Relevance of anisotropy and spatial variability of gas diffusivity for soil-gas transport

NASA Astrophysics Data System (ADS)

Schack-Kirchner, Helmer; Kühne, Anke; Lang, Friederike

2017-04-01

Models of soil gas transport generally do not consider neither direction dependence of gas diffusivity, nor its small-scale variability. However, in a recent study, we could provide evidence for anisotropy favouring vertical gas diffusion in natural soils. We hypothesize that gas transport models based on gas diffusion data measured with soil rings are strongly influenced by both, anisotropy and spatial variability and the use of averaged diffusivities could be misleading. To test this we used a 2-dimensional model of soil gas transport to under compacted wheel tracks to model the soil-air oxygen distribution in the soil. The model was parametrized with data obtained from soil-ring measurements with its central tendency and variability. The model includes vertical parameter variability as well as variation perpendicular to the elongated wheel track. Different parametrization types have been tested: [i)]Averaged values for wheel track and undisturbed. em [ii)]Random distribution of soil cells with normally distributed variability within the strata. em [iii)]Random distributed soil cells with uniformly distributed variability within the strata. All three types of small-scale variability has been tested for [j)] isotropic gas diffusivity and em [jj)]reduced horizontal gas diffusivity (constant factor), yielding in total six models. As expected the different parametrizations had an important influence to the aeration state under wheel tracks with the strongest oxygen depletion in case of uniformly distributed variability and anisotropy towards higher vertical diffusivity. The simple simulation approach clearly showed the relevance of anisotropy and spatial variability in case of identical central tendency measures of gas diffusivity. However, until now it did not consider spatial dependency of variability, that could even aggravate effects. To consider anisotropy and spatial variability in gas transport models we recommend a) to measure soil-gas transport parameters spatially explicit including different directions and b) to use random-field stochastic models to assess the possible effects for gas-exchange models.

Deposition on disordered substrates with precursor layer diffusion

NASA Astrophysics Data System (ADS)

Filipe, J. A. N.; Rodgers, G. J.; Tavassoli, Z.

1998-09-01

Recently we introduced a one-dimensional accelerated random sequential adsorption process as a model for chemisorption with precursor layer diffusion. In this paper we consider this deposition process on disordered or impure substrates. The problem is solved exactly on both the lattice and continuum and for various impurity distributions. The results are compared with those from the standard random sequential adsorption model.

Diffusion in random networks: Asymptotic properties, and numerical and engineering approximations

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

The ensemble phase averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of a set of pockets connected by tortuous channels. Inside a channel, we assume that fluid transport is governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pores mass density. The so-called dual porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain, whose solution is sought numerically. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt- 1 / 4 rather than xt- 1 / 2 as in the traditional theory. This early time sub-diffusive similarity can be explained by random walk theory through the network. In addition, by applying concepts of fractional calculus, we show that, for small time, the governing equation reduces to a fractional diffusion equation with known solution. We recast this solution in terms of special functions easier to compute. Comparison of the numerical and exact solutions shows excellent agreement.

Effective Stochastic Model for Reactive Transport

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Random walks and diffusion on networks

NASA Astrophysics Data System (ADS)

Masuda, Naoki; Porter, Mason A.; Lambiotte, Renaud

2017-11-01

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.

Technology diffusion in hospitals: a log odds random effects regression model.

PubMed

Blank, Jos L T; Valdmanis, Vivian G

2015-01-01

This study identifies the factors that affect the diffusion of hospital innovations. We apply a log odds random effects regression model on hospital micro data. We introduce the concept of clustering innovations and the application of a log odds random effects regression model to describe the diffusion of technologies. We distinguish a number of determinants, such as service, physician, and environmental, financial and organizational characteristics of the 60 Dutch hospitals in our sample. On the basis of this data set on Dutch general hospitals over the period 1995-2002, we conclude that there is a relation between a number of determinants and the diffusion of innovations underlining conclusions from earlier research. Positive effects were found on the basis of the size of the hospitals, competition and a hospital's commitment to innovation. It appears that if a policy is developed to further diffuse innovations, the external effects of demand and market competition need to be examined, which would de facto lead to an efficient use of technology. For the individual hospital, instituting an innovations office appears to be the most prudent course of action. © 2013 The Authors. International Journal of Health Planning and Management published by John Wiley & Sons, Ltd.

Time-delayed feedback control of diffusion in random walkers.

PubMed

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

2017-07-01

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

Nonequilibrium Statistical Mechanics in One Dimension

NASA Astrophysics Data System (ADS)

Privman, Vladimir

2005-08-01

Part I. Reaction-Diffusion Systems and Models of Catalysis; 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner; 2. The coalescence process, A+A->A, and the method of interparticle distribution functions D. ben-Avraham; 3. Critical phenomena at absorbing states R. Dickman; Part II. Kinetic Ising Models; 4. Kinetic ising models with competing dynamics: mappings, correlations, steady states, and phase transitions Z. Racz; 5. Glauber dynamics of the ising model N. Ito; 6. 1D Kinetic ising models at low temperatures - critical dynamics, domain growth, and freezing S. Cornell; Part III. Ordering, Coagulation, Phase Separation; 7. Phase-ordering dynamics in one dimension A. J. Bray; 8. Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics V. Privman; 9. Stochastic models of aggregation with injection H. Takayasu and M. Takayasu; Part IV. Random Sequential Adsorption and Relaxation Processes; 10. Random and cooperative sequential adsorption: exactly solvable problems on 1D lattices, continuum limits, and 2D extensions J. W. Evans; 11. Lattice models of irreversible adsorption and diffusion P. Nielaba; 12. Deposition-evaporation dynamics: jamming, conservation laws and dynamical diversity M. Barma; Part V. Fluctuations In Particle and Surface Systems; 13. Microscopic models of macroscopic shocks S. A. Janowsky and J. L. Lebowitz; 14. The asymmetric exclusion model: exact results through a matrix approach B. Derrida and M. R. Evans; 15. Nonequilibrium surface dynamics with volume conservation J. Krug; 16. Directed walks models of polymers and wetting J. Yeomans; Part VI. Diffusion and Transport In One Dimension; 17. Some recent exact solutions of the Fokker-Planck equation H. L. Frisch; 18. Random walks, resonance, and ratchets C. R. Doering and T. C. Elston; 19. One-dimensional random walks in random environment K. Ziegler; Part VII. Experimental Results; 20. Diffusion-limited exciton kinetics in one-dimensional systems R. Kroon and R. Sprik; 21. Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems R. Kopelman and A. L. Lin; 22. Luminescence quenching as a probe of particle distribution S. H. Bossmann and L. S. Schulman; Index.

Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode.

PubMed

Abellán, C; Amaya, W; Jofre, M; Curty, M; Acín, A; Capmany, J; Pruneri, V; Mitchell, M W

2014-01-27

We demonstrate a high bit-rate quantum random number generator by interferometric detection of phase diffusion in a gain-switched DFB laser diode. Gain switching at few-GHz frequencies produces a train of bright pulses with nearly equal amplitudes and random phases. An unbalanced Mach-Zehnder interferometer is used to interfere subsequent pulses and thereby generate strong random-amplitude pulses, which are detected and digitized to produce a high-rate random bit string. Using established models of semiconductor laser field dynamics, we predict a regime of high visibility interference and nearly complete vacuum-fluctuation-induced phase diffusion between pulses. These are confirmed by measurement of pulse power statistics at the output of the interferometer. Using a 5.825 GHz excitation rate and 14-bit digitization, we observe 43 Gbps quantum randomness generation.

Time scale of random sequential adsorption.

PubMed

Erban, Radek; Chapman, S Jonathan

2007-04-01

A simple multiscale approach to the diffusion-driven adsorption from a solution to a solid surface is presented. The model combines two important features of the adsorption process: (i) The kinetics of the chemical reaction between adsorbing molecules and the surface and (ii) geometrical constraints on the surface made by molecules which are already adsorbed. The process (i) is modeled in a diffusion-driven context, i.e., the conditional probability of adsorbing a molecule provided that the molecule hits the surface is related to the macroscopic surface reaction rate. The geometrical constraint (ii) is modeled using random sequential adsorption (RSA), which is the sequential addition of molecules at random positions on a surface; one attempt to attach a molecule is made per one RSA simulation time step. By coupling RSA with the diffusion of molecules in the solution above the surface the RSA simulation time step is related to the real physical time. The method is illustrated on a model of chemisorption of reactive polymers to a virus surface.

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

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2008-12-01

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

Lévy walks

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

Heterogeneous continuous-time random walks

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.; Tupikina, Liubov

2018-01-01

We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.

Plasma fluctuations as Markovian noise.

PubMed

Li, B; Hazeltine, R D; Gentle, K W

2007-12-01

Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments.

Reconciling transport models across scales: The role of volume exclusion

NASA Astrophysics Data System (ADS)

Taylor, P. R.; Yates, C. A.; Simpson, M. J.; Baker, R. E.

2015-10-01

Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the role of volume exclusion, which can significantly alter diffusive transport, particularly within biological systems where the diffusing particles might occupy a significant fraction of the available space. In this work we use a random walk approach to provide a means to reconcile models that incorporate crowding effects on different spatial scales. Our work demonstrates that coarse-grained models incorporating simplified descriptions of excluded volume can be used in many circumstances, but that care must be taken in pushing the coarse-graining process too far.

Bayesian approach to non-Gaussian field statistics for diffusive broadband terahertz pulses.

PubMed

Pearce, Jeremy; Jian, Zhongping; Mittleman, Daniel M

2005-11-01

We develop a closed-form expression for the probability distribution function for the field components of a diffusive broadband wave propagating through a random medium. We consider each spectral component to provide an individual observation of a random variable, the configurationally averaged spectral intensity. Since the intensity determines the variance of the field distribution at each frequency, this random variable serves as the Bayesian prior that determines the form of the non-Gaussian field statistics. This model agrees well with experimental results.

Knowledge diffusion of dynamical network in terms of interaction frequency.

PubMed

Liu, Jian-Guo; Zhou, Qing; Guo, Qiang; Yang, Zhen-Hua; Xie, Fei; Han, Jing-Ti

2017-09-07

In this paper, we present a knowledge diffusion (SKD) model for dynamic networks by taking into account the interaction frequency which always used to measure the social closeness. A set of agents, which are initially interconnected to form a random network, either exchange knowledge with their neighbors or move toward a new location through an edge-rewiring procedure. The activity of knowledge exchange between agents is determined by a knowledge transfer rule that the target node would preferentially select one neighbor node to transfer knowledge with probability p according to their interaction frequency instead of the knowledge distance, otherwise, the target node would build a new link with its second-order neighbor preferentially or select one node in the system randomly with probability 1 - p. The simulation results show that, comparing with the Null model defined by the random selection mechanism and the traditional knowledge diffusion (TKD) model driven by knowledge distance, the knowledge would spread more fast based on SKD driven by interaction frequency. In particular, the network structure of SKD would evolve as an assortative one, which is a fundamental feature of social networks. This work would be helpful for deeply understanding the coevolution of the knowledge diffusion and network structure.

Diffusion-advection within dynamic biological gaps driven by structural motion

NASA Astrophysics Data System (ADS)

Asaro, Robert J.; Zhu, Qiang; Lin, Kuanpo

2018-04-01

To study the significance of advection in the transport of solutes, or particles, within thin biological gaps (channels), we examine theoretically the process driven by stochastic fluid flow caused by random thermal structural motion, and we compare it with transport via diffusion. The model geometry chosen resembles the synaptic cleft; this choice is motivated by the cleft's readily modeled structure, which allows for well-defined mechanical and physical features that control the advection process. Our analysis defines a Péclet-like number, AD, that quantifies the ratio of time scales of advection versus diffusion. Another parameter, AM, is also defined by the analysis that quantifies the full potential extent of advection in the absence of diffusion. These parameters provide a clear and compact description of the interplay among the well-defined structural, geometric, and physical properties vis-a ̀-vis the advection versus diffusion process. For example, it is found that AD˜1 /R2 , where R is the cleft diameter and hence diffusion distance. This curious, and perhaps unexpected, result follows from the dependence of structural motion that drives fluid flow on R . AM, on the other hand, is directly related (essentially proportional to) the energetic input into structural motion, and thereby to fluid flow, as well as to the mechanical stiffness of the cleftlike structure. Our model analysis thus provides unambiguous insight into the prospect of competition of advection versus diffusion within biological gaplike structures. The importance of the random, versus a regular, nature of structural motion and of the resulting transient nature of advection under random motion is made clear in our analysis. Further, by quantifying the effects of geometric and physical properties on the competition between advection and diffusion, our results clearly demonstrate the important role that metabolic energy (ATP) plays in this competitive process.

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.

Numerical simulation model of hyperacute/acute stage white matter infarction.

PubMed

Sakai, Koji; Yamada, Kei; Oouchi, Hiroyuki; Nishimura, Tsunehiko

2008-01-01

Although previous studies have revealed the mechanisms of changes in diffusivity (apparent diffusion coefficient [ADC]) in acute brain infarction, changes in diffusion anisotropy (fractional anisotropy [FA]) in white matter have not been examined. We hypothesized that membrane permeability as well as axonal swelling play important roles, and we therefore constructed a simulation model using random walk simulation to replicate the diffusion of water molecules. We implemented a numerical diffusion simulation model of normal and infarcted human brains using C++ language. We constructed this 2-pool model using simple tubes aligned in a single direction. Random walk simulation diffused water. Axon diameters and membrane permeability were then altered in step-wise fashion. To estimate the effects of axonal swelling, axon diameters were changed from 6 to 10 microm. Membrane permeability was altered from 0% to 40%. Finally, both elements were combined to explain increasing FA in the hyperacute stage of white matter infarction. The simulation demonstrated that simple water shift into the intracellular space reduces ADC and increases FA, but not to the extent expected from actual human cases (ADC approximately 50%; FA approximately +20%). Similarly, membrane permeability alone was insufficient to explain this phenomenon. However, a combination of both factors successfully replicated changes in diffusivity indices. Both axonal swelling and reduced membrane permeability appear important in explaining changes in ADC and FA based on eigenvalues in hyperacute-stage white matter infarction.

Magnetic field line random walk in models and simulations of reduced magnetohydrodynamic turbulence

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

Snodin, A. P.; Ruffolo, D.; Oughton, S.

2013-12-10

The random walk of magnetic field lines is examined numerically and analytically in the context of reduced magnetohydrodynamic (RMHD) turbulence, which provides a useful description of plasmas dominated by a strong mean field, such as in the solar corona. A recently developed non-perturbative theory of magnetic field line diffusion is compared with the diffusion coefficients obtained by accurate numerical tracing of magnetic field lines for both synthetic models and direct numerical simulations of RMHD. Statistical analysis of an ensemble of trajectories confirms the applicability of the theory, which very closely matches the numerical field line diffusion coefficient as a functionmore » of distance z along the mean magnetic field for a wide range of the Kubo number R. This theory employs Corrsin's independence hypothesis, sometimes thought to be valid only at low R. However, the results demonstrate that it works well up to R = 10, both for a synthetic RMHD model and an RMHD simulation. The numerical results from the RMHD simulation are compared with and without phase randomization, demonstrating a clear effect of coherent structures on the field line random walk for a very low Kubo number.« less

The hydrogen diffusion in liquid aluminum alloys from ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Jakse, N.; Pasturel, A.

2014-09-01

We study the hydrogen diffusion in liquid aluminum alloys through extensive ab initio molecular dynamics simulations. At the microscopic scale, we show that the hydrogen motion is characterized by a broad distribution of spatial jumps that does not correspond to a Brownian motion. To determine the self-diffusion coefficient of hydrogen in liquid aluminum alloys, we use a generalized continuous time random walk model recently developed to describe the hydrogen diffusion in pure aluminum. In particular, we show that the model successfully accounts the effects of alloying elements on the hydrogen diffusion in agreement with experimental features.

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.

Numerical Simulation of the Perrin-Like Experiments

ERIC Educational Resources Information Center

Mazur, Zygmunt; Grech, Dariusz

2008-01-01

A simple model of the random Brownian walk of a spherical mesoscopic particle in viscous liquids is proposed. The model can be solved analytically and simulated numerically. The analytic solution gives the known Einstein-Smoluchowski diffusion law r[superscript 2] = 2Dt, where the diffusion constant D is expressed by the mass and geometry of a…

Random-Walk Model of Diffusion in Three Dimensions in Brain Extracellular Space: Comparison with Microfiberoptic Photobleaching Measurements

PubMed Central

Jin, Songwan; Zador, Zsolt; Verkman, A. S.

2008-01-01

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises ∼20% of brain parenchymal volume and contains cell-cell gaps ∼50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (α), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (Do/D). Experimental Do/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. Do/D for the small solute calcein in different regions of brain was in the range 3.0–4.1, and increased with brain cell swelling after water intoxication. Do/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured Do/D using realistic α, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted Do/D for different solute sizes. Also, the modeling showed unanticipated effects on Do/D of changing ECS and cell dimensions that implicated solute trapping by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS. PMID:18469079

Random-walk model of diffusion in three dimensions in brain extracellular space: comparison with microfiberoptic photobleaching measurements.

PubMed

Jin, Songwan; Zador, Zsolt; Verkman, A S

2008-08-01

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises approximately 20% of brain parenchymal volume and contains cell-cell gaps approximately 50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (alpha), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (D(o)/D). Experimental D(o)/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. D(o)/D for the small solute calcein in different regions of brain was in the range 3.0-4.1, and increased with brain cell swelling after water intoxication. D(o)/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured D(o)/D using realistic alpha, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted D(o)/D for different solute sizes. Also, the modeling showed unanticipated effects on D(o)/D of changing ECS and cell dimensions that implicated solute trapping by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS.

Improved knowledge diffusion model based on the collaboration hypernetwork

NASA Astrophysics Data System (ADS)

Wang, Jiang-Pan; Guo, Qiang; Yang, Guang-Yong; Liu, Jian-Guo

2015-06-01

The process for absorbing knowledge becomes an essential element for innovation in firms and in adapting to changes in the competitive environment. In this paper, we present an improved knowledge diffusion hypernetwork (IKDH) model based on the idea that knowledge will spread from the target node to all its neighbors in terms of the hyperedge and knowledge stock. We apply the average knowledge stock V(t) , the variable σ2(t) , and the variance coefficient c(t) to evaluate the performance of knowledge diffusion. By analyzing different knowledge diffusion ways, selection ways of the highly knowledgeable nodes, hypernetwork sizes and hypernetwork structures for the performance of knowledge diffusion, results show that the diffusion speed of IKDH model is 3.64 times faster than that of traditional knowledge diffusion (TKDH) model. Besides, it is three times faster to diffuse knowledge by randomly selecting "expert" nodes than that by selecting large-hyperdegree nodes as "expert" nodes. Furthermore, either the closer network structure or smaller network size results in the faster knowledge diffusion.

Influence Function Learning in Information Diffusion Networks.

PubMed

Du, Nan; Liang, Yingyu; Balcan, Maria-Florina; Song, Le

2014-06-01

Can we learn the influence of a set of people in a social network from cascades of information diffusion? This question is often addressed by a two-stage approach: first learn a diffusion model, and then calculate the influence based on the learned model. Thus, the success of this approach relies heavily on the correctness of the diffusion model which is hard to verify for real world data. In this paper, we exploit the insight that the influence functions in many diffusion models are coverage functions, and propose a novel parameterization of such functions using a convex combination of random basis functions. Moreover, we propose an efficient maximum likelihood based algorithm to learn such functions directly from cascade data, and hence bypass the need to specify a particular diffusion model in advance. We provide both theoretical and empirical analysis for our approach, showing that the proposed approach can provably learn the influence function with low sample complexity, be robust to the unknown diffusion models, and significantly outperform existing approaches in both synthetic and real world data.

Interplay between inhibited transport and reaction in nanoporous materials

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

Ackerman, David Michael

2013-01-01

This work presents a detailed formulation of reaction and diffusion dynamics of molecules in confined pores such as mesoporous silica and zeolites. A general reaction-diffusion model and discrete Monte Carlo simulations are presented. Both transient and steady state behavior is covered. Failure of previous mean-field models for these systems is explained and discussed. A coarse-grained, generalized hydrodynamic model is developed that accurately captures the interplay between reaction and restricted transport in these systems. This method incorporates the non-uniform chemical diffusion behavior present in finite pores with multi-component diffusion. Two methods of calculating these diffusion values are developed: a random walkmore » based approach and a driven diffusion model based on an extension of Fick's law. The effects of reaction, diffusion, pore length, and catalytic site distribution are investigated. In addition to strictly single file motion, quasi-single file diffusion is incorporated into the model to match a range of experimental systems. The connection between these experimental systems and model parameters is made through Langevin dynamics modeling of particles in confined pores.« less

Constraining Thermal Histories by Monte Carlo Simulation of Mg-Fe Isotopic Profiles in Olivine

NASA Astrophysics Data System (ADS)

Sio, C. K. I.; Dauphas, N.

2016-12-01

In thermochronology, random time-temperature (t-T) paths are generated and used as inputs to model fission track data. This random search method is used to identify a range of acceptable thermal histories that can describe the data. We have extended this modeling approach to magmatic systems. This approach utilizes both the chemical and stable isotope profiles measured in crystals as model constraints. Specifically, the isotopic profiles are used to determine the relative contribution of crystal growth vs. diffusion in generating chemical profiles, and to detect changes in melt composition. With this information, tighter constraints can be placed on the thermal evolution of magmatic bodies. We use an olivine phenocryst from the Kilauea Iki lava lake, HI, to demonstrate proof of concept. We treat this sample as one with little geologic context, then compare our modeling results to the known thermal history experienced by that sample. To complete forward modeling, we use MELTS to estimate the boundary condition, initial and quench temperatures. We also assume a simple relationship between crystal growth and cooling rate. Another important parameter is the isotopic effect for diffusion (i.e., the relative diffusivity of the light vs. heavy isotope of an element). The isotopic effects for Mg and Fe diffusion in olivine have been estimated based on natural samples; experiments to better constrain these parameters are underway. We find that 40% of the random t-T paths can be used to fit the Mg-Fe chemical profiles. However, only a few can be used to simultaneously fit the Mg-Fe isotopic profiles. These few t-T paths are close to the independently determined t-T history of the sample. This modeling approach can be further extended other igneous and metamorphic systems where data exist for diffusion rates, crystal growth rates, and isotopic effects for diffusion.

