The thermoelectric transport coefficients are calculated in a generic lattice model of multi-Weyl semimetals with a broken time-reversal symmetry by using the Kubo's linear response theory. The contributions connected with the Berry curvature-induced electromagnetic orbital and heat magnetizations are systematically taken into account. It is shown that the thermoelectric transport is profoundly affected by the nontrivial topology of multi-Weyl semimetals. In particular, the calculation reveals a number of thermal coefficients of the topological origin which describe the anomalous Nernst and thermal Hall effects in the absence of background magnetic fields. Similarly to the anomalous Hall effect, all anomalous thermoelectric coefficients are proportional to the integer topological charge of the Weyl nodes. The dependence of the thermoelectric coefficients on the chemical potential and temperature is also studied.

Beam-plasma instability in the presence of low-frequency turbulence. [during type 3 solar emission

NASA Technical Reports Server (NTRS)

Goldman, M. V.; Dubois, D. F.

1982-01-01

General equations are derived for a linear beam-plasma instability in the presence of low-frequency turbulence. Within a 'quasi-linear' statistical approximation, these equations contain Langmuir wave scattering, diffusion, resonant and nonresonant anomalous absorption, and a 'plasma laser' effect. It is proposed that naturally occurring density irregularities in the solar wind may stabilize the beam-unstable Langmuir waves which occur during type III solar emissions.

Effects of various boundary conditions on the response of Poisson-Nernst-Planck impedance spectroscopy analysis models and comparison with a continuous-time random-walk model.

PubMed

Macdonald, J Ross

2011-11-24

Various electrode reaction rate boundary conditions suitable for mean-field Poisson-Nernst-Planck (PNP) mobile charge frequency response continuum models are defined and incorporated in the resulting Chang-Jaffe (CJ) CJPNP model, the ohmic OHPNP one, and a simplified GPNP one in order to generalize from full to partial blocking of mobile charges at the two plane parallel electrodes. Model responses using exact synthetic PNP data involving only mobile negative charges are discussed and compared for a wide range of CJ dimensionless reaction rate values. The CJPNP and OHPNP ones are shown to be fully equivalent, except possibly for the analysis of nanomaterial structures. The dielectric strengths associated with the CJPNP diffuse double layers at the electrodes were found to decrease toward 0 as the reaction rate increased, consistent with fewer blocked charges and more reacting ones. Parameter estimates from GPNP fits of CJPNP data were shown to lead to accurate calculated values of the CJ reaction rate and of some other CJPNP parameters. Best fits of CaCu(3)Ti(4)O(12) (CCTO) single-crystal data, an electronic conductor, at 80 and 140 K, required the anomalous diffusion model, CJPNPA, and led to medium-size rate estimates of about 0.12 and 0.03, respectively, as well as good estimates of the values of other important CJPNPA parameters such as the independently verified concentration of neutral dissociable centers. These continuum-fit results were found to be only somewhat comparable to those obtained from a composite continuous-time random-walk hopping/trapping semiuniversal UN model.

The behaviour of tributyl phosphate in an organic diluent

NASA Astrophysics Data System (ADS)

Leay, Laura; Tucker, Kate; Del Regno, Annalaura; Schroeder, Sven L. M.; Sharrad, Clint A.; Masters, Andrew J.

2014-09-01

Tributyl phosphate (TBP) is used as a complexing agent in the Plutonium Uranium Extraction (PUREX) liquid-liquid phase extraction process for recovering uranium and plutonium from spent nuclear reactor fuel. Here, we address the molecular and microstructure of the organic phases involved in the extraction process, using molecular dynamics to show that when TBP is mixed with a paraffinic diluent, the TBP self-assembles into a bi-continuous phase. The underlying self-association of TBP is driven by intermolecular interaction between its polar groups, resulting in butyl moieties radiating out into the organic solvent. Simulation predicts a TBP diffusion constant that is anomalously low compared to what might normally be expected for its size; experimental nuclear magnetic resonance (NMR) studies also indicate an extremely low diffusion constant, consistent with a molecular aggregation model. Simulation of TBP at an oil/water interface shows the formation of a bilayer system at low TBP concentrations. At higher concentrations, a bulk bi-continuous structure is observed linking to this surface bilayer. We suggest that this structure may be intimately connected with the surprisingly rapid kinetics of the interfacial mass transport of uranium and plutonium from the aqueous to the organic phase in the PUREX process.

