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.

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.

Apparent Anomalous Diffusion in the Cytoplasm of Human Cells: The Effect of Probes' Polydispersity.

PubMed

Kalwarczyk, Tomasz; Kwapiszewska, Karina; Szczepanski, Krzysztof; Sozanski, Krzysztof; Szymanski, Jedrzej; Michalska, Bernadeta; Patalas-Krawczyk, Paulina; Duszynski, Jerzy; Holyst, Robert

2017-10-26

This work, based on in vivo and in vitro measurements, as well as in silico simulations, provides a consistent analysis of diffusion of polydisperse nanoparticles in the cytoplasm of living cells. Using the example of fluorescence correlation spectroscopy (FCS), we show the effect of polydispersity of probes on the experimental results. Although individual probes undergo normal diffusion, in the ensemble of probes, an effective broadening of the distribution of diffusion times occurs-similar to anomalous diffusion. We introduced fluorescently labeled dextrans into the cytoplasm of HeLa cells and found that cytoplasmic hydrodynamic drag, exponentially dependent on probe size, extraordinarily broadens the distribution of diffusion times across the focal volume. As a result, the in vivo FCS data were effectively fitted with the anomalous subdiffusion model while for a monodisperse probe the normal diffusion model was most suitable. Diffusion time obtained from the anomalous diffusion model corresponds to a probe whose size is determined by the weight-average molecular weight of the polymer. The apparent anomaly exponent decreases with increasing polydispersity of the probes. Our results and methodology can be applied in intracellular studies of the mobility of nanoparticles, polymers, or oligomerizing proteins.

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

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 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.

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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).

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.

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

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.

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.

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 .

Anomalous scaling of stochastic processes and the Moses effect

NASA Astrophysics Data System (ADS)

Chen, Lijian; Bassler, Kevin E.; McCauley, Joseph L.; Gunaratne, Gemunu H.

2017-04-01

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t1/2. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

Anomalous scaling of stochastic processes and the Moses effect.

PubMed

Chen, Lijian; Bassler, Kevin E; McCauley, Joseph L; Gunaratne, Gemunu H

2017-04-01

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t^{1/2}. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

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.

Anomalous scaling of passive scalars in rotating flows.

PubMed

Rodriguez Imazio, P; Mininni, P D

2011-06-01

We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric decomposition of velocity and passive scalar structure functions. The passive scalar is more anisotropic than the velocity field, and its power spectrum follows a spectral law consistent with ~ k[Please see text](-3/2). This scaling is explained with phenomenological arguments that consider the effect of rotation. Intermittency is characterized using scaling exponents and probability density functions of velocity and passive scalar increments. In the presence of rotation, intermittency in the velocity field decreases more noticeably than in the passive scalar. The scaling exponents show good agreement with Kraichnan's prediction for passive scalar intermittency in two dimensions, after correcting for the observed scaling of the second-order exponent.

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.

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.

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.

Anomalous diffusion on a random comblike structure

NASA Astrophysics Data System (ADS)

Havlin, Shlomo; Kiefer, James E.; Weiss, George H.

1987-08-01

We have recently studied a random walk on a comblike structure as an analog of diffusion on a fractal structure. In our earlier work, the comb was assumed to have a deterministic structure, the comb having teeth of infinite length. In the present paper we study diffusion on a one-dimensional random comb, the length of whose teeth are random variables with an asymptotic stable law distribution φ(L)~L-(1+γ) where 0<γ<=1. Two mean-field methods are used for the analysis, one based on the continuous-time random walk, and the second a self-consistent scaling theory. Both lead to the same conclusions. We find that the diffusion exponent characterizing the mean-square displacement along the backbone of the comb is dw=4/(1+γ) for γ<1 and dw=2 for γ>=1. The probability of being at the origin at time t is P0(t)~t-ds/2 for large t with ds=(3-γ)/2 for γ<1 and ds=1 for γ>1. When a field is applied along the backbone of the comb the diffusion exponent is dw=2/(1+γ) for γ<1 and dw=1 for γ>=1. The theoretical results are confirmed using the exact enumeration method.

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.

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

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

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.

Poincaré recurrences of DNA sequences

NASA Astrophysics Data System (ADS)

Frahm, K. M.; Shepelyansky, D. L.

2012-01-01

We analyze the statistical properties of Poincaré recurrences of Homo sapiens, mammalian, and other DNA sequences taken from the Ensembl Genome data base with up to 15 billion base pairs. We show that the probability of Poincaré recurrences decays in an algebraic way with the Poincaré exponent β≈4 even if the oscillatory dependence is well pronounced. The correlations between recurrences decay with an exponent ν≈0.6 that leads to an anomalous superdiffusive walk. However, for Homo sapiens sequences, with the largest available statistics, the diffusion coefficient converges to a finite value on distances larger than one million base pairs. We argue that the approach based on Poncaré recurrences determines new proximity features between different species and sheds a new light on their evolution history.

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.

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.

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.

Intrinsic anomalous surface roughening of TiN films deposited by reactive sputtering

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

Auger, M. A.; Centro Nacional de Investigaciones Metalurgicas; Vazquez, L.

2006-01-15

We study surface kinetic roughening of TiN films grown on Si(100) substrates by dc reactive sputtering. The surface morphology of films deposited for different growth times under the same experimental conditions were analyzed by atomic force microscopy. The TiN films exhibit intrinsic anomalous scaling and multiscaling. The film kinetic roughening is characterized by a set of local exponent values {alpha}{sub loc}=1.0 and {beta}{sub loc}=0.39, and global exponent values {alpha}=1.7 and {beta}=0.67, with a coarsening exponent of 1/z=0.39. These properties are correlated to the local height-difference distribution function obeying power-law statistics. We associate this intrinsic anomalous scaling with the instability duemore » to nonlocal shadowing effects that take place during thin-film growth by sputtering.« less

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.

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.

1 / f α noise and generalized diffusion in random Heisenberg spin systems

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

Agarwal, Kartiek; Demler, Eugene; Martin, Ivar

2015-11-01

We study the “flux-noise” spectrum of random-bond quantum Heisenberg spin systems using a real-space renormalization group (RSRG) procedure that accounts for both the renormalization of the system Hamiltonian and of a generic probe that measures the noise. For spin chains, we find that the dynamical structure factor Sq (f ), at finite wave vector q, exhibits a power-law behavior both at high and low frequencies f , with exponents that are connected to one another and to an anomalous dynamical exponent through relations that differ at T = 0 and T =∞. The low-frequency power-law behavior of the structure factormore » is inherited by any generic probe with a finite bandwidth and is of the form 1/f α with 0.5 < α < 1. An analytical calculation of the structure factor, assuming a limiting distribution of the RG flow parameters (spin size, length, bond strength) confirms numerical findings.More generally, we demonstrate that this form of the structure factor, at high temperatures, is a manifestation of anomalous diffusionwhich directly follows from a generalized spin-diffusion propagator.We also argue that 1/f -noise is intimately connected to many-body-localization at finite temperatures. In two dimensions, the RG procedure is less reliable; however, it becomes convergent for quasi-one-dimensional geometries where we find that one-dimensional 1/f α behavior is recovered at low frequencies; the latter configurations are likely representative of paramagnetic spin networks that produce 1/f α noise in SQUIDs.« less

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.

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.

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.

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.

Anomalous scaling of a scalar field advected by turbulence

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

Kraichnan, R.H.

Recent work leading to deduction of anomalous scaling exponents for the inertial range of an advected passive field from the equations of motion is reviewed. Implications for other turbulence problems are discussed.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

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.

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.

Anomalous diffusion of a probe in a bath of active granular chains

NASA Astrophysics Data System (ADS)

Jerez, Michael Jade Y.; Confesor, Mark Nolan P.; Carpio-Bernido, M. Victoria; Bernido, Christopher C.

2017-08-01

We investigate the dynamics of a passive probe particle in a bath of active granular chains (AGC). The bath and the probe are enclosed in an experimental compartment with a sinusoidal boundary to prevent AGC congestion along the boundary while connected to an electrodynamic shaker. Single AGC trajectory analysis reveals a persistent type of motion compared to a purely Brownian motion as seen in its mean squared displacement (MSD). It was found that at small concentration, Φ ≤ 0.44, the MSD exhibits two dynamical regimes characterized by two different scaling exponents. For small time scales, the dynamics is superdiffusive (1.32-1.63) with the MSD scaling exponent increasing monotonically with increasing AGC concentration. On the other hand, at long time, we recover the Brownian dynamics regime, MSD = DΔt, where the mobility D ∝ Φ. We quantify the probe dynamics at short time scale by modeling it as a fractional Brownian motion. The analytical form of the MSD agrees with experimental results.

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.

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.

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 transport in Charney-Hasegawa-Mima flows

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

Leoncini, Xavier; Agullo, Olivier; Benkadda, Sadruddin

2005-08-01

The transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a nonlinear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow. All characteristic transport exponents have a similar value around {mu}=1.75, which is also the one found for simple point vortex flows in the literature, indicating some kind of universality. Moreover, the law {gamma}={mu}+1 linking the trapping-time exponent within jets to the transport exponent is confirmed, and an accumulation toward zero ofmore » the spectrum of the finite-time Lyapunov exponent is observed. The localization of a jet is performed, and its structure is analyzed. It is clearly shown that despite a regular coarse-grained picture of the jet, the motion within the jet appears as chaotic, but that chaos is bounded on successive small scales.« less

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.

Non-Porod scattering and non-integer scaling of resistance in rough films

NASA Astrophysics Data System (ADS)

Bupathy, Arunkumar; Verma, Rupesh; Banerjee, Varsha; Puri, Sanjay

2017-04-01

In many physical systems, films are rough due to the stochastic behavior of depositing particles. They are characterized by non-Porod power law decays in the structure factor S (k) . Theoretical studies predict anomalous diffusion in such morphologies, with important implications for diffusivity, conductivity, etc. We use the non-Porod decay to accurately determine the fractal properties of two prototypical nanoparticle films: (i) Palladium (Pd) and (ii) Cu2O. Using scaling arguments, we find that the resistance of rough films of lateral size L obeys a non-integer power law R ∼L-ζ , in contrast to integer power laws for compact structures. The exponent ζ is anisotropic. We confirm our predictions by re-analyzing experimental data from Cu2O nano-particle films. Our results are valuable for understanding recent experiments that report anisotropic electrical properties in (rough) thin films.

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.

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.

Creep properties of Pb-free solder joints

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

Song, H.G.; Morris Jr., J.W.; Hua, F.

2002-04-01

Describes the creep behavior of three Sn-rich solders that have become candidates for use in Pb-free solder joints: Sn-3.5Ag, Sn-3Ag-0.5Cu and Sn-0.7Cu. The three solders show the same general behavior when tested in thin joints between Cu and Ni/Au metallized pads at temperatures between 60 and 130 C. Their steady-state creep rates are separated into two regimes with different stress exponents(n). The low-stress exponents range from {approx}3-6, while the high-stress exponents are anomalously high (7-12). Strikingly, the high-stress exponent has a strong temperature dependence near room temperature, increasing significantly as the temperature drops from 95 to 60 C. The anomalousmore » creep behavior of the solders appears to be due to the dominant Sn constituent. Joints of pure Sn have stress exponents, n, that change with stress and temperature almost exactly like those of the Sn-rich solder joints. Research on creep in bulk samples of pure Sn suggests that the anomalous temperature dependence of the stress exponent may show a change in the dominant mechanism of creep. Whatever its source, it has the consequence that conventional constitutive relations for steady-state creep must be used with caution in treating Sn-rich solder joints, and qualification tests that are intended to verify performance should be carefully designed.« less

Rectified brownian transport in corrugated channels: Fractional brownian motion and Lévy flights.

PubMed

Ai, Bao-quan; Shao, Zhi-gang; Zhong, Wei-rong

2012-11-07

We study fractional brownian motion and Lévy flights in periodic corrugated channels without any external driving forces. From numerical simulations, we find that both fractional gaussian noise and Lévy-stable noise in asymmetric corrugated channels can break thermodynamical equilibrium and induce directed transport. The rectified mechanisms for fractional brownian motion and Lévy flights are different. The former is caused by non-uniform spectral distribution (low or high frequencies) of fractional gaussian noise, while the latter is due to the nonthermal character (occasional long jumps) of the Lévy-stable noise. For fractional brownian motion, average velocity increases with the Hurst exponent for the persistent case, while for the antipersistent case there exists an optimal value of Hurst exponent at which average velocity takes its maximal value. For Lévy flights, the group velocity decreases monotonically as the Lévy index increases. In addition, for both cases, the optimized periodicity and radius at the bottleneck can facilitate the directed transport. Our results could be implemented in constrained structures with narrow channels and pores where the particles undergo anomalous diffusion.

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.

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.

Higher-order phase transitions on financial markets

NASA Astrophysics Data System (ADS)

Kasprzak, A.; Kutner, R.; Perelló, J.; Masoliver, J.

2010-08-01

Statistical and thermodynamic properties of the anomalous multifractal structure of random interevent (or intertransaction) times were thoroughly studied by using the extended continuous-time random walk (CTRW) formalism of Montroll, Weiss, Scher, and Lax. Although this formalism is quite general (and can be applied to any interhuman communication with nontrivial priority), we consider it in the context of a financial market where heterogeneous agent activities can occur within a wide spectrum of time scales. As the main general consequence, we found (by additionally using the Saddle-Point Approximation) the scaling or power-dependent form of the partition function, Z(q'). It diverges for any negative scaling powers q' (which justifies the name anomalous) while for positive ones it shows the scaling with the general exponent τ(q'). This exponent is the nonanalytic (singular) or noninteger power of q', which is one of the pilar of higher-order phase transitions. In definition of the partition function we used the pausing-time distribution (PTD) as the central one, which takes the form of convolution (or superstatistics used, e.g. for describing turbulence as well as the financial market). Its integral kernel is given by the stretched exponential distribution (often used in disordered systems). This kernel extends both the exponential distribution assumed in the original version of the CTRW formalism (for description of the transient photocurrent measured in amorphous glassy material) as well as the Gaussian one sometimes used in this context (e.g. for diffusion of hydrogen in amorphous metals or for aging effects in glasses). Our most important finding is the third- and higher-order phase transitions, which can be roughly interpreted as transitions between the phase where high frequency trading is most visible and the phase defined by low frequency trading. The specific order of the phase transition directly depends upon the shape exponent α defining the stretched exponential integral kernel. On this basis a simple practical hint for investors was formulated.

Anomalous Kinetics of Diffusion-Controlled Defect Annealing in Irradiated Ionic Solids.

PubMed

Kotomin, Eugene; Kuzovkov, Vladimir; Popov, Anatoli I; Maier, Joachim; Vila, Rafael

2018-01-11

The annealing kinetics of the primary electronic F-type color centers (oxygen vacancies with trapped one or two electrons) is analyzed for three ionic materials (Al 2 O 3 , MgO, and MgF 2 ) exposed to intensive irradiation by electrons, neutrons, and heavy swift ions. Phenomenological theory of diffusion-controlled recombination of the F-type centers with much more mobile interstitial ions (complementary hole centers) allows us to extract from experimental data the migration energy of interstitials and pre-exponential factor of diffusion. The obtained migration energies are compared with available first-principles calculations. It is demonstrated that with the increase of radiation fluence both the migration energy and pre-exponent are decreasing in all three materials, irrespective of the type of irradiation. Their correlation satisfies the Meyer-Neldel rule observed earlier in glasses, liquids, and disordered materials.The origin of this effect is discussed. This study demonstrates that in the quantitative analysis of the radiation damage of real materials the dependence of the defect migration parameters on the radiation fluence plays an important role and cannot be neglected.

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

NASA Astrophysics Data System (ADS)

Gross, Markus

2018-03-01

A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards–Wilkinson equation with non-conserved noise and the Mullins–Herring equation with conserved noise. The profile is subject to either periodic or Dirichlet (no-flux) boundary conditions. We determine the noise-driven time-evolution of the profile between an initially flat configuration and the instant at which the profile reaches a given height M for the first time. The shape of the averaged profile agrees well with the prediction of weak-noise theory (WNT), which describes the most-likely trajectory to a fixed first-passage time. Furthermore, in agreement with WNT, on average the profile approaches the height M algebraically in time, with an exponent that is essentially independent of the boundary conditions. However, the actual value of the dynamic exponent turns out to be significantly smaller than predicted by WNT. This ‘renormalization’ of the exponent is explained in terms of the entropic repulsion exerted by the impenetrable boundary on the fluctuations of the profile around its most-likely path. The entropic repulsion mechanism is analyzed in detail for a single (fractional) Brownian walker, which describes the anomalous diffusion of a tagged monomer of the interface as it approaches the absorbing boundary. The present study sheds light on the accuracy and the limitations of the weak-noise approximation for the description of the full first-passage dynamics.

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

Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: effects of strong compressibility and large-scale anisotropy.

PubMed

Antonov, N V; Kostenko, M M

2014-12-01

The field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities (the density and the tracer fields) advected by a random turbulent velocity field. The latter is governed by the Navier-Stokes equation for compressible fluid, subject to external random force with the covariance ∝δ(t-t')k(4-d-y), where d is the dimension of space and y is an arbitrary exponent. The original stochastic problems are reformulated as multiplicatively renormalizable field theoretic models; the corresponding renormalization group equations possess infrared attractive fixed points. It is shown that various correlation functions of the scalar field, its powers and gradients, demonstrate anomalous scaling behavior in the inertial-convective range already for small values of y. The corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields ("operators" in the quantum-field terminology), can be systematically calculated as series in y. The practical calculation is performed in the leading one-loop approximation, including exponents in anisotropic contributions. It should be emphasized that, in contrast to Gaussian ensembles with finite correlation time, the model and the perturbation theory presented here are manifestly Galilean covariant. The validity of the one-loop approximation and comparison with Gaussian models are briefly discussed.

Transport properties of elastically coupled fractional Brownian motors

NASA Astrophysics Data System (ADS)

Lv, Wangyong; Wang, Huiqi; Lin, Lifeng; Wang, Fei; Zhong, Suchuan

2015-11-01

Under the background of anomalous diffusion, which is characterized by the sub-linear or super-linear mean-square displacement in time, we proposed the coupled fractional Brownian motors, in which the asymmetrical periodic potential as ratchet is coupled mutually with elastic springs, and the driving source is the external harmonic force and internal thermal fluctuations. The transport mechanism of coupled particles in the overdamped limit is investigated as the function of the temperature of baths, coupling constant and natural length of the spring, the amplitude and frequency of driving force, and the asymmetry of ratchet potential by numerical stimulations. The results indicate that the damping force involving the information of historical velocity leads to the nonlocal memory property and blocks the traditional dissipative motion behaviors, and it even plays a cooperative role of driving force in drift motion of the coupled particles. Thus, we observe various non-monotonic resonance-like behaviors of collective directed transport in the mediums with different diffusion exponents.

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.

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.

FAST TRACK COMMUNICATION: Suppressing anomalous diffusion by cooperation

NASA Astrophysics Data System (ADS)

Dybiec, Bartłomiej

2010-08-01

Within a continuous time random walk scenario we consider a motion of a complex of particles which moves coherently. The motion of every particle is characterized by the waiting time and jump length distributions which are of the power-law type. Due to the interactions between particles it is assumed that the waiting time is adjusted to the shortest or to the longest waiting time. Analogously, the jump length is adjusted to the shortest or to the longest jump length. We show that adjustment to the shortest waiting time can suppress the subdiffusive behavior even in situations when the exponent characterizing the waiting time distribution assures subdiffusive motion of a single particle. Finally, we demonstrate that the characteristic of the motion depends on the number of particles building a complex.

Anomalous quantum heat transport in a one-dimensional harmonic chain with random couplings.

PubMed

Yan, Yonghong; Zhao, Hui

2012-07-11

We investigate quantum heat transport in a one-dimensional harmonic system with random couplings. In the presence of randomness, phonon modes may normally be classified as ballistic, diffusive or localized. We show that these modes can roughly be characterized by the local nearest-neighbor level spacing distribution, similarly to their electronic counterparts. We also show that the thermal conductance G(th) through the system decays rapidly with the system size (G(th) ∼ L(-α)). The exponent α strongly depends on the system size and can change from α < 1 to α > 1 with increasing system size, indicating that the system undergoes a transition from a heat conductor to a heat insulator. This result could be useful in thermal control of low-dimensional systems.

Revisiting point FRAP to quantitatively characterize anomalous diffusion in live cells.

PubMed

Daddysman, Matthew K; Fecko, Christopher J

2013-02-07

Fluorescence recovery after photobleaching (FRAP) is widely used to interrogate diffusion and binding of proteins in live cells. Herein, we apply two-photon excited FRAP with a diffraction limited bleaching and observation volume to study anomalous diffusion of unconjugated green fluorescence protein (GFP) in vitro and in cells. Experiments performed on dilute solutions of GFP reveal that reversible fluorophore bleaching can be mistakenly interpreted as anomalous diffusion. We derive a reaction-diffusion FRAP model that includes reversible photobleaching, and demonstrate that it properly accounts for these photophysics. We then apply this model to investigate the diffusion of GFP in HeLa cells and polytene cells of Drosophila larval salivary glands. GFP exhibits anomalous diffusion in the cytoplasm of both cell types and in HeLa nuclei. Polytene nuclei contain optically resolvable chromosomes, permitting FRAP experiments that focus separately on chromosomal or interchrosomal regions. We find that GFP exhibits anomalous diffusion in chromosomal regions but diffuses normally in regions devoid of chromatin. This observation indicates that obstructed transport through chromatin and not crowding by macromolecules is a source of anomalous diffusion in polytene nuclei. This behavior is likely true in other cells, so it will be important to account for this type of transport physics and for reversible photobleaching to properly interpret future FRAP experiments on DNA-binding proteins.

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.

New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains

NASA Astrophysics Data System (ADS)

Damanik, David; Lemm, Marius; Lukic, Milivoje; Yessen, William

2014-09-01

We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson (LR) bound for an isotropic XY chain in a quasiperiodic transversal magnetic field. Instead of the usual effective light cone |x|≤v|t|, we obtain |x|≤v|t|α for some 0<α <1. We can characterize the allowed values of α exactly as those exceeding the upper transport exponent αu+ of a one-body Schrödinger operator. To our knowledge, this is the first rigorous derivation of anomalous quantum many-body transport. We also discuss anomalous LR bounds with power-law tails for a random dimer field.

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 bifractal nature of reticular patterns induced by oxygen plasma on polymer films

NASA Astrophysics Data System (ADS)

Bae, Junwan; Lee, I. J.

2015-05-01

Plasma etching was demonstrated to be a promising tool for generating self-organized nano-patterns on various commercial films. Unfortunately, dynamic scaling approach toward fundamental understanding of the formation and growth of the plasma-induced nano-structure has not always been straightforward. The temporal evolution of self-aligned nano-patterns may often evolve with an additional scale-invariance, which leads to breakdown of the well-established dynamic scaling law. The concept of a bifractal interface is successfully applied to reticular patterns induced by oxygen plasma on the surface of polymer films. The reticular pattern, composed of nano-size self-aligned protuberances and underlying structure, develops two types of anomalous dynamic scaling characterized by super-roughening and intrinsic anomalous scaling, respectively. The diffusion and aggregation of short-cleaved chains under the plasma environment are responsible for the regular distribution of the nano-size protuberances. Remarkably, it is uncovered that the dynamic roughening of the underlying structure is governed by a relaxation mechanism described by the Edwards-Wilkinson universality class with a conservative noise. The evidence for the basic phase, characterized by the negative roughness and growth exponents, has been elusive since its first theoretical consideration more than two decades ago.

Randomly diluted xy and resistor networks near the percolation threshold

NASA Astrophysics Data System (ADS)

Harris, A. B.; Lubensky, T. C.

1987-05-01

A formulation based on that of Stephen for randomly diluted systems near the percolation threshold is analyzed in detail. By careful consideration of various limiting procedures, a treatment of xy spin models and resistor networks is given which shows that previous calculations (which indicate that these systems having continuous symmetry have the same crossover exponents as the Ising model) are in error. By studying the limit wherein the energy gap goes to zero, we exhibit the mathematical mechanism which leads to qualitatively different results for xy-like as contrasted to Ising-like systems. A distinctive feature of the results is that there is an infinite sequence of crossover exponents needed to completely describe the probability distribution for R(x,x'), the resistance between sites x and x'. Because of the difference in symmetry between the xy model and the resistor network, the former has an infinite sequence of crossover exponents in addition to those of the resistor network. The first crossover exponent φ1=1+ɛ/42 governs the scaling behavior of R(x,x') with ||x-x'||≡r: [R(x,x')]c~xφ1/ν, where [ ]c indicates a conditional average, subject to x and x' being in the same cluster, ν is the correlation length exponent for percolation, and ɛ=6-d, where d is the spatial dimensionality. We give a detailed analysis of the scaling properties of the bulk conductivity and the anomalous diffusion constant introduced by Gefen et al. Our results show conclusively that the Alexander-Orbach conjecture, while numerically quite accurate, is not exact, at least in high spatial dimension. We also evaluate various amplitude ratios associated with susceptibilities, χn involving the nth power of the resistance R(x,x'), e.g., &χ2χ0/χ21=2[1+(19ɛ/420)]. In an appendix we outline how the calculation can be extended to treat the diluted m-component spin model for m>2. As expected, the results for φ1 remain valid for m>2. The techniques described here have led to several recent calculations of various infinite families of exponents.

Critical decay exponent of the pair contact process with diffusion

NASA Astrophysics Data System (ADS)

Park, Su-Chan

2014-11-01

We investigate the one-dimensional pair contact process with diffusion (PCPD) by extensive Monte Carlo simulations, mainly focusing on the critical density decay exponent δ . To obtain an accurate estimate of δ , we first find the strength of corrections to scaling using the recently introduced method [S.-C. Park. J. Korean Phys. Soc. 62, 469 (2013), 10.3938/jkps.62.469]. For small diffusion rate (d ≤0.5 ), the leading corrections-to-scaling term is found to be ˜t-0.15, whereas for large diffusion rate (d =0.95 ) it is found to be ˜t-0.5. After finding the strength of corrections to scaling, effective exponents are systematically analyzed to conclude that the value of critical decay exponent δ is 0.173 (3 ) irrespective of d . This value should be compared with the critical decay exponent of the directed percolation, 0.1595. In addition, we study two types of crossover. At d =0 , the phase boundary is discontinuous and the crossover from the pair contact process to the PCPD is found to be described by the crossover exponent ϕ =2.6 (1 ) . We claim that the discontinuity of the phase boundary cannot be consistent with the theoretical argument supporting the hypothesis that the PCPD should belong to the DP. At d =1 , the crossover from the mean field PCPD to the PCPD is described by ϕ =2 which is argued to be exact.