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.

Oxygen self-diffusion mechanisms in monoclinic Zr O2 revealed and quantified by density functional theory, random walk analysis, and kinetic Monte Carlo calculations

NASA Astrophysics Data System (ADS)

Yang, Jing; Youssef, Mostafa; Yildiz, Bilge

2018-01-01

In this work, we quantify oxygen self-diffusion in monoclinic-phase zirconium oxide as a function of temperature and oxygen partial pressure. A migration barrier of each type of oxygen defect was obtained by first-principles calculations. Random walk theory was used to quantify the diffusivities of oxygen interstitials by using the calculated migration barriers. Kinetic Monte Carlo simulations were used to calculate diffusivities of oxygen vacancies by distinguishing the threefold- and fourfold-coordinated lattice oxygen. By combining the equilibrium defect concentrations obtained in our previous work together with the herein calculated diffusivity of each defect species, we present the resulting oxygen self-diffusion coefficients and the corresponding atomistically resolved transport mechanisms. The predicted effective migration barriers and diffusion prefactors are in reasonable agreement with the experimentally reported values. This work provides insights into oxygen diffusion engineering in Zr O2 -related devices and parametrization for continuum transport modeling.

Random walk on lattices: Graph-theoretic approach to simulating long-range diffusion-attachment growth models

NASA Astrophysics Data System (ADS)

Limkumnerd, Surachate

2014-03-01

Interest in thin-film fabrication for industrial applications have driven both theoretical and computational aspects of modeling its growth. One of the earliest attempts toward understanding the morphological structure of a film's surface is through a class of solid-on-solid limited-mobility growth models such as the Family, Wolf-Villain, or Das Sarma-Tamborenea models, which have produced fascinating surface roughening behaviors. These models, however, restrict the motion of an incidence atom to be within the neighborhood of its landing site, which renders them inept for simulating long-distance surface diffusion such as that observed in thin-film growth using a molecular-beam epitaxy technique. Naive extension of these models by repeatedly applying the local diffusion rules for each hop to simulate large diffusion length can be computationally very costly when certain statistical aspects are demanded. We present a graph-theoretic approach to simulating a long-range diffusion-attachment growth model. Using the Markovian assumption and given a local diffusion bias, we derive the transition probabilities for a random walker to traverse from one lattice site to the others after a large, possibly infinite, number of steps. Only computation with linear-time complexity is required for the surface morphology calculation without other probabilistic measures. The formalism is applied, as illustrations, to simulate surface growth on a two-dimensional flat substrate and around a screw dislocation under the modified Wolf-Villain diffusion rule. A rectangular spiral ridge is observed in the latter case with a smooth front feature similar to that obtained from simulations using the well-known multiple registration technique. An algorithm for computing the inverse of a class of substochastic matrices is derived as a corollary.

Weakly anomalous diffusion with non-Gaussian propagators

NASA Astrophysics Data System (ADS)

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

2012-08-01

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

Global diffusion of cosmic rays in random magnetic fields

NASA Astrophysics Data System (ADS)

Snodin, A. P.; Shukurov, A.; Sarson, G. R.; Bushby, P. J.; Rodrigues, L. F. S.

2016-04-01

The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius RL and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g. there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of the order of 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least 106 times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to 10-2 ≲ RL/lc ≲ 103, where lc is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for RL/lc ≪ 1, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.

Communication: Memory effects and active Brownian diffusion

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

Ghosh, Pulak K.; Li, Yunyun, E-mail: yunyunli@tongji.edu.cn; Marchegiani, Giampiero

A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer’s diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer’s propulsion are exponentially correlated in time, whereas in the second one, we account for possiblemore » damped fluctuations of the propulsion velocity around the swimmer’s axis. The corresponding swimmer’s diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.« less

Communication: Memory effects and active Brownian diffusion

NASA Astrophysics Data System (ADS)

Ghosh, Pulak K.; Li, Yunyun; Marchegiani, Giampiero; Marchesoni, Fabio

2015-12-01

A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer's diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer's propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer's axis. The corresponding swimmer's diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.

Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

NASA Astrophysics Data System (ADS)

Feres, Renato; Ng, Jasmine; Zhang, Hong-Kun

2013-10-01

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P h , depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that ( P h - I)/ h converges for small h to a second order elliptic differential operator on compactly supported functions and that the Markov chain process associated to P h converges to a diffusion with infinitesimal generator . Both P h and are self-adjoint (densely) defined on the space of square-integrable functions over the (lower) half-space in , where η is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.

Pattern formations and optimal packing.

PubMed

Mityushev, Vladimir

2016-04-01

Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary value problems. We demonstrate an intimate connection between pattern formations and optimal random packing on the plane. The main study is based on the following two points. First, the diffusive flux in reaction-diffusion systems is approximated by piecewise linear functions in the framework of structural approximations. This leads to a discrete network approximation of the considered continuous problem. Second, the discrete energy minimization yields optimal random packing of the domains (disks) in the representative cell. Therefore, the general problem of pattern formations based on the reaction-diffusion equations is reduced to the geometric problem of random packing. It is demonstrated that all random packings can be divided onto classes associated with classes of isomorphic graphs obtained from the Delaunay triangulation. The unique optimal solution is constructed in each class of the random packings. If the number of disks per representative cell is finite, the number of classes of isomorphic graphs, hence, the number of optimal packings is also finite. Copyright © 2016 Elsevier Inc. All rights reserved.

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).

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.

The Locomotion of Mouse Fibroblasts in Tissue Culture

PubMed Central

Gail, Mitchell H.; Boone, Charles W.

1970-01-01

Time-lapse cinematography was used to investigate the motion of mouse fibroblasts in tissue culture. Observations over successive short time intervals revealed a tendency for the cells to persist in their direction of motion from one 2.5 hr time interval to the next. Over 5.0-hr time intervals, however, the direction of motion appeared random. This fact suggested that D, the diffusion constant of a random walk model, might serve to characterize cellular motility if suitably long observation times were used. We therefore investigated the effect of “persistence” on the pure random walk model, and we found theoretically and confirmed experimentally that the motility of a persisting cell could indeed be characterized by an augmented diffusion constant, D*. A method for determining confidence limits on D* was also developed. Thus a random walk model, modified to comprehend the persistence effect, was found to describe the motion of fibroblasts in tissue culture and to provide a numerical measure of cellular motility. PMID:5531614

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

PubMed

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

2012-07-21

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

A random walk model to evaluate autism

NASA Astrophysics Data System (ADS)

Moura, T. R. S.; Fulco, U. L.; Albuquerque, E. L.

2018-02-01

A common test administered during neurological examination in children is the analysis of their social communication and interaction across multiple contexts, including repetitive patterns of behavior. Poor performance may be associated with neurological conditions characterized by impairments in executive function, such as the so-called pervasive developmental disorders (PDDs), a particular condition of the autism spectrum disorders (ASDs). Inspired in these diagnosis tools, mainly those related to repetitive movements and behaviors, we studied here how the diffusion regimes of two discrete-time random walkers, mimicking the lack of social interaction and restricted interests developed for children with PDDs, are affected. Our model, which is based on the so-called elephant random walk (ERW) approach, consider that one of the random walker can learn and imitate the microscopic behavior of the other with probability f (1 - f otherwise). The diffusion regimes, measured by the Hurst exponent (H), is then obtained, whose changes may indicate a different degree of autism.

Influence Function Learning in Information Diffusion Networks

PubMed Central

Du, Nan; Liang, Yingyu; Balcan, Maria-Florina; Song, Le

2015-01-01

Can we learn the influence of a set of people in a social network from cascades of information diffusion? This question is often addressed by a two-stage approach: first learn a diffusion model, and then calculate the influence based on the learned model. Thus, the success of this approach relies heavily on the correctness of the diffusion model which is hard to verify for real world data. In this paper, we exploit the insight that the influence functions in many diffusion models are coverage functions, and propose a novel parameterization of such functions using a convex combination of random basis functions. Moreover, we propose an efficient maximum likelihood based algorithm to learn such functions directly from cascade data, and hence bypass the need to specify a particular diffusion model in advance. We provide both theoretical and empirical analysis for our approach, showing that the proposed approach can provably learn the influence function with low sample complexity, be robust to the unknown diffusion models, and significantly outperform existing approaches in both synthetic and real world data. PMID:25973445

Money creation process in a random redistribution model

NASA Astrophysics Data System (ADS)

Chen, Siyan; Wang, Yougui; Li, Keqiang; Wu, Jinshan

2014-01-01

In this paper, the dynamical process of money creation in a random exchange model with debt is investigated. The money creation kinetics are analyzed by both the money-transfer matrix method and the diffusion method. From both approaches, we attain the same conclusion: the source of money creation in the case of random exchange is the agents with neither money nor debt. These analytical results are demonstrated by computer simulations.

Random element method for numerical modeling of diffusional processes

NASA Technical Reports Server (NTRS)

Ghoniem, A. F.; Oppenheim, A. K.

1982-01-01

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Field Line Random Walk in Isotropic Magnetic Turbulence up to Infinite Kubo Number

NASA Astrophysics Data System (ADS)

Sonsrettee, W.; Wongpan, P.; Ruffolo, D. J.; Matthaeus, W. H.; Chuychai, P.; Rowlands, G.

2013-12-01

In astrophysical plasmas, the magnetic field line random walk (FLRW) plays a key role in the transport of energetic particles. In the present, we consider isotropic magnetic turbulence, which is a reasonable model for interstellar space. Theoretical conceptions of the FLRW have been strongly influenced by studies of the limit of weak fluctuations (or a strong mean field) (e.g, Isichenko 1991a, b). In this case, the behavior of FLRW can be characterized by the Kubo number R = (b/B0)(l_∥ /l_ \\bot ) , where l∥ and l_ \\bot are turbulence coherence scales parallel and perpendicular to the mean field, respectively, and b is the root mean squared fluctuation field. In the 2D limit (R ≫ 1), there has been an apparent conflict between concepts of Bohm diffusion, which is based on the Corrsin's independence hypothesis, and percolative diffusion. Here we have used three non-perturbative analytic techniques based on Corrsin's independence hypothesis for B0 = 0 (R = ∞ ): diffusive decorrelation (DD), random ballistic decorrelation (RBD) and a general ordinary differential equation (ODE), and compared them with direct computer simulations. All the analytical models and computer simulations agree that isotropic turbulence for R = ∞ has a field line diffusion coefficient that is consistent with Bohm diffusion. Partially supported by the Thailand Research Fund, NASA, and NSF.

Master equation for She-Leveque scaling and its classification in terms of other Markov models of developed turbulence

NASA Astrophysics Data System (ADS)

Nickelsen, Daniel

2017-07-01

The statistics of velocity increments in homogeneous and isotropic turbulence exhibit universal features in the limit of infinite Reynolds numbers. After Kolmogorov’s scaling law from 1941, many turbulence models aim for capturing these universal features, some are known to have an equivalent formulation in terms of Markov processes. We derive the Markov process equivalent to the particularly successful scaling law postulated by She and Leveque. The Markov process is a jump process for velocity increments u(r) in scale r in which the jumps occur randomly but with deterministic width in u. From its master equation we establish a prescription to simulate the She-Leveque process and compare it with Kolmogorov scaling. To put the She-Leveque process into the context of other established turbulence models on the Markov level, we derive a diffusion process for u(r) using two properties of the Navier-Stokes equation. This diffusion process already includes Kolmogorov scaling, extended self-similarity and a class of random cascade models. The fluctuation theorem of this Markov process implies a ‘second law’ that puts a loose bound on the multipliers of the random cascade models. This bound explicitly allows for instances of inverse cascades, which are necessary to satisfy the fluctuation theorem. By adding a jump process to the diffusion process, we go beyond Kolmogorov scaling and formulate the most general scaling law for the class of Markov processes having both diffusion and jump parts. This Markov scaling law includes She-Leveque scaling and a scaling law derived by Yakhot.

Correlated random walks induced by dynamical wavefunction collapse

NASA Astrophysics Data System (ADS)

Bedingham, Daniel

2015-03-01

Wavefunction collapse models modify Schrödinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a genuine physical process [PRA 42, 78 (1990)]. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Furthermore, the diffusions of two sufficiently nearby particles are positively correlated -- it is more likely that the particles diffuse in the same direction than would happen if they behaved independently [PRA 89, 032713 (2014)]. The use of this effect is proposed as an experimental test of wave function collapse models in which pairs of nanoparticles are simultaneously released from nearby traps and allowed a brief period of free fall. The random displacements of the particles are then measured. The experiment must be carried out at sufficiently low temperature and pressure for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large class of viable wavefunction collapse models. Work supported by the Templeton World Charity Foundation.

Collision Models for Particle Orbit Code on SSX

NASA Astrophysics Data System (ADS)

Fisher, M. W.; Dandurand, D.; Gray, T.; Brown, M. R.; Lukin, V. S.

2011-10-01

Coulomb collision models are being developed and incorporated into the Hamiltonian particle pushing code (PPC) for applications to the Swarthmore Spheromak eXperiment (SSX). A Monte Carlo model based on that of Takizuka and Abe [JCP 25, 205 (1977)] performs binary collisions between test particles and thermal plasma field particles randomly drawn from a stationary Maxwellian distribution. A field-based electrostatic fluctuation model scatters particles from a spatially uniform random distribution of positive and negative spherical potentials generated throughout the plasma volume. The number, radii, and amplitude of these potentials are chosen to mimic the correct particle diffusion statistics without the use of random particle draws or collision frequencies. An electromagnetic fluctuating field model will be presented, if available. These numerical collision models will be benchmarked against known analytical solutions, including beam diffusion rates and Spitzer resistivity, as well as each other. The resulting collisional particle orbit models will be used to simulate particle collection with electrostatic probes in the SSX wind tunnel, as well as particle confinement in typical SSX fields. This work has been supported by US DOE, NSF and ONR.

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.

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.

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

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

Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.

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

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

PubMed

Berezhkovskii, Alexander M; Shvartsman, Stanislav Y

2016-05-28

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

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.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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

PubMed

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

2017-09-01

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

Evolution of the concentration PDF in random environments modeled by global random walk

NASA Astrophysics Data System (ADS)

Suciu, Nicolae; Vamos, Calin; Attinger, Sabine; Knabner, Peter

2013-04-01

The evolution of the probability density function (PDF) of concentrations of chemical species transported in random environments is often modeled by ensembles of notional particles. The particles move in physical space along stochastic-Lagrangian trajectories governed by Ito equations, with drift coefficients given by the local values of the resolved velocity field and diffusion coefficients obtained by stochastic or space-filtering upscaling procedures. A general model for the sub-grid mixing also can be formulated as a system of Ito equations solving for trajectories in the composition space. The PDF is finally estimated by the number of particles in space-concentration control volumes. In spite of their efficiency, Lagrangian approaches suffer from two severe limitations. Since the particle trajectories are constructed sequentially, the demanded computing resources increase linearly with the number of particles. Moreover, the need to gather particles at the center of computational cells to perform the mixing step and to estimate statistical parameters, as well as the interpolation of various terms to particle positions, inevitably produce numerical diffusion in either particle-mesh or grid-free particle methods. To overcome these limitations, we introduce a global random walk method to solve the system of Ito equations in physical and composition spaces, which models the evolution of the random concentration's PDF. The algorithm consists of a superposition on a regular lattice of many weak Euler schemes for the set of Ito equations. Since all particles starting from a site of the space-concentration lattice are spread in a single numerical procedure, one obtains PDF estimates at the lattice sites at computational costs comparable with those for solving the system of Ito equations associated to a single particle. The new method avoids the limitations concerning the number of particles in Lagrangian approaches, completely removes the numerical diffusion, and speeds up the computation by orders of magnitude. The approach is illustrated for the transport of passive scalars in heterogeneous aquifers, with hydraulic conductivity modeled as a random field.

Polymer diffusion in quenched disorder: A renormalization group approach

NASA Astrophysics Data System (ADS)

Ebert, Ute

1996-01-01

We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second moment v and the excluded-volume interaction u of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion in u and v are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interaction w≔u-v≥0 and for small effective disorder couplingbar v(l) on the intermediate length scale l. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as[Figure not available: see fulltext.] forbar v(l) ≪ 1.

Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

PubMed

Hössjer, Ola; Tyvand, Peder A; Miloh, Touvia

2016-02-01

The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates. Copyright © 2015 Elsevier Inc. All rights reserved.

Rumor Diffusion in an Interests-Based Dynamic Social Network

PubMed Central

Mao, Xinjun; Guessoum, Zahia; Zhou, Huiping

2013-01-01

To research rumor diffusion in social friend network, based on interests, a dynamic friend network is proposed, which has the characteristics of clustering and community, and a diffusion model is also proposed. With this friend network and rumor diffusion model, based on the zombie-city model, some simulation experiments to analyze the characteristics of rumor diffusion in social friend networks have been conducted. The results show some interesting observations: (1) positive information may evolve to become a rumor through the diffusion process that people may modify the information by word of mouth; (2) with the same average degree, a random social network has a smaller clustering coefficient and is more beneficial for rumor diffusion than the dynamic friend network; (3) a rumor is spread more widely in a social network with a smaller global clustering coefficient than in a social network with a larger global clustering coefficient; and (4) a network with a smaller clustering coefficient has a larger efficiency. PMID:24453911

Rumor diffusion in an interests-based dynamic social network.

PubMed

Tang, Mingsheng; Mao, Xinjun; Guessoum, Zahia; Zhou, Huiping

2013-01-01

To research rumor diffusion in social friend network, based on interests, a dynamic friend network is proposed, which has the characteristics of clustering and community, and a diffusion model is also proposed. With this friend network and rumor diffusion model, based on the zombie-city model, some simulation experiments to analyze the characteristics of rumor diffusion in social friend networks have been conducted. The results show some interesting observations: (1) positive information may evolve to become a rumor through the diffusion process that people may modify the information by word of mouth; (2) with the same average degree, a random social network has a smaller clustering coefficient and is more beneficial for rumor diffusion than the dynamic friend network; (3) a rumor is spread more widely in a social network with a smaller global clustering coefficient than in a social network with a larger global clustering coefficient; and (4) a network with a smaller clustering coefficient has a larger efficiency.

Angular intensity and polarization dependence of diffuse transmission through random media

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

Eliyahu, D.; Rosenbluh, M.; Feund, I.

1993-03-01

A simple theoretical model involving only a single sample parameter, the depolarization ratio [rho] for linearly polarized normally incident and normally scattered light, is developed to describe the angular intensity and all other polarization-dependent properties of diffuse transmission through multiple-scattering media. Initial experimental results that tend to support the theory are presented. Results for diffuse reflection are also described. 63 refs., 15 figs.

A diffusion approximation for ocean wave scatterings by randomly distributed ice floes

NASA Astrophysics Data System (ADS)

Zhao, Xin; Shen, Hayley

2016-11-01

This study presents a continuum approach using a diffusion approximation method to solve the scattering of ocean waves by randomly distributed ice floes. In order to model both strong and weak scattering, the proposed method decomposes the wave action density function into two parts: the transmitted part and the scattered part. For a given wave direction, the transmitted part of the wave action density is defined as the part of wave action density in the same direction before the scattering; and the scattered part is a first order Fourier series approximation for the directional spreading caused by scattering. An additional approximation is also adopted for simplification, in which the net directional redistribution of wave action by a single scatterer is assumed to be the reflected wave action of a normally incident wave into a semi-infinite ice cover. Other required input includes the mean shear modulus, diameter and thickness of ice floes, and the ice concentration. The directional spreading of wave energy from the diffusion approximation is found to be in reasonable agreement with the previous solution using the Boltzmann equation. The diffusion model provides an alternative method to implement wave scattering into an operational wave model.

Modelling wildland fire propagation by tracking random fronts

NASA Astrophysics Data System (ADS)

Pagnini, G.; Mentrelli, A.

2013-11-01

Wildland fire propagation is studied in literature by two alternative approaches, namely the reaction-diffusion equation and the level-set method. These two approaches are considered alternative each other because the solution of the reaction-diffusion equation is generally a continuous smooth function that has an exponential decay and an infinite support, while the level-set method, which is a front tracking technique, generates a sharp function with a finite support. However, these two approaches can indeed be considered complementary and reconciled. Turbulent hot-air transport and fire spotting are phenomena with a random character that are extremely important in wildland fire propagation. As a consequence the fire front gets a random character, too. Hence a tracking method for random fronts is needed. In particular, the level-set contourn is here randomized accordingly to the probability density function of the interface particle displacement. Actually, when the level-set method is developed for tracking a front interface with a random motion, the resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterizing role proper to the level-set approach. The resulting model emerges to be suitable to simulate effects due to turbulent convection as fire flank and backing fire, the faster fire spread because of the actions by hot air pre-heating and by ember landing, and also the fire overcoming a firebreak zone that is a case not resolved by models based on the level-set method. Moreover, from the proposed formulation it follows a correction for the rate of spread formula due to the mean jump-length of firebrands in the downwind direction for the leeward sector of the fireline contour.

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

Long-range correlations in time series generated by time-fractional diffusion: A numerical study

NASA Astrophysics Data System (ADS)

Barbieri, Davide; Vivoli, Alessandro

2005-09-01

Time series models showing power law tails in autocorrelation functions are common in econometrics. A special non-Markovian model for such kind of time series is provided by the random walk introduced by Gorenflo et al. as a discretization of time fractional diffusion. The time series so obtained are analyzed here from a numerical point of view in terms of autocorrelations and covariance matrices.

A Mass Diffusion Model for Dry Snow Utilizing a Fabric Tensor to Characterize Anisotropy

NASA Astrophysics Data System (ADS)

Shertzer, Richard H.; Adams, Edward E.