Mode and polarization state selected guided wave spectroscopy of orientational anisotrophy in model membrane cellulosic polymer films: relevance to lab-on-a-chip

NASA Astrophysics Data System (ADS)

Andrews, Mark P.; Kanigan, Tanya

2007-06-01

Orientation anisotropies in structural properties relevant to the use of cellulosic polymers as membranes for lab-on-chips were investigated for cellulose acetate (CA) and regenerated cellulose (RC) films deposited as slab waveguides. Anisotropy was probed with mode and polarization state selected guided wave Raman spectroscopy. CA exhibits partial chain orientation in the plane of the film, and this orientation is independent of sample substrate and film preparation conditions. RC films also show in-plane anisotropy, where the hexose sugar rings lie roughly in the plane of the film. Explanations are given of the role of artifacts in interpreting waveguide Raman spectra, including anomalous contributions to Raman spectra that arise from deviations from right angle scattering geometry, mode-dependent contributions to longitudinal electric field components and TE<-->TM mode conversion. We explore diffusion profiles of small molecules in cellulosic films by adaptations of an inverse-Wentzel-Kramers-Brillouin (iWKB) recursive, noninteger virtual mode index algorithm. Perturbations in the refractive index distribution, n(z), are recovered from the measured relative propagation constants, neffective,m, of the planar waveguide. The refractive index distribution then yields the diffusion profile.

What sets the minimum tokamak scrape-off layer width?

NASA Astrophysics Data System (ADS)

Joseph, Ilon

2016-10-01

The heat flux width of the tokamak scrape-off layer is on the order of the poloidal ion gyroradius, but the ``heuristic drift'' physics model is still not completely understood. In the absence of anomalous transport, neoclassical transport sets the minimum width. For plateau collisionality, the ion temperature width is set by qρi , while the electron temperature width scales as the geometric mean q(ρeρi) 1 / 2 and is close to qρi in magnitude. The width is enhanced because electrons are confined by the sheath potential and have a much longer time to radially diffuse before escaping to the wall. In the Pfirsch-Schluter regime, collisional diffusion increases the width by the factor (qR / λ) 1 / 2 where qR is the connection length and λ is the mean free path. This qualitatively agrees with the observed transition in the scaling law for detached plasmas. The radial width of the SOL electric field is determined by Spitzer parallel and ``neoclassical'' radial electric conductivity and has a similar scaling to that for thermal transport. Prepared under US DOE contract DE-AC52-07NA27344.

Molecular dynamics study on glycolic acid in the physiological salt solution

NASA Astrophysics Data System (ADS)

Matsunaga, S.

2018-05-01

Molecular dynamics (MD) study on glycolic acid in the physiological salt solution has been performed, which is a model of a biofuel cell. The structure and charge distribution of glycolic acid in aqueous solution used in MD is beforehand optimized by Gaussian09 utilizing the density functional theory. MD is performed in the NTV constant condition, i.e. the number of particles, temperature, and volume of MD cell are definite. The structure difference of the glycolic acid and oxalic acid is detected by the water distribution around the molecules using the pair distribution functions, gij(r), and the frequency dependent diffusion coefficients, Di(ν). The anomalous dielectric constant of the solution, i.e. about 12 times larger than that of water, has been obtained, which may be attributed to the ion pair formation in the solution.

Communication: Quantum molecular dynamics simulation of liquid para-hydrogen by nuclear and electron wave packet approach.