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

PubMed

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

2016-07-27

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.

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.

Anomalous Fluctuations in Autoregressive Models with Long-Term Memory

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Honjo, Haruo

2015-10-01

An autoregressive model with a power-law type memory kernel is studied as a stochastic process that exhibits a self-affine-fractal-like behavior for a small time scale. We find numerically that the root-mean-square displacement Δ(m) for the time interval m increases with a power law as mα with α < 1/2 for small m but saturates at sufficiently large m. The exponent α changes with the power exponent of the memory kernel.

Theoretical Investigation Leading to Energy Storage in Atomic and Molecular Systems

DTIC Science & Technology

1990-12-01

can be calculated in a single run. 21 j) Non-gradient optimization of basis function exponents is possible. The source code can be modified to carry...basis. The 10s3p/5s3p basis consists of the 9s/4s contraction of Siegbahn and Liu (Reference 91) augmented by a diffuse s-type function ( exponent ...vibrational modes. Introduction of diffuse basis functions and optimization of the d-orbital exponents have a small but important effect on the

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise.

PubMed

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Cusping, transport and variance of solutions to generalized Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Carnaffan, Sean; Kawai, Reiichiro

2017-06-01

We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.

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

Anomalous bulk behavior in the free parafermion Z (N ) spin chain

NASA Astrophysics Data System (ADS)

Alcaraz, Francisco C.; Batchelor, Murray T.

2018-06-01

We demonstrate using direct numerical diagonalization and extrapolation methods that boundary conditions have a profound effect on the bulk properties of a simple Z (N ) model for N ≥3 for which the model Hamiltonian is non-Hermitian. For N =2 the model reduces to the well-known quantum Ising model in a transverse field. For open boundary conditions, the Z (N ) model is known to be solved exactly in terms of free parafermions. Once the ends of the open chain are connected by considering the model on a ring, the bulk properties, including the ground-state energy per site, are seen to differ dramatically with increasing N . Other properties, such as the leading finite-size corrections to the ground-state energy, the mass gap exponent, and the specific-heat exponent, are also seen to be dependent on the boundary conditions. We speculate that this anomalous bulk behavior is a topological effect.

Resonant behavior of the generalized Langevin system with tempered Mittag–Leffler memory kernel

NASA Astrophysics Data System (ADS)

Chen, Yao; Wang, Xudong; Deng, Weihua

2018-05-01

The generalized Langevin equation describes anomalous dynamics. Noise is not only the origin of uncertainty but also plays a positive role in helping to detect signals with information, termed stochastic resonance (SR). This paper analyzes the anomalous resonant behaviors of the generalized Langevin system with a multiplicative dichotomous noise and an internal tempered Mittag–Leffler noise. For a system with a fluctuating harmonic potential, we obtain the exact expressions of several types of SR such as the first moment, the amplitude and autocorrelation function for the output signal as well as the signal–noise ratio. We analyze the influence of the tempering parameter and memory exponent on the bona fide SR and the general SR. Moreover, it is detected that the critical memory exponent changes regularly with the increase of the tempering parameter. Almost all the theoretical results are validated by numerical simulations.

Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs.

PubMed

Iubini, Stefano; Di Cintio, Pierfrancesco; Lepri, Stefano; Livi, Roberto; Casetti, Lapo

2018-03-01

We investigate thermal conduction in arrays of long-range interacting rotors and Fermi-Pasta-Ulam (FPU) oscillators coupled to two reservoirs at different temperatures. The strength of the interaction between two lattice sites decays as a power α of the inverse of their distance. We point out the necessity of distinguishing between energy flows towards or from the reservoirs and those within the system. We show that energy flow between the reservoirs occurs via a direct transfer induced by long-range couplings and a diffusive process through the chain. To this aim, we introduce a decomposition of the steady-state heat current that explicitly accounts for such direct transfer of energy between the reservoir. For 0≤α<1, the direct transfer term dominates, meaning that the system can be effectively described as a set of oscillators each interacting with the thermal baths. Also, the heat current exchanged with the reservoirs depends on the size of the thermalized regions: In the case in which such size is proportional to the system size N, the stationary current is independent on N. For α>1, heat transport mostly occurs through diffusion along the chain: For the rotors transport is normal, while for FPU the data are compatible with an anomalous diffusion, possibly with an α-dependent characteristic exponent.

Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

NASA Astrophysics Data System (ADS)

Iubini, Stefano; Di Cintio, Pierfrancesco; Lepri, Stefano; Livi, Roberto; Casetti, Lapo

2018-03-01

We investigate thermal conduction in arrays of long-range interacting rotors and Fermi-Pasta-Ulam (FPU) oscillators coupled to two reservoirs at different temperatures. The strength of the interaction between two lattice sites decays as a power α of the inverse of their distance. We point out the necessity of distinguishing between energy flows towards or from the reservoirs and those within the system. We show that energy flow between the reservoirs occurs via a direct transfer induced by long-range couplings and a diffusive process through the chain. To this aim, we introduce a decomposition of the steady-state heat current that explicitly accounts for such direct transfer of energy between the reservoir. For 0 ≤α <1 , the direct transfer term dominates, meaning that the system can be effectively described as a set of oscillators each interacting with the thermal baths. Also, the heat current exchanged with the reservoirs depends on the size of the thermalized regions: In the case in which such size is proportional to the system size N , the stationary current is independent on N . For α >1 , heat transport mostly occurs through diffusion along the chain: For the rotors transport is normal, while for FPU the data are compatible with an anomalous diffusion, possibly with an α -dependent characteristic exponent.

Rad4 recognition-at-a-distance: Physical basis of conformation-specific anomalous diffusion of DNA repair proteins.

PubMed

Kong, Muwen; Van Houten, Bennett

2017-08-01

Since Robert Brown's first observations of random walks by pollen particles suspended in solution, the concept of diffusion has been subject to countless theoretical and experimental studies in diverse fields from finance and social sciences, to physics and biology. Diffusive transport of macromolecules in cells is intimately linked to essential cellular functions including nutrient uptake, signal transduction, gene expression, as well as DNA replication and repair. Advancement in experimental techniques has allowed precise measurements of these diffusion processes. Mathematical and physical descriptions and computer simulations have been applied to model complicated biological systems in which anomalous diffusion, in addition to simple Brownian motion, was observed. The purpose of this review is to provide an overview of the major physical models of anomalous diffusion and corresponding experimental evidence on the target search problem faced by DNA-binding proteins, with an emphasis on DNA repair proteins and the role of anomalous diffusion in DNA target recognition. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

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.

Critical short-time dynamics in a system with interacting static and diffusive populations

NASA Astrophysics Data System (ADS)

Argolo, C.; Quintino, Yan; Gleria, Iram; Lyra, M. L.

2012-01-01

We study the critical short-time dynamical behavior of a one-dimensional model where diffusive individuals can infect a static population upon contact. The model presents an absorbing phase transition from an active to an inactive state. Previous calculations of the critical exponents based on quasistationary quantities have indicated an unusual crossover from the directed percolation to the diffusive contact process universality classes. Here we show that the critical exponents governing the slow short-time dynamic evolution of several relevant quantities, including the order parameter, its relative fluctuations, and correlation function, reinforce the lack of universality in this model. Accurate estimates show that the critical exponents are distinct in the regimes of low and high recovery rates.

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).

Numerical schemes for anomalous diffusion of single-phase fluids in porous media

NASA Astrophysics Data System (ADS)

Awotunde, Abeeb A.; Ghanam, Ryad A.; Al-Homidan, Suliman S.; Tatar, Nasser-eddine

2016-10-01

Simulation of fluid flow in porous media is an indispensable part of oil and gas reservoir management. Accurate prediction of reservoir performance and profitability of investment rely on our ability to model the flow behavior of reservoir fluids. Over the years, numerical reservoir simulation models have been based mainly on solutions to the normal diffusion of fluids in the porous reservoir. Recently, however, it has been documented that fluid flow in porous media does not always follow strictly the normal diffusion process. Small deviations from normal diffusion, called anomalous diffusion, have been reported in some experimental studies. Such deviations can be caused by different factors such as the viscous state of the fluid, the fractal nature of the porous media and the pressure pulse in the system. In this work, we present explicit and implicit numerical solutions to the anomalous diffusion of single-phase fluids in heterogeneous reservoirs. An analytical solution is used to validate the numerical solution to the simple homogeneous case. The conventional wellbore flow model is modified to account for anomalous behavior. Example applications are used to show the behavior of wellbore and wellblock pressures during the single-phase anomalous flow of fluids in the reservoirs considered.

Revealing mesoscopic structural universality with diffusion.

PubMed

Novikov, Dmitry S; Jensen, Jens H; Helpern, Joseph A; Fieremans, Els

2014-04-08

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke.

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.

Clearing out a maze: A model of chemotactic motion in porous media

NASA Astrophysics Data System (ADS)

Schilling, Tanja; Voigtmann, Thomas

2017-12-01

We study the anomalous dynamics of a biased "hungry" (or "greedy") random walk on a percolating cluster. The model mimics chemotaxis in a porous medium: In close resemblance to the 1980s arcade game PAC-MA N ®, the hungry random walker consumes food, which is initially distributed in the maze, and biases its movement towards food-filled sites. We observe that the mean-squared displacement of the process follows a power law with an exponent that is different from previously known exponents describing passive or active microswimmer dynamics. The change in dynamics is well described by a dynamical exponent that depends continuously on the propensity to move towards food. It results in slower differential growth when compared to the unbiased random walk.

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 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.

Revealing mesoscopic structural universality with diffusion

PubMed Central

Novikov, Dmitry S.; Jensen, Jens H.; Helpern, Joseph A.; Fieremans, Els

2014-01-01

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke. PMID:24706873

Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

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

Litvinenko, Yuri E.; Fichtner, Horst; Walter, Dominik

2017-05-20

We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatmentmore » of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.« less

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.

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.

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

Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in O(N) models

NASA Astrophysics Data System (ADS)

Péli, Zoltán; Nagy, Sándor; Sailer, Kornel

2018-02-01

The effect of the O(partial4) terms of the gradient expansion on the anomalous dimension η and the correlation length's critical exponent ν of the Wilson-Fisher fixed point has been determined for the Euclidean 3-dimensional O( N) models with N≥ 2 . Wetterich's effective average action renormalization group method is used with field-independent derivative couplings and Litim's optimized regulator. It is shown that the critical theory is well approximated by the effective average action preserving O( N) symmetry with an accuracy of O(η).

Concentration-Encoded Subdiffusive Molecular Communication: Theory, Channel Characteristics, and Optimum Signal Detection.

PubMed

Mahfuz, Mohammad Upal; Makrakis, Dimitrios; Mouftah, Hussein T

2016-09-01

Unlike normal diffusion, in anomalous diffusion, the movement of a molecule is described by the correlated random walk model where the mean square displacement of a molecule depends on the power law of time. In molecular communication (MC), there are many scenarios when the propagation of molecules cannot be described by normal diffusion process, where anomalous diffusion is a better fit. In this paper, the effects of anomalous subdiffusion on concentration-encoded molecular communication (CEMC) are investigated. Although classical (i.e., normal) diffusion is a widely-used model of diffusion in molecular communication (MC) research, anomalous subdiffusion is quite common in biological media involving bio-nanomachines, yet inadequately addressed as a research issue so far. Using the fractional diffusion approach, the molecular propagation effects in the case of pure subdiffusion occurring in an unbounded three-dimensional propagation medium have been shown in detail in terms of temporal dispersion parameters of the impulse response of the subdiffusive channel. Correspondingly, the bit error rate (BER) performance of a CEMC system is investigated with sampling-based (SD) and strength (i.e., energy)-based (ED) signal detection methods. It is found that anomalous subdiffusion has distinctive time-dispersive properties that play a vital role in accurately designing a subdiffusive CEMC system. Unlike normal diffusion, to detect information symbols in subdiffusive CEMC, a receiver requires larger memory size to operate correctly and hence a more complex structure. An in-depth analysis has been made on the performances of SD and ED optimum receiver models under diffusion noise and intersymbol interference (ISI) scenarios when communication range, transmission data rate, and memory size vary. In subdiffusive CEMC, the SD method.

Evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy.

PubMed

Zhang, Wenqing; Qiu, Lu; Xiao, Qin; Yang, Huijie; Zhang, Qingjun; Wang, Jianyong

2012-11-01

By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments (∼0.8). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages (∼0.7). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series (∼10^{2}), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions.

Evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy

NASA Astrophysics Data System (ADS)

Zhang, Wenqing; Qiu, Lu; Xiao, Qin; Yang, Huijie; Zhang, Qingjun; Wang, Jianyong

2012-11-01

By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments (˜0.8). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages (˜0.7). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series (˜102), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions.

Mechanisms underlying anomalous diffusion in the plasma membrane.

PubMed

Krapf, Diego

2015-01-01

The plasma membrane is a complex fluid where lipids and proteins undergo diffusive motion critical to biochemical reactions. Through quantitative imaging analyses such as single-particle tracking, it is observed that diffusion in the cell membrane is usually anomalous in the sense that the mean squared displacement is not linear with time. This chapter describes the different models that are employed to describe anomalous diffusion, paying special attention to the experimental evidence that supports these models in the plasma membrane. We review models based on anticorrelated displacements, such as fractional Brownian motion and obstructed diffusion, and nonstationary models such as continuous time random walks. We also emphasize evidence for the formation of distinct compartments that transiently form on the cell surface. Finally, we overview heterogeneous diffusion processes in the plasma membrane, which have recently attracted considerable interest. Copyright © 2015. Published by Elsevier Inc.

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.

Critical exponents of the explosive percolation transition

NASA Astrophysics Data System (ADS)

da Costa, R. A.; Dorogovtsev, S. N.; Goltsev, A. V.; Mendes, J. F. F.

2014-04-01

In a new type of percolation phase transition, which was observed in a set of nonequilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential merging of small components and delays the emergence of the percolation cluster. First simulations led to a conclusion that a percolation cluster in this irreversible process is born discontinuously, by a discontinuous phase transition, which results in the term "explosive percolation transition." We have shown that this transition is actually continuous (second order) though with an anomalously small critical exponent of the percolation cluster. Here we propose an efficient numerical method enabling us to find the critical exponents and other characteristics of this second-order transition for a representative set of explosive percolation models with different number of choices. The method is based on gluing together the numerical solutions of evolution equations for the cluster size distribution and power-law asymptotics. For each of the models, with high precision, we obtain critical exponents and the critical point.

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.

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

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.

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

The applications of Complexity Theory and Tsallis Non-extensive Statistics at Solar Plasma Dynamics

NASA Astrophysics Data System (ADS)

Pavlos, George

2015-04-01

As the solar plasma lives far from equilibrium it is an excellent laboratory for testing complexity theory and non-equilibrium statistical mechanics. In this study, we present the highlights of complexity theory and Tsallis non extensive statistical mechanics as concerns their applications at solar plasma dynamics, especially at sunspot, solar flare and solar wind phenomena. Generally, when a physical system is driven far from equilibrium states some novel characteristics can be observed related to the nonlinear character of dynamics. Generally, the nonlinearity in space plasma dynamics can generate intermittent turbulence with the typical characteristics of the anomalous diffusion process and strange topologies of stochastic space plasma fields (velocity and magnetic fields) caused by the strange dynamics and strange kinetics (Zaslavsky, 2002). In addition, according to Zelenyi and Milovanov (2004) the complex character of the space plasma system includes the existence of non-equilibrium (quasi)-stationary states (NESS) having the topology of a percolating fractal set. The stabilization of a system near the NESS is perceived as a transition into a turbulent state determined by self-organization processes. The long-range correlation effects manifest themselves as a strange non-Gaussian behavior of kinetic processes near the NESS plasma state. The complex character of space plasma can also be described by the non-extensive statistical thermodynamics pioneered by Tsallis, which offers a consistent and effective theoretical framework, based on a generalization of Boltzmann - Gibbs (BG) entropy, to describe far from equilibrium nonlinear complex dynamics (Tsallis, 2009). In a series of recent papers, the hypothesis of Tsallis non-extensive statistics in magnetosphere, sunspot dynamics, solar flares, solar wind and space plasma in general, was tested and verified (Karakatsanis et al., 2013; Pavlos et al., 2014; 2015). Our study includes the analysis of solar plasma time series at three cases: sunspot index, solar flare and solar wind data. The non-linear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis (1988; 2004; 2009). The q-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum f(a), the generalized Renyi dimension spectrum D(q) and the spectrum J(p) of the structure function exponents were estimated experimentally and theoretically by using the q-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2000, 2001). Our analysis showed clearly the following: (a) a phase transition process in the solar dynamics from high dimensional non-Gaussian SOC state to a low dimensional non-Gaussian chaotic state, (b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes a phase transition to low dimensional chaos in accordance to Ruzmaikin, Zelenyi and Milovanov's studies (Zelenyi and Milovanov, 1991; Milovanov and Zelenyi, 1993; Ruzmakin et al., 1996), (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of: (i) non-Gaussian probability distribution function P(x), (ii) multifractal scaling exponent spectrum f(a) and generalized Renyi dimension spectrum Dq, (iii) exponent spectrum J(p) of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics. Also, the q-triplet of Tsallis as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the singular value decomposition (SVD) components of the solar flares timeseries. Also the multifractal scaling exponent spectrum f(a), the generalized Renyi dimension spectrum D(q) and the spectrum J(p) of the structure function exponents were estimated experimentally and theoretically by using the q-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2000). Our analysis showed clearly the following: (a) a phase transition process in the solar flare dynamics from a high dimensional non-Gaussian self-organized critical (SOC) state to a low dimensional also non-Gaussian chaotic state, (b) strong intermittent solar corona turbulence and an anomalous (multifractal) diffusion solar corona process, which is strengthened as the solar corona dynamics makes a phase transition to low dimensional chaos, (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of the functions: (i) non-Gaussian probability distribution function P(x), (ii) f(a) and D(q), and (iii) J(p) for the solar flares timeseries and its underlying non-equilibrium solar dynamics, and (d) the solar flare dynamical profile is revealed similar to the dynamical profile of the solar corona zone as far as the phase transition process from self-organized criticality (SOC) to chaos state. However the solar low corona (solar flare) dynamical characteristics can be clearly discriminated from the dynamical characteristics of the solar convection zone. At last we present novel results revealing non-equilibrium phase transition processes in the solar wind plasma during a strong shock event, which can take place in Solar wind plasma system. The solar wind plasma as well as the entire solar plasma system is a typical case of stochastic spatiotemporal distribution of physical state variables such as force fields ( ) and matter fields (particle and current densities or bulk plasma distributions). This study shows clearly the non-extensive and non-Gaussian character of the solar wind plasma and the existence of multi-scale strong correlations from the microscopic to the macroscopic level. It also underlines the inefficiency of classical magneto-hydro-dynamic (MHD) or plasma statistical theories, based on the classical central limit theorem (CLT), to explain the complexity of the solar wind dynamics, since these theories include smooth and differentiable spatial-temporal functions (MHD theory) or Gaussian statistics (Boltzmann-Maxwell statistical mechanics). On the contrary, the results of this study indicate the presence of non-Gaussian non-extensive statistics with heavy tails probability distribution functions, which are related to the q-extension of CLT. Finally, the results of this study can be understood in the framework of modern theoretical concepts such as non-extensive statistical mechanics (Tsallis, 2009), fractal topology (Zelenyi and Milovanov, 2004), turbulence theory (Frisch, 1996), strange dynamics (Zaslavsky, 2002), percolation theory (Milovanov, 1997), anomalous diffusion theory and anomalous transport theory (Milovanov, 2001), fractional dynamics (Tarasov, 2013) and non-equilibrium phase transition theory (Chang, 1992). References 1. T. Arimitsu, N. Arimitsu, Tsallis statistics and fully developed turbulence, J. Phys. A: Math. Gen. 33 (2000) L235. 2. T. Arimitsu, N. Arimitsu, Analysis of turbulence by statistics based on generalized entropies, Physica A 295 (2001) 177-194. 3. T. Chang, Low-dimensional behavior and symmetry braking of stochastic systems near criticality can these effects be observed in space and in the laboratory, IEEE 20 (6) (1992) 691-694. 4. U. Frisch, Turbulence, Cambridge University Press, Cambridge, UK, 1996, p. 310. 5. L.P. Karakatsanis, G.P. Pavlos, M.N. Xenakis, Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar flares dynamics, Physica A 392 (2013) 3920-3944. 6. A.V. Milovanov, Topological proof for the Alexander-Orbach conjecture, Phys. Rev. E 56 (3) (1997) 2437-2446. 7. A.V. Milovanov, L.M. Zelenyi, Fracton excitations as a driving mechanism for the self-organized dynamical structuring in the solar wind, Astrophys. Space Sci. 264 (1-4) (1999) 317-345. 8. A.V. Milovanov, Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation: large-scale behavior of the turbulent transport coefficient, Phys. Rev. E 63 (2001) 047301. 9. G.P. Pavlos, et al., Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications, Physica A 395 (2014) 58-95. 10. G.P. Pavlos, et al., Tsallis non-extensive statistics and solar wind plasma complexity, Physica A 422 (2015) 113-135. 11. A.A. Ruzmaikin, et al., Spectral properties of solar convection and diffusion, ApJ 471 (1996) 1022. 12. V.E. Tarasov, Review of some promising fractional physical models, Internat. J. Modern Phys. B 27 (9) (2013) 1330005. 13. C. Tsallis, Possible generalization of BG statistics, J. Stat. Phys. J 52 (1-2) (1988) 479-487. 14. C. Tsallis, Nonextensive statistical mechanics: construction and physical interpretation, in: G.M. Murray, C. Tsallis (Eds.), Nonextensive Entropy-Interdisciplinary Applications, Oxford Univ. Press, 2004, pp. 1-53. 15. C. Tsallis, Introduction to Non-Extensive Statistical Mechanics, Springer, 2009. 16. G.M. Zaslavsky, Chaos, fractional kinetics, and anomalous transport, Physics Reports 371 (2002) 461-580. 17. L.M. Zelenyi, A.V. Milovanov, Fractal properties of sunspots, Sov. Astron. Lett. 17 (6) (1991) 425. 18. L.M. Zelenyi, A.V. Milovanov, Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics, Phys.-Usp. 47 (8), (2004) 749-788.

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.

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.

Emergence of Multiscaling in a Random-Force Stirred Fluid

NASA Astrophysics Data System (ADS)

Yakhot, Victor; Donzis, Diego

2017-07-01

We consider the transition to strong turbulence in an infinite fluid stirred by a Gaussian random force. The transition is defined as a first appearance of anomalous scaling of normalized moments of velocity derivatives (dissipation rates) emerging from the low-Reynolds-number Gaussian background. It is shown that, due to multiscaling, strongly intermittent rare events can be quantitatively described in terms of an infinite number of different "Reynolds numbers" reflecting a multitude of anomalous scaling exponents. The theoretically predicted transition disappears at Rλ≤3 . The developed theory is in quantitative agreement with the outcome of large-scale numerical simulations.

Anomalous scaling in an age-dependent branching model.

PubMed

Keller-Schmidt, Stephanie; Tuğrul, Murat; Eguíluz, Víctor M; Hernández-García, Emilio; Klemm, Konstantin

2015-02-01

We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ(-α). Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)(2). This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.

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.

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.

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.

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

USGS Publications Warehouse

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

2015-01-01

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

Effect of temperature and grain size on the dominant diffusion process for superplastic flow in an AZ61 magnesium alloy

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

Watanabe, H.; Mukai, T.; Kohzu, M.

1999-10-26

The effect of temperature and grain size on superplastic flow was investigated using a relatively coarse-grained ({approximately}20 {micro}m) Mg-Al-Zn alloy for the inclusive understanding of the dominant diffusion process. Tensile tests revealed that the strain rate was inversely proportional to the square of the grain size and to the second power of stress. The activation energy was close to that for grain boundary diffusion at 523--573 K, and was close to that for lattice diffusion at 598--673 K. From the analysis of the stress exponent, the grain size exponent and activation energy, it was suggested that the dominant diffusion processmore » was influenced by temperature and grain size. It was demonstrated that the notion of effective diffusivity explained the experimental results.« less

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.

A new coarse-grained model for E. coli cytoplasm: accurate calculation of the diffusion coefficient of proteins and observation of anomalous diffusion.

PubMed

Hasnain, Sabeeha; McClendon, Christopher L; Hsu, Monica T; Jacobson, Matthew P; Bandyopadhyay, Pradipta

2014-01-01

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.

Opinion dynamics in two dimensions: domain coarsening leads to stable bi-polarization and anomalous scaling exponents

NASA Astrophysics Data System (ADS)

Velásquez-Rojas, F.; Vazquez, F.

2018-04-01

We study an opinion dynamics model that explores the competition between persuasion and compromise in a population of agents with nearest-neighbor interactions on a two-dimensional square lattice. Each agent can hold either a positive or a negative opinion orientation, and can have two levels of intensity—moderate and extremist. When two interacting agents have the same orientation they become extremists with persuasion probability p, while if they have opposite orientations they become moderate with compromise probability q. These updating rules lead to the formation of same-opinion domains with a coarsening dynamics that depends on the ratio r  =  p/q. The population initially evolves to a centralized state for small r, where domains are composed of moderate agents and coarsening is without surface tension, and to a bi-polarized state for large r, where domains are formed by extremist agents and coarsening is driven by curvature. Consensus in an extreme opinion is finally reached in a time that scales with the population size N and r as for small r and as for large r. Bi-polarization could be quite stable when the system falls into a striped state where agents organize into single-opinion horizontal, vertical or diagonal bands. An analysis of the stripe dynamics towards consensus allows us to obtain an approximate expression for τ, which shows that the exponent 1.64 is a result of the diffusion of the stripe interfaces combined with their roughness properties.

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.

Analysis of Bacteriophage Motion Through a Non-Static Medium

NASA Astrophysics Data System (ADS)

Dickey, Samuel A.