2018-03-01

A homogenization algorithm for randomly distributed microstructures is applied to develop a mass diffusion model for dry snow. Homogenization is a multiscale approach linking constituent behavior at the microscopic level—among ice and air—to the macroscopic material—snow. Principles of continuum mechanics at the microscopic scale describe water vapor diffusion across an ice grain's surface to the air-filled pore space. Volume averaging and a localization assumption scale up and down, respectively, between microscopic and macroscopic scales. The model yields a mass diffusivity expression at the macroscopic scale that is, in general, a second-order tensor parameterized by both bulk and microstructural variables. The model predicts a mass diffusivity of water vapor through snow that is less than that through air. Mass diffusivity is expected to decrease linearly with ice volume fraction. Potential anisotropy in snow's mass diffusivity is captured due to the tensor representation. The tensor is built from directional data assigned to specific, idealized microstructural features. Such anisotropy has been observed in the field and laboratories in snow morphologies of interest such as weak layers of depth hoar and near-surface facets.

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

High-fidelity meshes from tissue samples for diffusion MRI simulations.

PubMed

Panagiotaki, Eleftheria; Hall, Matt G; Zhang, Hui; Siow, Bernard; Lythgoe, Mark F; Alexander, Daniel C

2010-01-01

This paper presents a method for constructing detailed geometric models of tissue microstructure for synthesizing realistic diffusion MRI data. We construct three-dimensional mesh models from confocal microscopy image stacks using the marching cubes algorithm. Random-walk simulations within the resulting meshes provide synthetic diffusion MRI measurements. Experiments optimise simulation parameters and complexity of the meshes to achieve accuracy and reproducibility while minimizing computation time. Finally we assess the quality of the synthesized data from the mesh models by comparison with scanner data as well as synthetic data from simple geometric models and simplified meshes that vary only in two dimensions. The results support the extra complexity of the three-dimensional mesh compared to simpler models although sensitivity to the mesh resolution is quite robust.

Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

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

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

2016-07-15

We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficientsmore » and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.« less

Simulation of diffuse-charge capacitance in electric double layer capacitors

NASA Astrophysics Data System (ADS)

Sun, Ning; Gersappe, Dilip

2017-01-01

We use a Lattice Boltzmann Model (LBM) in order to simulate diffuse-charge dynamics in Electric Double Layer Capacitors (EDLCs). Simulations are carried out for both the charge and the discharge processes on 2D systems of complex random electrode geometries (pure random, random spheres and random fibers). The steric effect of concentrated solutions is considered by using a Modified Poisson-Nernst-Planck (MPNP) equations and compared with regular Poisson-Nernst-Planck (PNP) systems. The effects of electrode microstructures (electrode density, electrode filler morphology, filler size, etc.) on the net charge distribution and charge/discharge time are studied in detail. The influence of applied potential during discharging process is also discussed. Our studies show how electrode morphology can be used to tailor the properties of supercapacitors.

Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor

NASA Astrophysics Data System (ADS)

Miyaguchi, Tomoshige

2017-10-01

There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here a method is developed to elucidate this fluctuating diffusivity from trajectory data. Time-averaged mean-square displacement (MSD), a common tool in single-particle-tracking (SPT) experiments, is generalized to a second-order tensor with which both magnitude and orientation fluctuations of the diffusivity can be clearly detected. This method is used to analyze the center-of-mass motion of four fundamental polymer models: the Rouse model, the Zimm model, a reptation model, and a rigid rodlike polymer. It is found that these models exhibit distinctly different types of magnitude and orientation fluctuations of diffusivity. This is an advantage of the present method over previous ones, such as the ergodicity-breaking parameter and a non-Gaussian parameter, because with either of these parameters it is difficult to distinguish the dynamics of the four polymer models. Also, the present method of a time-averaged MSD tensor could be used to analyze trajectory data obtained in SPT experiments.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

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

A new fundamental model of moving particle for reinterpreting Schroedinger equation

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

Umar, Muhamad Darwis

2012-06-20

The study of Schroedinger equation based on a hypothesis that every particle must move randomly in a quantum-sized volume has been done. In addition to random motion, every particle can do relative motion through the movement of its quantum-sized volume. On the other way these motions can coincide. In this proposed model, the random motion is one kind of intrinsic properties of the particle. The every change of both speed of randomly intrinsic motion and or the velocity of translational motion of a quantum-sized volume will represent a transition between two states, and the change of speed of randomly intrinsicmore » motion will generate diffusion process or Brownian motion perspectives. Diffusion process can take place in backward and forward processes and will represent a dissipative system. To derive Schroedinger equation from our hypothesis we use time operator introduced by Nelson. From a fundamental analysis, we find out that, naturally, we should view the means of Newton's Law F(vector sign) = ma(vector sign) as no an external force, but it is just to describe both the presence of intrinsic random motion and the change of the particle energy.« less

Lagrangian particles with mixing. I. Simulating scalar transport

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2009-06-01

The physical similarity and mathematical equivalence of continuous diffusion and particle random walk forms one of the cornerstones of modern physics and the theory of stochastic processes. The randomly walking particles do not need to posses any properties other than location in physical space. However, particles used in many models dealing with simulating turbulent transport and turbulent combustion do posses a set of scalar properties and mixing between particle properties is performed to reflect the dissipative nature of the diffusion processes. We show that the continuous scalar transport and diffusion can be accurately specified by means of localized mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. Particles with scalar properties and localized mixing represent an alternative formulation for the process, which is selected to represent the continuous diffusion. Simulating diffusion by Lagrangian particles with mixing involves three main competing requirements: minimizing stochastic uncertainty, minimizing bias introduced by numerical diffusion, and preserving independence of particles. These requirements are analyzed for two limited cases of mixing between two particles and mixing between a large number of particles. The problem of possible dependences between particles is most complicated. This problem is analyzed using a coupled chain of equations that has similarities with Bogolubov-Born-Green-Kirkwood-Yvon chain in statistical physics. Dependences between particles can be significant in close proximity of the particles resulting in a reduced rate of mixing. This work develops further ideas introduced in the previously published letter [Phys. Fluids 19, 031702 (2007)]. Paper I of this work is followed by Paper II [Phys. Fluids 19, 065102 (2009)] where modeling of turbulent reacting flows by Lagrangian particles with localized mixing is specifically considered.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Normal and tumoral melanocytes exhibit q-Gaussian random search patterns.

PubMed

da Silva, Priscila C A; Rosembach, Tiago V; Santos, Anésia A; Rocha, Márcio S; Martins, Marcelo L

2014-01-01

In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, failures in its regulation potentiates numerous diseases. Here, cell migration assays on plastic 2D surfaces were performed using normal (Melan A) and tumoral (B16F10) murine melanocytes in random motility conditions. The trajectories of the centroids of the cell perimeters were tracked through time-lapse microscopy. The statistics of these trajectories was analyzed by building velocity and turn angle distributions, as well as velocity autocorrelations and the scaling of mean-squared displacements. We find that these cells exhibit a crossover from a normal to a super-diffusive motion without angular persistence at long time scales. Moreover, these melanocytes move with non-Gaussian velocity distributions. This major finding indicates that amongst those animal cells supposedly migrating through Lévy walks, some of them can instead perform q-Gaussian walks. Furthermore, our results reveal that B16F10 cells infected by mycoplasmas exhibit essentially the same diffusivity than their healthy counterparts. Finally, a q-Gaussian random walk model was proposed to account for these melanocytic migratory traits. Simulations based on this model correctly describe the crossover to super-diffusivity in the cell migration tracks.

Modeling the migration of platinum nanoparticles on surfaces using a kinetic Monte Carlo approach

DOE PAGES

Li, Lin; Plessow, Philipp N.; Rieger, Michael; ...

2017-02-15

We propose a kinetic Monte Carlo (kMC) model for simulating the movement of platinum particles on supports, based on atom-by-atom diffusion on the surface of the particle. The proposed model was able to reproduce equilibrium cluster shapes predicted using Wulff-construction. The diffusivity of platinum particles was simulated both purely based on random motion and assisted using an external field that causes a drift velocity. The overall particle diffusivity increases with temperature; however, the extracted activation barrier appears to be temperature independent. Additionally, this barrier was found to increase with particle size, as well as, with the adhesion between the particlemore » and the support.« less

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

PubMed

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

2008-08-14

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

Simulation of xenon, uranium vacancy and interstitial diffusion and grain boundary segregation in UO 2

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

Andersson, Anders D.; Tonks, Michael R.; Casillas, Luis

2014-10-31

In light water reactor fuel, gaseous fission products segregate to grain boundaries, resulting in the nucleation and growth of large intergranular fission gas bubbles. Based on the mechanisms established from density functional theory (DFT) and empirical potential calculations 1, continuum models for diffusion of xenon (Xe), uranium (U) vacancies and U interstitials in UO 2 have been derived for both intrinsic conditions and under irradiation. Segregation of Xe to grain boundaries is described by combining the bulk diffusion model with a model for the interaction between Xe atoms and three different grain boundaries in UO 2 ( Σ5 tilt, Σ5more » twist and a high angle random boundary),as derived from atomistic calculations. All models are implemented in the MARMOT phase field code, which is used to calculate effective Xe and U diffusivities as well as redistribution for a few simple microstructures.« less

A mathematical model of single target site location by Brownian movement in subcellular compartments.

PubMed

Kuthan, Hartmut

2003-03-07

The location of distinct sites is mandatory for many cellular processes. In the subcompartments of the cell nucleus, only very small numbers of diffusing macromolecules and specific target sites of some types may be present. In this case, we are faced with the Brownian movement of individual macromolecules and their "random search" for single/few specific target sites, rather than bulk-averaged diffusion and multiple sites. In this article, I consider the location of a distant central target site, e.g. a globular protein, by individual macromolecules executing unbiased (i.e. drift-free) random walks in a spherical compartment. For this walk-and-capture model, the closed-form analytic solution of the first passage time probability density function (p.d.f.) has been obtained as well as the first and second moment. In the limit of a large ratio of the radii of the spherical diffusion space and central target, well-known relations for the variance and the first two moments for the exponential p.d.f. were found to hold with high accuracy. These calculations reinforce earlier numerical results and Monte Carlo simulations. A major implication derivable from the model is that non-directed random movement is an effective means for locating single sites in submicron-sized compartments, even when the diffusion coefficients are comparatively small and the diffusing species are present in one copy only. These theoretical conclusions are underscored numerically for effective diffusion constants ranging from 0.5 to 10.0 microm(2) s(-1), which have been reported for a couple of nuclear proteins in their physiological environment. Spherical compartments of submicron size are, for example, the Cajal bodies (size: 0.1-1.0 microm), which are present in 1-5 copies in the cell nucleus. Within a small Cajal body of radius 0.1 microm a single diffusing protein molecule (with D=0.5 microm(2) s(-1)) would encounter a medium-sized protein of radius 2.5 nm within 1 s with a probability near certainty (p=0.98).

Analysis of the Yule-Nielsen effect with the multiple-path point spread function in a frequency-modulated halftone.

PubMed

Rogers, Geoffrey

2018-06-01

The Yule-Nielsen effect is an influence on halftone color caused by the diffusion of light within the paper upon which the halftone ink is printed. The diffusion can be characterized by a point spread function. In this paper, a point spread function for paper is derived using the multiple-path model of reflection. This model treats the interaction of light with turbid media as a random walk. Using the multiple-path point spread function, a general expression is derived for the average reflectance of light from a frequency-modulated halftone, in which dot size is constant and the number of dots is varied, with the arrangement of dots random. It is also shown that the line spread function derived from the multiple-path model has the form of a Lorentzian function.

Sustained currents in coupled diffusive systems

NASA Astrophysics Data System (ADS)

Larralde, Hernán; Sanders, David P.

2014-08-01

Coupling two diffusive systems may give rise to a nonequilibrium stationary state (NESS) with a non-trivial persistent, circulating current. We study a simple example that is exactly soluble, consisting of random walkers with different biases towards a reflecting boundary, modelling, for example, Brownian particles with different charge states in an electric field. We obtain analytical expressions for the concentrations and currents in the NESS for this model, and exhibit the main features of the system by numerical simulation.

Superdiffusive Dispersals Impart the Geometry of Underlying Random Walks

NASA Astrophysics Data System (ADS)

Zaburdaev, V.; Fouxon, I.; Denisov, S.; Barkai, E.

2016-12-01

It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

Turing patterns and a stochastic individual-based model for predator-prey systems

NASA Astrophysics Data System (ADS)

Nagano, Seido

2012-02-01

Reaction-diffusion theory has played a very important role in the study of pattern formations in biology. However, a group of individuals is described by a single state variable representing population density in reaction-diffusion models and interaction between individuals can be included only phenomenologically. Recently, we have seamlessly combined individual-based models with elements of reaction-diffusion theory. To include animal migration in the scheme, we have adopted a relationship between the diffusion and the random numbers generated according to a two-dimensional bivariate normal distribution. Thus, we have observed the transition of population patterns from an extinction mode, a stable mode, or an oscillatory mode to the chaotic mode as the population growth rate increases. We show our phase diagram of predator-prey systems and discuss the microscopic mechanism for the stable lattice formation in detail.

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.

Hydrogen diffusion in liquid aluminum from ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Jakse, N.; Pasturel, A.

2014-05-01

Ab initio molecular dynamics simulations are used to describe the diffusion of hydrogen in liquid aluminum at different temperatures. Quasi-instantaneous jumps separating periods of localized vibrations around a mean position are found to characterize the hydrogen motion at the microscopic scale. The hydrogen motion is furthermore analyzed using the van Hove function. We highlight a non-Fickian behavior for the hydrogen diffusion due to a large spatial distribution of hydrogen jumps. We show that a generalized continuous time random walk (CTRW) model describes the experimental diffusion coefficients in a satisfactory manner. Finally, the impact of impurities and alloying elements on hydrogen diffusion in aluminum is discussed.

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.

Establishment of a Physical Model for Solute Diffusion in Hydrogel: Understanding the Diffusion of Proteins in Poly(sulfobetaine methacrylate) Hydrogel.

PubMed

Zhou, Yuhang; Li, Junjie; Zhang, Ying; Dong, Dianyu; Zhang, Ershuai; Ji, Feng; Qin, Zhihui; Yang, Jun; Yao, Fanglian

2017-02-02

Prediction of the diffusion coefficient of solute, especially bioactive molecules, in hydrogel is significant in the biomedical field. Considering the randomness of solute movement in a hydrogel network, a physical diffusion RMP-1 model based on obstruction theory was established in this study. The physical properties of the solute and the polymer chain and their interactions were introduced into this model. Furthermore, models RMP-2 and RMP-3 were established to understand and predict the diffusion behaviors of proteins in hydrogel. In addition, zwitterionic poly(sulfobetaine methacrylate) (PSBMA) hydrogels with wide range and fine adjustable mesh sizes were prepared and used as efficient experimental platforms for model validation. The Flory characteristic ratios, Flory-Huggins parameter, mesh size, and polymer chain radii of PSBMA hydrogels were determined. The diffusion coefficients of the proteins (bovine serum albumin, immunoglobulin G, and lysozyme) in PSBMA hydrogels were studied by the fluorescence recovery after photobleaching technique. The measured diffusion coefficients were compared with the predictions of obstruction models, and it was found that our model presented an excellent predictive ability. Furthermore, the assessment of our model revealed that protein diffusion in PSBMA hydrogel would be affected by the physical properties of the protein and the PSBMA network. It was also confirmed that the diffusion behaviors of protein in zwitterionic hydrogels can be adjusted by changing the cross-linking density of the hydrogel and the ionic strength of the swelling medium. Our model is expected to possess accurate predictive ability for the diffusion coefficient of solute in hydrogel, which will be widely used in the biomedical field.

Multiscale simulation of xenon diffusion and grain boundary segregation in UO₂

DOE PAGES

Andersson, David A.; Tonks, Michael R.; Casillas, Luis; ...

2015-07-01

In light water reactor fuel, gaseous fission products segregate to grain boundaries, resulting in the nucleation and growth of large intergranular fission gas bubbles. The segregation rate is controlled by diffusion of fission gas atoms through the grains and interaction with the boundaries. Based on the mechanisms established from earlier density functional theory (DFT) and empirical potential calculations, diffusion models for xenon (Xe), uranium (U) vacancies and U interstitials in UO₂ have been derived for both intrinsic (no irradiation) and irradiation conditions. Segregation of Xe to grain boundaries is described by combining the bulk diffusion model with a model formore » the interaction between Xe atoms and three different grain boundaries in UO₂ (Σ5 tilt, Σ5 twist and a high angle random boundary), as derived from atomistic calculations. The present model does not attempt to capture nucleation or growth of fission gas bubbles at the grain boundaries. The point defect and Xe diffusion and segregation models are implemented in the MARMOT phase field code, which is used to calculate effective Xe and U diffusivities as well as to simulate Xe redistribution for a few simple microstructures.« less

Random walks on cubic lattices with bond disorder

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

Ernst, M.H.; van Velthoven, P.F.J.

1986-12-01

The authors consider diffusive systems with static disorder, such as Lorentz gases, lattice percolation, ants in a labyrinth, termite problems, random resistor networks, etc. In the case of diluted randomness the authors can apply the methods of kinetic theory to obtain systematic expansions of dc and ac transport properties in powers of the impurity concentration c. The method is applied to a hopping model on a d-dimensional cubic lattice having two types of bonds with conductivity sigma and sigma/sub 0/ = 1, with concentrations c and 1-c, respectively. For the square lattice the authors explicitly calculate the diffusion coefficient D(c,sigma)more » as a function of c, to O(c/sup 2/) terms included for different ratios of the bond conductivity sigma. The probability of return at long times is given by P/sub 0/(t) approx. (4..pi..D(c,sigma)t)/sup -d/2/, which is determined by the diffusion coefficient of the disordered system.« less

Modeling of batch sorber system: kinetic, mechanistic, and thermodynamic modeling

NASA Astrophysics Data System (ADS)

Mishra, Vishal

2017-10-01

The present investigation has dealt with the biosorption of copper and zinc ions on the surface of egg-shell particles in the liquid phase. Various rate models were evaluated to elucidate the kinetics of copper and zinc biosorptions, and the results indicated that the pseudo-second-order model was more appropriate than the pseudo-first-order model. The curve of the initial sorption rate versus the initial concentration of copper and zinc ions also complemented the results of the pseudo-second-order model. Models used for the mechanistic modeling were the intra-particle model of pore diffusion and Bangham's model of film diffusion. The results of the mechanistic modeling together with the values of pore and film diffusivities indicated that the preferential mode of the biosorption of copper and zinc ions on the surface of egg-shell particles in the liquid phase was film diffusion. The results of the intra-particle model showed that the biosorption of the copper and zinc ions was not dominated by the pore diffusion, which was due to macro-pores with open-void spaces present on the surface of egg-shell particles. The thermodynamic modeling reproduced the fact that the sorption of copper and zinc was spontaneous, exothermic with the increased order of the randomness at the solid-liquid interface.

Random walk on a leash: a simple single-molecule diffusion model for surface-tethered redox molecules with flexible linkers.

PubMed

Huang, Kuan-Chun; White, Ryan J

2013-08-28

We develop a random walk model to simulate the Brownian motion and the electrochemical response of a single molecule confined to an electrode surface via a flexible molecular tether. We use our simple model, which requires no prior knowledge of the physics of the molecular tether, to predict and better understand the voltammetric response of surface-confined redox molecules when motion of the redox molecule becomes important. The single molecule is confined to a hemispherical volume with a maximum radius determined by the flexible molecular tether (5-20 nm) and is allowed to undergo true three-dimensional diffusion. Distance- and potential-dependent electron transfer probabilities are evaluated throughout the simulations to generate cyclic voltammograms of the model system. We find that at sufficiently slow cyclic voltammetric scan rates the electrochemical reaction behaves like an adsorbed redox molecule with no mass transfer limitation; thus, the peak current is proportional to the scan rate. Conversely, at faster scan rates the diffusional motion of the molecule limits the simulated peak current, which exhibits a linear dependence on the square root of the scan rate. The switch between these two limiting regimes occurs when the diffusion layer thickness, (2Dt)(1/2), is ~10 times the tether length. Finally, we find that our model predicts the voltammetric behavior of a redox-active methylene blue tethered to an electrode surface via short flexible single-stranded, polythymine DNAs, allowing the estimation of diffusion coefficients for the end-tethered molecule.

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.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

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

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

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

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

PubMed

Fouxon, Itzhak; Holzner, Markus

2016-08-01

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

Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium

NASA Astrophysics Data System (ADS)

Wang, Ken Kang-Hsin; Ye, Zhen

2003-10-01

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan et al. [J. Opt. Soc. Am. B 10, 391 (1993)]. A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of, and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with traveling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases where the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems [Asatryan et al., Phys. Rev. E 67, 036605 (2003)].

Nonparametric estimates of drift and diffusion profiles via Fokker-Planck algebra.

PubMed

Lund, Steven P; Hubbard, Joseph B; Halter, Michael

2014-11-06

Diffusion processes superimposed upon deterministic motion play a key role in understanding and controlling the transport of matter, energy, momentum, and even information in physics, chemistry, material science, biology, and communications technology. Given functions defining these random and deterministic components, the Fokker-Planck (FP) equation is often used to model these diffusive systems. Many methods exist for estimating the drift and diffusion profiles from one or more identifiable diffusive trajectories; however, when many identical entities diffuse simultaneously, it may not be possible to identify individual trajectories. Here we present a method capable of simultaneously providing nonparametric estimates for both drift and diffusion profiles from evolving density profiles, requiring only the validity of Langevin/FP dynamics. This algebraic FP manipulation provides a flexible and robust framework for estimating stationary drift and diffusion coefficient profiles, is not based on fluctuation theory or solved diffusion equations, and may facilitate predictions for many experimental systems. We illustrate this approach on experimental data obtained from a model lipid bilayer system exhibiting free diffusion and electric field induced drift. The wide range over which this approach provides accurate estimates for drift and diffusion profiles is demonstrated through simulation.

The non-random walk of stock prices: the long-term correlation between signs and sizes

NASA Astrophysics Data System (ADS)

La Spada, G.; Farmer, J. D.; Lillo, F.

2008-08-01

We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.