PubMed

Hyeon-Deuk, Kim; Ando, Koji

2014-05-07

Liquid para-hydrogen (p-H2) is a typical quantum liquid which exhibits strong nuclear quantum effects (NQEs) and thus anomalous static and dynamic properties. We propose a real-time simulation method of wave packet (WP) molecular dynamics (MD) based on non-empirical intra- and inter-molecular interactions of non-spherical hydrogen molecules, and apply it to condensed-phase p-H2. The NQEs, such as WP delocalization and zero-point energy, are taken into account without perturbative expansion of prepared model potential functions but with explicit interactions between nuclear and electron WPs. The developed MD simulation for 100 ps with 1200 hydrogen molecules is realized at feasible computational cost, by which basic experimental properties of p-H2 liquid such as radial distribution functions, self-diffusion coefficients, and shear viscosities are all well reproduced.

Thermodynamics of Surface Nanobubbles.

PubMed

Zargarzadeh, Leila; Elliott, Janet A W

2016-11-01

In this paper, we examine the thermodynamic stability of surface nanobubbles. The appropriate free energy is defined for the system of nanobubbles on a solid surface submerged in a supersaturated liquid solution at constant pressure and temperature, under conditions where an individual nanobubble is not in diffusive contact with a gas phase outside of the system or with other nanobubbles on the time scale of the experiment. The conditions under which plots of free energy versus the radius of curvature of the nanobubbles show a global minimum, which denotes the stable equilibrium state, are explored. Our investigation shows that supersaturation and an anomalously high contact angle (measured through the liquid) are required to have stable surface nanobubbles. In addition, the anomalously high contact angle of surface nanobubbles is discussed from the standpoint of a framework recently proposed by Koch, Amirfazli, and Elliott that relates advancing and receding contact angles to thermodynamic equilibrium contact angles, combined with the existence of a gas enrichment layer.

Sheared E×B flow and plasma turbulence viscosity in a Reversed Field Pinch

NASA Astrophysics Data System (ADS)

Vianello, N.; Antoni, V.; Spada, E.; Spolaore, M.; Serianni, G.; Regnoli, G.; Zuin, M.; Cavazzana, R.; Bergsåker, H.; Cecconello, M.; Drake, J. R.

2004-11-01

The relationship between electromagnetic turbulence and sheared plasma flow in Reversed Field Pinch configuration is addressed. The momentum balance equation for a compressible plasma is considered and the terms involved are measured in the outer region of Extrap-T2R RFP device. It results that electrostatic fluctuations determine the plasma flow through the electrostatic component of Reynolds Stress tensor. This term involves spatial and temporal scales comparable to those of MHD activity. The derived experimental perpendicular viscosity is consistent with anomalous diffusion, the latter being discussed in terms of electrostatic turbulence background and coherent structures emerging from fluctuations. The results indicate a dynamical interplay between turbulence, anomalous transport and mean E×B profiles. The momentum balance has been studied also in non-stationary condition during the application of Pulsed Poloidal Current Drive, which is known to reduce the amplitude of MHD modes.

Anomalous radon emission as precursor of medium to strong earthquakes

NASA Astrophysics Data System (ADS)

Zoran, Maria

2016-03-01

Anomalous radon (Rn222) emissions enhanced by forthcoming earthquakes is considered to be a precursory phenomenon related to an increased geotectonic activity in seismic areas. Rock microfracturing in the Earth's crust preceding a seismic rupture may cause local surface deformation fields, rock dislocations, charged particle generation and motion, electrical conductivity changes, radon and other gases emission, fluid diffusion, electrokinetic, piezomagnetic and piezoelectric effects as well as climate fluctuations. Space-time anomalies of radon gas emitted in underground water, soil and near the ground air weeks to days in the epicentral areas can be associated with the strain stress changes that occurred before the occurrence of medium and strong earthquakes. This paper aims to investigate temporal variations of radon concentration levels in air near or in the ground by the use of solid state nuclear track detectors (SSNTD) CR-39 and LR-115 in relation with some important seismic events recorded in Vrancea region, Romania.