In this work, I investigated the motion of bacteriophages (phages) through their mucosal environment. Recently, biologists here at San Diego State University have proposed a model in which phages move sub-diffusively through mucosal fibers in their hunt for bacteria to prey upon. Through a Hoc protein located upon the capsid of the wild type phages, these phages are allowed to bind to mucosal fibers, and extend the amount of time spent in a single location hunting for bacteria. Contrarily, the delta hoc phages are unable to. The ability of the wild type phages to attach itself to mucosal fibers is what enables its subdiffusive behavior. This study investigates the diffusive behavior of these phages in different mucus concentrations. It expands on previous studies in which only short tracks could be observed. In the study at hand, phages are imaged in a highly doped optical fiber with varying concentrations of mucus present in solution. Through rigorous image processing techniques, trajectories of these phages are created with a minimized noise level. We developed code that created position-versus-time files for each phage present in the experimental data. These files were then further analyzed. The sub-diffusive behavior is investigated via mean squared displacement versus time. The diffusive exponent can be obtained from fits to these data. For large enough time intervals, I always obtained an exponent of one for space and time averaged data. This indicates that the diffusion is normal, or sub-diffusive of the CTRW type. CTRW sub-diffusive motion is characterized by waiting times that resemble a power law distribution and have long tails. I investigate these stuck time distributions, however am unable to determine if a power law or exponential fits the data best. Moreover, the distribution gives the same power law exponent for phages moving through water, or mucus, for wild type and delta hoc phages. These exponents would predict super-diffusive instead of sub-diffusive behavior. We conclude that many of these problems result from the small amount of data available to us and the still primitive conditions of the setup at the time the data were collected.

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.

Dielectric spectroscopy of polymer-metal composites across the percolation threshold

NASA Astrophysics Data System (ADS)

Panda, Maheswar; Srinivas, V.; Thakur, A. K.

2014-11-01

Polymer (polar/nonpolar)/metal composites (PMC) were prepared under different process conditions. In polar PMC, dipolar relaxation plays a predominant role below percolation threshold (fc) and anomalous low frequency dispersion (ALFD) becomes dominant above fc while ALFD is the only likely possibility for nonpolar PMC above fc. The magnitude of relaxation exponents "m", "p" and "n", evaluated from the experimental results using Jonscher's universal dielectric response (JUDR) laws, falls within the universal limit [0, 1] with additional feature of strong dependence on volume fraction of conductor (fcon). The decrease in the relaxation exponent "m" with an increase of fcon is directly linked with decrease in the number of dipoles of the polymer in the composite and is accompanied by a distribution of relaxation time due to increased heterogeneity of the system. The magnitude of the relaxation exponent "n" decreases at fc, due to the prevalence of Maxwell-Wagner-Sillar polarization contributed by uncorrelated electrons.

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.

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

PubMed

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

2015-01-01

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

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).

Emergence of multi-scaling in fluid turbulence

NASA Astrophysics Data System (ADS)

Donzis, Diego; Yakhot, Victor

2017-11-01

We present new theoretical and numerical results on the transition to strong turbulence in an infinite fluid stirred by a Gaussian random force. The transition is defined as a first appearance of anomalous scaling of normalized moments of velocity derivatives (or dissipation rates) emerging from the low-Reynolds-number Gaussian background. It is shown that due to multi-scaling, strongly intermittent rare events can be quantitatively described in terms of an infinite number of different ``Reynolds numbers'' reflecting a multitude of anomalous scaling exponents. We found that anomalous scaling for high order moments emerges at very low Reynolds numbers implying that intense dissipative-range fluctuations are established at even lower Reynolds number than that required for an inertial range. Thus, our results suggest that information about inertial range dynamics can be obtained from dissipative scales even when the former does not exit. We discuss our further prediction that transition to fully anomalous turbulence disappears at Rλ < 3 . Support from NSF is acknowledged.

Quenching and anisotropy of hydromagnetic turbulent transport

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

Karak, Bidya Binay; Brandenburg, Axel; Rheinhardt, Matthias

2014-11-01

Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the α effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for themore » quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the α effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the Ω×J effect nearly the same quenching exponent is obtained as for α. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.« less

Numerical study of anomalous dynamic scaling behaviour of (1+1)-dimensional Das Sarma-Tamborenea model

NASA Astrophysics Data System (ADS)

Xun, Zhi-Peng; Tang, Gang; Han, Kui; Hao, Da-Peng; Xia, Hui; Zhou, Wei; Yang, Xi-Quan; Wen, Rong-Ji; Chen, Yu-Ling

2010-07-01

In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model, the (1+1)-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by using the kinetic Monte-Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the (1+1)-dimensional Das Sarma-Tamborenea model systematically decreases with system size L increasing when L > 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma-Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour.

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.

Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Lučivjanský, T.

2017-03-01

We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field-theoretic renormalization group. In this approach, scaling properties are related to the fixed points of the renormalization group equations. Previous analysis of this model near the real-world space dimension 3 identified a scaling regime [N. V. Antonov et al., Theor. Math. Phys. 110, 305 (1997), 10.1007/BF02630456]. The aim of the present paper is to explore the existence of additional regimes, which could not be found using the direct perturbative approach of the previous work, and to analyze the crossover between different regimes. It seems possible to determine them near the special value of space dimension 4 in the framework of double y and ɛ expansion, where y is the exponent associated with the random force and ɛ =4 -d is the deviation from the space dimension 4. Our calculations show that there exists an additional fixed point that governs scaling behavior. Turbulent advection of a passive scalar (density) field by this velocity ensemble is considered as well. We demonstrate that various correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. The corresponding anomalous exponents, identified as scaling dimensions of certain composite fields, can be systematically calculated as a series in y and ɛ . All calculations are performed in the leading one-loop approximation.

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.

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 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.

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 charge storage exponents of organic bulk heterojunction solar cells.

NASA Astrophysics Data System (ADS)

Nair, Pradeep; Dwivedi, Raaz; Kumar, Goutam; Dept of Electrical Engineering, IIT Bombay Team

2013-03-01

Organic bulk heterojunction (BHJ) devices are increasingly being researched for low cost solar energy conversion. The efficiency of such solar cells is dictated by various recombination processes involved. While it is well known that the ideality factor and hence the charge storage exponents of conventional PN junction diodes are influenced by the recombination processes, the same aspects are not so well understood for organic solar cells. While dark currents of such devices typically show an ideality factor of 1 (after correcting for shunt resistance effects, if any), surprisingly, a wide range of charge storage exponents for such devices are reported in literature alluding to apparent concentration dependence for bi-molecular recombination rates. In this manuscript we critically analyze the role of bi-molecular recombination processes on charge storage exponents of organic solar cells. Our results indicate that the charge storage exponents are fundamentally influenced by the electrostatics and recombination processes and can be correlated to the dark current ideality factors. We believe that our findings are novel, and advance the state-of the art understanding on various recombination processes that dictate the performance limits of organic solar cells. The authors would like to thank the Centre of Excellence in Nanoelectronics (CEN) and the National Centre for Photovoltaic Research and Education (NCPRE), IIT Bombay for computational and financial support

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.

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.

Critical spreading dynamics of parity conserving annihilating random walks with power-law branching

NASA Astrophysics Data System (ADS)

Laise, T.; dos Anjos, F. C.; Argolo, C.; Lyra, M. L.

2018-09-01

We investigate the critical spreading of the parity conserving annihilating random walks model with Lévy-like branching. The random walks are considered to perform normal diffusion with probability p on the sites of a one-dimensional lattice, annihilating in pairs by contact. With probability 1 - p, each particle can also produce two offspring which are placed at a distance r from the original site following a power-law Lévy-like distribution P(r) ∝ 1 /rα. We perform numerical simulations starting from a single particle. A finite-time scaling analysis is employed to locate the critical diffusion probability pc below which a finite density of particles is developed in the long-time limit. Further, we estimate the spreading dynamical exponents related to the increase of the average number of particles at the critical point and its respective fluctuations. The critical exponents deviate from those of the counterpart model with short-range branching for small values of α. The numerical data suggest that continuously varying spreading exponents sets up while the branching process still results in a diffusive-like spreading.

Fibonacci family of dynamical universality classes.

PubMed

Popkov, Vladislav; Schadschneider, Andreas; Schmidt, Johannes; Schütz, Gunter M

2015-10-13

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent [Formula: see text], another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with [Formula: see text]. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents [Formula: see text] are given by ratios of neighboring Fibonacci numbers, starting with either [Formula: see text] (if a KPZ mode exist) or [Formula: see text] (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean [Formula: see text] as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.

Modeling anomalous radial transport in kinetic transport codes

NASA Astrophysics Data System (ADS)

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

2009-11-01

Anomalous transport is typically the dominant component of the radial transport in magnetically confined plasmas, where the physical origin of this transport is believed to be plasma turbulence. A model is presented for anomalous transport that can be used in continuum kinetic edge codes like TEMPEST, NEO and the next-generation code being developed by the Edge Simulation Laboratory. The model can also be adapted to particle-based codes. It is demonstrated that the model with a velocity-dependent diffusion and convection terms can match a diagonal gradient-driven transport matrix as found in contemporary fluid codes, but can also include off-diagonal effects. The anomalous transport model is also combined with particle drifts and a particle/energy-conserving Krook collision operator to study possible synergistic effects with neoclassical transport. For the latter study, a velocity-independent anomalous diffusion coefficient is used to mimic the effect of long-wavelength ExB turbulence.

The relation of turbulence to diffusion in open-channel flows

USGS Publications Warehouse

Keefer, Thomas N.

1971-01-01

The exponent in the power-law equation describing the decay of scalar quantities downstream of a jet is a linear function of the shear velocity of the channel. The length of the core region of a jet is a power-law function of the jet strength with the exponent depending on boundary roughness.

Scaling exponent and dispersity of polymers in solution by diffusion NMR.

PubMed

Williamson, Nathan H; Röding, Magnus; Miklavcic, Stanley J; Nydén, Magnus

2017-05-01

Molecular mass distribution measurements by pulsed gradient spin echo nuclear magnetic resonance (PGSE NMR) spectroscopy currently require prior knowledge of scaling parameters to convert from polymer self-diffusion coefficient to molecular mass. Reversing the problem, we utilize the scaling relation as prior knowledge to uncover the scaling exponent from within the PGSE data. Thus, the scaling exponent-a measure of polymer conformation and solvent quality-and the dispersity (M w /M n ) are obtainable from one simple PGSE experiment. The method utilizes constraints and parametric distribution models in a two-step fitting routine involving first the mass-weighted signal and second the number-weighted signal. The method is developed using lognormal and gamma distribution models and tested on experimental PGSE attenuation of the terminal methylene signal and on the sum of all methylene signals of polyethylene glycol in D 2 O. Scaling exponent and dispersity estimates agree with known values in the majority of instances, leading to the potential application of the method to polymers for which characterization is not possible with alternative techniques. Copyright © 2017 Elsevier Inc. All rights reserved.

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

Jedrecy, N., E-mail: jedrecy@insp.jussieu.fr; Hamieh, M.; Hebert, C.

We show that the well-established universal scaling σ{sub xy}{sup AHE} ∼ σ{sub xx}{sup 1.6} between anomalous Hall and longitudinal conductivities in the low conductivity regime (σ{sub xx} < 10{sup 4} Ω{sup −1} cm{sup −1}) transforms into the scaling σ{sub xy}{sup AHE} ∼ σ{sub xx}{sup 2} at the onset of strong electron localization. The crossover between the two relations is observed in magnetite-derived Zn{sub x}Fe{sub 3-x}O{sub 4} thin films where an insulating/hopping regime follows a bad metal/hopping regime below the Verwey transition temperature T{sub v}. Our results demonstrate that electron localization effects come into play in the anomalous Hall effect (AHE)more » modifying significantly the scaling exponent. In addition, the thermal evolution of the anomalous Hall resistivity suggests the existence of spin polarons whose size would decrease below T{sub v}.« less

Transport equations for subdiffusion with nonlinear particle interaction.

PubMed

Straka, P; Fedotov, S

2015-02-07

We show how the nonlinear interaction effects 'volume filling' and 'adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with anomalous trapping and systematically derive generic non-Markovian and nonlinear governing equations for the mean concentrations of the subdiffusive cells or organisms. We uncover an interesting interaction between the nonlinearities and the non-Markovian nature of the transport. In the subdiffusive case, this interaction manifests itself in a nontrivial combination of nonlinear terms with fractional derivatives. In the long time limit, however, these equations simplify to a form without fractional operators. This provides an easy method for the study of aggregation phenomena. In particular, this enables us to show that volume filling can prevent "anomalous aggregation," which occurs in subdiffusive systems with a spatially varying anomalous exponent. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Energy Current Cumulants in One-Dimensional Systems in Equilibrium

NASA Astrophysics Data System (ADS)

Dhar, Abhishek; Saito, Keiji; Roy, Anjan

2018-06-01

A recent theory based on fluctuating hydrodynamics predicts that one-dimensional interacting systems with particle, momentum, and energy conservation exhibit anomalous transport that falls into two main universality classes. The classification is based on behavior of equilibrium dynamical correlations of the conserved quantities. One class is characterized by sound modes with Kardar-Parisi-Zhang scaling, while the second class has diffusive sound modes. The heat mode follows Lévy statistics, with different exponents for the two classes. Here we consider heat current fluctuations in two specific systems, which are expected to be in the above two universality classes, namely, a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Numerical simulations show completely different system-size dependence of current cumulants in these two systems. We explain this numerical observation using a phenomenological model of Lévy walkers with inputs from fluctuating hydrodynamics. This consistently explains the system-size dependence of heat current fluctuations. For the latter system, we derive the cumulant-generating function from a more microscopic theory, which also gives the same system-size dependence of cumulants.

Lyophilised wafers as vehicles for the topical release of chlorhexidine digluconate--release kinetics and efficacy against Pseudomonas aeruginosa.

PubMed

Labovitiadi, Olga; Lamb, Andrew J; Matthews, Kerr H

2012-12-15

There is a requirement to deliver accurate amounts of broad spectrum antimicrobial compounds locally to exuding wounds. Varying amounts of exudate complicates this process by limiting the residence and therefore efficacy of active substances. Minimum bactericidal concentrations (MBC) of antimicrobials are necessary to suppress infection and lessen the chances of resistant strains of potentially pathogenic bacteria from prevailing. Polysaccharide wafers can adhere to exudating wound beds, absorbing fluids and forming highly viscous gels that remain in situ for prolonged periods of time to release sustained amounts of antimicrobial. In this study, five different formulations were produced containing the antimicrobial, chlorhexidine digluconate (CHD). Absorption of simulated wound fluid, resultant rheological properties of gels and efficacy against plated cultures of Pseudomonas aeruginosa were measured and compared. CHD reduced the 'water uptake' of wafers by 11-50% (w/w) and decreased the rheological consistency of non-SA containing gels by 10-65%. Release studies indicated that karaya wafers gave the highest sustained release of CHD, >60 μg/mL in 24 h, well in excess of the MBC for P. aeruginosa. Release kinetics indicated an anomalous diffusion mechanism according to Korsmeyer-Peppas, with diffusion exponents varying from 0.31 to 0.41 for most wafers except xanthan (0.65). Copyright © 2012 Elsevier B.V. All rights reserved.

End-monomer Dynamics in Semiflexible Polymers

PubMed Central

Hinczewski, Michael; Schlagberger, Xaver; Rubinstein, Michael; Krichevsky, Oleg; Netz, Roland R.

2009-01-01

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) 〈r2(t)〉 ~ t1/2 at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling 〈r2(t)〉 ~ t2/3 in the same time range. Using hydrodynamic simulations, analytical and scaling theories, we find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, α(t) = d log〈r2(t)〉/d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, found in simulations and in an improved mean-field theory for semiflexible polymers, in particular the variation of α(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent α are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales. PMID:21359118

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 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

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

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.

Spin diffusion from an inhomogeneous quench in an integrable system.

PubMed

Ljubotina, Marko; Žnidarič, Marko; Prosen, Tomaž

2017-07-13

Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional discrete symmetries. Here we perform large scale numerical simulations of spin dynamics in the anisotropic Heisenberg XXZ spin 1/2 chain starting from an inhomogeneous mixed initial state which is symmetric with respect to a combination of spin reversal and spatial reflection. In the isotropic and easy-axis regimes we find non-ballistic spin transport which we analyse in detail in terms of scaling exponents of the transported magnetization and scaling profiles of the spin density. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to 2/3, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time.

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.

Scaling behavior of the surface roughness of platinum films grown by oblique angle deposition

NASA Astrophysics Data System (ADS)

Dolatshahi-Pirouz, A.; Hovgaard, M. B.; Rechendorff, K.; Chevallier, J.; Foss, M.; Besenbacher, F.

2008-03-01

Thin platinum films with well-controlled rough surface morphologies are grown by e-gun evaporation at an oblique angle of incidence between the deposition flux and the substrate normal. Atomic force microscopy is used to determine the root-mean-square value w of the surface roughness on the respective surfaces. From the scaling behavior of w , we find that while the roughness exponent α remains nearly unchanged at about 0.90, the growth exponent β changes from 0.49±0.04 to 0.26±0.01 as the deposition angle approaches grazing incidence. The values of the growth exponent β indicate that the film growth is influenced by both surface diffusion and shadowing effects, while the observed change from 0.49 to 0.26 can be attributed to differences in the relative importance of diffusion and shadowing with the deposition angle.

How main-chains of proteins explore the free-energy landscape in native states.

PubMed

Senet, Patrick; Maisuradze, Gia G; Foulie, Colette; Delarue, Patrice; Scheraga, Harold A

2008-12-16

Understanding how a single native protein diffuses on its free-energy landscape is essential to understand protein kinetics and function. The dynamics of a protein is complex, with multiple relaxation times reflecting a hierarchical free-energy landscape. Using all-atom molecular dynamics simulations of an alpha/beta protein (crambin) and a beta-sheet polypeptide (BS2) in their "native" states, we demonstrate that the mean-square displacement of dihedral angles, defined by 4 successive C(alpha) atoms, increases as a power law of time, t(alpha), with an exponent alpha between 0.08 and 0.39 (alpha = 1 corresponds to Brownian diffusion), at 300 K. Residues with low exponents are located mainly in well-defined secondary elements and adopt 1 conformational substate. Residues with high exponents are found in loops/turns and chain ends and exist in multiple conformational substates, i.e., they move on multiple-minima free-energy profiles.

How main-chains of proteins explore the free-energy landscape in native states

PubMed Central

Senet, Patrick; Maisuradze, Gia G.; Foulie, Colette; Delarue, Patrice; Scheraga, Harold A.

2008-01-01

Understanding how a single native protein diffuses on its free-energy landscape is essential to understand protein kinetics and function. The dynamics of a protein is complex, with multiple relaxation times reflecting a hierarchical free-energy landscape. Using all-atom molecular dynamics simulations of an α/β protein (crambin) and a β-sheet polypeptide (BS2) in their “native” states, we demonstrate that the mean-square displacement of dihedral angles, defined by 4 successive Cα atoms, increases as a power law of time, tα, with an exponent α between 0.08 and 0.39 (α = 1 corresponds to Brownian diffusion), at 300 K. Residues with low exponents are located mainly in well-defined secondary elements and adopt 1 conformational substate. Residues with high exponents are found in loops/turns and chain ends and exist in multiple conformational substates, i.e., they move on multiple-minima free-energy profiles. PMID:19073932

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

Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Niry, M. D.; Bozorg, B.; Tabar, M. Reza Rahimi; Sahimi, Muhammad

2008-03-01

A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.

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.

On the influence of anharmonicity on the isotope effect

NASA Astrophysics Data System (ADS)

Galbaatar, T.; Drechsler, S. L.; Plakida, N. M.; Vujicic, G. M.

1991-12-01

The effect of double-well type lattice anharmonicity on the superconducting temperature and its isotope effect is investigated beyond the two-level approximation (TLA) within the Eliashberg theory. It is shown that anharmonicity can greatly modify the isotope effect; In particular anomalously large as well as negative values of the isotope effect exponent α are obtained in the strong and weak coupling limits, respectively.

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.

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.

The foreign exchange market: return distributions, multifractality, anomalous multifractality and the Epps effect

NASA Astrophysics Data System (ADS)

Drożdż, Stanisław; Kwapień, Jarosław; Oświȩcimka, Paweł; Rak, Rafał

2010-10-01

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all of the pairs considered are well described by the non-extensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the non-extensivity q-parameter values for different exchange rates (which depend also on the time scales studied), and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all of the exchange rates, with a varying degree of symmetry of the singularity spectrum f(α), however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations, which excludes description in terms of q-Gaussians. The multifractal characteristics of these residual returns reveal such anomalous properties as negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with diffusion-limited aggregation and with turbulence. Studying the cross-correlations among different exchange rates, we found that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales, but comparable to the ones for the stock market. Although the currency market is much more liquid than the stock markets and has a much greater transaction frequency, the building up of correlations takes up to several hours—a duration that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect.

Molecular Dynamics Calculations of Optical Nonlinear Properties of Materials

DTIC Science & Technology

1991-12-20

by saturating the hydrogens with five sets each of d and p functions with exponents of 1.0, 0.5, 0.25, 0.125, 0.0625 but for a molecule like ASH 3...of d polarization functions using the exponents suggested by Dykstra et al. A similar calculation was also performed in which a second diffuse p set...one set each of d and p functions with exponents of 0.05 as suggested by DuPuis et al. for larger molecules was used. There was a loss in & of only

Fibonacci family of dynamical universality classes

PubMed Central

Popkov, Vladislav; Schadschneider, Andreas; Schmidt, Johannes; Schütz, Gunter M.

2015-01-01

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent z=2, another prominent example is the superdiffusive Kardar−Parisi−Zhang (KPZ) class with z=3/2. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents zα are given by ratios of neighboring Fibonacci numbers, starting with either z1=3/2 (if a KPZ mode exist) or z1=2 (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean z=(1+5)/2 as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement. PMID:26424449

Enhanced diffusion with abnormal temperature dependence in underdamped space-periodic systems subject to time-periodic driving

NASA Astrophysics Data System (ADS)

Marchenko, I. G.; Marchenko, I. I.; Zhiglo, A. V.

2018-01-01

We present a study of the diffusion enhancement of underdamped Brownian particles in a one-dimensional symmetric space-periodic potential due to external symmetric time-periodic driving with zero mean. We show that the diffusivity can be enhanced by many orders of magnitude at an appropriate choice of the driving amplitude and frequency. The diffusivity demonstrates abnormal (decreasing) temperature dependence at the driving amplitudes exceeding a certain value. At any fixed driving frequency Ω normal temperature dependence of the diffusivity is restored at low enough temperatures, T

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.

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.

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.

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.

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.

Observation of the Quantum Anomalous Hall Insulator to Anderson Insulator Quantum Phase Transition and its Scaling Behavior.

PubMed

Chang, Cui-Zu; Zhao, Weiwei; Li, Jian; Jain, J K; Liu, Chaoxing; Moodera, Jagadeesh S; Chan, Moses H W

2016-09-16

Fundamental insight into the nature of the quantum phase transition from a superconductor to an insulator in two dimensions, or from one plateau to the next or to an insulator in the quantum Hall effect, has been revealed through the study of its scaling behavior. Here, we report on the experimental observation of a quantum phase transition from a quantum-anomalous-Hall insulator to an Anderson insulator in a magnetic topological insulator by tuning the chemical potential. Our experiment demonstrates the existence of scaling behavior from which we extract the critical exponent for this quantum phase transition. We expect that our work will motivate much further investigation of many properties of quantum phase transition in this new context.

F4 symmetric ϕ3 theory at four loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.

2017-03-01

The renormalization group functions for six dimensional scalar ϕ3 theory with an F4 symmetry are provided at four loops in the modified minimal subtraction (MS ¯ ) scheme. Aside from the anomalous dimension of ϕ and the β -function this includes the mass operator and a ϕ2-type operator. The anomalous dimension of the latter is computed explicitly at four loops for the 26 and 324 representations of F4. The ɛ expansion of all the related critical exponents are determined to O (ɛ4). For instance the value for Δϕ agrees with recent conformal bootstrap estimates in 5 and 5.95 dimensions. The renormalization group functions are also provided at four loops for the group E6.

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

Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling

NASA Astrophysics Data System (ADS)

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

2015-10-01

In this work we study the generalization of the problem considered in [Phys. Rev. E 91, 013002 (2015), 10.1103/PhysRevE.91.013002] to the case of finite correlation time of the environment (velocity) field. The model describes a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow. Inertial-range asymptotic behavior is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and preassigned pair correlation function. Due to the presence of distinguished direction n , all the multiloop diagrams in this model vanish, so that the results obtained are exact. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to the two nontrivial fixed points of the RG equations. Their stability depends on the relation between the exponents in the energy spectrum E ∝k⊥1 -ξ and the dispersion law ω ∝k⊥2 -η . 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 corrections to ordinary scaling are polynomials of logarithms of the integral turbulence scale L .

The use of the Hurst exponent to investigate the global maximum of the Warsaw Stock Exchange WIG20 index

NASA Astrophysics Data System (ADS)

Domino, Krzysztof

2012-01-01

The WIG20 index-the index of the 20 biggest companies traded on the Warsaw Stock Exchange-reached the global maximum on 29th October 2007. I have used the local DFA (Detrended Functional Analysis) to obtain the Hurst exponent (diffusion exponent) and investigate the signature of anti-correlation of share price evolution around the maximum. The analysis was applied to the share price evolution for variable DFA parameters. For many values of parameters, the evidence of anti-correlation near the WIG20 maximum was pointed out.

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.

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.

Ameba-like diffusion in two-dimensional polymer melts: how critical exponents determine the structural relaxation

NASA Astrophysics Data System (ADS)

Kreer, Torsten; Meyer, Hendrik; Baschnagel, Joerg

2008-03-01

By means of numerical investigations we demonstrate that the structural relaxation of linear polymers in two dimensional (space-filling) melts is characterized by ameba-like diffusion, where the chains relax via frictional dissipation at their interfacial contact lines. The perimeter length of the contact line determines a new length scale, which does not exist in three dimensions. We show how this length scale follows from the critical exponents, which hence characterize not only the static but also the dynamic properties of the melt. Our data is in agreement with recent theoretical predictions, concerning the time-dependence of single-monomer mean-square displacements and the scaling of concomitant relaxation times with the degree of polymerization. For the latter we demonstrate a density crossover-scaling as an additional test for ameba-like relaxation. We compare our results to the conceptually different Rouse model, which predicts numerically close exponents. Our data can clearly rule out the classical picture as the relevant relaxation mechanism in two-dimensional polymer melts.

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.

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

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 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.

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

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.

Effects of film growth kinetics on grain coarsening and grain shape.