Open quantum random walks: Bistability on pure states and ballistically induced diffusion

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2013-12-01

Open quantum random walks (OQRWs) deal with quantum random motions on a line for systems with internal and orbital degrees of freedom. The internal system behaves as a quantum random gyroscope coding for the direction of the orbital moves. We reveal the existence of a transition, depending on OQRW moduli, in the internal system behaviors from simple oscillations to random flips between two unstable pure states. This induces a transition in the orbital motions from the usual diffusion to ballistically induced diffusion with a large mean free path and large effective diffusion constant at large times. We also show that mixed states of the internal system are converted into random pure states during the process. We touch upon possible experimental realizations.

Nonholonomic diffusion of a stochastic sled

NASA Astrophysics Data System (ADS)

Jung, Peter; Marchegiani, Giampiero; Marchesoni, Fabio

2016-01-01

A sled is a stylized mechanical model of a system which is constrained to move in space in a specific orientation, i.e., in the direction of the runners of the sled or a blade. The negation of motion transverse to the runners renders the sled a nonholonomic mechanical system. In this paper we report on the unexpected and fascinating richness of the dynamics of such a sled if it is subject to random forces. Specifically we show that the ensuing random dynamics is characterized by relatively smooth sections of motion interspersed by episodes of persistent tumbling (change of orientation) and sharp reversals resembling the random walks of bacterial cells. In the presence of self-propulsion, the diffusivity of the sled can be enhanced and suppressed depending on the directionality and strength of the propulsive force.

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.

Distributional behavior of diffusion coefficients obtained by single trajectories in annealed transit time model

NASA Astrophysics Data System (ADS)

Akimoto, Takuma; Yamamoto, Eiji

2016-12-01

Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of single-particle-tracking measurements. Irreproducibility of time-averaged observables has been theoretically studied in the context of weak ergodicity breaking in stochastic processes. Here, we provide rigorous descriptions of equilibrium and non-equilibrium diffusion processes for the annealed transit time model, which is a heterogeneous diffusion model in living cells. We give analytical solutions for the mean square displacement (MSD) and the relative standard deviation of the time-averaged MSD for equilibrium and non-equilibrium situations. We find that the time-averaged MSD grows linearly with time and that the time-averaged diffusion coefficients are intrinsically random (irreproducible) even in the long-time measurements in non-equilibrium situations. Furthermore, the distribution of the time-averaged diffusion coefficients converges to a universal distribution in the sense that it does not depend on initial conditions. Our findings pave the way for a theoretical understanding of distributional behavior of the time-averaged diffusion coefficients in disordered systems.

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

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

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

2016-05-07

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

Observations of diffusion-limited aggregation-like patterns by atmospheric plasma jet

NASA Astrophysics Data System (ADS)

Chiu, Ching-Yang; Chu, Hong-Yu

2017-11-01

We report on the observations of diffusion-limited aggregation-like patterns during the thin film removal process by an atmospheric plasma jet. The fractal patterns are found to have various structures like dense branching and tree-like patterns. The determination of surface morphology reveals that the footprints of discharge bursts are not as random as expected. We propose a diffusion-limited aggregation model with a few extra requirements by analogy with the experimental results, and thereby present the beauty of nature. We show that the model simulates not only the shapes of the patterns similar to the experimental observations, but also the growing sequences of fluctuating, oscillatory, and zigzag traces.

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

Bivariate Gaussian bridges: directional factorization of diffusion in Brownian bridge models.

PubMed

Kranstauber, Bart; Safi, Kamran; Bartumeus, Frederic

2014-01-01

In recent years high resolution animal tracking data has become the standard in movement ecology. The Brownian Bridge Movement Model (BBMM) is a widely adopted approach to describe animal space use from such high resolution tracks. One of the underlying assumptions of the BBMM is isotropic diffusive motion between consecutive locations, i.e. invariant with respect to the direction. Here we propose to relax this often unrealistic assumption by separating the Brownian motion variance into two directional components, one parallel and one orthogonal to the direction of the motion. Our new model, the Bivariate Gaussian bridge (BGB), tracks movement heterogeneity across time. Using the BGB and identifying directed and non-directed movement within a trajectory resulted in more accurate utilisation distributions compared to dynamic Brownian bridges, especially for trajectories with a non-isotropic diffusion, such as directed movement or Lévy like movements. We evaluated our model with simulated trajectories and observed tracks, demonstrating that the improvement of our model scales with the directional correlation of a correlated random walk. We find that many of the animal trajectories do not adhere to the assumptions of the BBMM. The proposed model improves accuracy when describing the space use both in simulated correlated random walks as well as observed animal tracks. Our novel approach is implemented and available within the "move" package for R.

The Building Game: From Enumerative Combinatorics to Conformational Diffusion

NASA Astrophysics Data System (ADS)

Johnson-Chyzhykov, Daniel; Menon, Govind

2016-08-01

We study a discrete attachment model for the self-assembly of polyhedra called the building game. We investigate two distinct aspects of the model: (i) enumerative combinatorics of the intermediate states and (ii) a notion of Brownian motion for the polyhedral linkage defined by each intermediate that we term conformational diffusion. The combinatorial configuration space of the model is computed for the Platonic, Archimedean, and Catalan solids of up to 30 faces, and several novel enumerative results are generated. These represent the most exhaustive computations of this nature to date. We further extend the building game to include geometric information. The combinatorial structure of each intermediate yields a systems of constraints specifying a polyhedral linkage and its moduli space. We use a random walk to simulate a reflected Brownian motion in each moduli space. Empirical statistics of the random walk may be used to define the rates of transition for a Markov process modeling the process of self-assembly.

The Role of Cosmic-Ray Pressure in Accelerating Galactic Outflows

NASA Astrophysics Data System (ADS)

Simpson, Christine M.; Pakmor, Rüdiger; Marinacci, Federico; Pfrommer, Christoph; Springel, Volker; Glover, Simon C. O.; Clark, Paul C.; Smith, Rowan J.

2016-08-01

We study the formation of galactic outflows from supernova (SN) explosions with the moving-mesh code AREPO in a stratified column of gas with a surface density similar to the Milky Way disk at the solar circle. We compare different simulation models for SN placement and energy feedback, including cosmic rays (CRs), and find that models that place SNe in dense gas and account for CR diffusion are able to drive outflows with similar mass loading as obtained from a random placement of SNe with no CRs. Despite this similarity, CR-driven outflows differ in several other key properties including their overall clumpiness and velocity. Moreover, the forces driving these outflows originate in different sources of pressure, with the CR diffusion model relying on non-thermal pressure gradients to create an outflow driven by internal pressure and the random-placement model depending on kinetic pressure gradients to propel a ballistic outflow. CRs therefore appear to be non-negligible physics in the formation of outflows from the interstellar medium.

THE ROLE OF COSMIC-RAY PRESSURE IN ACCELERATING GALACTIC OUTFLOWS

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

Simpson, Christine M.; Pakmor, Rüdiger; Pfrommer, Christoph

We study the formation of galactic outflows from supernova (SN) explosions with the moving-mesh code AREPO in a stratified column of gas with a surface density similar to the Milky Way disk at the solar circle. We compare different simulation models for SN placement and energy feedback, including cosmic rays (CRs), and find that models that place SNe in dense gas and account for CR diffusion are able to drive outflows with similar mass loading as obtained from a random placement of SNe with no CRs. Despite this similarity, CR-driven outflows differ in several other key properties including their overallmore » clumpiness and velocity. Moreover, the forces driving these outflows originate in different sources of pressure, with the CR diffusion model relying on non-thermal pressure gradients to create an outflow driven by internal pressure and the random-placement model depending on kinetic pressure gradients to propel a ballistic outflow. CRs therefore appear to be non-negligible physics in the formation of outflows from the interstellar medium.« less

Mixed-order phase transition in a minimal, diffusion-based spin model.

PubMed

Fronczak, Agata; Fronczak, Piotr

2016-07-01

In this paper we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model diffusion based because its Hamiltonian can be recovered from a simple dynamic procedure, which can be seen as an equilibrium statistical mechanics representation of a biased random walk. We outline the derivation of the phase diagram of the model, in which the triple point has the hallmarks of the hybrid transition: discontinuity in the average magnetization and algebraically diverging susceptibilities. At this point, two second-order transition curves meet in equilibrium with the first-order curve, resulting in a prototypical mixed-order behavior.

Birth-jump processes and application to forest fire spotting.

PubMed

Hillen, T; Greese, B; Martin, J; de Vries, G

2015-01-01

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.

Accelerated tumor invasion under non-isotropic cell dispersal in glioblastomas

NASA Astrophysics Data System (ADS)

Fort, Joaquim; Solé, Ricard V.

2013-05-01

Glioblastomas are highly diffuse, malignant tumors that have so far evaded clinical treatment. The strongly invasive behavior of cells in these tumors makes them very resistant to treatment, and for this reason both experimental and theoretical efforts have been directed toward understanding the spatiotemporal pattern of tumor spreading. Although usual models assume a standard diffusion behavior, recent experiments with cell cultures indicate that cells tend to move in directions close to that of glioblastoma invasion, thus indicating that a biased random walk model may be much more appropriate. Here we show analytically that, for realistic parameter values, the speeds predicted by biased dispersal are consistent with experimentally measured data. We also find that models beyond reaction-diffusion-advection equations are necessary to capture this substantial effect of biased dispersal on glioblastoma spread.

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.

Molecular Dynamics Simulations of Grain Boundary and Bulk Diffusion in Metals.

NASA Astrophysics Data System (ADS)

Plimpton, Steven James

Diffusion is a microscopic mass transport mechanism that underlies many important macroscopic phenomena affecting the structural, electrical, and mechanical properties of metals. This thesis presents results from atomistic simulation studies of diffusion both in bulk and in the fast diffusion paths known as grain boundaries. Using the principles of molecular dynamics single boundaries are studied and their structure and dynamic properties characterized. In particular, tilt boundary bicrystal and bulk models of fcc Al and bcc alpha-Fe are simulated. Diffusion coefficients and activation energies for atomic motion are calculated for both models and compared to experimental data. The influence of the interatomic pair potential on the diffusion is studied in detail. A universal relation between the melting temperature that a pair potential induces in a simulated bulk model and the potential energy barrier height for atomic hopping is derived and used to correlate results for a wide variety of pair potentials. Using these techniques grain boundary and bulk diffusion coefficients for any fcc material can be estimated from simple static calculations without the need to perform more time-consuming dynamic simulations. The influences of two other factors on grain boundary diffusion are also studied because of the interest of the microelectronics industry in the diffusion related reliability problem known as electromigration. The first factor, known to affect the self diffusion rate of Al, is the presence of Cu impurity atoms in Al tilt boundaries. The bicrystal model for Al is seeded randomly with Cu atoms and a simple hybrid Morse potential used to model the Al-Cu interaction. While some effect due to the Cu is noted, it is concluded that pair potentials are likely an inadequate approximation for the alloy system. The second factor studied is the effect of the boundary orientation angle on the diffusion rate. Symmetric bcc Fe boundaries are relaxed to find optimal structures and their diffusion coefficients calculated. Good agreement is found with the dislocation pipe model for tilt boundary diffusion.

Generalized run-and-turn motions: From bacteria to Lévy walks

NASA Astrophysics Data System (ADS)

Detcheverry, François

2017-07-01

Swimming bacteria exhibit a repertoire of motility patterns, in which persistent motion is interrupted by turning events. What are the statistical properties of such random walks? If some particular instances have long been studied, the general case where turning times do not follow a Poisson process has remained unsolved. We present a generic extension of the continuous time random walks formalism relying on operators and noncommutative calculus. The approach is first applied to a unimodal model of bacterial motion. We examine the existence of a minimum in velocity correlation function and discuss the maximum of diffusivity at an optimal value of rotational diffusion. The model is then extended to bimodal patterns and includes as particular cases all swimming strategies: run-and-tumble, run-stop, run-reverse and run-reverse-flick. We characterize their velocity correlation functions and investigate how bimodality affects diffusivity. Finally, the wider applicability of the method is illustrated by considering curved trajectories and Lévy walks. Our results are relevant for intermittent motion of living beings, be they swimming micro-organisms or crawling cells.

Persistent random walk of cells involving anomalous effects and random death

NASA Astrophysics Data System (ADS)

Fedotov, Sergei; Tan, Abby; Zubarev, Andrey

2015-04-01

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

Three-Dimensional Modeling of the Brain's ECS by Minimum Configurational Energy Packing of Fluid Vesicles

PubMed Central

Nandigam, Ravi K.; Kroll, Daniel M.

2007-01-01

The extracellular space of the brain is the heterogeneous porous medium formed by the spaces between the brain cells. Diffusion in this interstitial space is the mechanism by which glucose and oxygen are delivered to the brain cells from the vascular system. It is also a medium for the transport of certain informational substances between the cells (called volume transmission), and for drug delivery. This work involves three-dimensional modeling of the extracellular space as void space in close-packed arrays of fluid membrane vesicles. These packings are generated by minimizing the configurational energy using a Monte Carlo procedure. Both regular and random packs of vesicles are considered. A random walk algorithm is then used to compute the geometric tortuosities, and the results are compared with published experimental data. For the random packings, it is found that although the absolute values for the tortuosities differ, the dependence of the tortuosity on pore volume fraction is very similar to that observed in experiment. The tortuosities we measure are larger than those computed in previous studies of packings of convex polytopes, and modeling improvements, which require higher resolution studies and an improved modeling of brain cell shapes and mechanical properties, could help resolve remaining discrepancies between model simulations and experiment. It is also shown that the specular reflection scheme is the appropriate technique for implementing zero-flux boundary conditions in random walk simulations commonly encountered in diffusion problems. PMID:17307830

Three-dimensional modeling of the brain's ECS by minimum configurational energy packing of fluid vesicles.

PubMed

Nandigam, Ravi K; Kroll, Daniel M

2007-05-15

The extracellular space of the brain is the heterogeneous porous medium formed by the spaces between the brain cells. Diffusion in this interstitial space is the mechanism by which glucose and oxygen are delivered to the brain cells from the vascular system. It is also a medium for the transport of certain informational substances between the cells (called volume transmission), and for drug delivery. This work involves three-dimensional modeling of the extracellular space as void space in close-packed arrays of fluid membrane vesicles. These packings are generated by minimizing the configurational energy using a Monte Carlo procedure. Both regular and random packs of vesicles are considered. A random walk algorithm is then used to compute the geometric tortuosities, and the results are compared with published experimental data. For the random packings, it is found that although the absolute values for the tortuosities differ, the dependence of the tortuosity on pore volume fraction is very similar to that observed in experiment. The tortuosities we measure are larger than those computed in previous studies of packings of convex polytopes, and modeling improvements, which require higher resolution studies and an improved modeling of brain cell shapes and mechanical properties, could help resolve remaining discrepancies between model simulations and experiment. It is also shown that the specular reflection scheme is the appropriate technique for implementing zero-flux boundary conditions in random walk simulations commonly encountered in diffusion problems.

Diffusion of flexible random-coil dextran polymers measured in anisotropic brain extracellular space by integrative optical imaging.

PubMed

Xiao, Fanrong; Nicholson, Charles; Hrabe, Jan; Hrabetová, Sabina

2008-08-01

There are a limited number of methods available to quantify the extracellular diffusion of macromolecules in an anisotropic brain region, e.g., an area containing numerous aligned fibers where diffusion is faster along the fibers than across. We applied the integrative optical imaging method to measure diffusion of the fluorophore Alexa Fluor 488 (molecular weight (MW) 547) and fluorophore-labeled flexible random-coil dextran polymers (dex3, MW 3000; dex75, MW 75,000; dex282, MW 282,000; dex525, MW 525,000) in the extracellular space (ECS) of the anisotropic molecular layer of the isolated turtle cerebellum. For all molecules, two-dimensional images acquired an elliptical shape with major and minor axes oriented along and across, respectively, the unmyelinated parallel fibers. The effective diffusion coefficients, D*(major) and D*(minor), decreased with molecular size. The diffusion anisotropy ratio (DAR = D*(major)/D*(minor)) increased for Alexa Fluor 488 through dex75 but then unexpectedly reached a plateau. We argue that dex282 and dex525 approach the ECS width and deform to diffuse. In support of this concept, scaling theory shows the diffusion behavior of dex282 and dex525 to be consistent with transition to a reptation regime, and estimates the average ECS width at approximately 31 nm. These findings have implications for the interstitial transport of molecules and drugs, and for modeling neurotransmitter diffusion during ectopic release and spillover.

Charged Particle Diffusion in Isotropic Random Static Magnetic Fields

NASA Astrophysics Data System (ADS)

Subedi, P.; Sonsrettee, W.; Matthaeus, W. H.; Ruffolo, D. J.; Wan, M.; Montgomery, D.

2013-12-01

Study of the transport and diffusion of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider Diffusion of charged particles in fully three dimensional statistically isotropic magnetic field turbulence with no mean field which is pertinent to many astrophysical situations. We classify different regions of particle energy depending upon the ratio of Larmor radius of the charged particle to the characteristic outer length scale of turbulence. We propose three different theoretical models to calculate the diffusion coefficient each applicable to a distinct range of particle energies. The theoretical results are compared with those from computer simulations, showing very good agreement.

Modelling wildland fire propagation by tracking random fronts

NASA Astrophysics Data System (ADS)

Pagnini, G.; Mentrelli, A.

2014-08-01

Wildland fire propagation is studied in the literature by two alternative approaches, namely the reaction-diffusion equation and the level-set method. These two approaches are considered alternatives to each other because the solution of the reaction-diffusion equation is generally a continuous smooth function that has an exponential decay, and it is not zero in an infinite domain, while the level-set method, which is a front tracking technique, generates a sharp function that is not zero inside a compact domain. However, these two approaches can indeed be considered complementary and reconciled. Turbulent hot-air transport and fire spotting are phenomena with a random nature and they are extremely important in wildland fire propagation. Consequently, the fire front gets a random character, too; hence, a tracking method for random fronts is needed. In particular, the level-set contour is randomised here according to the probability density function of the interface particle displacement. Actually, when the level-set method is developed for tracking a front interface with a random motion, the resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterising role that is typical of the level-set approach. The resulting model emerges to be suitable for simulating effects due to turbulent convection, such as fire flank and backing fire, the faster fire spread being because of the actions by hot-air pre-heating and by ember landing, and also due to the fire overcoming a fire-break zone, which is a case not resolved by models based on the level-set method. Moreover, from the proposed formulation, a correction follows for the formula of the rate of spread which is due to the mean jump length of firebrands in the downwind direction for the leeward sector of the fireline contour. The presented study constitutes a proof of concept, and it needs to be subjected to a future validation.

Superimposed Code Theoretic Analysis of Deoxyribonucleic Acid (DNA) Codes and DNA Computing

DTIC Science & Technology

2010-01-01

partitioned by font type) of sequences are allowed to be in each position (e.g., Arial = position 0, Comic = position 1, etc. ) and within each collection...movement was modeled by a Brownian motion 3 dimensional random walk. The one dimensional diffusion coefficient D for the ellipsoid shape with 3...temperature, kB is Boltzmann’s constant, and η is the viscosity of the medium. The random walk motion is modeled by assuming the oligo is on a three

Software for Teaching Physiology and Biophysics.

ERIC Educational Resources Information Center

Weiss, Thomas F.; And Others

1992-01-01

Describes a software library developed to teach biophysics and physiology undergraduates that includes software on (1) the Hodgkin-Huxley model for excitation of action potentials in electrically excitable cells; (2) a random-walk model of diffusion; (3) single voltage-gated ion channels; (4) steady-state chemically mediated transport; and (5)…

FAST TRACK COMMUNICATION: Polarization diffusion from spacetime uncertainty

NASA Astrophysics Data System (ADS)

Contaldi, Carlo R.; Dowker, Fay; Philpott, Lydia

2010-09-01

A model of Lorentz invariant random fluctuations in photon polarization is presented. The effects are frequency dependent and affect the polarization of photons as they propagate through space. We test for this effect by confronting the model with the latest measurements of polarization of cosmic microwave background photons.

Knowledge diffusion in the collaboration hypernetwork

NASA Astrophysics Data System (ADS)

Yang, Guang-Yong; Hu, Zhao-Long; Liu, Jian-Guo

2015-02-01

As knowledge constitutes a primary productive force, it is important to understand the performance of knowledge diffusion. In this paper, we present a knowledge diffusion model based on the local-world non-uniform hypernetwork, which introduces the preferential diffusion mechanism and the knowledge absorptive capability αj, where αj is correlated with the hyperdegree dH(j) of node j. At each time step, we randomly select a node i as the sender; a receiver node is selected from the set of nodes that the sender i has published with previously, with probability proportional to the number of papers they have published together. Applying the average knowledge stock V bar(t) , the variance σ2(t) and the variance coefficient c(t) of knowledge stock to measure the growth and diffusion of knowledge and the adequacy of knowledge diffusion, we have made 3 groups of comparative experiments to investigate how different network structures, hypernetwork sizes and knowledge evolution mechanisms affect the knowledge diffusion, respectively. As the diffusion mechanisms based on the hypernetwork combine with the hyperdegree of node, the hypernetwork is more suitable for investigating the performance of knowledge diffusion. Therefore, the proposed model could be helpful for deeply understanding the process of the knowledge diffusion in the collaboration hypernetwork.

Convergence of the Graph Allen-Cahn Scheme

NASA Astrophysics Data System (ADS)

Luo, Xiyang; Bertozzi, Andrea L.

2017-05-01

The graph Laplacian and the graph cut problem are closely related to Markov random fields, and have many applications in clustering and image segmentation. The diffuse interface model is widely used for modeling in material science, and can also be used as a proxy to total variation minimization. In Bertozzi and Flenner (Multiscale Model Simul 10(3):1090-1118, 2012), an algorithm was developed to generalize the diffuse interface model to graphs to solve the graph cut problem. This work analyzes the conditions for the graph diffuse interface algorithm to converge. Using techniques from numerical PDE and convex optimization, monotonicity in function value and convergence under an a posteriori condition are shown for a class of schemes under a graph-independent stepsize condition. We also generalize our results to incorporate spectral truncation, a common technique used to save computation cost, and also to the case of multiclass classification. Various numerical experiments are done to compare theoretical results with practical performance.

Computing diffusivities from particle models out of equilibrium

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Collaborative emitter tracking using Rao-Blackwellized random exchange diffusion particle filtering

NASA Astrophysics Data System (ADS)

Bruno, Marcelo G. S.; Dias, Stiven S.