Crystallization and preliminary X-ray crystallographic analysis of the variable domain of Scl2.3, a streptococcal collagen-like protein from invasive M3-type Streptococcus pyogenes.

PubMed

Squeglia, Flavia; Bachert, Beth; Romano, Maria; Lukomski, Slawomir; Berisio, Rita

2013-09-01

Streptococcal collagen-like proteins (Scls) are widely expressed by the well recognized human pathogen Streptococcus pyogenes. These surface proteins contain a signature central collagen-like region and an amino-terminal globular domain, termed the variable domain, which is protruded away from the cell surface by the collagen-like domain. Despite their recognized importance in bacterial pathogenicity, no structural information is presently available on proteins of the Scl class. The variable domain of Scl2 from invasive M3-type S. pyogenes has successfully been crystallized using vapour-diffusion methods. The crystals diffracted to 1.5 Å resolution and belonged to space group H32, with unit-cell parameters a = 44.23, b = 44.23, c = 227.83 Å. The crystal structure was solved by single-wavelength anomalous dispersion using anomalous signal from a europium chloride derivative.|

Anomalous transport from holography. Part I

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2016-11-01

We revisit the transport properties induced by the chiral anomaly in a charged plasma holographically dual to anomalous U(1) V ×U(1) A Maxwell theory in Schwarzschild-AdS5. Off-shell constitutive relations for vector and axial currents are derived using various approximations generalising most of known in the literature anomaly-induced phenomena and revealing some new ones. In a weak external field approximation, the constitutive relations have all-order derivatives resummed into six momenta-dependent transport co-efficient functions: the diffusion, the electric/magnetic conductivity, and three anomaly induced functions. The latter generalise the chiral magnetic and chiral separation effects. Nonlinear transport is studied assuming presence of constant background external fields. The chiral magnetic effect, including all order nonlinearity in magnetic field, is proven to be exact when the magnetic field is the only external field that is turned on. Non-linear corrections to the constitutive relations due to electric and axial external fields are computed.

Observation of anomalous Hall effect in a non-magnetic two-dimensional electron system

PubMed Central

Maryenko, D.; Mishchenko, A. S.; Bahramy, M. S.; Ernst, A.; Falson, J.; Kozuka, Y.; Tsukazaki, A.; Nagaosa, N.; Kawasaki, M.

2017-01-01

Anomalous Hall effect, a manifestation of Hall effect occurring in systems without time-reversal symmetry, has been mostly observed in ferromagnetically ordered materials. However, its realization in high-mobility two-dimensional electron system remains elusive, as the incorporation of magnetic moments deteriorates the device performance compared to non-doped structure. Here we observe systematic emergence of anomalous Hall effect in various MgZnO/ZnO heterostructures that exhibit quantum Hall effect. At low temperatures, our nominally non-magnetic heterostructures display an anomalous Hall effect response similar to that of a clean ferromagnetic metal, while keeping a large anomalous Hall effect angle θAHE≈20°. Such a behaviour is consistent with Giovannini–Kondo model in which the anomalous Hall effect arises from the skew scattering of electrons by localized paramagnetic centres. Our study unveils a new aspect of many-body interactions in two-dimensional electron systems and shows how the anomalous Hall effect can emerge in a non-magnetic system. PMID:28300133

Non-perturbative measurement of cross-field thermal diffusivity reduction at the O-point of 2/1 neoclassical tearing mode islands in the DIII-D tokamak

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

Bardóczi, L.; Rhodes, T. L.; Carter, T. A.