PubMed

Reis, F D A Aarão

2017-04-01

We study models of grain nucleation and coarsening during the deposition of a thin film using numerical simulations and scaling approaches. The incorporation of new particles in the film is determined by lattice growth models in three different universality classes, with no effect of the grain structure. The first model of grain coarsening is similar to that proposed by Saito and Omura [Phys. Rev. E 84, 021601 (2011)PLEEE81539-375510.1103/PhysRevE.84.021601], in which nucleation occurs only at the substrate, and the grain boundary evolution at the film surface is determined by a probabilistic competition of neighboring grains. The surface grain density has a power-law decay, with an exponent related to the dynamical exponent of the underlying growth kinetics, and the average radius of gyration scales with the film thickness with the same exponent. This model is extended by allowing nucleation of new grains during the deposition, with constant but small rates. The surface grain density crosses over from the initial power law decay to a saturation; at the crossover, the time, grain mass, and surface grain density are estimated as a function of the nucleation rate. The distributions of grain mass, height, and radius of gyration show remarkable power law decays, similar to other systems with coarsening and particle injection, with exponents also related to the dynamical exponent. The scaling of the radius of gyration with the height h relative to the base of the grain show clearly different exponents in growth dominated by surface tension and growth dominated by surface diffusion; thus it may be interesting for investigating the effects of kinetic roughening on grain morphology. In growth dominated by surface diffusion, the increase of grain size with temperature is observed.

Aggregation-fragmentation-diffusion model for trail dynamics

DOE PAGES

Kawagoe, Kyle; Huber, Greg; Pradas, Marc; ...

2017-07-21

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail P(w)~w –γ formore » small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. In conclusion, the exponent γ can be positive or negative, so that in one range of parameters small-weight trails are abundant and in the complementary range they are rare.« less

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.

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.

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.

Mean field approximation for biased diffusion on Japanese inter-firm trading network.

PubMed

Watanabe, Hayafumi

2014-01-01

By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7.

Gravity-darkening exponents in semi-detached binary systems from their photometric observations. II.

NASA Astrophysics Data System (ADS)

Djurašević, G.; Rovithis-Livaniou, H.; Rovithis, P.; Georgiades, N.; Erkapić, S.; Pavlović, R.

2006-01-01

This second part of our study concerning gravity-darkening presents the results for 8 semi-detached close binary systems. From the light-curve analysis of these systems the exponent of the gravity-darkening (GDE) for the Roche lobe filling components has been empirically derived. The method used for the light-curve analysis is based on Roche geometry, and enables simultaneous estimation of the systems' parameters and the gravity-darkening exponents. Our analysis is restricted to the black-body approximation which can influence in some degree the parameter estimation. The results of our analysis are: 1) For four of the systems, namely: TX UMa, β Per, AW Cam and TW Cas, there is a very good agreement between empirically estimated and theoretically predicted values for purely convective envelopes. 2) For the AI Dra system, the estimated value of gravity-darkening exponent is greater, and for UX Her, TW And and XZ Pup lesser than corresponding theoretical predictions, but for all mentioned systems the obtained values of the gravity-darkening exponent are quite close to the theoretically expected values. 3) Our analysis has proved generally that with the correction of the previously estimated mass ratios of the components within some of the analysed systems, the theoretical predictions of the gravity-darkening exponents for stars with convective envelopes are highly reliable. The anomalous values of the GDE found in some earlier studies of these systems can be considered as the consequence of the inappropriate method used to estimate the GDE. 4) The empirical estimations of GDE given in Paper I and in the present study indicate that in the light-curve analysis one can apply the recent theoretical predictions of GDE with high confidence for stars with both convective and radiative envelopes.

Correlation Structure of Fractional Pearson Diffusions.

PubMed

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

2013-09-01

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

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

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.

Ordering kinetics in two-dimensional hexagonal pattern of cylinder-forming PS-b -PMMA block copolymer thin films: Dependence on the segregation strength

NASA Astrophysics Data System (ADS)

Seguini, Gabriele; Zanenga, Fabio; Laus, Michele; Perego, Michele

2018-05-01

This paper reports the experimental determination of the growth exponents and activation enthalpies for the ordering process of standing cylinder-forming all-organic polystyrene-block-poly (methyl methacrylate) block copolymer (BCP) thin films as a function of the BCP degree of polymerization (N). The maximum growth exponent of 1/3 is observed for the BCP with the lowest N at the border of the order-disorder transition. Both the growth exponents and the activation enthalpies exponentially decrease with the BCP segregation strength (χN) following the same path of the diffusivity.

Modeling irradiation creep of graphite using rate theory

DOE PAGES

Sarkar, Apu; Eapen, Jacob; Raj, Anant; ...

2016-02-20

In this work we examined irradiation induced creep of graphite in the framework of transition state rate theory. Experimental data for two grades of nuclear graphite (H-337 and AGOT) were analyzed to determine the stress exponent (n) and activation energy (Q) for plastic flow under irradiation. Here we show that the mean activation energy lies between 0.14 and 0.32 eV with a mean stress-exponent of 1.0 ± 0.2. A stress exponent of unity and the unusually low activation energies strongly indicate a diffusive defect transport mechanism for neutron doses in the range of 3-4 x 10 22 n/cm 2.

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.

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.

Crossover behavior of stock returns and mean square displacements of particles governed by the Langevin equation

NASA Astrophysics Data System (ADS)

Ma, Wen-Jong; Wang, Shih-Chieh; Chen, Chi-Ning; Hu, Chin-Kun

2013-06-01

It is found that the mean square log-returns calculated from the high-frequency one-day moving average of US and Taiwan stocks with the time internal τ show ballistic behavior \\theta \\tau^{\\alpha_1} with the exponent \\alpha_1 \\approx 2 for small τ and show diffusion-like behavior D \\tau^{\\alpha_2} with the exponent \\alpha_2 \\approx 1 for large τ. Such a crossover behavior can be well described by the mean square displacements of particles governed by the Langevin equation of motion. Thus, θ and D can be considered, respectively, as the temperature-like and diffusivity-like kinetic parameters of the market, and they can be used to characterize the behavior of the market.

A Nonlinear Inversion Approach to Map the Magnetic Basement: A Case Study from Central India Using Aeromagnetic Data

NASA Astrophysics Data System (ADS)

Kumar, R.; Bansal, A. R.; Anand, S. P.; Rao, V. K.; Singh, U. K.

2016-12-01

The central India region is having complex geology covering various geological units e.g., Precambrian Bastar Craton (including Proterozoic Chhattisgarh Basin, granitic intrusions etc.) and Eastern Ghat Mobile Belt, Gondwana Godavari and Mahanadi Grabens, Late Cretaceous Deccan Traps etc. The central India is well covered by reconnaissance scale aeromagnetic data. We analyzed this data for mapping the basement by dividing into143 overlapping blocks of 100×100km using least square nonlinear inversion method for fractal distribution of sources. The scaling exponents and depth values are optimized using grid search method. We interpreted estimated depths of anomalous sources as magnetic basement and shallow anomalous magnetic sources. The shallow magnetic anomalies are found to vary from 1 to 3km whereas magnetic basement depths are found to vary from 2km to 7km. The shallowest basement depth of 2km found corresponding to Kanker granites a part of Bastar Craton whereas deepest basement depth of 7km is associated with Godavari Graben and south eastern part of Eastern Ghat Mobile Belts near the Parvatipuram Bobbili fault. The variation of magnetic basement, shallow depths and scaling exponent in the region indicate complex tectonic, heterogeneity and intrusive bodies at different depths which is due to different tectonic processes in the region. The detailed basement depth of central India is presented in this study.

Non-Abelian fermionization and fractional quantum Hall transitions

NASA Astrophysics Data System (ADS)

Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah

2018-02-01

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent ν ≈2.3 and that ν is observed to be superuniversal, i.e., the same in the vicinity of distinct critical points [Sondhi et al., Rev. Mod. Phys. 69, 315 (1997), 10.1103/RevModPhys.69.315]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with U (Nc) gauge group coupled to Nf=1 fermion. We study one class of theories in a controlled limit where Nf≫Nc and calculate ν to leading nontrivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent ν within the large Nf≫Nc expansion, they do offer a new parameter space of theories that is apparently different from prior works involving Abelian Chern-Simons gauge fields [Wen and Wu, Phys. Rev. Lett. 70, 1501 (1993), 10.1103/PhysRevLett.70.1501; Chen et al., Phys. Rev. B 48, 13749 (1993), 10.1103/PhysRevB.48.13749].

Scaling in the aggregation dynamics of a magnetorheological fluid.

PubMed

Domínguez-García, P; Melle, Sonia; Pastor, J M; Rubio, M A

2007-11-01

We present experimental results on the aggregation dynamics of a magnetorheological fluid, namely, an aqueous suspension of micrometer-sized superparamagnetic particles, under the action of a constant uniaxial magnetic field using video microscopy and image analysis. We find a scaling behavior in several variables describing the aggregation kinetics. The data agree well with the Family-Vicsek scaling ansatz for diffusion-limited cluster-cluster aggregation. The kinetic exponents z and z' are obtained from the temporal evolution of the mean cluster size S(t) and the number of clusters N(t), respectively. The crossover exponent Delta is calculated in two ways: first, from the initial slope of the scaling function; second, from the evolution of the nonaggregated particles, n1(t). We report on results of Brownian two-dimensional dynamics simulations and compare the results with the experiments. Finally, we discuss the differences obtained between the kinetic exponents in terms of the variation in the crossover exponent and relate this behavior to the physical interpretation of the crossover exponent.

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.

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.

Structure of physical crystalline membranes within the self-consistent screening approximation.

PubMed

Gazit, Doron

2009-10-01

The anomalous exponents governing the long-wavelength behavior of the flat phase of physical crystalline membranes are calculated within a self-consistent screening approximation (SCSA) applied to second order expansion in 1/dC ( dC is the codimension), extending the seminal work of Le Doussal and Radzihovsky [Phys. Rev. Lett. 69, 1209 (1992)]. In particular, the bending rigidity is found to harden algebraically in the long-wavelength limit with an exponent eta=0.789... , which is used to extract the elasticity softening exponent eta(u)=0.422... , and the roughness exponent zeta=0.605... . The scaling relation eta(u)=2-2eta is proven to hold to all orders in SCSA. Further, applying the SCSA to an expansion in 1/dC , is found to be essential, as no solution to the self-consistent equations is found in a two-bubble level, which is the naive second-order expansion. Surprisingly, even though the expansion parameter for physical membrane is 1/dC=1 , the SCSA applied to second-order expansion deviates only slightly from the first order, increasing zeta by mere 0.016. This supports the high quality of the SCSA for physical crystalline membranes, as well as improves the comparison to experiments and numerical simulations of these systems. The prediction of SCSA applied to first order expansion for the Poisson ratio is shown to be exact to all orders.

Domain-area distribution anomaly in segregating multicomponent superfluids

NASA Astrophysics Data System (ADS)

Takeuchi, Hiromitsu

2018-01-01

The domain-area distribution in the phase transition dynamics of Z2 symmetry breaking is studied theoretically and numerically for segregating binary Bose-Einstein condensates in quasi-two-dimensional systems. Due to the dynamic-scaling law of the phase ordering kinetics, the domain-area distribution is described by a universal function of the domain area, rescaled by the mean distance between domain walls. The scaling theory for general coarsening dynamics in two dimensions hypothesizes that the distribution during the coarsening dynamics has a hierarchy with the two scaling regimes, the microscopic and macroscopic regimes with distinct power-law exponents. The power law in the macroscopic regime, where the domain size is larger than the mean distance, is universally represented with the Fisher's exponent of the percolation theory in two dimensions. On the other hand, the power-law exponent in the microscopic regime is sensitive to the microscopic dynamics of the system. This conjecture is confirmed by large-scale numerical simulations of the coupled Gross-Pitaevskii equation for binary condensates. In the numerical experiments of the superfluid system, the exponent in the microscopic regime anomalously reaches to its theoretical upper limit of the general scaling theory. The anomaly comes from the quantum-fluid effect in the presence of circular vortex sheets, described by the hydrodynamic approximation neglecting the fluid compressibility. It is also found that the distribution of superfluid circulation along vortex sheets obeys a dynamic-scaling law with different power-law exponents in the two regimes. An analogy to quantum turbulence on the hierarchy of vorticity distribution and the applicability to chiral superfluid 3He in a slab are also discussed.

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 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.

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.

A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems

NASA Astrophysics Data System (ADS)

Caponetto, Riccardo; Fazzino, Stefano

2013-01-01

Fractional-order differential equations are interesting for their applications in the construction of mathematical models in finance, materials science or diffusion. In this paper, an application of a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equation is employed for calculating Lyapunov exponents of fractional order systems. It is known that the Lyapunov exponents, first introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dependence on initial conditions and the presence of chaotic attractors. The results reveal that the proposed method is very effective and simple and leads to accurate, approximately convergent solutions.

Anomalous Growth of Aging Populations

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.

2016-04-01

We consider a discrete-time population dynamics with age-dependent structure. At every time step, one of the alive individuals from the population is chosen randomly and removed with probability q_k depending on its age, whereas a new individual of age 1 is born with probability r. The model can also describe a single queue in which the service order is random while the service efficiency depends on a customer's "age" in the queue. We propose a mean field approximation to investigate the long-time asymptotic behavior of the mean population size. The age dependence is shown to lead to anomalous power-law growth of the population at the critical regime. The scaling exponent is determined by the asymptotic behavior of the probabilities q_k at large k. The mean field approximation is validated by Monte Carlo simulations.

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.

Lyapunov exponent and criticality in the Hamiltonian mean field model

NASA Astrophysics Data System (ADS)

Filho, L. H. Miranda; Amato, M. A.; Rocha Filho, T. M.

2018-03-01

We investigate the dependence of the largest Lyapunov exponent (LLE) of an N-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the LLE, although at variance with the theoretical estimate. The existence of strong chaos in the magnetized state evidenced by a positive Lyapunov exponent is explained by the coupling of individual particle oscillations to the diffusive motion of the center of mass of the system and also results in a change of the scaling of the LLE with the number of particles. We also discuss thoroughly for the model the validity and limits of the approximations made by a geometrical model for their analytic estimate.

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

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.

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

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.

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

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

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.

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.

Application of Bogolyubov's theory of weakly nonideal Bose gases to the A+A, A+B, B+B reaction-diffusion system

NASA Astrophysics Data System (ADS)

Konkoli, Zoran

2004-01-01

Theoretical methods for dealing with diffusion-controlled reactions inevitably rely on some kind of approximation, and to find the one that works on a particular problem is not always easy. Here the approximation used by Bogolyubov to study a weakly nonideal Bose gas, referred to as the weakly nonideal Bose gas approximation (WBGA), is applied in the analysis of three reaction-diffusion models: (i) A+A→Ø, (ii) A+B→Ø, and (iii) A+A,B+B,A+B→Ø (the ABBA model). Two types of WBGA are considered, the simpler WBGA-I and the more complicated WBGA-II. All models are defined on the lattice to facilitate comparison with computer experiment (simulation). It is found that the WBGA describes the A+B reaction well, it reproduces the correct d/4 density decay exponent. However, it fails in the case of the A+A reaction and the ABBA model. (To cure the deficiency of WBGA in dealing with the A+A model, a hybrid of the WBGA and Kirkwood superposition approximations is suggested.) It is shown that the WBGA-I is identical to the dressed-tree calculation suggested by Lee [J. Phys. A 27, 2633 (1994)], and that the dressed-tree calculation does not lead to the d/2 density decay exponent when applied to the A+A reaction, as normally believed, but it predicts the d/4 decay exponent. Last, the usage of the small n0 approximation suggested by Mattis and Glasser [Rev. Mod. Phys. 70, 979 (1998)] is questioned if used beyond the A+B reaction-diffusion model.

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.

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.

The mechanical spectra of β-relaxation and spontaneous densification effects in an amorphous polymer

NASA Astrophysics Data System (ADS)

Muzeau, Elisabeth; Johari, G. P.

1990-12-01

The dynamic mechanical spectra of shear modulus of poly(methyl methacrylate) have been measured at several temperatures over the frequency range 10 -4-1 Hz in order to study localized diffusion of chain segments which appears as β-relaxation. The shape of the spectra of both the real and imaginary components has been analyzed. It is described by a stretched exponential decay function with exponent of 0.18 and it shows nearly 50% change in the modulus over this frequency range. This exponent and the rate of relaxation are remarkably similar to those observed by dielectric methods. A procedure for obtaining the exponent of the decay function and the relaxation strength of the β-process has been outlined. The strength of the β-relaxation, or equivalently the number of molecular segments undergoing a thermally activated localized diffusion, decreases on structural relaxation during the isothermal ageing, and the magnitude of the modulus increases. Qualitatively speaking, these effects seem comparable to the effects of an increase in density that normally occurs with decrease in temperature or increase in pressure, and demonstrate that isothermal ageing causes collapse of "soft sites" in a rigid amorphous matrix.

Subleading Regge limit from a soft anomalous dimension

NASA Astrophysics Data System (ADS)

Brüser, Robin; Caron-Huot, Simon; Henn, Johannes M.

2018-04-01

Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N=4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop with a scalar inserted at the cusp, and we provide perturbative evidence for this proposal. We also analyze other limits of the amplitude and conjecture an exact formula for a total cross-section at high energies.

Relaxation and anomalous T- and H-dependence of the μ coefficient in (K,Ba)BiO3 superconductors

NASA Astrophysics Data System (ADS)

Klein, T.; Harneit, W.; Joumard, I.; Marcus, J.; Escribe-Filippini, C.; Feinberg, D.

1998-04-01

Ac shielding and classical dc relaxation experiments have been used to study the flux creep phenomena in the cubic (K,Ba)BiO3 superconductor (Tc ~ 30 K). The relaxation rate is found to be constant (S ~ 1.5%) at low temperature and magnetic field and increases sharply as the vortex-glass transition line is approached. This behavior can be attributed to an anomalous decrease of the μ exponent (U(J) = U0(J0/J)μ) close to Tg(H). In this regime, the temperature dependence of the apparent critical current J is then directly related to μ(T) as J(T) = J0/[kT/U0·ln (1/ωτ)]μ(T). A similar analysis can be made on the J(B) data recently published by Abulafia et al. (Phys. Rev. Lett., 77 (1996) 1597) on YBaCuO single crystals.

Diffusion-like recommendation with enhanced similarity of objects

NASA Astrophysics Data System (ADS)

An, Ya-Hui; Dong, Qiang; Sun, Chong-Jing; Nie, Da-Cheng; Fu, Yan

2016-11-01

In the last decade, diversity and accuracy have been regarded as two important measures in evaluating a recommendation model. However, a clear concern is that a model focusing excessively on one measure will put the other one at risk, thus it is not easy to greatly improve diversity and accuracy simultaneously. In this paper, we propose to enhance the Resource-Allocation (RA) similarity in resource transfer equations of diffusion-like models, by giving a tunable exponent to the RA similarity, and traversing the value of this exponent to achieve the optimal recommendation results. In this way, we can increase the recommendation scores (allocated resource) of many unpopular objects. Experiments on three benchmark data sets, MovieLens, Netflix and RateYourMusic show that the modified models can yield remarkable performance improvement compared with the original ones.

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.

Molecular dynamics study of nanodroplet diffusion on smooth solid surfaces

NASA Astrophysics Data System (ADS)

Niu, Zhao-Xia; Huang, Tao; Chen, Yong

2018-10-01

We perform molecular dynamics simulations of Lennard-Jones particles in a canonical ensemble to study the diffusion of nanodroplets on smooth solid surfaces. Using the droplet-surface interaction to realize a hydrophilic or hydrophobic surface and calculating the mean square displacement of the center-of-mass of the nanodroplets, the random motion of nanodroplets could be characterized by shorttime subdiffusion, intermediate-time superdiffusion, and long-time normal diffusion. The short-time subdiffusive exponent increases and almost reaches unity (normal diffusion) with decreasing droplet size or enhancing hydrophobicity. The diffusion coefficient of the droplet on hydrophobic surfaces is larger than that on hydrophilic surfaces.

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.

Critical behavior in graphene with Coulomb interactions.

PubMed

Wang, Jianhui; Fertig, H A; Murthy, Ganpathy

2010-05-07

We demonstrate that, in the presence of Coulomb interactions, electrons in graphene behave like a critical system, supporting power law correlations with interaction-dependent exponents. An asymptotic analysis shows that the origin of this behavior lies in particle-hole scattering, for which the Coulomb interaction induces anomalously close approaches. With increasing interaction strength the relevant power law changes from real to complex, leading to an unusual instability characterized by a complex-valued susceptibility in the thermodynamic limit. Measurable quantities, as well as the connection to classical two-dimensional systems, are discussed.

From webs to polylogarithms

NASA Astrophysics Data System (ADS)

Gardi, Einan

2014-04-01

We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of α ij , the exponential of the Minkowski cusp angle formed between the lines i and j. We show that beyond the obvious inversion symmetry α ij → 1 /α ij , at the level of the symbol the result also admits a crossing symmetry α ij → - α ij , relating spacelike and timelike kinematics, and hence argue that in this class of webs the symbol alphabet is restricted to α ij and . We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.

Island dynamics and anisotropy during vapor phase epitaxy of m-plane GaN

DOE PAGES

Perret, Edith; Xu, Dongwei; Highland, M. J.; ...

2017-12-04

Using in situ grazing-incidence x-ray scattering, we have measured the diffuse scattering from islands that form during layer-by-layer growth of GaN by metal-organic vapor phase epitaxy on the (10more » $$\\bar{1}$$0) m-plane surface. The diffuse scattering is extended in the (0001) in-plane direction in reciprocal space, indicating a strong anisotropy with islands elongated along [1$$\\bar{2}$$10] and closely spaced along [0001]. This is confirmed by atomic force microscopy of a quenched sample. Islands were characterized as a function of growth rate F and temperature. Furthermore, the island spacing along [0001] observed during the growth of the first monolayer obeys a power-law dependence on growth rate F -n, with an exponent n=0.25±0.02. Our results are in agreement with recent kinetic Monte Carlo simulations, indicating that elongated islands result from the dominant anisotropy in step edge energy and not from surface diffusion anisotropy. The observed power-law exponent can be explained using a simple steady-state model, which gives n = 1/4.« less

Island dynamics and anisotropy during vapor phase epitaxy of m-plane GaN

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

Perret, Edith; Xu, Dongwei; Highland, M. J.

Using in situ grazing-incidence x-ray scattering, we have measured the diffuse scattering from islands that form during layer-by-layer growth of GaN by metal-organic vapor phase epitaxy on the (1010) m-plane surface. The diffuse scattering is extended in the (0001) in-plane direction in reciprocal space, indicating a strong anisotropy with islands elongated along [1210] and closely spaced along [0001]. This is confirmed by atomic force microscopy of a quenched sample. Islands were characterized as a function of growth rate F and temperature. The island spacing along [0001] observed during the growth of the first monolayer obeys a power-law dependence on growthmore » rate F-n, with an exponent n = 0:25 + 0.02. The results are in agreement with recent kinetic Monte Carlo simulations, indicating that elongated islands result from the dominant anisotropy in step edge energy and not from surface diffusion anisotropy. The observed power-law exponent can be explained using a simple steady-state model, which gives n = 1/4.« less

Island dynamics and anisotropy during vapor phase epitaxy of m-plane GaN

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

Perret, Edith; Xu, Dongwei; Highland, M. J.

Using in situ grazing-incidence x-ray scattering, we have measured the diffuse scattering from islands that form during layer-by-layer growth of GaN by metal-organic vapor phase epitaxy on the (10more » $$\\bar{1}$$0) m-plane surface. The diffuse scattering is extended in the (0001) in-plane direction in reciprocal space, indicating a strong anisotropy with islands elongated along [1$$\\bar{2}$$10] and closely spaced along [0001]. This is confirmed by atomic force microscopy of a quenched sample. Islands were characterized as a function of growth rate F and temperature. Furthermore, the island spacing along [0001] observed during the growth of the first monolayer obeys a power-law dependence on growth rate F -n, with an exponent n=0.25±0.02. Our results are in agreement with recent kinetic Monte Carlo simulations, indicating that elongated islands result from the dominant anisotropy in step edge energy and not from surface diffusion anisotropy. The observed power-law exponent can be explained using a simple steady-state model, which gives n = 1/4.« less

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.

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.

Kinetics of Isothermal Reactive Diffusion Between Solid Cu and Liquid Sn

NASA Astrophysics Data System (ADS)

O, M.; Suzuki, T.; Kajihara, M.

2018-01-01

The Cu/Sn system is one of the most fundamental and important metallic systems for solder joints in electric devices. To realize reliable solder joints, information on reactive diffusion at the solder joint is very important. In the present study, we experimentally investigated the kinetics of the reactive diffusion between solid Cu and liquid Sn using semi-infinite Cu/Sn diffusion couples prepared by an isothermal bonding technique. Isothermal annealing of the diffusion couple was conducted in the temperature range of 533-603 K for various times up to 172.8 ks (48 h). Using annealing, an intermetallic layer composed of Cu6Sn5 with scallop morphology and Cu3Sn with rather uniform thickness is formed at the original Cu/Sn interface in the diffusion couple. The growth of the Cu6Sn5 scallop occurs much more quickly than that of the Cu3Sn layer and thus predominates in the overall growth of the intermetallic layer. This tendency becomes more remarkable at lower annealing temperatures. The total thickness of the intermetallic layer is proportional to a power function of the annealing time, and the exponent of the power function is close to unity at all the annealing temperatures. This means that volume diffusion controls the intermetallic growth and the morphology of the Cu6Sn5/Sn interface influences the rate-controlling process. Adopting a mean value of 0.99 for the exponent, we obtain a value of 26 kJ/mol for the activation enthalpy of the intermetallic growth.

Secular Variations of Soil CO2 Efflux at Santa Ana-Izalco-Coatepeque Volcanic Complex, El Salvador, Central America

NASA Astrophysics Data System (ADS)

Olmos, R.; Barahona, F.; Cartagena, R.; Soriano, T.; Salazar, J.; Hernandez, P.; Perez, N.; Lopez, D.