2014-12-01

We introduce in this paper the fully distributed, random exchange diffusion particle filter (ReDif-PF) to track a moving emitter using multiple received signal strength (RSS) sensors. We consider scenarios with both known and unknown sensor model parameters. In the unknown parameter case, a Rao-Blackwellized (RB) version of the random exchange diffusion particle filter, referred to as the RB ReDif-PF, is introduced. In a simulated scenario with a partially connected network, the proposed ReDif-PF outperformed a PF tracker that assimilates local neighboring measurements only and also outperformed a linearized random exchange distributed extended Kalman filter (ReDif-EKF). Furthermore, the novel ReDif-PF matched the tracking error performance of alternative suboptimal distributed PFs based respectively on iterative Markov chain move steps and selective average gossiping with an inter-node communication cost that is roughly two orders of magnitude lower than the corresponding cost for the Markov chain and selective gossip filters. Compared to a broadcast-based filter which exactly mimics the optimal centralized tracker or its equivalent (exact) consensus-based implementations, ReDif-PF showed a degradation in steady-state error performance. However, compared to the optimal consensus-based trackers, ReDif-PF is better suited for real-time applications since it does not require iterative inter-node communication between measurement arrivals.

Diffusion and mobility of atomic particles in a liquid

NASA Astrophysics Data System (ADS)

Smirnov, B. M.; Son, E. E.; Tereshonok, D. V.

2017-11-01

The diffusion coefficient of a test atom or molecule in a liquid is determined for the mechanism where the displacement of the test molecule results from the vibrations and motion of liquid molecules surrounding the test molecule and of the test particle itself. This leads to a random change in the coordinate of the test molecule, which eventually results in the diffusion motion of the test particle in space. Two models parameters of interaction of a particle and a liquid are used to find the activation energy of the diffusion process under consideration: the gas-kinetic cross section for scattering of test molecules in the parent gas and the Wigner-Seitz radius for test molecules. In the context of this approach, we have calculated the diffusion coefficient of atoms and molecules in water, where based on experimental data, we have constructed the dependence of the activation energy for the diffusion of test molecules in water on the interaction parameter and the temperature dependence for diffusion coefficient of atoms or molecules in water within the models considered. The statistically averaged difference of the activation energies for the diffusion coefficients of different test molecules in water that we have calculated based on each of the presented models does not exceed 10% of the diffusion coefficient itself. We have considered the diffusion of clusters in water and present the dependence of the diffusion coefficient on the cluster size. The accuracy of the presented formulas for the diffusion coefficient of atomic particles in water is estimated to be 50%.

Modeling and simulation of Cu diffusion and drift in porous CMOS backend dielectrics

NASA Astrophysics Data System (ADS)

Ali, R.; Fan, Y.; King, S.; Orlowski, M.

2018-06-01

With the advent of porous dielectrics, Cu drift-diffusion reliability issues in CMOS backend have only been exacerbated. In this regard, a modeling and simulation study of Cu atom/ion drift-diffusion in porous dielectrics is presented to assess the backend reliability and to explore conditions for a reliable Resistive Random Access Memory (RRAM) operation. The numerical computation, using elementary jump frequencies for a random walk in 2D and 3D, is based on an extended adjacency tensor concept. It is shown that Cu diffusion and drift transport are affected as much by the level of porosity as by the pore morphology. Allowance is made for different rates of Cu dissolution into the dielectric and for Cu absorption and transport at and on the inner walls of the pores. Most of the complex phenomena of the drift-diffusion transport in porous media can be understood in terms of local lateral and vertical gradients and the degree of their perturbation caused by the presence of pores in the transport domain. The impact of pore morphology, related to the concept of tortuosity, is discussed in terms of "channeling" and "trapping" effects. The simulations are calibrated to experimental results of porous SiCOH layers of 25 nm thickness, sandwiched between Cu and Pt(W) electrodes with experimental porosity levels of 0%, 8%, 12%, and 25%. We find that porous SICOH is more immune to Cu+ drift at 300 K than non-porous SICOH.

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.

Threshold-based epidemic dynamics in systems with memory

NASA Astrophysics Data System (ADS)

Bodych, Marcin; Ganguly, Niloy; Krueger, Tyll; Mukherjee, Animesh; Siegmund-Schultze, Rainer; Sikdar, Sandipan

2016-11-01

In this article we analyze an epidemic dynamics model (SI) where we assume that there are k susceptible states, that is a node would require multiple (k) contacts before it gets infected. In specific, we provide a theoretical framework for studying diffusion rate in complete graphs and d-regular trees with extensions to dense random graphs. We observe that irrespective of the topology, the diffusion process could be divided into two distinct phases: i) the initial phase, where the diffusion process is slow, followed by ii) the residual phase where the diffusion rate increases manifold. In fact, the initial phase acts as an indicator for the total diffusion time in dense graphs. The most remarkable lesson from this investigation is that such a diffusion process could be controlled and even contained if acted upon within its initial phase.

Cancerous tumor: the high frequency of a rare event.

PubMed

Galam, S; Radomski, J P

2001-05-01

A simple model for cancer growth is presented using cellular automata. Cells diffuse randomly on a two-dimensional square lattice. Individual cells can turn cancerous at a very low rate. During each diffusive step, local fights may occur between healthy and cancerous cells. Associated outcomes depend on some biased local rules, which are independent of the overall cancerous cell density. The models unique ingredients are the frequency of local fights and the bias amplitude. While each isolated cancerous cell is eventually destroyed, an initial two-cell tumor cluster is found to have a nonzero probabilty to spread over the whole system. The associated phase diagram for survival or death is obtained as a function of both the rate of fight and the bias distribution. Within the model, although the occurrence of a killing cluster is a very rare event, it turns out to happen almost systematically over long periods of time, e.g., on the order of an adults life span. Thus, after some age, survival from tumorous cancer becomes random.

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

DOE PAGES

Slattery, Stuart R.; Evans, Thomas M.; Wilson, Paul P. H.

2015-09-08

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakagemore » frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.« less

Relativistic diffusive motion in random electromagnetic fields

NASA Astrophysics Data System (ADS)

Haba, Z.

2011-08-01

We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Jüttner equilibrium at the inverse temperature β-1 = mc2. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).

Radial diffusion in magnetodiscs. [charged particle motion in planetary or stellar magnetosphere

NASA Technical Reports Server (NTRS)

Birmingham, T. J.

1985-01-01

The orbits of charged particles in magnetodiscs are considered. The bounce motion is assumed adiabatic except for transits of a small equatorial region of weak magnetic field strength and high field curvature. Previous theory and modeling have shown that particles scatter randomly in pitch angle with each passage through the equator. A peaked distribution thus diffuses in pitch angle on the time scale of many bounces. It is argued in this paper that spatial diffusion is a further consequence when the magnetodisc has a longitudinal asymmetry. A general expression for DLL, the diffusion of equatorial crossing radii, is derived. DLL is evaluated explicitly for ions in Jupiter's 20-35 radii magnetodisc, assumed to be represented by Connerney et al.'s (1982) Voyager model plus a small image dipole asymmetry. Rates are energy, species, and space dependent but can average as much as a few tenths of a planetary radius per bounce period.

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.

A deterministic Lagrangian particle separation-based method for advective-diffusion problems

NASA Astrophysics Data System (ADS)

Wong, Ken T. M.; Lee, Joseph H. W.; Choi, K. W.

2008-12-01

A simple and robust Lagrangian particle scheme is proposed to solve the advective-diffusion transport problem. The scheme is based on relative diffusion concepts and simulates diffusion by regulating particle separation. This new approach generates a deterministic result and requires far less number of particles than the random walk method. For the advection process, particles are simply moved according to their velocity. The general scheme is mass conservative and is free from numerical diffusion. It can be applied to a wide variety of advective-diffusion problems, but is particularly suited for ecological and water quality modelling when definition of particle attributes (e.g., cell status for modelling algal blooms or red tides) is a necessity. The basic derivation, numerical stability and practical implementation of the NEighborhood Separation Technique (NEST) are presented. The accuracy of the method is demonstrated through a series of test cases which embrace realistic features of coastal environmental transport problems. Two field application examples on the tidal flushing of a fish farm and the dynamics of vertically migrating marine algae are also presented.

Diffusion in randomly perturbed dissipative dynamics

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

Cellular automata model for drug release from binary matrix and reservoir polymeric devices.

PubMed

Johannes Laaksonen, Timo; Mikael Laaksonen, Hannu; Tapio Hirvonen, Jouni; Murtomäki, Lasse

2009-04-01

Kinetics of drug release from polymeric tablets, inserts and implants is an important and widely studied area. Here we present a new and widely applicable cellular automata model for diffusion and erosion processes occurring during drug release from polymeric drug release devices. The model divides a 2D representation of the release device into an array of cells. Each cell contains information about the material, drug, polymer or solvent that the domain contains. Cells are then allowed to rearrange according to statistical rules designed to match realistic drug release. Diffusion is modeled by a random walk of mobile cells and kinetics of chemical or physical processes by probabilities of conversion from one state to another. This is according to the basis of diffusion coefficients and kinetic rate constants, which are on fundamental level just probabilities for certain occurrences. The model is applied to three kinds of devices with different release mechanisms: erodable matrices, diffusion through channels or pores and membrane controlled release. The dissolution curves obtained are compared to analytical models from literature and the validity of the model is considered. The model is shown to be compatible with all three release devices, highlighting easy adaptability of the model to virtually any release system and geometry. Further extension and applications of the model are envisioned.

Modeling intragranular diffusion in low-connectivity granular media

NASA Astrophysics Data System (ADS)

Ewing, Robert P.; Liu, Chongxuan; Hu, Qinhong

2012-03-01

Characterizing the diffusive exchange of solutes between bulk water in an aquifer and water in the intragranular pores of the solid phase is still challenging despite decades of study. Many disparities between observation and theory could be attributed to low connectivity of the intragranular pores. The presence of low connectivity indicates that a useful conceptual framework is percolation theory. The present study was initiated to develop a percolation-based finite difference (FD) model, and to test it rigorously against both random walk (RW) simulations of diffusion starting from nonequilibrium, and data on Borden sand published by Ball and Roberts (1991a,b) and subsequently reanalyzed by Haggerty and Gorelick (1995) using a multirate mass transfer (MRMT) approach. The percolation-theoretical model is simple and readily incorporated into existing FD models. The FD model closely matches the RW results using only a single fitting parameter, across a wide range of pore connectivities. Simulation of the Borden sand experiment without pore connectivity effects reproduced the MRMT analysis, but including low pore connectivity effects improved the fit. Overall, the theory and simulation results show that low intragranular pore connectivity can produce diffusive behavior that appears as if the solute had undergone slow sorption, despite the absence of any sorption process, thereby explaining some hitherto confusing aspects of intragranular diffusion.

Scale-free network provides an optimal pattern for knowledge transfer

NASA Astrophysics Data System (ADS)

Lin, Min; Li, Nan

2010-02-01

We study numerically the knowledge innovation and diffusion process on four representative network models, such as regular networks, small-world networks, random networks and scale-free networks. The average knowledge stock level as a function of time is measured and the corresponding growth diffusion time, τ is defined and computed. On the four types of networks, the growth diffusion times all depend linearly on the network size N as τ∼N, while the slope for scale-free network is minimal indicating the fastest growth and diffusion of knowledge. The calculated variance and spatial distribution of knowledge stock illustrate that optimal knowledge transfer performance is obtained on scale-free networks. We also investigate the transient pattern of knowledge diffusion on the four networks, and a qualitative explanation of this finding is proposed.

Evolutionarily stable and convergent stable strategies in reaction-diffusion models for conditional dispersal.

PubMed

Lam, King-Yeung; Lou, Yuan

2014-02-01

We consider a mathematical model of two competing species for the evolution of conditional dispersal in a spatially varying, but temporally constant environment. Two species are different only in their dispersal strategies, which are a combination of random dispersal and biased movement upward along the resource gradient. In the absence of biased movement or advection, Hastings showed that the mutant can invade when rare if and only if it has smaller random dispersal rate than the resident. When there is a small amount of biased movement or advection, we show that there is a positive random dispersal rate that is both locally evolutionarily stable and convergent stable. Our analysis of the model suggests that a balanced combination of random and biased movement might be a better habitat selection strategy for populations.

A fractional motion diffusion model for grading pediatric brain tumors.

PubMed

Karaman, M Muge; Wang, He; Sui, Yi; Engelhard, Herbert H; Li, Yuhua; Zhou, Xiaohong Joe

2016-01-01

To demonstrate the feasibility of a novel fractional motion (FM) diffusion model for distinguishing low- versus high-grade pediatric brain tumors; and to investigate its possible advantage over apparent diffusion coefficient (ADC) and/or a previously reported continuous-time random-walk (CTRW) diffusion model. With approval from the institutional review board and written informed consents from the legal guardians of all participating patients, this study involved 70 children with histopathologically-proven brain tumors (30 low-grade and 40 high-grade). Multi- b -value diffusion images were acquired and analyzed using the FM, CTRW, and mono-exponential diffusion models. The FM parameters, D fm , φ , ψ (non-Gaussian diffusion statistical measures), and the CTRW parameters, D m , α , β (non-Gaussian temporal and spatial diffusion heterogeneity measures) were compared between the low- and high-grade tumor groups by using a Mann-Whitney-Wilcoxon U test. The performance of the FM model for differentiating between low- and high-grade tumors was evaluated and compared with that of the CTRW and the mono-exponential models using a receiver operating characteristic (ROC) analysis. The FM parameters were significantly lower ( p  < 0.0001) in the high-grade ( D fm : 0.81 ± 0.26, φ : 1.40 ± 0.10, ψ : 0.42 ± 0.11) than in the low-grade ( D fm : 1.52 ± 0.52, φ : 1.64 ± 0.13, ψ : 0.67 ± 0.13) tumor groups. The ROC analysis showed that the FM parameters offered better specificity (88% versus 73%), sensitivity (90% versus 82%), accuracy (88% versus 78%), and area under the curve (AUC, 93% versus 80%) in discriminating tumor malignancy compared to the conventional ADC. The performance of the FM model was similar to that of the CTRW model. Similar to the CTRW model, the FM model can improve differentiation between low- and high-grade pediatric brain tumors over ADC.

Noteworthy fractal features and transport properties of Cantor tartans

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Golmankhaneh, Alireza K.; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel

2018-06-01

This Letter is focused on the impact of fractal topology on the transport processes governed by different kinds of random walks on Cantor tartans. We establish that the spectral dimension of the infinitely ramified Cantor tartan ds is equal to its fractal (self-similarity) dimension D. Consequently, the random walk on the Cantor tartan leads to a normal diffusion. On the other hand, the fractal geometry of Cantor tartans allows for a natural definition of power-law distributions of the waiting times and step lengths of random walkers. These distributions are Lévy stable if D > 1.5. Accordingly, we found that the random walk with rests leads to sub-diffusion, whereas the Lévy walk leads to ballistic diffusion. The Lévy walk with rests leads to super-diffusion, if D >√{ 3 }, or sub-diffusion, if 1.5 < D <√{ 3 }.

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.

Results from the Biology Concept Inventory (BCI), and what they mean for biogeoscience literacy.

NASA Astrophysics Data System (ADS)

Garvin-Doxas, K.; Klymkowsky, M.

2008-12-01

While researching the Biology Concept Inventory (BCI) we found that a wide class of student difficulties in genetics and molecular biology can be traced to deep-seated misconceptions about random processes and molecular interactions. Students believe that random processes are inefficient, while biological systems are very efficient, and are therefore quick to propose their own rational explanations for various processes (from diffusion to evolution). These rational explanations almost always make recourse to a driver (natural selection in genetics, or density gradients in molecular biology) with the process only taking place when the driver is present. The concept of underlying random processes that are taking place all the time giving rise to emergent behaviour is almost totally absent. Even students who have advanced or college physics, and can discuss diffusion correctly in that context, cannot make the transfer to biological processes. Furthermore, their understanding of molecular interactions is purely geometric, with a lock-and-key model (rather than an energy minimization model) that does not allow for the survival of slight variations of the "correct" molecule. Together with the dominant misconception about random processes, this results in a strong conceptual barrier in understanding evolutionary processes, and can frustrate the success of education programs.

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.

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

Conserved linear dynamics of single-molecule Brownian motion.

PubMed

Serag, Maged F; Habuchi, Satoshi

2017-06-06

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance.

Conserved linear dynamics of single-molecule Brownian motion

PubMed Central

Serag, Maged F.; Habuchi, Satoshi

2017-01-01

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance. PMID:28585925

Conserved linear dynamics of single-molecule Brownian motion

NASA Astrophysics Data System (ADS)

Serag, Maged F.; Habuchi, Satoshi

2017-06-01

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance.

Ge auto-doping and out-diffusion in InGaP grown on Ge substrate and their effects on the ordering of InGaP

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

Wu, Hong-Ming; Ho, Hao-I; Tsai, Shi-Jane

2016-03-21

We report on the Ge auto-doping and out-diffusion in InGaP epilayer with Cu-Pt ordering grown on 4-in. Ge substrate. Ge profiles determined from secondary ion mass spectrometry indicate that the Ge out-diffusion depth is within 100 nm. However, the edge of the wafer suffers from stronger Ge gas-phase auto-doping than the center, leading to ordering deterioration in the InGaP epilayer. In the edge, we observed a residual Cu-Pt ordering layer left beneath the surface, suggesting that the ordering deterioration takes place after the deposition rather than during the deposition and In/Ga inter-diffusion enhanced by Ge vapor-phase auto-doping is responsible for themore » deterioration. We thus propose a di-vacancy diffusion model, in which the amphoteric Ge increases the di-vacancy density, resulting in a Ge density dependent diffusion. In the model, the In/Ga inter-diffusion and Ge out-diffusion are realized by the random hopping of In/Ga host atoms and Ge atoms to di-vacancies, respectively. Simulation based on this model well fits the Ge out-diffusion profiles, suggesting its validity. By comparing the Ge diffusion coefficient obtained from the fitting and the characteristic time constant of ordering deterioration estimated from the residual ordering layer, we found that the hopping rates of Ge and the host atoms are in the same order of magnitude, indicating that di-vacancies are bound in the vicinity of Ge atoms.« less

Comparison of Experimental Methods for Estimating Matrix Diffusion Coefficients for Contaminant Transport Modeling

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

Telfeyan, Katherine Christina; Ware, Stuart Douglas; Reimus, Paul William

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%,more » and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.« less

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

NASA Astrophysics Data System (ADS)

Telfeyan, Katherine; Ware, S. Doug; Reimus, Paul W.; Birdsell, Kay H.

2018-02-01

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

Prioritization of candidate disease genes by topological similarity between disease and protein diffusion profiles.

PubMed

Zhu, Jie; Qin, Yufang; Liu, Taigang; Wang, Jun; Zheng, Xiaoqi

2013-01-01

Identification of gene-phenotype relationships is a fundamental challenge in human health clinic. Based on the observation that genes causing the same or similar phenotypes tend to correlate with each other in the protein-protein interaction network, a lot of network-based approaches were proposed based on different underlying models. A recent comparative study showed that diffusion-based methods achieve the state-of-the-art predictive performance. In this paper, a new diffusion-based method was proposed to prioritize candidate disease genes. Diffusion profile of a disease was defined as the stationary distribution of candidate genes given a random walk with restart where similarities between phenotypes are incorporated. Then, candidate disease genes are prioritized by comparing their diffusion profiles with that of the disease. Finally, the effectiveness of our method was demonstrated through the leave-one-out cross-validation against control genes from artificial linkage intervals and randomly chosen genes. Comparative study showed that our method achieves improved performance compared to some classical diffusion-based methods. To further illustrate our method, we used our algorithm to predict new causing genes of 16 multifactorial diseases including Prostate cancer and Alzheimer's disease, and the top predictions were in good consistent with literature reports. Our study indicates that integration of multiple information sources, especially the phenotype similarity profile data, and introduction of global similarity measure between disease and gene diffusion profiles are helpful for prioritizing candidate disease genes. Programs and data are available upon request.

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

Slow diffusion by Markov random flights

NASA Astrophysics Data System (ADS)

Kolesnik, Alexander D.

2018-06-01

We present a conception of the slow diffusion processes in the Euclidean spaces Rm , m ≥ 1, based on the theory of random flights with small constant speed that are driven by a homogeneous Poisson process of small rate. The slow diffusion condition that, on long time intervals, leads to the stationary distributions, is given. The stationary distributions of slow diffusion processes in some Euclidean spaces of low dimensions, are presented.

Relativistic diffusion processes and random walk models

NASA Astrophysics Data System (ADS)

Dunkel, Jörn; Talkner, Peter; Hänggi, Peter

2007-02-01

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (noncontinuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the nonrelativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.

Diffusion in the presence of a local attracting factor: Theory and interdisciplinary applications.

PubMed

Veermäe, Hardi; Patriarca, Marco

2017-06-01

In many complex diffusion processes the drift of random walkers is not caused by an external force, as in the case of Brownian motion, but by local variations of fitness perceived by the random walkers. In this paper, a simple but general framework is presented that describes such a type of random motion and may be of relevance in different problems, such as opinion dynamics, cultural spreading, and animal movement. To this aim, we study the problem of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned position-dependent "attractiveness function." At variance with standard Brownian motion, the attractiveness function introduced here regulates both the advection and diffusion of the random walker, thus providing testable predictions for a specific form of fluctuation-relations. We discuss the relation between the drift-diffusion equation based on the attractiveness function and that describing standard Brownian motion, and we provide some explicit examples illustrating its relevance in different fields, such as animal movement, chemotactic diffusion, and social dynamics.

Diffusion in the presence of a local attracting factor: Theory and interdisciplinary applications

NASA Astrophysics Data System (ADS)

Veermäe, Hardi; Patriarca, Marco

2017-06-01

In many complex diffusion processes the drift of random walkers is not caused by an external force, as in the case of Brownian motion, but by local variations of fitness perceived by the random walkers. In this paper, a simple but general framework is presented that describes such a type of random motion and may be of relevance in different problems, such as opinion dynamics, cultural spreading, and animal movement. To this aim, we study the problem of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned position-dependent "attractiveness function." At variance with standard Brownian motion, the attractiveness function introduced here regulates both the advection and diffusion of the random walker, thus providing testable predictions for a specific form of fluctuation-relations. We discuss the relation between the drift-diffusion equation based on the attractiveness function and that describing standard Brownian motion, and we provide some explicit examples illustrating its relevance in different fields, such as animal movement, chemotactic diffusion, and social dynamics.