2016-05-15

Neoclassical tearing modes (NTMs) often lead to the decrease of plasma performance and can lead to disruptions, which makes them a major impediment in the development of operating scenarios in present toroidal fusion devices. Recent gyrokinetic simulations predict a decrease of plasma turbulence and cross-field transport at the O-point of the islands, which in turn affects the NTM dynamics. In this paper, a heat transport model of magnetic islands employing spatially non-uniform cross-field thermal diffusivity (χ{sub ⊥}) is presented. This model is used to derive χ{sub ⊥} at the O-point from electron temperature data measured across 2/1 NTM islands inmore » DIII-D. It was found that χ{sub ⊥} at the O-point is 1 to 2 orders of magnitude smaller than the background plasma transport, in qualitative agreement with gyrokinetic predictions. As the anomalously large values of χ{sub ⊥} are often attributed to turbulence driven transport, the reduction of the O-point χ{sub ⊥} is consistent with turbulence reduction found in recent experiments. Finally, the implication of reduced χ{sub ⊥} at the O-point on NTM dynamics was investigated using the modified Rutherford equation that predicts a significant effect of reduced χ{sub ⊥} at the O-point on NTM saturation.« less

Non-perturbative measurement of cross-field thermal diffusivity reduction at the O-point of 2/1 neoclassical tearing mode islands in the DIII-D tokamak

DOE PAGES

Bardóczi, Laszlo; Rhodes, Terry L.; Carter, Troy A.; ...

2016-05-09

Neoclassical Tearing Modes (NTMs) often lead to the decrease of plasma performance and can lead to disruptions, which makes them a major impediment in the development of operating scenarios in present toroidal fusion devices. Recent gyrokinetic simulations predict a decrease of plasma turbulence and cross- eld transport at the O-point of the islands, which in turn affects the NTM dynamics. In this paper a heat transport model of magnetic islands employing spatially non-uniform cross-field thermal diffusivity (χ more » $$\\perp$$) is presented. This model is used to derive χ $$\\perp$$ at the O-point from electron temperature data measured across 2/1 NTM islands in DIII-D. It was found that χ $$\\perp$$ at the O-point is 1 to 2 orders of magnitude smaller than the background plasma transport, in qualitative agreement with gyrokinetic predictions. As the anomalously large values of χ $$\\perp$$ are often attributed to turbulence driven transport, the reduction of the O-point χ $$\\perp$$ is consistent with turbulence reduction found in recent experiments. Lastly, the implication of reduced χ $$\\perp$$ at the O-point on NTM dynamics was investigated using the modi ed Rutherford equation that predicts a significant effect of reduced χ $$\\perp$$ at the O-point on NTM saturation.« less

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

DOE PAGES

Del-Castillo-Negrete, Diego B.; Moradi, Sara; Anderson, Johan

2016-09-01

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of -stable Levy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Levy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Levy fluctuations. The absolute value ofmore » the power law decay exponents are linearly proportional to the Levy index. Furthermore, the observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Levy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.« less

Nonequilibrium transport of charge carriers and transient electroluminescence in organic light-emitting diodes

NASA Astrophysics Data System (ADS)

Nikitenko, V. R.; von Seggern, H.

2007-11-01

An analytic theory of nonequilibrium hopping charge transport in disordered organic materials includes quasiequilibrium (normal) and extremely nonequilibrium (dispersive) regimes as limiting cases at long and short times, respectively. In the intermediate interval of time quasiequilibrium value of mobility is nearly established while the coefficient of field-assisted diffusion continues to increase (quasidispersive regime). Therefore, normalized time dependencies of transient current in time-of-flight (TOF) conditions are practically independent of field strength and sample thickness, in good agreement both with data of TOF experiments for molecularly doped polymers and results of numerical simulations of Gaussian disorder model. An analytic model of transient electroluminescence (TEL) is developed on the base of the mentioned theory. Strong asymmetry of mobilities is presumed. In analogy with TOF transients, dispersion parameter of normalized TEL intensity is anomalously large and almost field independent in the quasidispersive regime of transport. The method for determination of mobility from TEL data is proposed.

Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation.

PubMed

Berry, Hugues

2002-10-01

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes.

Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation.

PubMed Central

Berry, Hugues

2002-01-01

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes. PMID:12324410

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

NASA Astrophysics Data System (ADS)

Moradi, Sara; del-Castillo-Negrete, Diego; Anderson, Johan

2016-09-01

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of α-stable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents is linearly proportional to the Lévy index α. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Lévy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.

Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2017-03-01

The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins, including their non-markovian dynamics with memory. The known expressions valid for normal and anomalous diffusion are obtained as special cases in the long time approximation. The method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the Hahn spin echo experiment. The attenuation of the NMR signal is also evaluated providing that the random motion of particle is modeled by the generalized Langevin equation with the memory kernel exponentially decaying in time. The models considered in our paper assume massive particles driven by much smaller particles.

Anticipated Electrical Environment at Phobos: Nominal and Solar Storm Conditions

NASA Technical Reports Server (NTRS)

Farrell, W. M.; Halekas, J. S.; Fatemi, S.; Poppe, A. R.; Hartzell, C.; Marshall, J. R.; Stubbs, T. J.; Zimmerman, M. I.; Zheng, Y.

2017-01-01

A passing coronal mass ejection (CME) will manifest a different response at an airless body compared to a magnetized planet. Specifically,because the regolith-rich surfaces of airless bodies are directly exposed to the variations in the plasma flow, the surfaces are found to undergo anomalous surface charging during the passing of CME fast plasma events. In this study, we model the surface charging expected at Phobos for nominal solar wind conditions and also those associated with disturbed solar wind conditions during the passage of a CME similar to that observed by MAVEN at Mars in early March 2015. We use an ambipolar diffusion model to examine the development of the trailing wake void in the plasma flow behind Phobos and the formation of mini-wakes within obstruction regions like Stickney Crater. We also consider the roving of an astronaut in Stickney Crater for Phobos positioned near 10 hours Local Time relative to Mars. We examine the plasma dissipation of the collected astronaut charge from contact electrification with the regolith.

Anomalous single production of the fourth generation quarks at the CERN LHC

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

Ciftci, R.

Possible anomalous single productions of the fourth standard model generation up and down type quarks at CERN Large Hadron Collider are studied. Namely, pp{yields}u{sub 4}(d{sub 4})X with subsequent u{sub 4}{yields}bW{sup +} process followed by the leptonic decay of the W boson and d{sub 4}{yields}b{gamma} (and its H.c.) decay channel are considered. Signatures of these processes and corresponding standard model backgrounds are discussed in detail. Discovery limits for the quark mass and achievable values of the anomalous coupling strength are determined.

Parallel electric fields in extragalactic jets - Double layers and anomalous resistivity in symbiotic relationships

NASA Technical Reports Server (NTRS)

Borovsky, J. E.

1986-01-01

After examining the properties of Coulomb-collision resistivity, anomalous (collective) resistivity, and double layers, a hybrid anomalous-resistivity/double-layer model is introduced. In this model, beam-driven waves on both sides of a double layer provide electrostatic plasma-wave turbulence that greatly reduces the mobility of charged particles. These regions then act to hold open a density cavity within which the double layer resides. In the double layer, electrical energy is dissipated with 100 percent efficiency into high-energy particles, creating conditions optimal for the collective emission of polarized radio waves.

Spin Hall and Spin Swapping Torques in Diffusive Ferromagnets

NASA Astrophysics Data System (ADS)

Pauyac, Christian Ortiz; Chshiev, Mairbek; Manchon, Aurelien; Nikolaev, Sergey A.

2018-04-01

A complete set of the generalized drift-diffusion equations for a coupled charge and spin dynamics in ferromagnets in the presence of extrinsic spin-orbit coupling is derived from the quantum kinetic approach, covering major transport phenomena, such as the spin and anomalous Hall effects, spin swapping, spin precession, and relaxation processes. We argue that the spin swapping effect in ferromagnets is enhanced due to spin polarization, while the overall spin texture induced by the interplay of spin-orbital and spin precession effects displays a complex spatial dependence that can be exploited to generate torques and nucleate or propagate domain walls in centrosymmetric geometries without the use of external polarizers, as opposed to the conventional understanding of spin-orbit mediated torques.