2002-12-01

The Santa Ana-Izalco-Coatepeque volcanic complex (2,365 m elevation), located 40 Km west of San Salvador, consists of the Coatepeque collapse caldera (a 6.5 x 10.5 Km elliptical depression), the Santa Ana and Izalco stratovolcanoes, as well as numerous cinder cones and explosion craters. The summit of the Santa Ana volcano contains an acid lake where hot springs, gas bubbling and intense fumarolic emissions occur. A volcanic plume, usually driven by the NE trades, may be seen rising up to 500 m from the summit crater of the Santa Ana volcano. The goal of this study is to provide a multidisciplinary approach for the volcanic surveillance by means of performing geochemical continuous monitoring of diffuse CO2 emission rate in addition to seismic monitoring. Temporal variations of soil CO2 efflux measured at Cerro Pacho dome, Coatepeque caldera, by means of the accumulation chamber method and using a CO2 efflux continuous monitoring station developed by WEST Systems (Italy). From May 2001 till May 2002, CO2 efflux ranged from 4.3 to 327 gm-2d-1, with a median value of 98 and a quartile range of 26 gm-2d-1. Two distinct diffuse CO2 degassing periods have been observed: (1) an increasing trend from May to July 2001, and (2) a stationary period from November 2001 to May 2002. The increasing-trend period may be due to the anomalous plume degassing at the Santa Ana volcano during 2001 and soon after the January and February 2001 earthquakes. Temporal variations of CO2 efllux during the second period seem to be coupled with those of barometric pressure and wind speed at different time scales, though most of the variance is contained at diurnal and semi-diurnal frequencies. These observations can help to explain the existence of a persistent behavior (Hurst exponent, H=0.934 +/- 0.0039) within the diffuse CO2 degassing phenomena. However, further observations are in progress to understand the long-term memory of diffuse CO2 degassing at the Santa Ana volcanic complex.

A Brief Survey of the Equilibrium and Transport Properties of Critical Fluids and the Degree to Which Microgravity is Required for Their Experimental Investigation

NASA Technical Reports Server (NTRS)

Ferrell, Richard A.

1996-01-01

The modern theory of second order phase transitions is very successful in calculating the critical exponents as an asymptotic expansion in powers of epsilon = 4 - D, the deviation of D = 3, the spatial dimension of the actual physical system from that of the abstract four-dimensional reference model. This remarkable mathematical 'tour de force' leaves unanswered, however, many fundamental questions concerning the exact nature of how the fluctuations interact. I discuss here some experiments which would help to further our understanding of the equilibrium critical properties. Especially promising would be a measurement of the temperature dependence of the turbidity very close to the critical point. This has the promise of determining the small and elusive but fundamentally important anomalous dimension exponent eta. I also review various ways of measuring the critical transport coefficients and point out some cases where ground based experiments may usefully supplement flight experiments.

Extended slow dynamical regime close to the many-body localization transition

NASA Astrophysics Data System (ADS)

Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien

2016-02-01

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L =28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth S (t ) ∝t1 /z with a disorder-dependent exponent z ≥1 , in contrast with the pure ballistic growth z =1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance I (t ) ∝t-ζ with a continuously varying disorder-dependent exponent ζ , vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.

Fluctuations uncover a distinct class of traveling waves

PubMed Central

Korolev, Kirill S.

2018-01-01

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction–diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semipushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semipushed, and fully pushed waves occur at universal ratios of the wave velocity to the Fisher velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of diversity loss, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We analytically calculate this exponent, taking into account the fluctuations in the shape of the wave front. For fully pushed waves, the exponent is −1, consistent with the central limit theorem. In semipushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 toward the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in the position of the front occur, even for populations with cooperative growth and other forms of an Allee effect. The evolutionary outcome of spatial spreading in such populations could therefore be less predictable than previously thought. PMID:29610340

Fluctuations uncover a distinct class of traveling waves.

PubMed

Birzu, Gabriel; Hallatschek, Oskar; Korolev, Kirill S

2018-04-17

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction-diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semipushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semipushed, and fully pushed waves occur at universal ratios of the wave velocity to the Fisher velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of diversity loss, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We analytically calculate this exponent, taking into account the fluctuations in the shape of the wave front. For fully pushed waves, the exponent is -1, consistent with the central limit theorem. In semipushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 toward the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in the position of the front occur, even for populations with cooperative growth and other forms of an Allee effect. The evolutionary outcome of spatial spreading in such populations could therefore be less predictable than previously thought. Copyright © 2018 the Author(s). Published by PNAS.

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.

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.

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.

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

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.

Anomalous elasticity, fluctuations and disorder in elastic membranes

NASA Astrophysics Data System (ADS)

Le Doussal, Pierre; Radzihovsky, Leo

2018-05-01

Motivated by freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters (Le Doussal and Radzihovsky, 1992; 1993). The experimental realization atom-thin graphene sheets (Novoselov et al., 2004) have driven a resurgence in this fascinating subject, making our dated predictions and their detailed derivations timely. To this end we analyze the statistical mechanics of a generalized D-dimensional elastic "membrane" embedded in d dimensions using a self-consistent screening approximation (SCSA), that has proved to be unprecedentedly accurate in this system, exact in three complementary limits: (i) d → ∞, (ii) D → 4, and (iii) D = d. Focusing on the critical "flat" phase, for a homogeneous two-dimensional (D = 2) membrane embedded in three dimensions (d = 3), we predict its universal roughness exponent ζ = 0 . 590, length-scale dependent elastic moduli exponents η = 0 . 821 and ηu = 0 . 358, and an anomalous Poisson ratio, σ = - 1 / 3. In the presence of random uncorrelated heterogeneity the membrane exhibits a glassy wrinkled ground state, characterized by ζ‧ = 0 . 775 ,η‧ = 0 . 449, ηu‧ = 1 . 101 and a Poisson ratio σ‧ = - 1 / 3. Motivated by a number of physical realizations (charged impurities, disclinations and dislocations) we also study power-law correlated quenched disorder that leads to a variety of distinct glassy wrinkled phases. Finally, neglecting self-avoiding interaction we demonstrate that at high temperature a "phantom" sheet undergoes a continuous crumpling transition, characterized by a radius of gyration exponent, ν = 0 . 732 and η = 0 . 535. Many of these universal predictions have received considerable support from simulations. We hope that this detailed presentation of the SCSA theory will be useful to further theoretical developments and corresponding experimental investigations on freely suspended graphene.

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.

Light-induced metal-insulator transition in a switchable mirror.

PubMed

Hoekstra, A F; Roy, A S; Rosenbaum, T F; Griessen, R; Wijngaarden, R J; Koeman, N J

2001-06-04

Rare earth hydride films can be converted reversibly from metallic mirrors to insulating windows simply by changing the surrounding hydrogen gas pressure at room temperature. At low temperatures, in situ doping is not possible in this way as hydrogen cannot diffuse. However, our finding of persistent photoconductivity under ultraviolet illumination offers an attractive possibility to tune yttrium hydride through the T = 0 metal-insulator transition. Conductivity and Hall measurements are used to determine critical exponents. The unusually large value for the product of the static and dynamical critical exponents appears to signify the important role played by electron-electron interactions.

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

Understanding generalized inversions of nuclear magnetic resonance transverse relaxation time in porous media

NASA Astrophysics Data System (ADS)

Mitchell, J.; Chandrasekera, T. C.

2014-12-01

The nuclear magnetic resonance transverse relaxation time T2, measured using the Carr-Purcell-Meiboom-Gill (CPMG) experiment, is a powerful method for obtaining unique information on liquids confined in porous media. Furthermore, T2 provides structural information on the porous material itself and has many applications in petrophysics, biophysics, and chemical engineering. Robust interpretation of T2 distributions demands appropriate processing of the measured data since T2 is influenced by diffusion through magnetic field inhomogeneities occurring at the pore scale, caused by the liquid/solid susceptibility contrast. Previously, we introduced a generic model for the diffusion exponent of the form -ant_e^k (where n is the number and te the temporal separation of spin echoes, and a is a composite diffusion parameter) in order to distinguish the influence of relaxation and diffusion in CPMG data. Here, we improve the analysis by introducing an automatic search for the optimum power k that best describes the diffusion behavior. This automated method is more efficient than the manual trial-and-error grid search adopted previously, and avoids variability through subjective judgments of experimentalists. Although our method does not avoid the inherent assumption that the diffusion exponent depends on a single k value, we show through simulation and experiment that it is robust in measurements of heterogeneous systems that violate this assumption. In this way, we obtain quantitative T2 distributions from complicated porous structures and demonstrate the analysis with examples of ceramics used for filtration and catalysis, and limestone of relevance to the construction and petroleum industries.

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.

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’.

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.

Spike solutions in Gierer#x2013;Meinhardt model with a time dependent anomaly exponent

NASA Astrophysics Data System (ADS)

Nec, Yana

2018-01-01

Experimental evidence of complex dispersion regimes in natural systems, where the growth of the mean square displacement in time cannot be characterised by a single power, has been accruing for the past two decades. In such processes the exponent γ(t) in ⟨r2⟩ ∼ tγ(t) at times might be approximated by a piecewise constant function, or it can be a continuous function. Variable order differential equations are an emerging mathematical tool with a strong potential to model these systems. However, variable order differential equations are not tractable by the classic differential equations theory. This contribution illustrates how a classic method can be adapted to gain insight into a system of this type. Herein a variable order Gierer-Meinhardt model is posed, a generic reaction- diffusion system of a chemical origin. With a fixed order this system possesses a solution in the form of a constellation of arbitrarily situated localised pulses, when the components' diffusivity ratio is asymptotically small. The pattern was shown to exist subject to multiple step-like transitions between normal diffusion and sub-diffusion, as well as between distinct sub-diffusive regimes. The analytical approximation obtained permits qualitative analysis of the impact thereof. Numerical solution for typical cross-over scenarios revealed such features as earlier equilibration and non-monotonic excursions before attainment of equilibrium. The method is general and allows for an approximate numerical solution with any reasonably behaved γ(t).

Random walks on combs

NASA Astrophysics Data System (ADS)

Durhuus, Bergfinnur; Jonsson, Thordur; Wheater, John F.

2006-02-01

We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds, we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.

Avalanche Statistics Identify Intrinsic Stellar Processes near Criticality in KIC 8462852

NASA Astrophysics Data System (ADS)

Sheikh, Mohammed A.; Weaver, Richard L.; Dahmen, Karin A.

2016-12-01

The star KIC8462852 (Tabby's star) has shown anomalous drops in light flux. We perform a statistical analysis of the more numerous smaller dimming events by using methods found useful for avalanches in ferromagnetism and plastic flow. Scaling exponents for avalanche statistics and temporal profiles of the flux during the dimming events are close to mean field predictions. Scaling collapses suggest that this star may be near a nonequilibrium critical point. The large events are interpreted as avalanches marked by modified dynamics, limited by the system size, and not within the scaling regime.

On critical exponents without Feynman diagrams

NASA Astrophysics Data System (ADS)

Sen, Kallol; Sinha, Aninda

2016-11-01

In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov’s, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the O(n) model at the Wilson-Fisher fixed point in 4-ɛ dimensions up to O({ɛ }2). AS dedicates this work to the loving memory of his mother.

Hyperscaling violating black hole solutions and magneto-thermoelectric DC conductivities in holography

NASA Astrophysics Data System (ADS)

Ge, Xian-Hui; Tian, Yu; Wu, Shang-Yu; Wu, Shao-Feng

2017-08-01

We derive new black hole solutions in Einstein-Maxwell-axion-dilaton theory with a hyperscaling violation exponent. We then examine the corresponding anomalous transport exhibited by cuprate strange metals in the normal phase of high-temperature superconductors via gauge-gravity duality. Linear-temperature-dependence resistivity and quadratic-temperature-dependence inverse Hall angle can be achieved. In the high-temperature regime, the heat conductivity and Hall Lorenz ratio are proportional to the temperature. The Nernst signal first increases as temperature goes up, but it then decreases with increasing temperature in the high-temperature regime.

Diffusive growth of a single droplet with three different boundary conditions

NASA Astrophysics Data System (ADS)

Tavassoli, Z.; Rodgers, G. J.

2000-02-01

We study a single, motionless three-dimensional droplet growing by adsorption of diffusing monomers on a 2D substrate. The diffusing monomers are adsorbed at the aggregate perimeter of the droplet with different boundary conditions. Models with both an adsorption boundary condition and a radiation boundary condition, as well as a phenomenological model, are considered and solved in a quasistatic approximation. The latter two models allow particle detachment. In the short time limit, the droplet radius grows as a power of the time with exponents of 1/4, 1/2 and 3/4 for the models with adsorption, radiation and phenomenological boundary conditions, respectively. In the long time limit a universal growth rate as $[t/\\ln(t)]^{1/3}$ is observed for the radius of the droplet for all models independent of the boundary conditions. This asymptotic behaviour was obtained by Krapivsky \\cite{krapquasi} where a similarity variable approach was used to treat the growth of a droplet with an adsorption boundary condition based on a quasistatic approximation. Another boundary condition with a constant flux of monomers at the aggregate perimeter is also examined. The results exhibit a power law growth rate with an exponent of 1/3 for all times.

Testing lyoequivalency for three commercially sustained-release tablets containing diltiazem hydrochloride.

PubMed

Maswadeh, Hamzah A; Al-Hanbali, Othman A; Kanaan, Reem A; Shakya, Ashok K; Maraqa, Anwar

2010-01-01

In vitro release kinetics of three commercially available sustained release tablets (SR) diltiazem hydrochloride were studied at pH 1.1 for 2 h and for another 6 h at pH 6.8 using the USP dissolution apparatus with the paddle assemble. The kinetics of the dissolution process was studied by analyzing the dissolution data using five kinetic equations: the zero-order equation, the first-order equation, the Higuchi square root equation, the Hixson-Crowell cube root law and the Peppas equation. Analyses of the dissolution kinetic data for diltiazem hydrochloride commercial SR tablets showed that both Dilzacard and Dilzem SR tablets released drug by Non-Fickian (Anomalous transport) release with release exponent (n) equal to 0.59 and 0.54, respectively, which indicate the summation of both diffusion and dissolution controlled drug release. Bi-Tildiem SR tablets released drug by super case II (n = 1.29) which indicate zero-order release due to the dissolution of polymeric matrix and relaxation of the polymer chain. This finding was also in agreement with results obtained from application of zero-order and Hixson-Crowell equations. A dissolution profile comparative study was done to test the lyoequivelancy of the three products by using the mean dissolution time (MDT), dissimilarity factor f1 and similarity factor f2. Results showed that the three products are different and not lyoequivalent.

Fickian dispersion is anomalous

DOE PAGES

Cushman, John H.; O’Malley, Dan

2015-06-22

The thesis put forward here is that the occurrence of Fickian dispersion in geophysical settings is a rare event and consequently should be labeled as anomalous. What people classically call anomalous is really the norm. In a Lagrangian setting, a process with mean square displacement which is proportional to time is generally labeled as Fickian dispersion. With a number of counter examples we show why this definition is fraught with difficulty. In a related discussion, we show an infinite second moment does not necessarily imply the process is super dispersive. By employing a rigorous mathematical definition of Fickian dispersion wemore » illustrate why it is so hard to find a Fickian process. We go on to employ a number of renormalization group approaches to classify non-Fickian dispersive behavior. Scaling laws for the probability density function for a dispersive process, the distribution for the first passage times, the mean first passage time, and the finite-size Lyapunov exponent are presented for fixed points of both deterministic and stochastic renormalization group operators. The fixed points of the renormalization group operators are p-self-similar processes. A generalized renormalization group operator is introduced whose fixed points form a set of generalized self-similar processes. Finally, power-law clocks are introduced to examine multi-scaling behavior. Several examples of these ideas are presented and discussed.« less

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.

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.

The use of the Hurst exponent to predict changes in trends on the Warsaw Stock Exchange

NASA Astrophysics Data System (ADS)

Domino, Krzysztof

2011-01-01

The local properties of the time series of the evolution of share prices of 126 significant companies traded on the Warsaw Stock Exchange during the period between 1991-2008 have been investigated. The analysis was applied to daily financial returns. I have used the local DFA to obtain the Hurst exponent (diffusion coefficient) while searching for negative correlations by which changes of long-term trends would be effected. A certain evidence, proving that after the signature of anti-correlation-the drop in the Hurst exponent-the change in the trend and in the return rate of an investment is probable, was pointed out. Hence after further investigation this method may be useful as a part of an investment strategy. As the Warsaw Stock Exchange is relatively smaller and younger than other significant world Stock Exchanges-and as the developing market is less efficient-the generalization for others markets needs further investigation.

Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux

NASA Astrophysics Data System (ADS)

Liu, Bingchen; Dong, Mengzhen; Li, Fengjie

2018-04-01

This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.

Coarsening of Inter- and Intra-granular Proeutectoid Cementite in an Initially Pearlitic 2C-4Cr Ultrahigh Carbon Steel

NASA Astrophysics Data System (ADS)

Hecht, Matthew D.; Picard, Yoosuf N.; Webler, Bryan A.

2017-05-01

We have examined spheroidization and coarsening of cementite in an initially pearlitic 2C-4Cr ultrahigh carbon steel containing a cementite network. Coarsening kinetics of spheroidized cementite and growth of denuded zones adjacent to the cementite network were investigated by analyzing particle sizes from digital micrographs of water-quenched steel etched with Nital. Denuded zones grew at a rate proportional to t 1/4- t 1/5. Spheroidization of pearlite was completed within 90 minutes at 1073 K and 1173 K (800 °C and 900 °C), and within 5 minutes at 1243 K (970 °C). Bimodal particle size distributions were identified in most of the samples and were more pronounced at higher temperatures and hold times. Peaks in the distributions were attributed to the coarsening of intragranular and grain boundary particles at different rates. A third, non-coarsening peak of particles was present at 1073 K (800 °C) only and was attributed to particles existing prior to the heat treatment. Particle sizes were plotted vs time to investigate possible coarsening mechanisms. The coarsening exponent for the growth of grain boundary carbides was closest to 4, indicating grain boundary diffusion control. The coarsening exponent was closest to 5 for intragranular carbides, indicating suppression of volumetric diffusion (possibly due to reduced effective diffusivity because of Cr alloying) and control by dislocation diffusion.

Unstable vicinal crystal growth from cellular automata

NASA Astrophysics Data System (ADS)

Krasteva, A.; Popova, H.; KrzyŻewski, F.; Załuska-Kotur, M.; Tonchev, V.

2016-03-01

In order to study the unstable step motion on vicinal crystal surfaces we devise vicinal Cellular Automata. Each cell from the colony has value equal to its height in the vicinal, initially the steps are regularly distributed. Another array keeps the adatoms, initially distributed randomly over the surface. The growth rule defines that each adatom at right nearest neighbor position to a (multi-) step attaches to it. The update of whole colony is performed at once and then time increases. This execution of the growth rule is followed by compensation of the consumed particles and by diffusional update(s) of the adatom population. Two principal sources of instability are employed - biased diffusion and infinite inverse Ehrlich-Schwoebel barrier (iiSE). Since these factors are not opposed by step-step repulsion the formation of multi-steps is observed but in general the step bunches preserve a finite width. We monitor the developing surface patterns and quantify the observations by scaling laws with focus on the eventual transition from diffusion-limited to kinetics-limited phenomenon. The time-scaling exponent of the bunch size N is 1/2 for the case of biased diffusion and 1/3 for the case of iiSE. Additional distinction is possible based on the time-scaling exponents of the sizes of multi-step Nmulti, these are 0.36÷0.4 (for biased diffusion) and 1/4 (iiSE).

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

Thermal diffusivity and butterfly velocity in anisotropic Q-lattice models

NASA Astrophysics Data System (ADS)

Jeong, Hyun-Sik; Ahn, Yongjun; Ahn, Dujin; Niu, Chao; Li, Wei-Jia; Kim, Keun-Young

2018-01-01

We study a relation between the thermal diffusivity ( D T ) and two quantum chaotic properties, Lyapunov time (τ L ) and butterfly velocity ( v B ) in strongly correlated systems by using a holographic method. Recently, it was shown that E_i:={D}_{T,i}/({v}{^{B,i}}^2{τ}_L)(i=x,y) is universal in the sense that it is determined only by some scaling exponents of the IR metric in the low temperature limit regardless of the matter fields and ultraviolet data. Inspired by this observation, by analyzing the anisotropic IR scaling geometry carefully, we find the concrete expressions for E_i in terms of the critical dynamical exponents z i in each direction, E_i={z}_i/2({z}_i-1) . Furthermore, we find the lower bound of E_i is always 1 /2, which is not affected by anisotropy, contrary to the η/s case. However, there may be an upper bound determined by given fixed anisotropy.

Influence of enteric-coated lactose on the release profile of 4-aminopyridine from HPMC matrix tablets.

PubMed

Martínez-González, Ilona; Villafuerte-Robles, Leopoldo

2004-01-01

A weakly basic experimental drug, 4-aminopyridine, was taken as a model to study the influence of enteric-coated lactose (EL) on the release profile from hydroxypropyl methylcellulose matrices. Powder mixtures were wet-granulated with water. The dried granulation was compressed with a hydraulic press at 85 MPa. Dissolution studies were made using HCl 0.1 N and then phosphate buffer pH 7.4. Dissolution curves were described by M(t)/M(inf) = k*t(N). A trend toward increasing exponent (n) and decreasing release constant (k) values is observed with increasing EL concentrations up to 9%; this is attributed to an increasing obstruction of the diffusion path by isolated EL particles that are insoluble in HCl and are surrounded by a water-filled space. After a critical EL concentration, the water-filled spaces surrounding EL particles percolate, producing the opposite effect, increasing the release constant and decreasing the exponent (n) values as the EL proportion increases from 10% to 50%. EL particles (2% to 9%) decrease the drug and water transport in matrices dissolving in HCl. Thereafter, at pH 7.4, the pores formed by dissolution of EL particles produce the opposite. Both processes contribute to flattening the release profile. Release profiles with decreasing release constant values show a logarithmic trend toward increasing values of the exponent (n), changing from diffusion toward relaxation-erosion-controlled processes.

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

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

Slow kinetics of Brownian maxima.

PubMed

Ben-Naim, E; Krapivsky, P L

2014-07-18

We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t and find the algebraic decay P ∼ t(-β) with exponent β = 1/4. When the two particles have diffusion constants D(1) and D(2), the exponent depends on the mobilities, β = (1/π) arctan sqrt[D(2)/D(1)]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest extension of particles in higher dimensions.

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

Understanding generalized inversions of nuclear magnetic resonance transverse relaxation time in porous media

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

Mitchell, J., E-mail: JMitchell16@slb.com; Chandrasekera, T. C.

2014-12-14

The nuclear magnetic resonance transverse relaxation time T{sub 2}, measured using the Carr-Purcell-Meiboom-Gill (CPMG) experiment, is a powerful method for obtaining unique information on liquids confined in porous media. Furthermore, T{sub 2} provides structural information on the porous material itself and has many applications in petrophysics, biophysics, and chemical engineering. Robust interpretation of T{sub 2} distributions demands appropriate processing of the measured data since T{sub 2} is influenced by diffusion through magnetic field inhomogeneities occurring at the pore scale, caused by the liquid/solid susceptibility contrast. Previously, we introduced a generic model for the diffusion exponent of the form −ant{sub e}{supmore » k} (where n is the number and t{sub e} the temporal separation of spin echoes, and a is a composite diffusion parameter) in order to distinguish the influence of relaxation and diffusion in CPMG data. Here, we improve the analysis by introducing an automatic search for the optimum power k that best describes the diffusion behavior. This automated method is more efficient than the manual trial-and-error grid search adopted previously, and avoids variability through subjective judgments of experimentalists. Although our method does not avoid the inherent assumption that the diffusion exponent depends on a single k value, we show through simulation and experiment that it is robust in measurements of heterogeneous systems that violate this assumption. In this way, we obtain quantitative T{sub 2} distributions from complicated porous structures and demonstrate the analysis with examples of ceramics used for filtration and catalysis, and limestone of relevance to the construction and petroleum industries.« less

Dynamic scaling in natural swarms

NASA Astrophysics Data System (ADS)

Cavagna, Andrea; Conti, Daniele; Creato, Chiara; Del Castello, Lorenzo; Giardina, Irene; Grigera, Tomas S.; Melillo, Stefania; Parisi, Leonardo; Viale, Massimiliano

2017-09-01

Collective behaviour in biological systems presents theoretical challenges beyond the borders of classical statistical physics. The lack of concepts such as scaling and renormalization is particularly problematic, as it forces us to negotiate details whose relevance is often hard to assess. In an attempt to improve this situation, we present here experimental evidence of the emergence of dynamic scaling laws in natural swarms of midges. We find that spatio-temporal correlation functions in different swarms can be rescaled by using a single characteristic time, which grows with the correlation length with a dynamical critical exponent z ~ 1, a value not found in any other standard statistical model. To check whether out-of-equilibrium effects may be responsible for this anomalous exponent, we run simulations of the simplest model of self-propelled particles and find z ~ 2, suggesting that natural swarms belong to a novel dynamic universality class. This conclusion is strengthened by experimental evidence of the presence of non-dissipative modes in the relaxation, indicating that previously overlooked inertial effects are needed to describe swarm dynamics. The absence of a purely dissipative regime suggests that natural swarms undergo a near-critical censorship of hydrodynamics.

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.

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.

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.

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.

Evaluation of scaling invariance embedded in short time series.

PubMed

Pan, Xue; Hou, Lei; Stephen, Mutua; Yang, Huijie; Zhu, Chenping

2014-01-01

Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2). Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03) and sharp confidential interval (standard deviation ≤0.05). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.

Evaluation of Scaling Invariance Embedded in Short Time Series

PubMed Central

Pan, Xue; Hou, Lei; Stephen, Mutua; Yang, Huijie; Zhu, Chenping

2014-01-01

Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length . Calculations with specified Hurst exponent values of show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias () and sharp confidential interval (standard deviation ). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records. PMID:25549356

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.

Hidden Area and Mechanical Nonlinearities in Freestanding Graphene.

PubMed

Nicholl, Ryan J T; Lavrik, Nickolay V; Vlassiouk, Ivan; Srijanto, Bernadeta R; Bolotin, Kirill I

2017-06-30

We investigated the effect of out-of-plane crumpling on the mechanical response of graphene membranes. In our experiments, stress was applied to graphene membranes using pressurized gas while the strain state was monitored through two complementary techniques: interferometric profilometry and Raman spectroscopy. By comparing the data obtained through these two techniques, we determined the geometric hidden area which quantifies the crumpling strength. While the devices with hidden area ∼0% obeyed linear mechanics with biaxial stiffness 428±10  N/m, specimens with hidden area in the range 0.5%-1.0% were found to obey an anomalous nonlinear Hooke's law with an exponent ∼0.1.

Hidden Area and Mechanical Nonlinearities in Freestanding Graphene

NASA Astrophysics Data System (ADS)

Nicholl, Ryan J. T.; Lavrik, Nickolay V.; Vlassiouk, Ivan; Srijanto, Bernadeta R.; Bolotin, Kirill I.