A molecule-centered method for accelerating the calculation of hydrodynamic interactions in Brownian dynamics simulations containing many flexible biomolecules

PubMed Central

Elcock, Adrian H.

2013-01-01

Inclusion of hydrodynamic interactions (HIs) is essential in simulations of biological macromolecules that treat the solvent implicitly if the macromolecules are to exhibit correct translational and rotational diffusion. The present work describes the development and testing of a simple approach aimed at allowing more rapid computation of HIs in coarse-grained Brownian dynamics simulations of systems that contain large numbers of flexible macromolecules. The method combines a complete treatment of intramolecular HIs with an approximate treatment of the intermolecular HIs which assumes that the molecules are effectively spherical; all of the HIs are calculated at the Rotne-Prager-Yamakawa level of theory. When combined with Fixman’s Chebyshev polynomial method for calculating correlated random displacements, the proposed method provides an approach that is simple to program but sufficiently fast that it makes it computationally viable to include HIs in large-scale simulations. Test calculations performed on very coarse-grained models of the pyruvate dehydrogenase (PDH) E2 complex and on oligomers of ParM (ranging in size from 1 to 20 monomers) indicate that the method reproduces the translational diffusion behavior seen in more complete HI simulations surprisingly well; the method performs less well at capturing rotational diffusion but its discrepancies diminish with increasing size of the simulated assembly. Simulations of residue-level models of two tetrameric protein models demonstrate that the method also works well when more structurally detailed models are used in the simulations. Finally, test simulations of systems containing up to 1024 coarse-grained PDH molecules indicate that the proposed method rapidly becomes more efficient than the conventional BD approach in which correlated random displacements are obtained via a Cholesky decomposition of the complete diffusion tensor. PMID:23914146

Transitions between strongly correlated and random steady-states for catalytic CO-oxidation on surfaces at high-pressure

DOE PAGES

Liu, Da -Jiang; Evans, James W.

2015-04-02

We explore simple lattice-gas reaction models for CO-oxidation on 1D and 2D periodic arrays of surface adsorption sites. The models are motivated by studies of CO-oxidation on RuO 2(110) at high-pressures. Although adspecies interactions are neglected, the effective absence of adspecies diffusion results in kinetically-induced spatial correlations. A transition occurs from a random mainly CO-populated steady-state at high CO-partial pressure p CO, to a strongly-correlated near-O-covered steady-state for low p CO as noted. In addition, we identify a second transition to a random near-O-covered steady-state at very low p CO.

Active motion assisted by correlated stochastic torques.

PubMed

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

2011-07-01

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

Quantum random number generation for loophole-free Bell tests

NASA Astrophysics Data System (ADS)

Mitchell, Morgan; Abellan, Carlos; Amaya, Waldimar

2015-05-01

We describe the generation of quantum random numbers at multi-Gbps rates, combined with real-time randomness extraction, to give very high purity random numbers based on quantum events at most tens of ns in the past. The system satisfies the stringent requirements of quantum non-locality tests that aim to close the timing loophole. We describe the generation mechanism using spontaneous-emission-driven phase diffusion in a semiconductor laser, digitization, and extraction by parity calculation using multi-GHz logic chips. We pay special attention to experimental proof of the quality of the random numbers and analysis of the randomness extraction. In contrast to widely-used models of randomness generators in the computer science literature, we argue that randomness generation by spontaneous emission can be extracted from a single source.

Modeling emerald ash borer dispersal using percolation theory: estimating the rate of range expansion in a fragmented landscape

Treesearch

Robin A. J. Taylor; Daniel A. Herms; Louis R. Iverson

2008-01-01

The dispersal of organisms is rarely random, although diffusion processes can be useful models for movement in approximately homogeneous environments. However, the environments through which all organisms disperse are far from uniform at all scales. The emerald ash borer (EAB), Agrilus planipennis, is obligate on ash (Fraxinus spp...

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

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

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

2010-11-01

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

A Model with Darwinian Dynamics on a Rugged Landscape

NASA Astrophysics Data System (ADS)

Brotto, Tommaso; Bunin, Guy; Kurchan, Jorge

2017-02-01

We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase diagram in terms of the size of the population and the diffusion rate, with a glass phase inside which the dynamics keeps searching for better configurations, and outside which deleterious `mutations' spoil the performance. The phase diagram is analogous to that of dense active matter in terms of temperature and drive.

Epidemic spreading on complex networks with community structures

PubMed Central

Stegehuis, Clara; van der Hofstad, Remco; van Leeuwaarden, Johan S. H.

2016-01-01

Many real-world networks display a community structure. We study two random graph models that create a network with similar community structure as a given network. One model preserves the exact community structure of the original network, while the other model only preserves the set of communities and the vertex degrees. These models show that community structure is an important determinant of the behavior of percolation processes on networks, such as information diffusion or virus spreading: the community structure can both enforce as well as inhibit diffusion processes. Our models further show that it is the mesoscopic set of communities that matters. The exact internal structures of communities barely influence the behavior of percolation processes across networks. This insensitivity is likely due to the relative denseness of the communities. PMID:27440176

Spatiotemporal pattern formation in a prey-predator model under environmental driving forces

NASA Astrophysics Data System (ADS)

Sirohi, Anuj Kumar; Banerjee, Malay; Chakraborti, Anirban

2015-09-01

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this paper, we focus on the spatiotemporal patterns produced by the predator-prey model with ratio-dependent functional response and density dependent death rate of predator. We get the reaction-diffusion equations incorporating the self-diffusion terms, corresponding to random movement of the individuals within two dimensional habitats, into the growth equations for the prey and predator population. In order to have the noise added model, small amplitude heterogeneous perturbations to the linear intrinsic growth rates are introduced using uncorrelated Gaussian white noise terms. For the noise added system, we then observe spatial patterns for the parameter values lying outside the Turing instability region. With thorough numerical simulations we characterize the patterns corresponding to Turing and Turing-Hopf domain and study their dependence on different system parameters like noise-intensity, etc.

Block effect on HCV infection by HMGB1 released from virus-infected cells: An insight from mathematical modeling

NASA Astrophysics Data System (ADS)

Wang, Wei; Ma, Wanbiao

2018-06-01

The nuclear protein high-mobility group box 1 (HMGB1) can have an active role in deoxyribonucleic acid (DNA) organization and the regulation of transcription. Based on the new findings from a recent experimental study, the blocking effect on HCV infection by HMGB1 released from virus-infected cells is investigated using a diffusive model for viral infection dynamics. In the model, the diffusion of the virus depends not only on its concentration gradient, but also on the concentration of HMGB1. The basic reproduction number, threshold dynamics, stability properties of the steady states, travelling wave solutions, and spreading speed for the proposed model are studied. We show that the HMGB1-induced blocking of HCV infection slows the spread of virus compared with random diffusion only. Numerically, it is shown that a high concentration of HMGB1 can block the spread of virus and this confirms, not only qualitatively but also quantitatively, the experimental result.

The Coalescent Process in Models with Selection

PubMed Central

Kaplan, N. L.; Darden, T.; Hudson, R. R.

1988-01-01

Statistical properties of the process describing the genealogical history of a random sample of genes are obtained for a class of population genetics models with selection. For models with selection, in contrast to models without selection, the distribution of this process, the coalescent process, depends on the distribution of the frequencies of alleles in the ancestral generations. If the ancestral frequency process can be approximated by a diffusion, then the mean and the variance of the number of segregating sites due to selectively neutral mutations in random samples can be numerically calculated. The calculations are greatly simplified if the frequencies of the alleles are tightly regulated. If the mutation rates between alleles maintained by balancing selection are low, then the number of selectively neutral segregating sites in a random sample of genes is expected to substantially exceed the number predicted under a neutral model. PMID:3066685

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.

Data-driven analysis for the temperature and momentum dependence of the heavy-quark diffusion coefficient in relativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Xu, Yingru; Bernhard, Jonah E.; Bass, Steffen A.; Nahrgang, Marlene; Cao, Shanshan

2018-01-01

By applying a Bayesian model-to-data analysis, we estimate the temperature and momentum dependence of the heavy quark diffusion coefficient in an improved Langevin framework. The posterior range of the diffusion coefficient is obtained by performing a Markov chain Monte Carlo random walk and calibrating on the experimental data of D -meson RAA and v2 in three different collision systems at the Relativistic Heavy-Ion Collidaer (RHIC) and the Large Hadron Collider (LHC): Au-Au collisions at 200 GeV and Pb-Pb collisions at 2.76 and 5.02 TeV. The spatial diffusion coefficient is found to be consistent with lattice QCD calculations and comparable with other models' estimation. We demonstrate the capability of our improved Langevin model to simultaneously describe the RAA and v2 at both RHIC and the LHC energies, as well as the higher order flow coefficient such as D meson v3. We show that by applying a Bayesian analysis, we are able to quantitatively and systematically study the heavy flavor dynamics in heavy-ion collisions.

Rewiring the network. What helps an innovation to diffuse?

NASA Astrophysics Data System (ADS)

Sznajd-Weron, Katarzyna; Szwabiński, Janusz; Weron, Rafał; Weron, Tomasz

2014-03-01

A fundamental question related to innovation diffusion is how the structure of the social network influences the process. Empirical evidence regarding real-world networks of influence is very limited. On the other hand, agent-based modeling literature reports different, and at times seemingly contradictory, results. In this paper we study innovation diffusion processes for a range of Watts-Strogatz networks in an attempt to shed more light on this problem. Using the so-called Sznajd model as the backbone of opinion dynamics, we find that the published results are in fact consistent and allow us to predict the role of network topology in various situations. In particular, the diffusion of innovation is easier on more regular graphs, i.e. with a higher clustering coefficient. Moreover, in the case of uncertainty—which is particularly high for innovations connected to public health programs or ecological campaigns—a more clustered network will help the diffusion. On the other hand, when social influence is less important (i.e. in the case of perfect information), a shorter path will help the innovation to spread in the society and—as a result—the diffusion will be easiest on a random graph.

Adaptive hierarchical grid model of water-borne pollutant dispersion

NASA Astrophysics Data System (ADS)

Borthwick, A. G. L.; Marchant, R. D.; Copeland, G. J. M.

Water pollution by industrial and agricultural waste is an increasingly major public health issue. It is therefore important for water engineers and managers to be able to predict accurately the local behaviour of water-borne pollutants. This paper describes the novel and efficient coupling of dynamically adaptive hierarchical grids with standard solvers of the advection-diffusion equation. Adaptive quadtree grids are able to focus on regions of interest such as pollutant fronts, while retaining economy in the total number of grid elements through selective grid refinement. Advection is treated using Lagrangian particle tracking. Diffusion is solved separately using two grid-based methods; one is by explicit finite differences, the other a diffusion-velocity approach. Results are given in two dimensions for pure diffusion of an initially Gaussian plume, advection-diffusion of the Gaussian plume in the rotating flow field of a forced vortex, and the transport of species in a rectangular channel with side wall boundary layers. Close agreement is achieved with analytical solutions of the advection-diffusion equation and simulations from a Lagrangian random walk model. An application to Sepetiba Bay, Brazil is included to demonstrate the method with complex flows and topography.

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

PubMed Central

Marshall, Wallace F.; Fung, Jennifer C.

2016-01-01

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

Phylogeography Takes a Relaxed Random Walk in Continuous Space and Time

PubMed Central

Lemey, Philippe; Rambaut, Andrew; Welch, John J.; Suchard, Marc A.

2010-01-01

Research aimed at understanding the geographic context of evolutionary histories is burgeoning across biological disciplines. Recent endeavors attempt to interpret contemporaneous genetic variation in the light of increasingly detailed geographical and environmental observations. Such interest has promoted the development of phylogeographic inference techniques that explicitly aim to integrate such heterogeneous data. One promising development involves reconstructing phylogeographic history on a continuous landscape. Here, we present a Bayesian statistical approach to infer continuous phylogeographic diffusion using random walk models while simultaneously reconstructing the evolutionary history in time from molecular sequence data. Moreover, by accommodating branch-specific variation in dispersal rates, we relax the most restrictive assumption of the standard Brownian diffusion process and demonstrate increased statistical efficiency in spatial reconstructions of overdispersed random walks by analyzing both simulated and real viral genetic data. We further illustrate how drawing inference about summary statistics from a fully specified stochastic process over both sequence evolution and spatial movement reveals important characteristics of a rabies epidemic. Together with recent advances in discrete phylogeographic inference, the continuous model developments furnish a flexible statistical framework for biogeographical reconstructions that is easily expanded upon to accommodate various landscape genetic features. PMID:20203288

Phonons, Diffusons, and the Boson Peak in Two-Dimensional Lattices with Random Bonds

NASA Astrophysics Data System (ADS)

Konyukh, D. A.; Bel'tyukov, Ya. M.; Parshin, D. A.

2018-02-01

Within the model of stable random matrices possessing translational invariance, a two-dimensional (on a square lattice) disordered oscillatory system with random strongly fluctuating bonds is considered. By a numerical analysis of the dynamic structure factor S( q, ω), it is shown that vibrations with frequencies below the Ioffe-Regel frequency ωIR are ordinary phonons with a linear dispersion law ω( q) ∝ q and a reciprocal lifetime б q 3. Vibrations with frequencies above ωIR, although being delocalized, cannot be described by plane waves with a definite dispersion law ω( q). They are characterized by a diffusion structure factor with a reciprocal lifetime б q 2, which is typical of a diffusion process. In the literature, they are often referred to as diffusons. It is shown that, as in the three-dimensional model, the boson peak at the frequency ωb in the reduced density of vibrational states g(ω)/ω is on the order of the frequency ωIR. It is located in the transition region between phonons and diffusons and is proportional to the Young's modulus of the lattice, ω b ≃ E.

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

NASA Astrophysics Data System (ADS)

Marshall, Wallace F.; Fung, Jennifer C.

2016-04-01

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

Mathematical modelling of complex contagion on clustered networks

NASA Astrophysics Data System (ADS)

O'sullivan, David J.; O'Keeffe, Gary; Fennell, Peter; Gleeson, James

2015-09-01

The spreading of behavior, such as the adoption of a new innovation, is influenced bythe structure of social networks that interconnect the population. In the experiments of Centola (Science, 2010), adoption of new behavior was shown to spread further and faster across clustered-lattice networks than across corresponding random networks. This implies that the “complex contagion” effects of social reinforcement are important in such diffusion, in contrast to “simple” contagion models of disease-spread which predict that epidemics would grow more efficiently on random networks than on clustered networks. To accurately model complex contagion on clustered networks remains a challenge because the usual assumptions (e.g. of mean-field theory) regarding tree-like networks are invalidated by the presence of triangles in the network; the triangles are, however, crucial to the social reinforcement mechanism, which posits an increased probability of a person adopting behavior that has been adopted by two or more neighbors. In this paper we modify the analytical approach that was introduced by Hebert-Dufresne et al. (Phys. Rev. E, 2010), to study disease-spread on clustered networks. We show how the approximation method can be adapted to a complex contagion model, and confirm the accuracy of the method with numerical simulations. The analytical results of the model enable us to quantify the level of social reinforcement that is required to observe—as in Centola’s experiments—faster diffusion on clustered topologies than on random networks.

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

Controllability of social networks and the strategic use of random information.

PubMed

Cremonini, Marco; Casamassima, Francesca

2017-01-01

This work is aimed at studying realistic social control strategies for social networks based on the introduction of random information into the state of selected driver agents. Deliberately exposing selected agents to random information is a technique already experimented in recommender systems or search engines, and represents one of the few options for influencing the behavior of a social context that could be accepted as ethical, could be fully disclosed to members, and does not involve the use of force or of deception. Our research is based on a model of knowledge diffusion applied to a time-varying adaptive network and considers two well-known strategies for influencing social contexts: One is the selection of few influencers for manipulating their actions in order to drive the whole network to a certain behavior; the other, instead, drives the network behavior acting on the state of a large subset of ordinary, scarcely influencing users. The two approaches have been studied in terms of network and diffusion effects. The network effect is analyzed through the changes induced on network average degree and clustering coefficient, while the diffusion effect is based on two ad hoc metrics which are defined to measure the degree of knowledge diffusion and skill level, as well as the polarization of agent interests. The results, obtained through simulations on synthetic networks, show a rich dynamics and strong effects on the communication structure and on the distribution of knowledge and skills. These findings support our hypothesis that the strategic use of random information could represent a realistic approach to social network controllability, and that with both strategies, in principle, the control effect could be remarkable.

Photoinduced random molecular reorientation by nonradiative energy relaxation: An experimental test

NASA Astrophysics Data System (ADS)

Manzo, C.; Paparo, D.; Marrucci, L.

2004-11-01

By measuring the time-resolved fluorescence depolarization as a function of light excitation wavelength we address the question of a possible photoinduced orientational randomization of amino-anthraquinone dyes in liquid solutions. We find no significant dependence within the experimental uncertainties of both the initial molecule anisotropy and of the subsequent rotational diffusion dynamics on the photon energy. This indicates that this effect, if present, must be very small. A simple model of photoinduced local heating and corresponding enhanced rotational diffusion is in accordance with this result. This null result rules out some recent proposals that photoinduced local heating may contribute significantly to molecular reorientation effects in different materials. A small but statistically significant effect of photon energy is instead found in the excited-state lifetime of the dye.

Deep Learning Role in Early Diagnosis of Prostate Cancer

PubMed Central

Reda, Islam; Khalil, Ashraf; Elmogy, Mohammed; Abou El-Fetouh, Ahmed; Shalaby, Ahmed; Abou El-Ghar, Mohamed; Elmaghraby, Adel; Ghazal, Mohammed; El-Baz, Ayman

2018-01-01

The objective of this work is to develop a computer-aided diagnostic system for early diagnosis of prostate cancer. The presented system integrates both clinical biomarkers (prostate-specific antigen) and extracted features from diffusion-weighted magnetic resonance imaging collected at multiple b values. The presented system performs 3 major processing steps. First, prostate delineation using a hybrid approach that combines a level-set model with nonnegative matrix factorization. Second, estimation and normalization of diffusion parameters, which are the apparent diffusion coefficients of the delineated prostate volumes at different b values followed by refinement of those apparent diffusion coefficients using a generalized Gaussian Markov random field model. Then, construction of the cumulative distribution functions of the processed apparent diffusion coefficients at multiple b values. In parallel, a K-nearest neighbor classifier is employed to transform the prostate-specific antigen results into diagnostic probabilities. Finally, those prostate-specific antigen–based probabilities are integrated with the initial diagnostic probabilities obtained using stacked nonnegativity constraint sparse autoencoders that employ apparent diffusion coefficient–cumulative distribution functions for better diagnostic accuracy. Experiments conducted on 18 diffusion-weighted magnetic resonance imaging data sets achieved 94.4% diagnosis accuracy (sensitivity = 88.9% and specificity = 100%), which indicate the promising results of the presented computer-aided diagnostic system. PMID:29804518

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

DOE PAGES

Telfeyan, Katherine Christina; Ware, Stuart Doug; Reimus, Paul William; ...

2018-01-31

Here, diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged frommore » 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.« less

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

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

Telfeyan, Katherine Christina; Ware, Stuart Doug; Reimus, Paul William

Here, diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged frommore » 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.« less

Transport of Internetwork Magnetic Flux Elements in the Solar Photosphere

NASA Astrophysics Data System (ADS)

Agrawal, Piyush; Rast, Mark P.; Gošić, Milan; Bellot Rubio, Luis R.; Rempel, Matthias

2018-02-01

The motions of small-scale magnetic flux elements in the solar photosphere can provide some measure of the Lagrangian properties of the convective flow. Measurements of these motions have been critical in estimating the turbulent diffusion coefficient in flux-transport dynamo models and in determining the Alfvén wave excitation spectrum for coronal heating models. We examine the motions of internetwork flux elements in Hinode/Narrowband Filter Imager magnetograms and study the scaling of their mean squared displacement and the shape of their displacement probability distribution as a function of time. We find that the mean squared displacement scales super-diffusively with a slope of about 1.48. Super-diffusive scaling has been observed in other studies for temporal increments as small as 5 s, increments over which ballistic scaling would be expected. Using high-cadence MURaM simulations, we show that the observed super-diffusive scaling at short increments is a consequence of random changes in barycenter positions due to flux evolution. We also find that for long temporal increments, beyond granular lifetimes, the observed displacement distribution deviates from that expected for a diffusive process, evolving from Rayleigh to Gaussian. This change in distribution can be modeled analytically by accounting for supergranular advection along with granular motions. These results complicate the interpretation of magnetic element motions as strictly advective or diffusive on short and long timescales and suggest that measurements of magnetic element motions must be used with caution in turbulent diffusion or wave excitation models. We propose that passive tracer motions in measured photospheric flows may yield more robust transport statistics.

Bayesian Nonparametric Prediction and Statistical Inference

DTIC Science & Technology

1989-09-07

Kadane, J. (1980), "Bayesian decision theory and the sim- plification of models," in Evaluation of Econometric Models, J. Kmenta and J. Ramsey , eds...the random model and weighted least squares regression," in Evaluation of Econometric Models, ed. by J. Kmenta and J. Ramsey , Academic Press, 197-217...likelihood function. On the other hand, H. Jeffreys’s theory of hypothesis testing covers the most important situations in which the prior is not diffuse. See

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

NASA Astrophysics Data System (ADS)

Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

2018-05-01

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

How Do Biology Teacher Candidates Know Particulate Movements & Random Nature of Matter and Their Effects to Diffusion

ERIC Educational Resources Information Center

Oztas, Fulya; Oztas, Haydar

2016-01-01

The previous researches results seem to suggest that some aspects of learning of diffusion and osmosis concepts such as membranes, kinetic energy of matter, and elements of the particulate and random nature of matter could lead to misconceptions. The concept of diffusion is very common in science instruction, and understanding the concept is an…

Transport of Charged Particles in Turbulent Magnetic Fields

NASA Astrophysics Data System (ADS)

Parashar, T.; Subedi, P.; Sonsrettee, W.; Blasi, P.; Ruffolo, D. J.; Matthaeus, W. H.; Montgomery, D.; Chuychai, P.; Dmitruk, P.; Wan, M.; Chhiber, R.