2017-06-01

We investigated the effect of out-of-plane crumpling on the mechanical response of graphene membranes. In our experiments, stress was applied to graphene membranes using pressurized gas while the strain state was monitored through two complementary techniques: interferometric profilometry and Raman spectroscopy. By comparing the data obtained through these two techniques, we determined the geometric hidden area which quantifies the crumpling strength. While the devices with hidden area ˜0 % obeyed linear mechanics with biaxial stiffness 428 ±10 N /m , specimens with hidden area in the range 0.5%-1.0% were found to obey an anomalous nonlinear Hooke's law with an exponent ˜0.1 .

Fractional Diffusion, Low Exponent Lévy Stable Laws, and 'Slow Motion' Denoising of Helium Ion Microscope Nanoscale Imagery.

PubMed

Carasso, Alfred S; Vladár, András E

2012-01-01

Helium ion microscopes (HIM) are capable of acquiring images with better than 1 nm resolution, and HIM images are particularly rich in morphological surface details. However, such images are generally quite noisy. A major challenge is to denoise these images while preserving delicate surface information. This paper presents a powerful slow motion denoising technique, based on solving linear fractional diffusion equations forward in time. The method is easily implemented computationally, using fast Fourier transform (FFT) algorithms. When applied to actual HIM images, the method is found to reproduce the essential surface morphology of the sample with high fidelity. In contrast, such highly sophisticated methodologies as Curvelet Transform denoising, and Total Variation denoising using split Bregman iterations, are found to eliminate vital fine scale information, along with the noise. Image Lipschitz exponents are a useful image metrology tool for quantifying the fine structure content in an image. In this paper, this tool is applied to rank order the above three distinct denoising approaches, in terms of their texture preserving properties. In several denoising experiments on actual HIM images, it was found that fractional diffusion smoothing performed noticeably better than split Bregman TV, which in turn, performed slightly better than Curvelet denoising.

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.

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.

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.

The Anomalous Accretion Disk of the Cataclysmic Variable RW Sextantis

NASA Astrophysics Data System (ADS)

Linnell, Albert P.; Godon, P.; Hubeny, I.; Sion, E. M.; Szkody, P.

2011-01-01

The standard model for stable Cataclysmic Variable (CV) accretion disks (Frank, King and Raine 1992) derives an explicit analytic expression for the disk effective temperature as function of radial distance from the white dwarf (WD). That model specifies that the effective temperature, Teff(R), varies with R as ()0.25, where () represents a combination of parameters including R, the mass transfer rate M(dot), and other parameters. It is well known that fits of standard model synthetic spectra to observed CV spectra find almost no instances of agreement. We have derived a generalized expression for the radial temperature gradient, which preserves the total disk luminosity as function of M(dot) but permits a different exponent from the theoretical value of 0.25, and have applied it to RW Sex (Linnell et al.,2010,ApJ, 719,271). We find an excellent fit to observed FUSE and IUE spectra for an exponent of 0.125, curiously close to 1/2 the theoretical value. Our annulus synthetic spectra, combined to represent the accretion disk, were produced with program TLUSTY, were non-LTE and included H, He, C, Mg, Al, Si, and Fe as explicit ions. We illustrate our results with a plot showing the failure to fit RW Sex for a range of M(dot) values, our model fit to the observations, and a chi2 plot showing the selection of the exponent 0.125 as the best fit for the M(dot) range shown. (For the final model parameters see the paper cited.)

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

NASA Astrophysics Data System (ADS)

Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying

2018-04-01

Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.

Shock-wave flow regimes at entry into the diffuser of a hypersonic ramjet engine: Influence of physical properties of the gas medium

NASA Astrophysics Data System (ADS)

Tarnavskii, G. A.

2006-07-01

The physical aspects of the effective-adiabatic-exponent model making it possible to decompose the total problem on modeling of high-velocity gas flows into individual subproblems (“physicochemical processes” and “ aeromechanics”), which ensures the creation of a universal and efficient computer complex divided into a number of independent units, have been analyzed. Shock-wave structures appearing at entry into the duct of a hypersonic aircraft have been investigated based on this methodology, and the influence of the physical properties of the gas medium in a wide range of variations of the effective adiabatic exponent has been studied.

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.

Transport, diffusion, and energy studies in the Arnold-Beltrami-Childress map

NASA Astrophysics Data System (ADS)

Das, Swetamber; Gupte, Neelima

2017-09-01

We study the transport and diffusion properties of passive inertial particles described by a six-dimensional dissipative bailout embedding map. The base map chosen for the study is the three-dimensional incompressible Arnold-Beltrami-Childress (ABC) map chosen as a representation of volume preserving flows. There are two distinct cases: the two-action and the one-action cases, depending on whether two or one of the parameters (A ,B ,C ) exceed 1. The embedded map dynamics is governed by two parameters (α ,γ ), which quantify the mass density ratio and dissipation, respectively. There are important differences between the aerosol (α <1 ) and the bubble (α >1 ) regimes. We have studied the diffusive behavior of the system and constructed the phase diagram in the parameter space by computing the diffusion exponents η . Three classes have been broadly classified—subdiffusive transport (η <1 ), normal diffusion (η ≈1 ), and superdiffusion (η >1 ) with η ≈2 referred to as the ballistic regime. Correlating the diffusive phase diagram with the phase diagram for dynamical regimes seen earlier, we find that the hyperchaotic bubble regime is largely correlated with normal and superdiffusive behavior. In contrast, in the aerosol regime, ballistic superdiffusion is seen in regions that largely show periodic dynamical behaviors, whereas subdiffusive behavior is seen in both periodic and chaotic regimes. The probability distributions of the diffusion exponents show power-law scaling for both aerosol and bubbles in the superdiffusive regimes. We further study the Poincáre recurrence times statistics of the system. Here, we find that recurrence time distributions show power law regimes due to the existence of partial barriers to transport in the phase space. Moreover, the plot of average particle kinetic energies versus the mass density ratio for the two-action case exhibits a devil's staircase-like structure for higher dissipation values. We explain these results and discuss their implications for realistic systems.

Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.

PubMed

Leibovich, N; Dechant, A; Lutz, E; Barkai, E

2016-11-01

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

Stretching Diagnostics and Mixing Properties In The Stratosphere

NASA Astrophysics Data System (ADS)

Legras, B.; Shuckburgh, E.

The "finite size Lyapunov exponent" and the "effective diffusivity" are two diagnos- tics of mixing which have been recently introduced to investigate atmospheric flows. Both have been used to successfully identify the barriers to transport, for instance at the edge of the stratospheric polar vortex. Here we compare the two diagnostics in detail. The equivalent length has the advantage of arising as a mixing quantification from a rigid theoretical framework, however it has the disadvantage of being an aver- age quantity (the average around a tracer contour). The finite size Lyapunov exponent may be defined at any point in the flow, and quantifies the stretching properties expe- rienced by a fluid parcel both in its past and future evolution. In particular, the lines of maximum stretching at any time delineate the building blocks of the chaotic stirring. However the interpretation of the finite size Lyapunov exponent as a mixing time is less direct and depends on the alignment of tracer contours with the stretching lines.

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.

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.

Deterministic chaos in atmospheric radon dynamics

NASA Astrophysics Data System (ADS)

Cuculeanu, Vasile; Lupu, Alexandru

2001-08-01

The correlation dimension and Lyapunov exponents have been calculated for two time series of atmospheric radon daughter concentrations obtained from four daily measurements during the period 1993-1996. A number of about 6000 activity concentration values of 222Rn and 220Rn daughters have been used. The measuring method is based on aerosol collection on filters. In order to determine the filter activity, a low background gross beta measuring device with Geiger-Müller counter tubes in anticoincidence was used. The small noninteger value of the correlation dimension (≃2.2) and the existence of a positive Lyapunov exponent prove that deterministic chaos is present in the time series of atmospheric 220Rn daughters. This shows that a simple diffusion equation with a parameterized turbulent diffusion coefficient is insufficient for describing the dynamics in the near-ground layer where turbulence is not fully developed and coherent structures dominate. The analysis of 222Rn series confirms that the dynamics of the boundary layer cannot be described by a system of ordinary differential equations with a low number of independent variables.

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.

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.

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.

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

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

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.

Universality classes for unstable crystal growth

NASA Astrophysics Data System (ADS)

Biagi, Sofia; Misbah, Chaouqi; Politi, Paolo

2014-06-01

Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with nonequilibrium problems, however, the distinction in universality classes is not as clear and few are the examples, such as phase separation and kinetic roughening, for which universality has allowed to classify results in a general spirit. Here we focus on an out-of-equilibrium case, unstable crystal growth, lying in between phase ordering and pattern formation. We consider a well-established 2+1-dimensional family of continuum nonlinear equations for the local height h(x,t) of a crystal surface having the general form ∂th(x,t)=-∇.[j(∇h)+∇(∇2h)]: j (∇h) is an arbitrary function, which is linear for small ∇h, and whose structure expresses instabilities which lead to the formation of pyramidlike structures of planar size L and height H. Our task is the choice and calculation of the quantities that can operate as critical exponents, together with the discussion of what is relevant or not to the definition of our universality class. These aims are achieved by means of a perturbative, multiscale analysis of our model, leading to phase diffusion equations whose diffusion coefficients encapsulate all relevant information on dynamics. We identify two critical exponents: (i) the coarsening exponent, n, controlling the increase in time of the typical size of the pattern, L ˜tn; (ii) the exponent β, controlling the increase in time of the typical slope of the pattern, M ˜tβ, where M ≈H/L. Our study reveals that there are only two different universality classes, according to the presence (n =1/3, β =0) or the absence (n =1/4, β >0) of faceting. The symmetry of the pattern, as well as the symmetry of the surface mass current j (∇h) and its precise functional form, is irrelevant. Our analysis seems to support the idea that also space dimensionality is irrelevant.

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.

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.

Diffusive dynamics of nanoparticles in ultra-confined media

DOE PAGES

Jacob, Jack Deodato; Conrad, Jacinta; Krishnamoorti, Ramanan; ...

2015-08-10

Differential dynamic microscopy (DDM) was used to investigate the diffusive dynamics of nanoparticles of diameter 200 400 nm that were strongly confined in a periodic square array of cylindrical nanoposts. The minimum distance between posts was 1.3 5 times the diameter of the nanoparticles. The image structure functions obtained from the DDM analysis were isotropic and could be fit by a stretched exponential function. The relaxation time scaled diffusively across the range of wave vectors studied, and the corresponding scalar diffusivities decreased monotonically with increased confinement. The decrease in diffusivity could be described by models for hindered diffusion that accountedmore » for steric restrictions and hydrodynamic interactions. The stretching exponent decreased linearly as the nanoparticles were increasingly confined by the posts. Altogether, these results are consistent with a picture in which strongly confined nanoparticles experience a heterogeneous spatial environment arising from hydrodynamics and volume exclusion on time scales comparable to cage escape, leading to multiple relaxation processes and Fickian but non-Gaussian diffusive dynamics.« less

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.

Shoreline Position Dynamics: Measurement and Analysis

NASA Astrophysics Data System (ADS)

Barton, C. C.; Rigling, B.; Hunter, N.; Tebbens, S. F.

2012-12-01

The dynamics of sandy shoreline position is a fundamental property of complex beach face processes and is characterized by the power scaling exponent. Spectral analysis was performed on the temporal position of four sandy shorelines extracted from four shore perpendicular profiles each resurveyed approximately seven times per year over twenty-seven years at the Field Research Facility (FRF) by the U.S. Army Corps of Engineers, located at Kitty Hawk, NC. The four shorelines we studied are mean-higher-high-water (MHHW), mean-high-water (MHW), and mean-low-water (MLW) and mean-lower-low-water (MLLW) with elevations of 0.75m, 0.65m, -0.33m, and -0.37m respectively, relative to the NGVD29 geodetic datum. Spectral analysis used to quantify scaling exponents requires data evenly spaced in time. Our previous studies of shoreline dynamics used the Lomb Periodogram method for spectral analysis, which we now show does not return the correct scaling exponent for unevenly spaced data. New to this study is the use of slotted resampling and a linear predictor to construct an evenly spaced data set from an unevenly spaced data set which has been shown with synthetic data to return correct values of the scaling exponents. A periodogram linear regression (PLR) estimate is used to determine the scaling exponent β of the constructed evenly spaced time series. This study shows that sandy shoreline position exhibits nonlinear self-affine dynamics through time. The times series of each of the four shorelines has scaling exponents ranging as follows: MHHW, β = 1.3-2.2; MHW, β = 1.3-2.1; MLW, β = 1.2-1.6; and MLLW, β = 1.2-1.6. Time series with β greater than 1 are non-stationary (mean and standard deviation are not constant through time) and are increasingly internally correlated with increasing β. The range of scaling exponents of the MLW and MLLW shorelines, near β = 1.5, is indicative of a diffusion process. The range of scaling exponents for the MHW and MHHW shorelines indicates spatially variable dynamics higher on the beach face.

Translocation of polymers into crowded media with dynamic attractive nanoparticles.

PubMed

Cao, Wei-Ping; Ren, Qing-Bao; Luo, Meng-Bo

2015-07-01

The translocation of polymers through a small pore into crowded media with dynamic attractive nanoparticles is simulated. Results show that the nanoparticles at the trans side can affect the translocation by influencing the free-energy landscape and the diffusion of polymers. Thus the translocation time τ is dependent on the polymer-nanoparticle attraction strength ɛ and the mobility of nanoparticles V. We observe a power-law relation of τ with V, but the exponent is dependent on ɛ and nanoparticle concentration. In addition, we find that the effect of attractive dynamic nanoparticles on the dynamics of polymers is dependent on the time scale. At a short time scale, subnormal diffusion is observed at strong attraction and the diffusion is slowed down by the dynamic nanoparticles. However, the diffusion of polymers is normal at a long time scale and the diffusion constant increases with the increase in V.

Correlated diffusion of colloidal particles near a liquid-liquid interface.

PubMed

Zhang, Wei; Chen, Song; Li, Na; Zhang, Jia Zheng; Chen, Wei

2014-01-01

Optical microscopy and multi-particle tracking are used to investigate the cross-correlated diffusion of quasi two-dimensional colloidal particles near an oil-water interface. The behaviors of the correlated diffusion along longitudinal and transverse direction are asymmetric. It is shown that the characteristic length for longitudinal and transverse correlated diffusion are particle diameter d and the distance z from particle center to the interface, respectively, for large particle separation z. The longitudinal and transverse correlated diffusion coefficient D||(r) and D[perpendicular](r) are independent of the colloidal area fraction n when n < 0.3, which indicates that the hydrodynamic interactions(HIs) among the particles are dominated by HIs through the surrounding fluid for small n. For high area fraction n > 0.4 the power law exponent for the spatial decay of [Formula: see text] begins to decrease, which suggests the HIs are more contributed from the 2D particle monolayer self for large n.

Nonequilibrium fluctuations during diffusion in liquid layers

NASA Astrophysics Data System (ADS)

Brogioli, Doriano; Vailati, Alberto

2017-07-01

Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H =1 . We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

Nonequilibrium fluctuations during diffusion in liquid layers.

PubMed

Brogioli, Doriano; Vailati, Alberto

2017-07-01

Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H=1. We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

Self-consistent molecular dynamics calculation of diffusion in higher n-alkanes.

PubMed

Kondratyuk, Nikolay D; Norman, Genri E; Stegailov, Vladimir V

2016-11-28

Diffusion is one of the key subjects of molecular modeling and simulation studies. However, there is an unresolved lack of consistency between Einstein-Smoluchowski (E-S) and Green-Kubo (G-K) methods for diffusion coefficient calculations in systems of complex molecules. In this paper, we analyze this problem for the case of liquid n-triacontane. The non-conventional long-time tails of the velocity autocorrelation function (VACF) are found for this system. Temperature dependence of the VACF tail decay exponent is defined. The proper inclusion of the long-time tail contributions to the diffusion coefficient calculation results in the consistency between G-K and E-S methods. Having considered the major factors influencing the precision of the diffusion rate calculations in comparison with experimental data (system size effects and force field parameters), we point to hydrogen nuclear quantum effects as, presumably, the last obstacle to fully consistent n-alkane description.

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

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.

On the channel width-dependence of the thermal conductivity in ultra-narrow graphene nanoribbons

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

Karamitaheri, Hossein; Neophytou, Neophytos, E-mail: N.Neophytou@warwick.ac.uk

The thermal conductivity of low-dimensional materials and graphene nanoribbons, in particular, is limited by the strength of line-edge-roughness scattering. One way to characterize the roughness strength is the dependency of the thermal conductivity on the channel's width in the form W{sup β}. Although in the case of electronic transport, this dependency is very well studied, resulting in W{sup 6} for nanowires and quantum wells and W{sup 4} for nanoribbons, in the case of phonon transport it is not yet clear what this dependence is. In this work, using lattice dynamics and Non-Equilibrium Green's Function simulations, we examine the width dependencemore » of the thermal conductivity of ultra-narrow graphene nanoribbons under the influence of line edge-roughness. We show that the exponent β is in fact not a single well-defined number, but it is different for different parts of the phonon spectrum depending on whether phonon transport is ballistic, diffusive, or localized. The exponent β takes values β < 1 for semi-ballistic phonon transport, values β ≫ 1 for sub-diffusive or localized phonons, and β = 1 only in the case where the transport is diffusive. The overall W{sup β} dependence of the thermal conductivity is determined by the width-dependence of the dominant phonon modes (usually the acoustic ones). We show that due to the long phonon mean-free-paths, the width-dependence of thermal conductivity becomes a channel length dependent property, because the channel length determines whether transport is ballistic, diffusive, or localized.« less

Boundary Information Inflow Enhances Correlation in Flocking

NASA Astrophysics Data System (ADS)

Cavagna, Andrea; Giardina, Irene; Ginelli, Francesco

2013-04-01

The most conspicuous trait of collective animal behavior is the emergence of highly ordered structures. Less obvious to the eye, but perhaps more profound a signature of self-organization, is the presence of long-range spatial correlations. Experimental data on starling flocks in 3D show that the exponent ruling the decay of the velocity correlation function, C(r)˜1/rγ, is extremely small, γ≪1. This result can neither be explained by equilibrium field theory nor by off-equilibrium theories and simulations of active systems. Here, by means of numerical simulations and theoretical calculations, we show that a dynamical field applied to the boundary of a set of Heisenberg spins on a 3D lattice gives rise to a vanishing exponent γ, as in starling flocks. The effect of the dynamical field is to create an information inflow from border to bulk that triggers long-range spin-wave modes, thus giving rise to an anomalously long-ranged correlation. The biological origin of this phenomenon can be either exogenous—information produced by environmental perturbations is transferred from boundary to bulk of the flock—or endogenous—the flock keeps itself in a constant state of dynamical excitation that is beneficial to correlation and collective response.

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.

Moessbauer effect: Study of disordered magnetic systems

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

Chang, Xiao Sha.

1989-01-01

This dissertation describes Moessbauer spectroscopy studies of two chemically disordered binary, crystalline alloys having the composition A{sub 1-x}B{sub x}. Both systems are random 3d Heisenberg ferromagnets. In each case both A and B atoms carry a magnetic moment. The first study concerns a Moessbauer absorber experiment on Fe{sub 1-x} V{sub x}, in which the disorder in the critical region is of the annealed random exchange type. To eliminate the effect of concentration inhomogeneity, the measurement of the critical exponent {beta} was done on the alloy with x = 0.125, where dT{sub C}/dx = 0, yielding {beta} = 0.362(8) over themore » reduced temperature range 1.4 {times} 10{sup {minus}3} < t < 4.88 {times} 10{sup {minus}1}. This result confirms the theoretical prediction that the annealed disorder is irrelevant to critical behavior in this case. As expected the critical exponent {beta} is consistent with the expectation for the 3d Heisenberg model as well as the measured exponent of pure Fe. The second study involves a Moessbauer source experiment on {sup 57} CoPd{sub 0.80}Co{sub 0.20}, in which disorder is of the quenched random exchange type perturbed by a very weak random anisotropy interaction. The critical exponent {beta} deduced over the range 1 {times} 10{sup {minus}2} < t < 2 {times} 10{sup {minus}1} is 0.385(20), and is consistent with the theoretical prediction for quenched disordered 3d Heisenberg systems: the disorder is irrelevant to the critical behavior. However, because of the restricted range of reduced temperature, the result is insufficiently asymptotic to serve as a conclusive test of the theory. Outside the critical region the distribution of Fe{sup 57} hyperfine field in Pd{sub 0.80}Co{sub 0.20} is observed to have an anomalous temperature dependence characterized by a linear increase in the width of the field distribution for T/T{sub C} {ge} 0.6.« less

How large a dataset should be in order to estimate scaling exponents and other statistics correctly in studies of solar wind turbulence

NASA Astrophysics Data System (ADS)

Rowlands, G.; Kiyani, K. H.; Chapman, S. C.; Watkins, N. W.

2009-12-01

Quantitative analysis of solar wind fluctuations are often performed in the context of intermittent turbulence and center around methods to quantify statistical scaling, such as power spectra and structure functions which assume a stationary process. The solar wind exhibits large scale secular changes and so the question arises as to whether the timeseries of the fluctuations is non-stationary. One approach is to seek a local stationarity by parsing the time interval over which statistical analysis is performed. Hence, natural systems such as the solar wind unavoidably provide observations over restricted intervals. Consequently, due to a reduction of sample size leading to poorer estimates, a stationary stochastic process (time series) can yield anomalous time variation in the scaling exponents, suggestive of nonstationarity. The variance in the estimates of scaling exponents computed from an interval of N observations is known for finite variance processes to vary as ~1/N as N becomes large for certain statistical estimators; however, the convergence to this behavior will depend on the details of the process, and may be slow. We study the variation in the scaling of second-order moments of the time-series increments with N for a variety of synthetic and “real world” time series, and we find that in particular for heavy tailed processes, for realizable N, one is far from this ~1/N limiting behavior. We propose a semiempirical estimate for the minimum N needed to make a meaningful estimate of the scaling exponents for model stochastic processes and compare these with some “real world” time series from the solar wind. With fewer datapoints the stationary timeseries becomes indistinguishable from a nonstationary process and we illustrate this with nonstationary synthetic datasets. Reference article: K. H. Kiyani, S. C. Chapman and N. W. Watkins, Phys. Rev. E 79, 036109 (2009).

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

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.

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.

Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

NASA Astrophysics Data System (ADS)

Ge, Xian-Hui; Sin, Sang-Jin; Tian, Yu; Wu, Shao-Feng; Wu, Shang-Yu

2018-01-01

We show that there exists a class of charged BTZ-like black hole solutions in Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ black hole is characterized by a charge-dependent logarithmic term in the metric function. As concrete examples, we give five such charged BTZ-like black hole solutions and the standard charged BTZ metric can be regarded as a special instance of them. In order to check the recent proposed universal relations between diffusivity and the butterfly velocity, we first compute the diffusion constants of the standard charged BTZ black holes and then extend our calculation to arbitrary dimension d, exponents z and θ. Remarkably, the case d = θ and z = 2 is a very special in that the charge diffusion D c is a constant and the energy diffusion D e might be ill-defined, but v B 2 τ diverges. We also compute the diffusion constants for the case that the DC conductivity is finite but in the absence of momentum relaxation.

Gradual Crossover from Subdiffusion to Normal Diffusion: A Many-Body Effect in Protein Surface Water

NASA Astrophysics Data System (ADS)

Tan, Pan; Liang, Yihao; Xu, Qin; Mamontov, Eugene; Li, Jinglai; Xing, Xiangjun; Hong, Liang

2018-06-01

Dynamics of hydration water is essential for the function of biomacromolecules. Previous studies have demonstrated that water molecules exhibit subdiffusion on the surface of biomacromolecules; yet the microscopic mechanism remains vague. Here, by performing neutron scattering, molecular dynamics simulations, and analytic modeling on hydrated perdeuterated protein powders, we found water molecules jump randomly between trapping sites on protein surfaces, whose waiting times obey a broad distribution, resulting in subdiffusion. Moreover, the subdiffusive exponent gradually increases with observation time towards normal diffusion due to a many-body volume-exclusion effect.

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.

Impact of density-dependent migration flows on epidemic outbreaks in heterogeneous metapopulations

NASA Astrophysics Data System (ADS)

Ripoll, J.; Avinyó, A.; Pellicer, M.; Saldaña, J.

2015-08-01

We investigate the role of migration patterns on the spread of epidemics in complex networks. We enhance the SIS-diffusion model on metapopulations to a nonlinear diffusion. Specifically, individuals move randomly over the network but at a rate depending on the population of the departure patch. In the absence of epidemics, the migration-driven equilibrium is described by quantifying the total number of individuals living in heavily or lightly populated areas. Our analytical approach reveals that strengthening the migration from populous areas contains the infection at the early stage of the epidemic. Moreover, depending on the exponent of the nonlinear diffusion rate, epidemic outbreaks do not always occur in the most populated areas as one might expect.

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.

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.

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].

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.

The Relationship of Dynamical Heterogeneity to the Adam-Gibbs and Random First-Order Transition Theories of Glass Formation

NASA Astrophysics Data System (ADS)

Starr, Francis; Douglas, Jack; Sastry, Srikanth

2013-03-01

We examine measures of dynamical heterogeneity for a bead-spring polymer melt and test how these scales compare with the scales hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories. We show that the time scale of the high-mobility clusters and strings is associated with a diffusive time scale, while the low-mobility particles' time scale relates to a structural relaxation time. The difference of the characteristic times naturally explains the decoupling of diffusion and structural relaxation time scales. We examine the appropriateness of identifying the size scales of mobile particle clusters or strings with the size of cooperatively rearranging regions (CRR) in the AG and RFOT theories. We find that the string size appears to be the most consistent measure of CRR for both the AG and RFOT models. Identifying strings or clusters with the``mosaic'' length of the RFOT model relaxes the conventional assumption that the``entropic droplet'' are compact. We also confirm the validity of the entropy formulation of the AG theory, constraining the exponent values of the RFOT theory. This constraint, together with the analysis of size scales, enables us to estimate the characteristic exponents of RFOT.

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.

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.

Self-affinity in the dengue fever time series

NASA Astrophysics Data System (ADS)

Azevedo, S. M.; Saba, H.; Miranda, J. G. V.; Filho, A. S. Nascimento; Moret, M. A.