2017-12-01

Magnetic fields permeate the Universe. They are found in planets, stars, galaxies, and the intergalactic medium. The magnetic field found in these astrophysical systems are usually chaotic, disordered, and turbulent. The investigation of the transport of cosmic rays in magnetic turbulence is a subject of considerable interest. One of the important aspects of cosmic ray transport is to understand their diffusive behavior and to calculate the diffusion coefficient in the presence of these turbulent fields. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here, we will particularly focus on calculating diffusion coefficients of charged particles and magnetic field lines in a fully three-dimensional isotropic turbulent magnetic field with no mean field, which may be pertinent to many astrophysical situations. For charged particles in isotropic turbulence we identify different ranges of particle energy depending upon the ratio of the Larmor radius of the charged particle to the characteristic outer length scale of the turbulence. Different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical ideas are tested against results of detailed numerical experiments using Monte-Carlo simulations of particle propagation in stochastic magnetic fields. We also discuss two different methods of generating random magnetic field to study charged particle propagation using numerical simulation. One method is the usual way of generating random fields with a specified power law in wavenumber space, using Gaussian random variables. Turbulence, however, is non-Gaussian, with variability that comes in bursts called intermittency. We therefore devise a way to generate synthetic intermittent fields which have many properties of realistic turbulence. Possible applications of such synthetically generated intermittent fields are discussed.

Optimal resource diffusion for suppressing disease spreading in multiplex networks

NASA Astrophysics Data System (ADS)

Chen, Xiaolong; Wang, Wei; Cai, Shimin; Stanley, H. Eugene; Braunstein, Lidia A.

2018-05-01

Resource diffusion is a ubiquitous phenomenon, but how it impacts epidemic spreading has received little study. We propose a model that couples epidemic spreading and resource diffusion in multiplex networks. The spread of disease in a physical contact layer and the recovery of the infected nodes are both strongly dependent upon resources supplied by their counterparts in the social layer. The generation and diffusion of resources in the social layer are in turn strongly dependent upon the state of the nodes in the physical contact layer. Resources diffuse preferentially or randomly in this model. To quantify the degree of preferential diffusion, a bias parameter that controls the resource diffusion is proposed. We conduct extensive simulations and find that the preferential resource diffusion can change phase transition type of the fraction of infected nodes. When the degree of interlayer correlation is below a critical value, increasing the bias parameter changes the phase transition from double continuous to single continuous. When the degree of interlayer correlation is above a critical value, the phase transition changes from multiple continuous to first discontinuous and then to hybrid. We find hysteresis loops in the phase transition. We also find that there is an optimal resource strategy at each fixed degree of interlayer correlation under which the threshold reaches a maximum and the disease can be maximally suppressed. In addition, the optimal controlling parameter increases as the degree of inter-layer correlation increases.

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.

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

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

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

2017-04-01

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

Computational investigation of longitudinal diffusion, eddy dispersion, and trans-particle mass transfer in bulk, random packings of core-shell particles with varied shell thickness and shell diffusion coefficient.

PubMed

Daneyko, Anton; Hlushkou, Dzmitry; Baranau, Vasili; Khirevich, Siarhei; Seidel-Morgenstern, Andreas; Tallarek, Ulrich

2015-08-14

In recent years, chromatographic columns packed with core-shell particles have been widely used for efficient and fast separations at comparatively low operating pressure. However, the influence of the porous shell properties on the mass transfer kinetics in core-shell packings is still not fully understood. We report on results obtained with a modeling approach to simulate three-dimensional advective-diffusive transport in bulk random packings of monosized core-shell particles, covering a range of reduced mobile phase flow velocities from 0.5 up to 1000. The impact of the effective diffusivity of analyte molecules in the porous shell and the shell thickness on the resulting plate height was investigated. An extension of Giddings' theory of coupled eddy dispersion to account for retention of analyte molecules due to stagnant regions in porous shells with zero mobile phase flow velocity is presented. The plate height equation involving a modified eddy dispersion term excellently describes simulated data obtained for particle-packings with varied shell thickness and shell diffusion coefficient. It is confirmed that the model of trans-particle mass transfer resistance of core-shell particles by Kaczmarski and Guiochon [42] is applicable up to a constant factor. We analyze individual contributions to the plate height from different mass transfer mechanisms in dependence of the shell parameters. The simulations demonstrate that a reduction of plate height in packings of core-shell relative to fully porous particles arises mainly due to reduced trans-particle mass transfer resistance and transchannel eddy dispersion. Copyright © 2015 Elsevier B.V. All rights reserved.

Diffusion of innovations in Axelrod’s model

NASA Astrophysics Data System (ADS)

Tilles, Paulo F. C.; Fontanari, José F.

2015-11-01

Axelrod's model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e., individuals become more similar when they interact) and homophily (i.e., individuals interact preferentially with similar others). The strength of these social influences are controlled by two parameters: $F$, the number of features that characterizes the cultures and $q$, the common number of states each feature can assume. Here we assume that the innovation is a new state of a cultural feature of a single individual -- the innovator -- and study how the innovation spreads through the networks among the individuals. For infinite regular lattices in one (1D) and two dimensions (2D), we find that initially the successful innovation spreads linearly with the time $t$, but in the long-time limit it spreads diffusively ($\\sim t^{1/2}$) in 1D and sub-diffusively ($\\sim t/\\ln t$) in 2D. For finite lattices, the growth curves for the number of adopters are typically concave functions of $t$. For random graphs with a finite number of nodes $N$, we argue that the classical S-shaped growth curves result from a trade-off between the average connectivity $K$ of the graph and the per feature diversity $q$. A large $q$ is needed to reduce the pace of the initial spreading of the innovation and thus delimit the early-adopters stage, whereas a large $K$ is necessary to ensure the onset of the take-off stage at which the number of adopters grows superlinearly with $t$. In an infinite random graph we find that the number of adopters of a successful innovation scales with $t^\\gamma$ with $\\gamma =1$ for $K> 2$ and $1/2 < \\gamma < 1$ for $K=2$. We suggest that the exponent $\\gamma$ may be a useful index to characterize the process of diffusion of successful innovations in diverse scenarios.

Slowdown of surface diffusion during early stages of bacterial colonization

NASA Astrophysics Data System (ADS)

Vourc'h, T.; Peerhossaini, H.; Léopoldès, J.; Méjean, A.; Chauvat, F.; Cassier-Chauvat, C.

2018-03-01

We study the surface diffusion of the model cyanobacterium Synechocystis sp. PCC6803 during the incipient stages of cell contact with a glass surface in the dilute regime. We observe a twitching motility with alternating immobile tumble and mobile run periods, resulting in a normal diffusion described by a continuous-time random walk with a coefficient of diffusion D . Surprisingly, D is found to decrease with time down to a plateau. This is observed only when the cyanobacterial cells are able to produce released extracellular polysaccharides, as shown by a comparative study between the wild-type strain and various polysaccharides-depleted mutants. The analysis of the trajectories taken by the bacterial cells shows that the temporal characteristics of their intermittent motion depend on the instantaneous fraction of visited sites during diffusion. This describes quantitatively the time dependence of D , related to the progressive surface coverage by the polysaccharides. The observed slowdown of the surface diffusion may constitute a basic precursor mechanism for microcolony formation and provides clues for controlling biofilm formation.

The angular distribution of diffusely backscattered light

NASA Astrophysics Data System (ADS)

Vera, M. U.; Durian, D. J.

1997-03-01

The diffusion approximation predicts the angular distribution of light diffusely transmitted through an opaque slab to depend only on boundary reflectivity, independent of scattering anisotropy, and this has been verified by experiment(M.U. Vera and D.J. Durian, Phys. Rev. E 53) 3215 (1996). Here, by contrast, we demonstrate that the angular distribution of diffusely backscattered light depends on scattering anisotropy as well as boundary reflectivity. To model this observation scattering anisotropy is added to the diffusion approximation by a discontinuity in the photon concentration at the source point that is proportional to the average cosine of the scattering angle. We compare the resulting predictions with random walk simulations and with measurements of diffusely backscattered intensity versus angle for glass frits and aqueous suspensions of polystyrene spheres held in air or immersed in a water bath. Increasing anisotropy and boundary reflectivity each tend to flatten the predicted distributions, and for different combinations of anisotropy and reflectivity the agreement between data and predictions ranges from qualitatively to quantitatively good.

Electronic Noise and Fluctuations in Solids

NASA Astrophysics Data System (ADS)

Kogan, Sh.

2008-07-01

Preface; Part I. Introduction. Some Basic Concepts of the Theory of Random Processes: 1. Probability density functions. Moments. Stationary processes; 2. Correlation function; 3. Spectral density of noise; 4. Ergodicity and nonergodicity of random processes; 5. Random pulses and shot noise; 6. Markov processes. General theory; 7. Discrete Markov processes. Random telegraph noise; 8. Quasicontinuous (Diffusion-like) Markov processes; 9. Brownian motion; 10. Langevin approach to the kinetics of fluctuations; Part II. Fluctuation-Dissipation Relations in Equilibrium Systems: 11. Derivation of fluctuation-dissipation relations; 12. Equilibrium noise in quasistationary circuits. Nyquist theorem; 13. Fluctuations of electromagnetic fields in continuous media; Part III. Fluctuations in Nonequilibrium Gases: 14. Some basic concepts of hot-electrons' physics; 15. Simple model of current fluctuations in a semiconductor with hot electrons; 16. General kinetic theory of quasiclassical fluctuations in a gas of particles. The Boltzmann-Langevin equation; 17. Current fluctuations and noise temperature; 18. Current fluctuations and diffusion in a gas of hot electrons; 19. One-time correlation in nonequilibrium gases; 20. Intervalley noise in multivalley semiconductors; 21. Noise of hot electrons emitting optical phonons in the streaming regime; 22. Noise in a semiconductor with a postbreakdown stable current filament; Part IV. Generation-recombination noise: 23. G-R noise in uniform unipolar semiconductors; 24. Noise produced by recombination and diffusion; Part V. Noise in quantum ballistic systems: 25. Introduction; 26. Equilibrium noise and shot noise in quantum conductors; 27. Modulation noise in quantum point contacts; 28. Transition from a ballistic conductor to a macroscopic one; 29. Noise in tunnel junctions; Part VI. Resistance noise in metals: 30. Incoherent scattering of electrons by mobile defects; 31. Effect of mobile scattering centers on the electron interference pattern; 32. Fluctuations of the number of diffusing scattering centers; 33. Temperature fluctuations and the corresponding noise; Part VII. Noise in strongly disordered conductors: 34. Basic ideas of the percolation theory; 35. Resistance fluctuations in percolation systems. 36. Experiments; Part VIII. Low-frequency noise with an 1/f-type spectrum and random telegraph noise: 37. Introduction; 38. Some general properties of 1/f noise; 39. Basic models of 1/f noise; 40./f noise in metals; 41. Low-frequency noise in semiconductors; 42. Magnetic noise in spin glasses and some other magnetic systems; 43. Temperature fluctuations as a possible source of 1/f noise; 44. Random telegraph noise; 45. Fluctuations with 1/f spectrum in other systems; 46. General conclusions on 1/f noise; Part IX. Noise in Superconductors and Superconducting Structures: 47. Noise in Josephson junctions; 48. Noise in type II superconductors; References; Subject index.

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.

Distribution of randomly diffusing particles in inhomogeneous media

NASA Astrophysics Data System (ADS)

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

2017-09-01

Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct particle hopping rates. Starting from the master equations (MEs) governing diffusion in inhomogeneous media we derive here, for arbitrary spatial dimensions, the deterministic lattice equations (DLEs) specifying the average particle number at each lattice site for randomly diffusing particles in inhomogeneous media. We consider the case of free (Fickian) diffusion with no steric constraints on the maximum particle number per lattice site as well as the case of diffusion under steric constraints imposing a maximum particle concentration. We find, for both transient and asymptotic regimes, excellent agreement between the DLEs and kinetic Monte Carlo simulations of the MEs. The DLEs provide a computationally efficient method for predicting the (average) distribution of randomly diffusing particles in inhomogeneous media, with the number of DLEs associated with a given system being independent of the number of particles in the system. From the DLEs we obtain general analytic expressions for the steady-state particle distributions for free diffusion and, in special cases, diffusion under steric constraints in inhomogeneous media. We find that, in the steady state of the system, the average fraction of particles in a given domain is independent of most system properties, such as the arrangement and shape of domains, and only depends on the number of lattice sites in each domain, the particle hopping rates, the number of distinct particle species in the system, and the total number of particles of each particle species in the system. Our results provide general insights into the role of spatially inhomogeneous particle hopping rates in setting the particle distributions in inhomogeneous media.

Network diffusion accurately models the relationship between structural and functional brain connectivity networks

PubMed Central

Abdelnour, Farras; Voss, Henning U.; Raj, Ashish

2014-01-01

The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brain’s long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways. PMID:24384152

Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species

NASA Astrophysics Data System (ADS)

Chen, Xiuqing; Daus, Esther S.; Jüngel, Ansgar

2018-02-01

The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The equations are considered in a bounded domain with homogeneous Neumann boundary conditions. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. Under detailed balance (and without reaction) the entropy is nonincreasing in time, but counter-examples show that the entropy may increase initially if detailed balance does not hold.

The role of educational trainings in the diffusion of smart metering platforms: An agent-based modeling approach

NASA Astrophysics Data System (ADS)

Weron, Tomasz; Kowalska-Pyzalska, Anna; Weron, Rafał

2018-09-01

Using an agent-based modeling approach we examine the impact of educational programs and trainings on the diffusion of smart metering platforms (SMPs). We also investigate how social responses, like conformity or independence, mass-media advertising as well as opinion stability impact the transition from predecisional and preactional behavioral stages (opinion formation) to actional and postactional stages (decision-making) of individual electricity consumers. We find that mass-media advertising (i.e., a global external field) and educational trainings (i.e., a local external field) lead to similar, though not identical adoption rates. Secondly, that spatially concentrated 'group' trainings are never worse than randomly scattered ones, and for a certain range of parameters are significantly better. Finally, that by manipulating the time required by an agent to make a decision, e.g., through promotions, we can speed up or slow down the diffusion of SMPs.

Random walk of passive tracers among randomly moving obstacles.

PubMed

Gori, Matteo; Donato, Irene; Floriani, Elena; Nardecchia, Ilaria; Pettini, Marco

2016-04-14

This study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles. The relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance. The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down.

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.

Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2016-11-01

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

Transport dissipative particle dynamics model for mesoscopic advection- diffusion-reaction problems

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

Zhen, Li; Yazdani, Alireza; Tartakovsky, Alexandre M.

2015-07-07

We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic DPD framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux and a random flux between particles, and an analytical formula is proposed to relate the mesoscopic concentration friction to the effective diffusion coefficient. To validate the present tDPD model and the boundary conditions, we perform three tDPDmore » simulations of one-dimensional diffusion with different boundary conditions, and the results show excellent agreement with the theoretical solutions. We also performed two-dimensional simulations of ADR systems and the tDPD simulations agree well with the results obtained by the spectral element method. Finally, we present an application of the tDPD model to the dynamic process of blood coagulation involving 25 reacting species in order to demonstrate the potential of tDPD in simulating biological dynamics at the mesoscale. We find that the tDPD solution of this comprehensive 25-species coagulation model is only twice as computationally expensive as the DPD simulation of the hydrodynamics only, which is a significant advantage over available continuum solvers.« less

Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy

NASA Astrophysics Data System (ADS)

Bizheva, Kostadinka K.; Siegel, Andy M.; Boas, David A.

1998-12-01

We used low coherence interferometry to measure Brownian motion within highly scattering random media. A coherence gate was applied to resolve the optical path-length distribution and to separate ballistic from diffusive light. Our experimental analysis provides details on the transition from single scattering to light diffusion and its dependence on the system parameters. We found that the transition to the light diffusion regime occurs at shorter path lengths for media with higher scattering anisotropy or for larger numerical aperture of the focusing optics.

Single-particle trajectories reveal two-state diffusion-kinetics of hOGG1 proteins on DNA.

PubMed

Vestergaard, Christian L; Blainey, Paul C; Flyvbjerg, Henrik

2018-03-16

We reanalyze trajectories of hOGG1 repair proteins diffusing on DNA. A previous analysis of these trajectories with the popular mean-squared-displacement approach revealed only simple diffusion. Here, a new optimal estimator of diffusion coefficients reveals two-state kinetics of the protein. A simple, solvable model, in which the protein randomly switches between a loosely bound, highly mobile state and a tightly bound, less mobile state is the simplest possible dynamic model consistent with the data. It yields accurate estimates of hOGG1's (i) diffusivity in each state, uncorrupted by experimental errors arising from shot noise, motion blur and thermal fluctuations of the DNA; (ii) rates of switching between states and (iii) rate of detachment from the DNA. The protein spends roughly equal time in each state. It detaches only from the loosely bound state, with a rate that depends on pH and the salt concentration in solution, while its rates for switching between states are insensitive to both. The diffusivity in the loosely bound state depends primarily on pH and is three to ten times higher than in the tightly bound state. We propose and discuss some new experiments that take full advantage of the new tools of analysis presented here.

Postural control model interpretation of stabilogram diffusion analysis

NASA Technical Reports Server (NTRS)

Peterka, R. J.

2000-01-01

Collins and De Luca [Collins JJ. De Luca CJ (1993) Exp Brain Res 95: 308-318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior.

Materials Outgassing Rate Decay in Vacuum at Isothermal Conditions

NASA Technical Reports Server (NTRS)

Huang, Alvin Y.; Kastanas, George N.; Kramer, Leonard; Soares, Carlos E.; Mikatarian, Ronald R.

2016-01-01

As a laboratory for scientific research, the International Space Station has been in Low Earth Orbit for nearly 20 years and is expected to be on-orbit for another 10 years. The ISS has been maintaining a relatively pristine contamination environment for science payloads. Materials outgassing induced contamination is currently the dominant source for sensitive surfaces on ISS and modeling the outgassing rate decay over a 20 to 30 year period is challenging. Materials outgassing is described herein as a diffusion-reaction process using ASTM E 1559 rate data. The observation of -1/2 (diffusion) or non-integers (reaction limited) as rate decay exponents for common ISS materials indicate classical reaction kinetics is unsatisfactory in modeling materials outgassing. Non-randomness of reactant concentrations at the interface is the source of this deviation from classical reaction kinetics. A diffusion limited decay was adopted as the result of the correlation of the contaminant layer thicknesses on returned ISS hardware, the existence of high outgassing silicone exhibiting near diffusion limited decay, and the confirmation of non-depleted material after ten years in the Low Earth Orbit.Keywords: Materials Outgassing, ASTM E 1559, Reaction Kinetics, Diffusion, Space Environments Effects, Contamination

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.

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.

Random-order fractional bistable system and its stochastic resonance

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Direct Simulation of Extinction in a Slab of Spherical Particles

NASA Technical Reports Server (NTRS)

Mackowski, D.W.; Mishchenko, Michael I.

2013-01-01

The exact multiple sphere superposition method is used to calculate the coherent and incoherent contributions to the ensemble-averaged electric field amplitude and Poynting vector in systems of randomly positioned nonabsorbing spherical particles. The target systems consist of cylindrical volumes, with radius several times larger than length, containing spheres with positional configurations generated by a Monte Carlo sampling method. Spatially dependent values for coherent electric field amplitude, coherent energy flux, and diffuse energy flux, are calculated by averaging of exact local field and flux values over multiple configurations and over spatially independent directions for fixed target geometry, sphere properties, and sphere volume fraction. Our results reveal exponential attenuation of the coherent field and the coherent energy flux inside the particulate layer and thereby further corroborate the general methodology of the microphysical radiative transfer theory. An effective medium model based on plane wave transmission and reflection by a plane layer is used to model the dependence of the coherent electric field on particle packing density. The effective attenuation coefficient of the random medium, computed from the direct simulations, is found to agree closely with effective medium theories and with measurements. In addition, the simulation results reveal the presence of a counter-propagating component to the coherent field, which arises due to the internal reflection of the main coherent field component by the target boundary. The characteristics of the diffuse flux are compared to, and found to be consistent with, a model based on the diffusion approximation of the radiative transfer theory.

Collective behavior of minus-ended motors in mitotic microtubule asters gliding toward DNA

NASA Astrophysics Data System (ADS)

Athale, Chaitanya A.; Dinarina, Ana; Nedelec, Francois; Karsenti, Eric

2014-02-01

Microtubules (MTs) nucleated by centrosomes form star-shaped structures referred to as asters. Aster motility and dynamics is vital for genome stability, cell division, polarization and differentiation. Asters move either toward the cell center or away from it. Here, we focus on the centering mechanism in a membrane independent system of Xenopus cytoplasmic egg extracts. Using live microscopy and single particle tracking, we find that asters move toward chromatinized DNA structures. The velocity and directionality profiles suggest a random-walk with drift directed toward DNA. We have developed a theoretical model that can explain this movement as a result of a gradient of MT length dynamics and MT gliding on immobilized dynein motors. In simulations, the antagonistic action of the motor species on the radial array of MTs leads to a tug-of-war purely due to geometric considerations and aster motility resembles a directed random-walk. Additionally, our model predicts that aster velocities do not change greatly with varying initial distance from DNA. The movement of asymmetric asters becomes increasingly super-diffusive with increasing motor density, but for symmetric asters it becomes less super-diffusive. The transition of symmetric asters from superdiffusive to diffusive mobility is the result of number fluctuations in bound motors in the tug-of-war. Overall, our model is in good agreement with experimental data in Xenopus cytoplasmic extracts and predicts novel features of the collective effects of motor-MT interactions.

Nonlocal operators, parabolic-type equations, and ultrametric random walks

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

Chacón-Cortes, L. F., E-mail: fchaconc@math.cinvestav.edu.mx; Zúñiga-Galindo, W. A., E-mail: wazuniga@math.cinvestav.edu.mx

2013-11-15

In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the numbermore » of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.« less

Enhanced hyperuniformity from random reorganization.