2016-06-01

Dengue is a complex public health problem that is common in tropical and subtropical regions. This disease has risen substantially in the last three decades, and the physical symptoms depict the self-affine behavior of the occurrences of reported dengue cases in Bahia, Brazil. This study uses detrended fluctuation analysis (DFA) to verify the scale behavior in a time series of dengue cases and to evaluate the long-range correlations that are characterized by the power law α exponent for different cities in Bahia, Brazil. The scaling exponent (α) presents different long-range correlations, i.e. uncorrelated, anti-persistent, persistent and diffusive behaviors. The long-range correlations highlight the complex behavior of the time series of this disease. The findings show that there are two distinct types of scale behavior. In the first behavior, the time series presents a persistent α exponent for a one-month period. For large periods, the time series signal approaches subdiffusive behavior. The hypothesis of the long-range correlations in the time series of the occurrences of reported dengue cases was validated. The observed self-affinity is useful as a forecasting tool for future periods through extrapolation of the α exponent behavior. This complex system has a higher predictability in a relatively short time (approximately one month), and it suggests a new tool in epidemiological control strategies. However, predictions for large periods using DFA are hidden by the subdiffusive behavior.

Anomalous Drag Reduction and Hydrodynamic Interactions of Nanoparticles in Polymer Nanocomposite Thin Films

NASA Astrophysics Data System (ADS)

Basu, Jaydeep; Begam, Nafisa; Chandran, Sivasurender; Sprung, Michael

2015-03-01

One of the central dogma of fluid physics is the no-slip boundary condition whose validity has come under intense scrutiny, especially in the fields of micro and nanofluidics. Although various studies show the violation of the no-slip condition its effect on flow of colloidal particles in viscous media has been rarely explored. Here we report unusually large reduction of effective drag experienced by polymer grafted nanoparticles moving through a highly viscous film of polymer, well above its glass transition temperature. The extent of drag reduction increases with decreasing temperature and polymer film thickness. We also observe apparent divergence of the wave vector dependent hydrodynamic interaction function of these nanoparticles with an anomalous power law exponent of ~ 2 at the lowest temperatures and film thickness. Such strong hydrodynamic interactions are not expected in polymer melts where these interactions are known to be screened to molecular dimensions. We provide evidence for the presence of large hydrodynamic slip at the nanoparticle-polymer interface and demonstrate its tunability with temperature and confinement. Our study suggests novel physics emerging in dynamics nanoparticles due to confinement and interface wettability in thin films of polymer nanocomposites.

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.

Universal deformation pathways and flexural hardening of nanoscale 2D-material standing folds

NASA Astrophysics Data System (ADS)

Chacham, Helio; Barboza, Ana Paula M.; de Oliveira, Alan B.; de Oliveira, Camilla K.; Batista, Ronaldo J. C.; Neves, Bernardo R. A.

2018-03-01

In the present work, we use atomic force microscopy nanomanipulation of 2D-material standing folds to investigate their mechanical deformation. Using graphene, h-BN and talc nanoscale wrinkles as testbeds, universal force-strain pathways are clearly uncovered and well-accounted for by an analytical model. Such universality further enables the investigation of each fold bending stiffness κ as a function of its characteristic height h 0. We observe a more than tenfold increase of κ as h 0 increases in the 10-100 nm range, with power-law behaviors of κ versus h 0 with exponents larger than unity for the three materials. This implies anomalous scaling of the mechanical responses of nano-objects made from these materials.

Universal Critical Dynamics in High Resolution Neuronal Avalanche Data

NASA Astrophysics Data System (ADS)

Friedman, Nir; Ito, Shinya; Brinkman, Braden A. W.; Shimono, Masanori; DeVille, R. E. Lee; Dahmen, Karin A.; Beggs, John M.; Butler, Thomas C.

2012-05-01

The tasks of neural computation are remarkably diverse. To function optimally, neuronal networks have been hypothesized to operate near a nonequilibrium critical point. However, experimental evidence for critical dynamics has been inconclusive. Here, we show that the dynamics of cultured cortical networks are critical. We analyze neuronal network data collected at the individual neuron level using the framework of nonequilibrium phase transitions. Among the most striking predictions confirmed is that the mean temporal profiles of avalanches of widely varying durations are quantitatively described by a single universal scaling function. We also show that the data have three additional features predicted by critical phenomena: approximate power law distributions of avalanche sizes and durations, samples in subcritical and supercritical phases, and scaling laws between anomalous exponents.

Using Noise and Fluctuations for In Situ Measurements of Nitrogen Diffusion Depth.

PubMed

Samoila, Cornel; Ursutiu, Doru; Schleer, Walter-Harald; Jinga, Vlad; Nascov, Victor

2016-10-05

In manufacturing processes involving diffusion (of C, N, S, etc.), the evolution of the layer depth is of the utmost importance: the success of the entire process depends on this parameter. Currently, nitriding is typically either calibrated using a "post process" method or controlled via indirect measurements (H2, O2, H2O + CO2). In the absence of "in situ" monitoring, any variation in the process parameters (gas concentration, temperature, steel composition, distance between sensors and furnace chamber) can cause expensive process inefficiency or failure. Indirect measurements can prevent process failure, but uncertainties and complications may arise in the relationship between the measured parameters and the actual diffusion process. In this paper, a method based on noise and fluctuation measurements is proposed that offers direct control of the layer depth evolution because the parameters of interest are measured in direct contact with the nitrided steel (represented by the active electrode). The paper addresses two related sets of experiments. The first set of experiments consisted of laboratory tests on nitrided samples using Barkhausen noise and yieded a linear relationship between the frequency exponent in the Hooge equation and the nitriding time. For the second set, a specific sensor based on conductivity noise (at the nitriding temperature) was built for shop-floor experiments. Although two different types of noise were measured in these two sets of experiments, the use of the frequency exponent to monitor the process evolution remained valid.

Using Noise and Fluctuations for In Situ Measurements of Nitrogen Diffusion Depth

PubMed Central

Samoila, Cornel; Ursutiu, Doru; Schleer, Walter-Harald; Jinga, Vlad; Nascov, Victor

2016-01-01

In manufacturing processes involving diffusion (of C, N, S, etc.), the evolution of the layer depth is of the utmost importance: the success of the entire process depends on this parameter. Currently, nitriding is typically either calibrated using a “post process” method or controlled via indirect measurements (H2, O2, H2O + CO2). In the absence of “in situ” monitoring, any variation in the process parameters (gas concentration, temperature, steel composition, distance between sensors and furnace chamber) can cause expensive process inefficiency or failure. Indirect measurements can prevent process failure, but uncertainties and complications may arise in the relationship between the measured parameters and the actual diffusion process. In this paper, a method based on noise and fluctuation measurements is proposed that offers direct control of the layer depth evolution because the parameters of interest are measured in direct contact with the nitrided steel (represented by the active electrode). The paper addresses two related sets of experiments. The first set of experiments consisted of laboratory tests on nitrided samples using Barkhausen noise and yielded a linear relationship between the frequency exponent in the Hooge equation and the nitriding time. For the second set, a specific sensor based on conductivity noise (at the nitriding temperature) was built for shop-floor experiments. Although two different types of noise were measured in these two sets of experiments, the use of the frequency exponent to monitor the process evolution remained valid. PMID:28773941

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

Turbulent vertical diffusivity in the sub-tropical stratosphere

NASA Astrophysics Data System (ADS)

Pisso, I.; Legras, B.

2008-02-01

Vertical (cross-isentropic) mixing is produced by small-scale turbulent processes which are still poorly understood and paramaterized in numerical models. In this work we provide estimates of local equivalent diffusion in the lower stratosphere by comparing balloon borne high-resolution measurements of chemical tracers with reconstructed mixing ratio from large ensembles of random Lagrangian backward trajectories using European Centre for Medium-range Weather Forecasts analysed winds and a chemistry-transport model (REPROBUS). We focus on a case study in subtropical latitudes using data from HIBISCUS campaign. An upper bound on the vertical diffusivity is found in this case study to be of the order of 0.5 m2 s-1 in the subtropical region, which is larger than the estimates at higher latitudes. The relation between diffusion and dispersion is studied by estimating Lyapunov exponents and studying their variation according to the presence of active dynamical structures.

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.

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

Thermodynamic scaling of dynamics in polymer melts: predictions from the generalized entropy theory.

PubMed

Xu, Wen-Sheng; Freed, Karl F

2013-06-21

Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of a unique scaling function of the ratio ρ(γ)∕T, where ρ is the density, T is the temperature, and γ is a material dependent constant. Interest in the scaling is also heightened because the exponent γ enters prominently into considerations of the relative contributions to the dynamics from pressure effects (e.g., activation barriers) vs. volume effects (e.g., free volume). Although this scaling is clearly of great practical use, a molecular understanding of the scaling remains elusive. Providing this molecular understanding would greatly enhance the utility of the empirically observed scaling in assisting the rational design of materials by describing how controllable molecular factors, such as monomer structures, interactions, flexibility, etc., influence the scaling exponent γ and, hence, the dynamics. Given the successes of the generalized entropy theory in elucidating the influence of molecular details on the universal properties of glass-forming polymers, this theory is extended here to investigate the thermodynamic scaling in polymer melts. The predictions of theory are in accord with the appearance of thermodynamic scaling for pressures not in excess of ~50 MPa. (The failure at higher pressures arises due to inherent limitations of a lattice model.) In line with arguments relating the magnitude of γ to the steepness of the repulsive part of the intermolecular potential, the abrupt, square-well nature of the lattice model interactions lead, as expected, to much larger values of the scaling exponent. Nevertheless, the theory is employed to study how individual molecular parameters affect the scaling exponent in order to extract a molecular understanding of the information content contained in the exponent. The chain rigidity, cohesive energy, chain length, and the side group length are all found to significantly affect the magnitude of the scaling exponent, and the computed trends agree well with available experiments. The variations of γ with these molecular parameters are explained by establishing a correlation between the computed molecular dependence of the scaling exponent and the fragility. Thus, the efficiency of packing the polymers is established as the universal physical mechanism determining both the fragility and the scaling exponent γ.

Effect of a solid solution on the steady-state creep behavior of an aluminum matrix composite

NASA Astrophysics Data System (ADS)

Pandey, A. B.; Mishra, R. S.; Mahajan, Y. R.

1996-02-01

The effect of an alloying element, 4 wt pct Mg, on the steady-state creep behavior of an Al-10 vol pct SiCp composite has been studied. The Al-4 wt pct Mg-10 vol pct SiCp composite has been tested under compression creep in the temperature range 573 to 673 K. The steady-state creep data of the composite show a transition in the creep behavior (regions I and II) depending on the applied stress at 623 and 673 K. The low stress range data (region I) exhibit a stress exponent of about 7 and an activation energy of 76.5 kJ mol-1. These values conform to the dislocation-climb-controlled creep model with pipe diffusion as a rate-controlling mechanism. The intermediate stress range data (region II) exhibit high and variable apparent stress exponents, 18 to 48, and activation energy, 266 kJ mol-1, at a constant stress, σ = 50 MPa, for creep of this composite. This behavior can be rationalized using a substructure-invariant model with a stress exponent of 8 and an activation energy close to the lattice self-diffusion of aluminum together with a threshold stress. The creep data of the Al-Mg-A12O3f composite reported by Dragone and Nix also conform to the substructure-invariant model. The threshold stress and the creep strength of the Al-Mg-SiCp, composite are compared with those of the Al-Mg-Al2O3f and 6061 Al-SiCp.w, composites and discussed in terms of the load-transfer mechanism. Magnesium has been found to be very effective in improving the creep resistance of the Al-SiCp composite.

Transient ensemble dynamics in time-independent galactic potentials

NASA Astrophysics Data System (ADS)

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

1995-07-01

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

Chaotic dynamics of large-scale double-diffusive convection in a porous medium

NASA Astrophysics Data System (ADS)

Kondo, Shutaro; Gotoda, Hiroshi; Miyano, Takaya; Tokuda, Isao T.

2018-02-01

We have studied chaotic dynamics of large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan-Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.

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.

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.

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.

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.

Spatio-temporal correlations in the Manna model in one, three and five dimensions

NASA Astrophysics Data System (ADS)

Willis, Gary; Pruessner, Gunnar

2018-02-01

Although the paradigm of criticality is centered around spatial correlations and their anomalous scaling, not many studies of self-organized criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche size and duration, are used, not least as to avoid complications due to the unavoidable lack of translational invariance. The present work is a survey of spatio-temporal correlation functions in the Manna Model of SOC, measured numerically in detail in d = 1,3 and 5 dimensions and compared to theoretical results, in particular relating them to “integrated” observables such as avalanche size and duration scaling, that measure them indirectly. Contrary to the notion held by some of SOC models organizing into a critical state by re-arranging their spatial structure avalanche by avalanche, which may be expected to result in large, nontrivial, system-spanning spatial correlations in the quiescent state (between avalanches), correlations of inactive particles in the quiescent state have a small amplitude that does not and cannot increase with the system size, although they display (noisy) power law scaling over a range linear in the system size. Self-organization, however, does take place as the (one-point) density of inactive particles organizes into a particular profile that is asymptotically independent of the driving location, also demonstrated analytically in one dimension. Activity and its correlations, on the other hand, display nontrivial long-ranged spatio-temporal scaling with exponents that can be related to established results, in particular avalanche size and duration exponents. The correlation length and amplitude are set by the system size (confirmed analytically for some observables), as expected in systems displaying finite size scaling. In one dimension, we find some surprising inconsistencies of the dynamical exponent. A (spatially extended) mean field theory (MFT) is recovered, with some corrections, in five dimensions.

Transport on percolation clusters with power-law distributed bond strengths.

PubMed

Alava, Mikko; Moukarzel, Cristian F

2003-05-01

The simplest transport problem, namely finding the maximum flow of current, or maxflow, is investigated on critical percolation clusters in two and three dimensions, using a combination of extremal statistics arguments and exact numerical computations, for power-law distributed bond strengths of the type P(sigma) approximately sigma(-alpha). Assuming that only cutting bonds determine the flow, the maxflow critical exponent v is found to be v(alpha)=(d-1)nu+1/(1-alpha). This prediction is confirmed with excellent accuracy using large-scale numerical simulation in two and three dimensions. However, in the region of anomalous bond capacity distributions (0< or =alpha< or =1) we demonstrate that, due to cluster-structure fluctuations, it is not the cutting bonds but the blobs that set the transport properties of the backbone. This "blob dominance" avoids a crossover to a regime where structural details, the distribution of the number of red or cutting bonds, would set the scaling. The restored scaling exponents, however, still follow the simplistic red bond estimate. This is argued to be due to the existence of a hierarchy of so-called minimum cut configurations, for which cutting bonds form the lowest level, and whose transport properties scale all in the same way. We point out the relevance of our findings to other scalar transport problems (i.e., conductivity).

One-dimensional long-range percolation: A numerical study

NASA Astrophysics Data System (ADS)

Gori, G.; Michelangeli, M.; Defenu, N.; Trombettoni, A.

2017-07-01

In this paper we study bond percolation on a one-dimensional chain with power-law bond probability C /rd +σ , where r is the distance length between distinct sites and d =1 . We introduce and test an order-N Monte Carlo algorithm and we determine as a function of σ the critical value Cc at which percolation occurs. The critical exponents in the range 0 <σ <1 are reported. Our analysis is in agreement, up to a numerical precision ≈10-3 , with the mean-field result for the anomalous dimension η =2 -σ , showing that there is no correction to η due to correlation effects. The obtained values for Cc are compared with a known exact bound, while the critical exponent ν is compared with results from mean-field theory, from an expansion around the point σ =1 and from the ɛ -expansion used with the introduction of a suitably defined effective dimension deff relating the long-range model with a short-range one in dimension deff. We finally present a formulation of our algorithm for bond percolation on general graphs, with order N efficiency on a large class of graphs including short-range percolation and translationally invariant long-range models in any spatial dimension d with σ >0 .

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

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Hanel, Rudolf

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

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.

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.

Structural and functional networks in complex systems with delay.

PubMed

Eguíluz, Víctor M; Pérez, Toni; Borge-Holthoefer, Javier; Arenas, Alex

2011-05-01

Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes) and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology γ is related to the exponent of the associated functional network as α=(2-γ)(-1) for γ<2. © 2011 American Physical Society

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,…

Three-dimensional kinetic Monte Carlo simulations of cubic transition metal nitride thin film growth

NASA Astrophysics Data System (ADS)

Nita, F.; Mastail, C.; Abadias, G.

2016-02-01

A three-dimensional kinetic Monte Carlo (KMC) model has been developed and used to simulate the microstructure and growth morphology of cubic transition metal nitride (TMN) thin films deposited by reactive magnetron sputtering. Results are presented for the case of stoichiometric TiN, chosen as a representative TMN prototype. The model is based on a NaCl-type rigid lattice and includes deposition and diffusion events for both N and Ti species. It is capable of reproducing voids and overhangs, as well as surface faceting. Simulations were carried out assuming a uniform flux of incoming particles approaching the surface at normal incidence. The ballistic deposition model is parametrized with an interaction parameter r0 that mimics the capture distance at which incoming particles may stick on the surface, equivalently to a surface trapping mechanism. Two diffusion models are implemented, based on the different ways to compute the site-dependent activation energy for hopping atoms. The influence of temperature (300-500 K), deposition flux (0.1-100 monolayers/s), and interaction parameter r0 (1.5-6.0 Å) on the obtained growth morphology are presented. Microstructures ranging from highly porous, [001]-oriented straight columns with smooth top surface to rough columns emerging with different crystallographic facets are reproduced, depending on kinetic restrictions, deposited energy (seemingly captured by r0), and shadowing effect. The development of facets is a direct consequence of the diffusion model which includes an intrinsic (minimum energy-based) diffusion anisotropy, although no crystallographic diffusion anisotropy was explicitly taken into account at this stage. The time-dependent morphological evolution is analyzed quantitatively to extract the growth exponent β and roughness exponent α , as indicators of kinetic roughening behavior. For dense TiN films, values of α ≈0.7 and β =0.24 are obtained in good agreement with existing experimental data. At this stage a single lattice is considered but the KMC model will be extended further to address more complex mechanisms, such as anisotropic surface diffusion and grain boundary migration at the origin of the competitive columnar growth observed in polycrystalline TiN-based films.

Confirming Time-reversal Symmetry of a Directed Percolation Phase Transition in a Model of Neutral Evolutionary Dynamics

NASA Astrophysics Data System (ADS)

Ordway, Stephen; King, Dawn; Bahar, Sonya

Reaction-diffusion processes, such as branching-coalescing random walks, can be used to describe the underlying dynamics of nonequilibrium phase transitions. In an agent-based, neutral model of evolutionary dynamics, we have previously shown that our system undergoes a continuous, nonequilibrium phase transition, from extinction to survival, as various system parameters were tuned. This model was shown to belong to the directed percolation (DP) universality class, by measuring the critical exponents corresponding to correlation length ξ⊥, correlation time ξ| |, and particle density β. The fourth critical exponent that defines the DP universality class is β', which measures the survival probability of growth from a single seed organism. Since DP universality is theorized to have time-reversal symmetry, it is assumed that β = β '. In order to confirm the existence of time-reversal symmetry in our model, we evaluate the system growth from a single asexually reproducing organism. Importantly, the critical exponent β' could be useful for comparison to experimental studies of phase transitions in biological systems, since observing growth of microbial populations is significantly easier than observing death. This research was supported by funding from the James S. McDonnell Foundation.

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

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).

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.

Numerical characterization of the edge transport conditions and limiter fluxes of the HIDRA stellarator

NASA Astrophysics Data System (ADS)

Marcinko, Steven; Curreli, Davide

2018-02-01

The Hybrid Illinois Device for Research and Applications (HIDRA) is a new device for education and Plasma-Material Interaction research at the University of Illinois at Urbana-Champaign. In advance of its first operational campaign, EMC3-EIRENE simulations have been run on the device. EMC3-EIRENE has been modified to calculate a per-plasma-cell relaxed Bohm-like diffusivity simultaneously with the electron temperature at each iteration. In our characterization, the electron temperature, diffusivity, heat fluxes, and particle fluxes have been obtained for varying power levels on a HIDRA magnetic grid, and scaling laws have been extracted, using constraints from previous experimental data taken when the device was operated in Germany (WEGA facility). Peak electron temperatures and heat fluxes were seen to follow a power-law dependence on the deposited radiofrequency (RF) power of type f (PR F)∝a PRF b , with typical exponents in the range of b ˜0.55 to 0.60. Higher magnetic fields have the tendency to linearize the heat flux dependence on the RF power, with exponents in the range of b ˜ 0.75. Particle fluxes are seen to saturate first, and then slightly decline for RF powers above 120 kW in the low-field case and 180 kW in the high-field case.

Local thermal energy as a structural indicator in glasses.

PubMed

Zylberg, Jacques; Lerner, Edan; Bar-Sinai, Yohai; Bouchbinder, Eran

2017-07-11

Identifying heterogeneous structures in glasses-such as localized soft spots-and understanding structure-dynamics relations in these systems remain major scientific challenges. Here, we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change caused by thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses-an intrinsic signature of glassy frustration-anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal [Formula: see text] density of states of quasilocalized low-frequency vibrational modes. When the spatial thermal energy field-a "softness field"-is considered, this power law tail manifests itself by highly localized spots, which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal modes-based approach. These results offer a general, system/model-independent, physical/observable-based approach to identify structural properties of quiescent glasses and relate them to glassy dynamics.

Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Drivas, Theodore D.

2018-02-01

We develop a first-principles theory of relativistic fluid turbulence at high Reynolds and Péclet numbers. We follow an exact approach pioneered by Onsager, which we explain as a nonperturbative application of the principle of renormalization-group invariance. We obtain results very similar to those for nonrelativistic turbulence, with hydrodynamic fields in the inertial range described as distributional or "coarse-grained" solutions of the relativistic Euler equations. These solutions do not, however, satisfy the naive conservation laws of smooth Euler solutions but are afflicted with dissipative anomalies in the balance equations of internal energy and entropy. The anomalies are shown to be possible by exactly two mechanisms, local cascade and pressure-work defect. We derive "4 /5 th-law" type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required for their not vanishing. We also investigate the Lorentz covariance of the inertial-range fluxes, which we find to be broken by our coarse-graining regularization but which is restored in the limit where the regularization is removed, similar to relativistic lattice quantum field theory. In the formal limit as speed of light goes to infinity, we recover the results of previous nonrelativistic theory. In particular, anomalous heat input to relativistic internal energy coincides in that limit with anomalous dissipation of nonrelativistic kinetic energy.

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Drivas, Theodore D.

2018-02-01

We investigate dissipative anomalies in a turbulent fluid governed by the compressible Navier-Stokes equation. We follow an exact approach pioneered by Onsager, which we explain as a nonperturbative application of the principle of renormalization-group invariance. In the limit of high Reynolds and Péclet numbers, the flow realizations are found to be described as distributional or "coarse-grained" solutions of the compressible Euler equations, with standard conservation laws broken by turbulent anomalies. The anomalous dissipation of kinetic energy is shown to be due not only to local cascade but also to a distinct mechanism called pressure-work defect. Irreversible heating in stationary, planar shocks with an ideal-gas equation of state exemplifies the second mechanism. Entropy conservation anomalies are also found to occur via two mechanisms: an anomalous input of negative entropy (negentropy) by pressure work and a cascade of negentropy to small scales. We derive "4 /5 th-law"-type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required to sustain the cascades. We compare our approach with alternative theories and empirical evidence. It is argued that the "Big Power Law in the Sky" observed in electron density scintillations in the interstellar medium is a manifestation of a forward negentropy cascade or an inverse cascade of usual thermodynamic entropy.

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.

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.

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.

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.

The high temperature creep deformation of Si3N4-6Y2O3-2Al2O3

NASA Technical Reports Server (NTRS)

Todd, J. A.; Xu, Zhi-Yue

1988-01-01

The creep properties of silicon nitride containing 6 wt percent yttria and 2 wt percent alumina have been determined in the temperature range 1573 to 1673 K. The stress exponent, n, in the equation epsilon dot varies as sigma sup n, was determined to be 2.00 + or - 0.15 and the true activation energy was found to be 692 + or - 25 kJ/mol. Transmission electron microscopy studies showed that deformation occurred in the grain boundary glassy phase accompanied by microcrack formation and cavitation. The steady state creep results are consistent with a diffusion controlled creep mechanism involving nitrogen diffusion through the grain boundary glassy phase.

Polymer translocation in solid-state nanopores: Dependence on hydrodynamic interactions and polymer configuration

NASA Astrophysics Data System (ADS)

Edmonds, Christopher M.; Hesketh, Peter J.; Nair, Sankar

2013-11-01

We present a Brownian dynamics investigation of 3-D Rouse and Zimm polymer translocation through solid-state nanopores. We obtain different scaling exponents α for both polymers using two initial configurations: minimum energy, and 'steady-state'. For forced translocation, Rouse polymers (no hydrodynamic interactions), shows a large dependence of α on initial configuration and voltage. Higher voltages result in crowding at the nanopore exit and reduced α. When the radius of gyration is in equilibrium at the beginning and end of translocation, α = 1 + υ where υ is the Flory exponent. For Zimm polymers (including hydrodynamic interactions), crowding is reduced and α = 2υ. Increased pore diameter does not affect α at moderate voltages that reduce diffusion effects. For unforced translocation using narrow pores, both polymers give α = 1 + 2υ. Due to increased polymer-pore interactions in the narrow pore, hydrodynamic drag effects are reduced, resulting in identical scaling.

Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions.

PubMed

Schnyder, Simon K; Horbach, Jürgen

2018-02-16

Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance transport when their density is increased, as disks cooperatively help each other over the finite energy barriers in the matrix. The system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded. Effective exponents in the mean-squared displacement can be observed over three decades in time but depend on the density of the disks and do not correspond to asymptotic behavior in the vicinity of a critical point, thus, showing that it is incorrect to relate them to the critical exponents in the Lorentz model scenario. The soft interactions are, therefore, responsible for a breakdown of the universality of the dynamics.

Landscape evolution models using the stream power incision model show unrealistic behavior when m / n equals 0.5

NASA Astrophysics Data System (ADS)

Kwang, Jeffrey S.; Parker, Gary

2017-12-01

Landscape evolution models often utilize the stream power incision model to simulate river incision: E = KAmSn, where E is the vertical incision rate, K is the erodibility constant, A is the upstream drainage area, S is the channel gradient, and m and n are exponents. This simple but useful law has been employed with an imposed rock uplift rate to gain insight into steady-state landscapes. The most common choice of exponents satisfies m / n = 0.5. Yet all models have limitations. Here, we show that when hillslope diffusion (which operates only on small scales) is neglected, the choice m / n = 0.5 yields a curiously unrealistic result: the predicted landscape is invariant to horizontal stretching. That is, the steady-state landscape for a 10 km2 horizontal domain can be stretched so that it is identical to the corresponding landscape for a 1000 km2 domain.

Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions

NASA Astrophysics Data System (ADS)

Schnyder, Simon K.; Horbach, Jürgen

2018-02-01

Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance transport when their density is increased, as disks cooperatively help each other over the finite energy barriers in the matrix. The system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded. Effective exponents in the mean-squared displacement can be observed over three decades in time but depend on the density of the disks and do not correspond to asymptotic behavior in the vicinity of a critical point, thus, showing that it is incorrect to relate them to the critical exponents in the Lorentz model scenario. The soft interactions are, therefore, responsible for a breakdown of the universality of the dynamics.

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.

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.

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

PubMed

Lei, Youming; Zheng, Fan

2016-12-01

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

A fractional reaction-diffusion description of supply and demand

NASA Astrophysics Data System (ADS)

Benzaquen, Michael; Bouchaud, Jean-Philippe

2018-02-01

We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t-β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Scaling behavior in corrosion and growth of a passive film.

PubMed

Aarão Reis, F D A; Stafiej, Janusz

2007-07-01

We study a simple model for metal corrosion controlled by the reaction rate of the metal with an anionic species and the diffusion of that species in the growing passive film between the solution and the metal. A crossover from the reaction-controlled to the diffusion-controlled growth regime with different roughening properties is observed. Scaling arguments provide estimates of the crossover time and film thickness as functions of the reaction and diffusion rates and the concentration of anionic species in the film-solution interface, including a nontrivial square-root dependence on that concentration. At short times, the metal-film interface exhibits Kardar-Parisi-Zhang (KPZ) scaling, which crosses over to a diffusion-limited erosion (Laplacian growth) regime at long times. The roughness of the metal-film interface at long times is obtained as a function of the rates of reaction and diffusion and of the KPZ growth exponent. The predictions have been confirmed by simulations of a lattice version of the model in two dimensions. Relations with other erosion and corrosion models and possible applications are discussed.

Notes on hyperscaling violating Lifshitz and shear diffusion

NASA Astrophysics Data System (ADS)

Kolekar, Kedar S.; Mukherjee, Debangshu; Narayan, K.

2017-07-01

We explore in greater detail our investigations of shear diffusion in hyperscaling violating Lifshitz theories in Phys. Lett. B 760, 86 (2016), 10.1016/j.physletb.2016.06.046. This adapts and generalizes the membrane-paradigm-like analysis of Kovtun, Son, and Starinets for shear gravitational perturbations in the near horizon region given certain self-consistent approximations, leading to the shear diffusion constant on an appropriately defined stretched horizon. In theories containing a gauge field, some of the metric perturbations mix with some of the gauge field perturbations and the above analysis is somewhat more complicated. We find a similar near-horizon analysis can be obtained in terms of new field variables involving a linear combination of the metric and the gauge field perturbation resulting in a corresponding diffusion equation. Thereby as before, for theories with Lifshitz and hyperscaling violating exponents z , θ satisfying z <4 -θ in four bulk dimensions, our analysis here results in a similar expression for the shear diffusion constant with power-law scaling with temperature suggesting universal behavior in relation to the viscosity bound. For z =4 -θ , we find logarithmic behavior.

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

Fraction of uninfected walkers in the one-dimensional Potts model

NASA Astrophysics Data System (ADS)

O'Donoghue, S. J.; Bray, A. J.

2002-05-01

The dynamics of the one-dimensional q-state Potts model, in the zero-temperature limit, can be formulated through the motion of random walkers which either annihilate (A+A-->∅) or coalesce (A+A-->A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is known to obey a power-law decay U(t)~t-φ(q), with a nontrivial exponent φ(q) [C. Monthus, Phys. Rev. E 54, 4844 (1996); S. N. Majumdar and S. J. Cornell, ibid. 57, 3757 (1998)]. We probe the numerical values of φ(q) to a higher degree of accuracy than previous simulations and relate the exponent φ(q) to the persistence exponent θ(q) [B. Derrida, V. Hakim, and V. Pasquier, Phys. Rev. Lett. 75, 751 (1995)], through the relation φ(q)=γ(q)θ(q) where γ is an exponent introduced in [S. J. O'Donoghue and A. J. Bray, preceding paper, Phys. Rev. E 65, XXXX (2002)]. Our study is extended to include the coupled diffusion-limited reaction A+A-->B, B+B-->A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as ρ(t)~t-1/2. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t)~t-θ with θ~=1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t)~t-φ, where φ~=1.13 when infection occurs between like particles only, and φ~=1.93 when we also include cross-species contamination. We find that the relation between φ and θ in this model can also be characterized by an exponent γ, where similarly, φ=γθ.

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

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

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.

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.

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.

A study of a diffusive model of asset returns and an empirical analysis of financial markets

NASA Astrophysics Data System (ADS)

Alejandro Quinones, Angel Luis

A diffusive model for market dynamics is studied and the predictions of the model are compared to real financial markets. The model has a non-constant diffusion coefficient which depends both on the asset value and the time. A general solution for the distribution of returns is obtained and shown to match the results of computer simulations for two simple cases, piecewise linear and quadratic diffusion. The effects of discreteness in the market dynamics on the model are also studied. For the quadratic diffusion case, a type of phase transition leading to fat tails is observed as the discrete distribution approaches the continuum limit. It is also found that the model captures some of the empirical stylized facts observed in real markets, including fat-tails and scaling behavior in the distribution of returns. An analysis of empirical data for the EUR/USD currency exchange rate and the S&P 500 index is performed. Both markets show time scaling behavior consistent with a value of 1/2 for the Hurst exponent. Finally, the results show that the distribution of returns for the two markets is well fitted by the model, and the corresponding empirical diffusion coefficients are determined.

Numerical study of the directed polymer in a 1 + 3 dimensional random medium

NASA Astrophysics Data System (ADS)

Monthus, C.; Garel, T.

2006-09-01

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length L, the high temperature phase is characterized by a diffusive behavior for the end-point displacement R2 ˜L and by free-energy fluctuations of order ΔF(L) ˜O(1). The low-temperature phase is characterized by an anomalous wandering exponent R2/L ˜Lω and by free-energy fluctuations of order ΔF(L) ˜Lω where ω˜0.18. In this paper, we first study the scaling behavior of various properties to localize the critical temperature Tc. Our results concerning R2/L and ΔF(L) point towards 0.76 < Tc ≤T2=0.79, so our conclusion is that Tc is equal or very close to the upper bound T2 derived by Derrida and coworkers (T2 corresponds to the temperature above which the ratio bar{Z_L^2}/(bar{Z_L})^2 remains finite as L ↦ ∞). We then present histograms for the free-energy, energy and entropy over disorder samples. For T ≫Tc, the free-energy distribution is found to be Gaussian. For T ≪Tc, the free-energy distribution coincides with the ground state energy distribution, in agreement with the zero-temperature fixed point picture. Moreover the entropy fluctuations are of order ΔS ˜L1/2 and follow a Gaussian distribution, in agreement with the droplet predictions, where the free-energy term ΔF ˜Lω is a near cancellation of energy and entropy contributions of order L1/2.

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

Fermi acceleration in time-dependent billiards: theory of the velocity diffusion in conformally breathing fully chaotic billiards

NASA Astrophysics Data System (ADS)

Batistić, Benjamin; Robnik, Marko

2011-09-01

We study aspects of the Fermi acceleration (the unbounded growth of the energy) in a certain class of time-dependent 2D billiards. Specifically, we look at the conformally breathing billiards (periodic oscillation of the boundary which preserves the shape of the billiard at all times), which are fully chaotic as static (frozen) billiards, and we show that for large velocities around v0 and for not too long times, we observe just normal diffusion of the velocity as a function of the physical (continuous) time, around v0. However, the diffusion is not homogeneous, as the diffusion constant D depends on v0 as a power law D∝1/v30. Taking this into account, we show that to the leading order the average velocity v(n) as a function of the number of collisions n obeys a power law v∝n1/6 thus, the Fermi acceleration exponent is β = 1/6, which is in excellent agreement with the numerical calculations of the fully chaotic oval billiard, the Sinai billiard and the cardioid billiard. The error of the velocity estimates is of the order 1/v2. Thus, the higher the velocity, the better our analytic approximation. Moreover, we derive the underlying universal equation of the velocity dynamics of the time-dependent conformally breathing billiards, correct up to and including the order 1/v in the regime of the large velocity of the particle v. This universal equation does not depend on the dynamical properties of the system (integrability, ergodicity, chaoticity). We present the results of the numerical simulations for three billiards in complete agreement with the theory. We believe that this is a first step towards theoretical understanding of the power law growth and the Fermi acceleration exponents in 2D billiards, although our theory is so far specialized to the conformally breathing fully chaotic billiards.

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.

Synchronized shocks in an inhomogeneous exclusion process

NASA Astrophysics Data System (ADS)

Arita, Chikashi

2015-11-01

We study an exclusion process with 4 segments, which was recently introduced by T. Banerjee, N. Sarkar and A. Basu (J. Stat. Mech. (2015) P01024). The segments have hopping rates 1, r(<1) , 1 and r, respectively. In a certain parameter region, two shocks appear, which are not static but synchronized. We explore dynamical properties of each shock and correlation of shocks, by means of the so-called second-class particle. The mean-squared displacement of shocks has three diffusive regimes, and the asymptotic diffusion coefficient is different from the known formula. In some time interval, it also exhibits sub-diffusion, being proportional to t1/2 . Furthermore we introduce a correlation function and a crossover time, in order to quantitatively characterize the synchronization. We numerically estimate the dynamical exponent for the crossover time. We also revisit the 2-segment case and the open boundary condition for comparison.

Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks.

PubMed

Lombardi, F; Herrmann, H J; de Arcangelis, L

2017-04-01

The 1/f-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitutes evidence of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here, we study the relationship between network inhibition and the scaling exponent β of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality. We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value β = 1 for a percentage of about 30%. More specifically, β is close to 2, namely, Brownian noise, for purely excitatory networks and decreases towards values in the interval [1, 1.4] as the percentage of inhibitory synapses ranges between 20% and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.

Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks

NASA Astrophysics Data System (ADS)

Lombardi, F.; Herrmann, H. J.; de Arcangelis, L.

2017-04-01

The 1/f-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitutes evidence of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here, we study the relationship between network inhibition and the scaling exponent β of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality. We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value β = 1 for a percentage of about 30%. More specifically, β is close to 2, namely, Brownian noise, for purely excitatory networks and decreases towards values in the interval [1, 1.4] as the percentage of inhibitory synapses ranges between 20% and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.

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.

Understanding scaling through history-dependent processes with collapsing sample space.

PubMed

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

2015-04-28

History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample space, or their set of possible outcomes, reduces as they age. We demonstrate that these sample-space-reducing (SSR) processes necessarily lead to Zipf's law in the rank distributions of their outcomes. We show that by adding noise to SSR processes the corresponding rank distributions remain exact power laws, p(x) ~ x(-λ), where the exponent directly corresponds to the mixing ratio of the SSR process and noise. This allows us to give a precise meaning to the scaling exponent in terms of the degree to which a given process reduces its sample space as it unfolds. Noisy SSR processes further allow us to explain a wide range of scaling exponents in frequency distributions ranging from α = 2 to ∞. We discuss several applications showing how SSR processes can be used to understand Zipf's law in word frequencies, and how they are related to diffusion processes in directed networks, or aging processes such as in fragmentation processes. SSR processes provide a new alternative to understand the origin of scaling in complex systems without the recourse to multiplicative, preferential, or self-organized critical processes.

Measurement of effective air diffusion coefficients for trichloroethene in undisturbed soil cores.

PubMed

Bartelt-Hunt, Shannon L; Smith, James A

2002-06-01

In this study, we measure effective diffusion coefficients for trichloroethene in undisturbed soil samples taken from Picatinny Arsenal, New Jersey. The measured effective diffusion coefficients ranged from 0.0053 to 0.0609 cm2/s over a range of air-filled porosity of 0.23-0.49. The experimental data were compared to several previously published relations that predict diffusion coefficients as a function of air-filled porosity and porosity. A multiple linear regression analysis was developed to determine if a modification of the exponents in Millington's [Science 130 (1959) 100] relation would better fit the experimental data. The literature relations appeared to generally underpredict the effective diffusion coefficient for the soil cores studied in this work. Inclusion of a particle-size distribution parameter, d10, did not significantly improve the fit of the linear regression equation. The effective diffusion coefficient and porosity data were used to recalculate estimates of diffusive flux through the subsurface made in a previous study performed at the field site. It was determined that the method of calculation used in the previous study resulted in an underprediction of diffusive flux from the subsurface. We conclude that although Millington's [Science 130 (1959) 100] relation works well to predict effective diffusion coefficients in homogeneous soils with relatively uniform particle-size distributions, it may be inaccurate for many natural soils with heterogeneous structure and/or non-uniform particle-size distributions.

Polymer scaling and dynamics in steady-state sedimentation at infinite Péclet number.

PubMed

Lehtola, V; Punkkinen, O; Ala-Nissila, T

2007-11-01

We consider the static and dynamical behavior of a flexible polymer chain under steady-state sedimentation using analytic arguments and computer simulations. The model system comprises a single coarse-grained polymer chain of N segments, which resides in a Newtonian fluid as described by the Navier-Stokes equations. The chain is driven into nonequilibrium steady state by gravity acting on each segment. The equations of motion for the segments and the Navier-Stokes equations are solved simultaneously using an immersed boundary method, where thermal fluctuations are neglected. To characterize the chain conformation, we consider its radius of gyration RG(N). We find that the presence of gravity explicitly breaks the spatial symmetry leading to anisotropic scaling of the components of RG with N along the direction of gravity RG, parallel and perpendicular to it RG, perpendicular, respectively. We numerically estimate the corresponding anisotropic scaling exponents nu parallel approximately 0.79 and nu perpendicular approximately 0.45, which differ significantly from the equilibrium scaling exponent nue=0.588 in three dimensions. This indicates that on the average, the chain becomes elongated along the sedimentation direction for large enough N. We present a generalization of the Flory scaling argument, which is in good agreement with the numerical results. It also reveals an explicit dependence of the scaling exponents on the Reynolds number. To study the dynamics of the chain, we compute its effective diffusion coefficient D(N), which does not contain Brownian motion. For the range of values of N used here, we find that both the parallel and perpendicular components of D increase with the chain length N, in contrast to the case of thermal diffusion in equilibrium. This is caused by the fluid-driven fluctuations in the internal configuration of the polymer that are magnified as polymer size becomes larger.

Creep Properties of the As-Cast Al-A319 Alloy: T4 and T7 Heat Treatment Effects

NASA Astrophysics Data System (ADS)

Erfanian-Naziftoosi, Hamid R.; Rincón, Ernesto J.; López, Hugo F.

2016-08-01

In this work, the creep behavior of a commercial Al-A319 alloy was investigated in the temperature range of 413 K to 533 K (140 °C to 260 °C). Tensile creep specimens in the as-cast condition and after heat treating by solid solution (T4) and by aging (T7) were tested in a stress range varying from 60 to 170 MPa. It was found that steady-state creep strain rate was significantly low in the T7 condition when compared with either the T4 or as-cast alloy conditions. As a result, the time to failure behavior considerably increased. The experimentally determined creep exponents measured from the stress-strain curves were 4 for the as-cast alloy, 7.5 in the solid solution, and 9.5 after aging. In particular, after solid solution a grain substructure was found to develop which indicated that creep in a constant subgrain structure was active, thus accounting for the n exponent of 7.5. In the aged condition, a stress threshold is considered to account for the power law creep exponent n of 9.5. Moreover, It was found that the creep activation energy values were rather similar for the alloys in the as-cast (134 kJ/mol) and T4 (146 kJ/mol) conditions. These values are close to the one corresponding to pure Al self-diffusion (143 kJ/mol). In the aged alloy, the apparent creep activation energy (202 kJ/mol) exceeded that corresponding to Al self-diffusion. This deviation in activation energy is attributed to the effect of temperature on the alloy elastic modulus. Microstructural observations using transmission electron microscopy provided further support for the various dislocation-microstructure interactions exhibited by the alloy under the investigated creep conditions and implemented heat treatments.

Correlation between information diffusion and opinion evolution on social media

NASA Astrophysics Data System (ADS)

Xiong, Fei; Liu, Yun; Zhang, Zhenjiang

2014-12-01

Information diffusion and opinion evolution are often treated as two independent processes. Opinion models assume the topic reaches each agent and agents initially have their own ideas. In fact, the processes of information diffusion and opinion evolution often intertwine with each other. Whether the influence between these two processes plays a role in the system state is unclear. In this paper, we collected more than one million real data from a well-known social platform, and analysed large-scale user diffusion behaviour and opinion formation. We found that user inter-event time follows a two-scaling power-law distribution with two different power exponents. Public opinion stabilizes quickly and evolves toward the direction of convergence, but the consensus state is prevented by a few opponents. We propose a three-state opinion model accompanied by information diffusion. Agents form and exchange their opinions during information diffusion. Conversely, agents' opinions also influence their diffusion actions. Simulations show that the model with a correlation of the two processes produces similar statistical characteristics as empirical results. A fast epidemic process drives individual opinions to converge more obviously. Unlike previous epidemic models, the number of infected agents does not always increase with the update rate, but has a peak with an intermediate value of the rate.

Quantification of tension to explain bias dependence of driven polymer translocation dynamics

NASA Astrophysics Data System (ADS)

Suhonen, P. M.; Piili, J.; Linna, R. P.

2017-12-01

Motivated by identifying the origin of the bias dependence of tension propagation, we investigate methods for measuring tension propagation quantitatively in computer simulations of driven polymer translocation. Here, the motion of flexible polymer chains through a narrow pore is simulated using Langevin dynamics. We measure tension forces, bead velocities, bead distances, and bond angles along the polymer at all stages of translocation with unprecedented precision. Measurements are done at a standard temperature used in simulations and at zero temperature to pin down the effect of fluctuations. The measured quantities were found to give qualitatively similar characteristics, but the bias dependence could be determined only using tension force. We find that in the scaling relation τ ˜Nβfdα for translocation time τ , the polymer length N , and the bias force fd, the increase of the exponent β with bias is caused by center-of-mass diffusion of the polymer toward the pore on the cis side. We find that this diffusion also causes the exponent α to deviate from the ideal value -1 . The bias dependence of β was found to result from combination of diffusion and pore friction and so be relevant for polymers that are too short to be considered asymptotically long. The effect is relevant in experiments all of which are made using polymers whose lengths are far below the asymptotic limit. Thereby, our results also corroborate the theoretical prediction by Sakaue's theory [Polymers 8, 424 (2016), 10.3390/polym8120424] that there should not be bias dependence of β for asymptotically long polymers. By excluding fluctuations we also show that monomer crowding at the pore exit cannot have a measurable effect on translocation dynamics under realistic conditions.

Sunlight Transmission through Desert Dust and Marine Aerosols: Diffuse Light Corrections to Sun Photometry and Pyrheliometry

NASA Technical Reports Server (NTRS)

Russell, P. B.; Livingston, J. M.; Dubovik, O.; Ramirez, S. A.; Wang, J.; Redemann, J.; Schmid, B.; Box, M.; Holben, B. N.

2003-01-01

Desert dust and marine aerosols are receiving increased scientific attention because of their prevalence on intercontinental scales and their potentially large effects on Earth radiation and climate, as well as on other aerosols, clouds, and precipitation. The relatively large size of desert dust and marine aerosols produces scattering phase functions that are strongly forward- peaked. Hence, Sun photometry and pyrheliometry of these aerosols are more subject to diffuse-light errors than is the case for smaller aerosols. Here we quantify these diffuse-light effects for common Sun photometer and pyrheliometer fields of view (FOV), using a data base on dust and marine aerosols derived from (1) AERONET measurements of sky radiance and solar beam transmission and (2) in situ measurements of aerosol layer size distribution and chemical composition. Accounting for particle non-sphericity is important when deriving dust size distribution from both AERONET and in situ aerodynamic measurements. We express our results in terms of correction factors that can be applied to Sun photometer and pyrheliometer measurements of aerosol optical depth (AOD). We find that the corrections are negligible (less than approximately 1% of AOD) for Sun photometers with narrow FOV (half-angle eta less than degree), but that they can be as large as 10% of AOD at 354 nm wavelength for Sun photometers with eta = 1.85 degrees. For pyrheliometers (which can have eta up to approximately 2.8 degrees), corrections can be as large as 16% at 354 nm. We find that AOD correction factors are well correlated with AOD wavelength dependence (hence Angstrom exponent). We provide best-fit equations for determining correction factors from Angstrom exponents of uncorrected AOD spectra, and we demonstrate their application to vertical profiles of multiwavelength AOD.

Elucidating the role of select cytoplasmic proteins in altering diffusion of integrin receptors.

PubMed

Sander, Suzanne; Arora, Neha; Smith, Emily A

2012-06-01

Cytoplasmic proteins that affect integrin diffusion in the cell membrane are identified using a combination of fluorescence recovery after photobleaching (FRAP) and RNA interference. Integrin receptors are essential for many cellular events, and alterations in lateral diffusion are one mechanism for modulating their function. In cells expressing native cytoplasmic protein concentrations and spread on a slide containing integrin extracellular ligand, 45 ± 2% of the integrin is mobile with a time-dependent 5.2 ± 0.9 × 10(-9) cm(2)/s diffusion coefficient at 1 s. The time exponent is 0.90 ± 0.07, indicating integrin diffusion moderately slows at longer times. The role of a specific cytoplasmic protein in altering integrin diffusion is revealed through changes in the FRAP curve after reducing the cytoplasmic protein's expression. Decreased expression of cytoplasmic proteins rhea, focal adhesion kinase (FAK), or steamer duck decreases the integrin mobile fraction. For rhea and FAK, there is a concomitant shift to Brownian (i.e., time-independent) diffusion at reduced concentrations of these proteins. In contrast, when the expression of actin 42A, dreadlocks, paxillin, integrin-linked kinase (ILK), or vinculin is reduced, integrin diffusion generally becomes more constrained with an increase in the integrin mobile fraction. This same change in integrin diffusion is measured in the absence of integrin extracellular ligand. The results indicate breaking the extracellular ligand-integrin-cytoskeletal linkage alters integrin diffusion properties, and, in most cases, there is no correlation between integrin and lipid diffusion properties.

The Phenomenology of Small-Scale Turbulence

NASA Astrophysics Data System (ADS)

Sreenivasan, K. R.; Antonia, R. A.

I have sometimes thought that what makes a man's work classic is often just this multiplicity [of interpretations], which invites and at the same time resists our craving for a clear understanding. Wright (1982, p. 34), on Wittgenstein's philosophy Small-scale turbulence has been an area of especially active research in the recent past, and several useful research directions have been pursued. Here, we selectively review this work. The emphasis is on scaling phenomenology and kinematics of small-scale structure. After providing a brief introduction to the classical notions of universality due to Kolmogorov and others, we survey the existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, intermittency models, and the structure and kinematics of small-scale structure - the latter aspect coming largely from the direct numerical simulation of homogeneous turbulence in a periodic box.

Unbinding Transition of Probes in Single-File Systems

NASA Astrophysics Data System (ADS)

Bénichou, Olivier; Démery, Vincent; Poncet, Alexis

2018-02-01

Single-file transport, arising in quasi-one-dimensional geometries where particles cannot pass each other, is characterized by the anomalous dynamics of a probe, notably its response to an external force. In these systems, the motion of several probes submitted to different external forces, although relevant to mixtures of charged and neutral or active and passive objects, remains unexplored. Here, we determine how several probes respond to external forces. We rely on a hydrodynamic description of the symmetric exclusion process to obtain exact analytical results at long times. We show that the probes can either move as a whole, or separate into two groups moving away from each other. In between the two regimes, they separate with a different dynamical exponent, as t1 /4. This unbinding transition also occurs in several continuous single-file systems and is expected to be observable.

Large-Scale Chaos and Fluctuations in Active Nematics

NASA Astrophysics Data System (ADS)

Ngo, Sandrine; Peshkov, Anton; Aranson, Igor S.; Bertin, Eric; Ginelli, Francesco; Chaté, Hugues

2014-07-01

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations describing these systems and of the self-propelled particle model they were derived from. We prove, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations. Revisiting the status of the strong fluctuations and long-range correlations in the particle model, we show that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation. However anomalous, curvature-driven number fluctuations are present in the homogeneous quasiordered nematic phase and characterized by a nontrivial scaling exponent.

Gravity Effects in Diffusive Coarsening of Bubble Lattices: von Neumann's Law

NASA Technical Reports Server (NTRS)

Noever, David A.

2000-01-01

von Neumann modelled the evolution of two-dimensional soap froths as a purely diffusive phenomenon; the area growth of a given cell was found to depend only on the geometry of the bubble lattice. In the model, hexagons are stable, pentagons shrink and heptagons grow. The simplest equivalent to the area growth law is / approximately t(sub beta). The result depends on assuming (1) an incompressible gas; (2) bubble walls which meet at 120 deg and (3) constant wall thickness and curvature. Each assumption is borne out in experiments except the last one: bubble wall thickness between connecting cells varies in unit gravity because of gravity drainage. The bottom part of the soap membrane is thickened, the top part is thinned, such that gas diffusion across the membrane shows a complex dependence on gravity. As a result, experimental tests of von Neumann's law have been influenced by effects of gravity; fluid behavior along cell borders can give non-uniform wall thicknesses and thus alter the effective area and gas diffusion rates between adjacent bubbles. For area plotted as a function of time, Glazier (J.A. Glazier, S.P. Gross, and I. Stavans, Phys. Rev. A. 36, 306 (1987); J. Stavans, J.A, Glazier, Phys. Rev. Lett. 62, 1318 (1989).) suggest that in some cases their failure to observe von Neumann's predicted growth exponent ((sup beta)theor(sup =1; beta)exp(sup =0.70 + 0.10)) may have been the result of such "fluid drainage onto the lower glass plate". Additional experiments which varied plate spacing gave different beta exponents in a fashion consistent with this suggestion. During preliminary long duration experiments (approximately 100 h) aboard Spacelab-J, a low-gravity test of froth coarsening has examined (1) power law scaling of von Neumann's law (beta values) in the appropriate diffusive limits; (2) new bubble lattice dynamics such as greater fluid wetting behavior on froth membranes in low gravity; and (3) explicit relations for the gravity dependence of the second moment (or disorder parameter) governing the geometric spread in cell-sidedness around the mean of perfect hexagonal filling. By reducing the gravity-induced distortion in lattice wall thickness, the diffusion-limited regime of bubble coarsening becomes available for performing critical tests of network dynamics.

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.

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

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.

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.

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.

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.