PubMed

Hexner, Daniel; Chaikin, Paul M; Levine, Dov

2017-04-25

Diffusion relaxes density fluctuations toward a uniform random state whose variance in regions of volume [Formula: see text] scales as [Formula: see text] Systems whose fluctuations decay faster, [Formula: see text] with [Formula: see text], are called hyperuniform. The larger [Formula: see text], the more uniform, with systems like crystals achieving the maximum value: [Formula: see text] Although finite temperature equilibrium dynamics will not yield hyperuniform states, driven, nonequilibrium dynamics may. Such is the case, for example, in a simple model where overlapping particles are each given a small random displacement. Above a critical particle density [Formula: see text], the system evolves forever, never finding a configuration where no particles overlap. Below [Formula: see text], however, it eventually finds such a state, and stops evolving. This "absorbing state" is hyperuniform up to a length scale [Formula: see text], which diverges at [Formula: see text] An important question is whether hyperuniformity survives noise and thermal fluctuations. We find that hyperuniformity of the absorbing state is not only robust against noise, diffusion, or activity, but that such perturbations reduce fluctuations toward their limiting behavior, [Formula: see text], a uniformity similar to random close packing and early universe fluctuations, but with arbitrary controllable density.

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.

Quantitative metrics for evaluating parallel acquisition techniques in diffusion tensor imaging at 3 Tesla.

PubMed

Ardekani, Siamak; Selva, Luis; Sayre, James; Sinha, Usha

2006-11-01

Single-shot echo-planar based diffusion tensor imaging is prone to geometric and intensity distortions. Parallel imaging is a means of reducing these distortions while preserving spatial resolution. A quantitative comparison at 3 T of parallel imaging for diffusion tensor images (DTI) using k-space (generalized auto-calibrating partially parallel acquisitions; GRAPPA) and image domain (sensitivity encoding; SENSE) reconstructions at different acceleration factors, R, is reported here. Images were evaluated using 8 human subjects with repeated scans for 2 subjects to estimate reproducibility. Mutual information (MI) was used to assess the global changes in geometric distortions. The effects of parallel imaging techniques on random noise and reconstruction artifacts were evaluated by placing 26 regions of interest and computing the standard deviation of apparent diffusion coefficient and fractional anisotropy along with the error of fitting the data to the diffusion model (residual error). The larger positive values in mutual information index with increasing R values confirmed the anticipated decrease in distortions. Further, the MI index of GRAPPA sequences for a given R factor was larger than the corresponding mSENSE images. The residual error was lowest in the images acquired without parallel imaging and among the parallel reconstruction methods, the R = 2 acquisitions had the least error. The standard deviation, accuracy, and reproducibility of the apparent diffusion coefficient and fractional anisotropy in homogenous tissue regions showed that GRAPPA acquired with R = 2 had the least amount of systematic and random noise and of these, significant differences with mSENSE, R = 2 were found only for the fractional anisotropy index. Evaluation of the current implementation of parallel reconstruction algorithms identified GRAPPA acquired with R = 2 as optimal for diffusion tensor imaging.

Modeling Transport of Cesium in Grimsel Granodiorite With Micrometer Scale Heterogeneities and Dynamic Update of Kd

NASA Astrophysics Data System (ADS)

Voutilainen, Mikko; Kekäläinen, Pekka; Siitari-Kauppi, Marja; Sardini, Paul; Muuri, Eveliina; Timonen, Jussi; Martin, Andrew

2017-11-01

Transport and retardation of cesium in Grimsel granodiorite taking into account heterogeneity of mineral and pore structure was studied using rock samples overcored from an in situ diffusion test at the Grimsel Test Site. The field test was part of the Long-Term Diffusion (LTD) project designed to characterize retardation properties (diffusion and distribution coefficients) under in situ conditions. Results of the LTD experiment for cesium showed that in-diffusion profiles and spatial concentration distributions were strongly influenced by the heterogeneous pore structure and mineral distribution. In order to study the effect of heterogeneity on the in-diffusion profile and spatial concentration distribution, a Time Domain Random Walk (TDRW) method was applied along with a feature for modeling chemical sorption in geological materials. A heterogeneous mineral structure of Grimsel granodiorite was constructed using X-ray microcomputed tomography (X-μCT) and the map was linked to previous results for mineral specific porosities and distribution coefficients (Kd) that were determined using C-14-PMMA autoradiography and batch sorption experiments, respectively. After this the heterogeneous structure contains information on local porosity and Kd in 3-D. It was found that the heterogeneity of the mineral structure on the micrometer scale affects significantly the diffusion and sorption of cesium in Grimsel granodiorite at the centimeter scale. Furthermore, the modeled in-diffusion profiles and spatial concentration distributions show similar shape and pattern to those from the LTD experiment. It was concluded that the use of detailed structure characterization and quantitative data on heterogeneity can significantly improve the interpretation and evaluation of transport experiments.

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.

Antipersistent dynamics in kinetic models of wealth exchange

NASA Astrophysics Data System (ADS)

Goswami, Sanchari; Chatterjee, Arnab; Sen, Parongama

2011-11-01

We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. An earlier work suggested that a walk in an abstract gain-loss space can be conceived for the agents. For models in which agents do not save, or save with uniform saving propensity, the walk has diffusive behavior. For the case in which the saving propensity λ is distributed randomly (0≤λ<1), the resultant walk showed a ballistic nature (except at a particular value of λ*≈0.47). Here we consider several other features of the walk with random λ. While some macroscopic properties of this walk are comparable to a biased random walk, at microscopic level, there are gross differences. The difference turns out to be due to an antipersistent tendency toward making a gain (loss) immediately after making a loss (gain). This correlation is in fact present in kinetic models without saving or with uniform saving as well, such that the corresponding walks are not identical to ordinary random walks. In the distributed saving case, antipersistence occurs with a simultaneous overall bias.

Ocean Turbulence V: Mesoscale Modeling in Level Coordinates. The Effect of Random Nature of Density

NASA Technical Reports Server (NTRS)

Canuto, V. M.; Dubovikov, M. S.

1998-01-01

The main result of this paper is the derivation of a new expression for the tracer subgrid term in level coordinates S(l) to be employed in O-GCM. The novel feature is the proper account of the random nature of the density field which strongly affects the transformation from isopycnal to level coordinates of the variables of interest, velocity and tracer fields, their correlation functions and ultimately the subgrid terms. In deriving our result we made use of measured properties of vertical ocean turbulence. The major new results are: 1) the new subgrid expression is different from that of the heuristic GM model, 2) u++(tracer)=1/2u+(thickness), where u++ and u+ are the tracer and thickness bolus velocities. In previous models, u++ = u+, 2) the subgrid for a tracer tau is not the same as that for the density rho even when one accounts for the obvious absence of a diffusion term in the latter. The difference stems from a new treatment of the stochastic nature of the density, 3) the mesoscale diffusivity enters both locally and non-locally, as the integral over all z's from the bottom of the ocean to the level z.

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.

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

PubMed

Kucza, Witold

2013-07-25

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

Different approach to the modeling of nonfree particle diffusion

NASA Astrophysics Data System (ADS)

Buhl, Niels

2018-03-01

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore networks to general geometric domains can be considered and that the (free random walk) central limit theorem can be generalized to cover also the nonfree case. The latter gives rise to a continuum-limit description of the diffusive motion where the effect of partially absorbing barriers is accounted for in a natural and non-Markovian way that, in contrast to the traditional approach, quantifies the absorptivity of a barrier in terms of a dimensionless parameter in the range 0 to 1. The generalized theorem gives two general analytic expressions for the continuum-limit propagator: an infinite sum of Gaussians and an infinite sum of plane waves. These expressions entail the known method-of-images and Laplace eigenfunction expansions as special cases and show how the presence of partially absorbing barriers can lead to phenomena such as line splitting and band gap formation in the plane wave wave-number spectrum.

Optical Interactions at Randomly Rough Surfaces

DTIC Science & Technology

2003-03-10

frequency range. The design of a random surface that acts as a Lambertian diffuser, especially in the infrared region of the optical spectrum, is...FTIR grazing angle microscopy. Recently, an experimental study was performed of the far-field scattering at small grazing angles, especially the enhanced...a specular component in the scattered light, in this frequency range. The design of a random surface that acts as a Lambertian diffuser, especially in

Magnetic orientation of nontronite clay in aqueous dispersions and its effect on water diffusion.

PubMed

Abrahamsson, Christoffer; Nordstierna, Lars; Nordin, Matias; Dvinskikh, Sergey V; Nydén, Magnus

2015-01-01

The diffusion rate of water in dilute clay dispersions depends on particle concentration, size, shape, aggregation and water-particle interactions. As nontronite clay particles magnetically align parallel to the magnetic field, directional self-diffusion anisotropy can be created within such dispersion. Here we study water diffusion in exfoliated nontronite clay dispersions by diffusion NMR and time-dependant 1H-NMR-imaging profiles. The dispersion clay concentration was varied between 0.3 and 0.7 vol%. After magnetic alignment of the clay particles in these dispersions a maximum difference of 20% was measured between the parallel and perpendicular self-diffusion coefficients in the dispersion with 0.7 vol% clay. A method was developed to measure water diffusion within the dispersion in the absence of a magnetic field (random clay orientation) as this is not possible with standard diffusion NMR. However, no significant difference in self-diffusion coefficient between random and aligned dispersions could be observed. Copyright © 2014 Elsevier Inc. All rights reserved.

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

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

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

Electrochemical Impedance Imaging via the Distribution of Diffusion Times

NASA Astrophysics Data System (ADS)

Song, Juhyun; Bazant, Martin Z.

2018-03-01

We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) or Gerischer (reaction-diffusion) circuit elements. A robust DDT inversion method is presented based on complex nonlinear least squares regression with Tikhonov regularization and illustrated for three cases of nanostructured electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow battery. The results demonstrate the feasibility of nondestructive "impedance imaging" to infer microstructural statistics of random, heterogeneous materials.

Cross-frequency and band-averaged response variance prediction in the hybrid deterministic-statistical energy analysis method

NASA Astrophysics Data System (ADS)

Reynders, Edwin P. B.; Langley, Robin S.

2018-08-01

The hybrid deterministic-statistical energy analysis method has proven to be a versatile framework for modeling built-up vibro-acoustic systems. The stiff system components are modeled deterministically, e.g., using the finite element method, while the wave fields in the flexible components are modeled as diffuse. In the present paper, the hybrid method is extended such that not only the ensemble mean and variance of the harmonic system response can be computed, but also of the band-averaged system response. This variance represents the uncertainty that is due to the assumption of a diffuse field in the flexible components of the hybrid system. The developments start with a cross-frequency generalization of the reciprocity relationship between the total energy in a diffuse field and the cross spectrum of the blocked reverberant loading at the boundaries of that field. By making extensive use of this generalization in a first-order perturbation analysis, explicit expressions are derived for the cross-frequency and band-averaged variance of the vibrational energies in the diffuse components and for the cross-frequency and band-averaged variance of the cross spectrum of the vibro-acoustic field response of the deterministic components. These expressions are extensively validated against detailed Monte Carlo analyses of coupled plate systems in which diffuse fields are simulated by randomly distributing small point masses across the flexible components, and good agreement is found.

A model for bacterial colonization of sinking aggregates.

PubMed

Bearon, R N

2007-01-01

Sinking aggregates provide important nutrient-rich environments for marine bacteria. Quantifying the rate at which motile bacteria colonize such aggregations is important in understanding the microbial loop in the pelagic food web. In this paper, a simple analytical model is presented to predict the rate at which bacteria undergoing a random walk encounter a sinking aggregate. The model incorporates the flow field generated by the sinking aggregate, the swimming behavior of the bacteria, and the interaction of the flow with the swimming behavior. An expression for the encounter rate is computed in the limit of large Péclet number when the random walk can be approximated by a diffusion process. Comparison with an individual-based numerical simulation is also given.

Diffuse Scattering from Lead-Containing Ferroelectric Perovskite Oxides

DOE PAGES

Goossens, D. J.

2013-01-01

Ferroelectric materials rely on some type of non-centrosymmetric displacement correlations to give rise to a macroscopic polarisation. These displacements can show short-range order (SRO) that is reflective of the local chemistry, and so studying it reveals important information about how the structure gives rise to the technologically useful properties. A key means of exploring this SRO is diffuse scattering. Conventional structural studies use Bragg peak intensitiesto determine the average structure. In a single crystal diffuse scattering (SCDS) experiment, the coherent scattered intensity is measured at non-integer Miller indices, and can be used to examine the population of local configurations. Thismore » is because the diffuse scattering is sensitive to two-body averages, whereas the Bragg intensity gives single-body averages. This review outlines key results of SCDS studies on several materials and explores the similarities and differences in their diffuse scattering. Random strains are considered, as are models based on a phonon-like picture or a more local-chemistry oriented picture. Limitations of the technique are discussed.« less

Effect of Polydispersity on Diffusion in Random Obstacle Matrices

NASA Astrophysics Data System (ADS)

Cho, Hyun Woo; Kwon, Gyemin; Sung, Bong June; Yethiraj, Arun

2012-10-01

The dynamics of tracers in disordered matrices is of interest in a number of diverse areas of physics such as the biophysics of crowding in cells and cell membranes, and the diffusion of fluids in porous media. To a good approximation the matrices can be modeled as a collection of spatially frozen particles. In this Letter, we consider the effect of polydispersity (in size) of the matrix particles on the dynamics of tracers. We study a two dimensional system of hard disks diffusing in a sea of hard disk obstacles, for different values of the polydispersity of the matrix. We find that for a given average size and area fraction, the diffusion of tracers is very sensitive to the polydispersity. We calculate the pore percolation threshold using Apollonius diagrams. The diffusion constant, D, follows a scaling relation D˜(ϕc-ϕm)μ-β for all values of the polydispersity, where ϕm is the area fraction and ϕc is the value of ϕm at the percolation threshold.

Effect of polydispersity on diffusion in random obstacle matrices.

PubMed

Cho, Hyun Woo; Kwon, Gyemin; Sung, Bong June; Yethiraj, Arun

2012-10-12

The dynamics of tracers in disordered matrices is of interest in a number of diverse areas of physics such as the biophysics of crowding in cells and cell membranes, and the diffusion of fluids in porous media. To a good approximation the matrices can be modeled as a collection of spatially frozen particles. In this Letter, we consider the effect of polydispersity (in size) of the matrix particles on the dynamics of tracers. We study a two dimensional system of hard disks diffusing in a sea of hard disk obstacles, for different values of the polydispersity of the matrix. We find that for a given average size and area fraction, the diffusion of tracers is very sensitive to the polydispersity. We calculate the pore percolation threshold using Apollonius diagrams. The diffusion constant, D, follows a scaling relation D~(φ(c)-φ(m))(μ-β) for all values of the polydispersity, where φ(m) is the area fraction and φ(c) is the value of φ(m) at the percolation threshold.

Diffusion of massive particles around an Abelian-Higgs string

NASA Astrophysics Data System (ADS)

Saha, Abhisek; Sanyal, Soma

2018-03-01

We study the diffusion of massive particles in the space time of an Abelian Higgs string. The particles in the early universe plasma execute Brownian motion. This motion of the particles is modeled as a two dimensional random walk in the plane of the Abelian Higgs string. The particles move randomly in the space time of the string according to their geodesic equations. We observe that for certain values of their energy and angular momentum, an overdensity of particles is observed close to the string. We find that the string parameters determine the distribution of the particles. We make an estimate of the density fluctuation generated around the string as a function of the deficit angle. Though the thickness of the string is small, the length is large and the overdensity close to the string may have cosmological consequences in the early universe.

Diffusion of water in the endosperm tissue of wheat grains as studied by pulsed field gradient nuclear magnetic resonance.

PubMed

Callaghan, P T; Jolley, K W; Lelievre, J

1979-10-01

Pulsed field gradient nuclear magnetic resonance has been used to measure water self-diffusion coefficients in the endosperm tissue of wheat grains as a function of the tissue water content. A model that confines the water molecules to a randomly oriented array of capillaries with both transverse dimension less than 100 nm has been used to fit the data and give a unique diffusion coefficient at each water content. The diffusion rates vary from 1.8 x 10(-10) m2s-1 at the lowest to 1.2 x 10(-9) m2s-1 at the highest moisture content. This variation can be explained in terms of an increase in water film thickness from approximately 0.5 to approximately 2.5 nm over the moisture range investigated (200-360 mg g-1).

Random walks of colloidal probes in viscoelastic materials

NASA Astrophysics Data System (ADS)

Khan, Manas; Mason, Thomas G.

2014-04-01

To overcome limitations of using a single fixed time step in random walk simulations, such as those that rely on the classic Wiener approach, we have developed an algorithm for exploring random walks based on random temporal steps that are uniformly distributed in logarithmic time. This improvement enables us to generate random-walk trajectories of probe particles that span a highly extended dynamic range in time, thereby facilitating the exploration of probe motion in soft viscoelastic materials. By combining this faster approach with a Maxwell-Voigt model (MVM) of linear viscoelasticity, based on a slowly diffusing harmonically bound Brownian particle, we rapidly create trajectories of spherical probes in soft viscoelastic materials over more than 12 orders of magnitude in time. Appropriate windowing of these trajectories over different time intervals demonstrates that random walk for the MVM is neither self-similar nor self-affine, even if the viscoelastic material is isotropic. We extend this approach to spatially anisotropic viscoelastic materials, using binning to calculate the anisotropic mean square displacements and creep compliances along different orthogonal directions. The elimination of a fixed time step in simulations of random processes, including random walks, opens up interesting possibilities for modeling dynamics and response over a highly extended temporal dynamic range.

Formation of parametric images using mixed-effects models: a feasibility study.

PubMed

Huang, Husan-Ming; Shih, Yi-Yu; Lin, Chieh

2016-03-01

Mixed-effects models have been widely used in the analysis of longitudinal data. By presenting the parameters as a combination of fixed effects and random effects, mixed-effects models incorporating both within- and between-subject variations are capable of improving parameter estimation. In this work, we demonstrate the feasibility of using a non-linear mixed-effects (NLME) approach for generating parametric images from medical imaging data of a single study. By assuming that all voxels in the image are independent, we used simulation and animal data to evaluate whether NLME can improve the voxel-wise parameter estimation. For testing purposes, intravoxel incoherent motion (IVIM) diffusion parameters including perfusion fraction, pseudo-diffusion coefficient and true diffusion coefficient were estimated using diffusion-weighted MR images and NLME through fitting the IVIM model. The conventional method of non-linear least squares (NLLS) was used as the standard approach for comparison of the resulted parametric images. In the simulated data, NLME provides more accurate and precise estimates of diffusion parameters compared with NLLS. Similarly, we found that NLME has the ability to improve the signal-to-noise ratio of parametric images obtained from rat brain data. These data have shown that it is feasible to apply NLME in parametric image generation, and the parametric image quality can be accordingly improved with the use of NLME. With the flexibility to be adapted to other models or modalities, NLME may become a useful tool to improve the parametric image quality in the future. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

A new mathematical solution for predicting char activation reactions

USGS Publications Warehouse

Rafsanjani, H.H.; Jamshidi, E.; Rostam-Abadi, M.

2002-01-01

The differential conservation equations that describe typical gas-solid reactions, such as activation of coal chars, yield a set of coupled second-order partial differential equations. The solution of these coupled equations by exact analytical methods is impossible. In addition, an approximate or exact solution only provides predictions for either reaction- or diffusion-controlling cases. A new mathematical solution, the quantize method (QM), was applied to predict the gasification rates of coal char when both chemical reaction and diffusion through the porous char are present. Carbon conversion rates predicted by the QM were in closer agreement with the experimental data than those predicted by the random pore model and the simple particle model. ?? 2002 Elsevier Science Ltd. All rights reserved.

Ionic conductivity and dielectric relaxation in Y doped La2Mo2O9 oxide-ion conductors

NASA Astrophysics Data System (ADS)

Paul, T.; Ghosh, A.

2014-10-01

In this work, we have studied electrical conductivity and dielectric properties of polycrystalline La2-xYxMo2O9 (0.05 ≤ x ≤ 0.3) compounds in the temperature range from 358 K to 1088 K and the frequency range from 10 Hz to 3 GHz. The bulk and grain boundary contributions to the overall conductivity of these compounds show Arrhenius type behavior at low temperatures. The random free-energy barrier model has been used to analyze the frequency dependence of the conductivity. The charge carrier relaxation time and its activation energy have been determined from the analysis of the conductivity spectra using this model. The results obtained from the random free-energy barrier model satisfy Barton-Nakajima-Namikawa relation. The conduction mechanism has been also predicted using random free-energy barrier model and the scaling formalism. We have observed that the dielectric relaxation peaks arise from the diffusion of oxygen ions via vacancies.

Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.

PubMed

Wang, Hongli; Ouyang, Qi

2007-11-23

The statistical properties of self-replicating spots in the reaction-diffusion Gray-Scott model are analyzed. In the chaotic regime of the system, the spots that dominate the spatiotemporal chaos grow and divide in two or decay into the background randomly and continuously. The rates at which the spots are created and decay are observed to be linearly dependent on the number of spots in the system. We derive a probabilistic description of the spot dynamics based on the statistical independence of spots and thus propose a characterization of the spatiotemporal chaos dominated by replicating spots.

Flow and diffusion of high-stakes test scores.

PubMed

Marder, M; Bansal, D

2009-10-13

We apply visualization and modeling methods for convective and diffusive flows to public school mathematics test scores from Texas. We obtain plots that show the most likely future and past scores of students, the effects of random processes such as guessing, and the rate at which students appear in and disappear from schools. We show that student outcomes depend strongly upon economic class, and identify the grade levels where flows of different groups diverge most strongly. Changing the effectiveness of instruction in one grade naturally leads to strongly nonlinear effects on student outcomes in subsequent grades.

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.

Measurements of True Leak Rates of MEMS Packages

PubMed Central

Han, Bongtae

2012-01-01

Gas transport mechanisms that characterize the hermetic behavior of MEMS packages are fundamentally different depending upon which sealing materials are used in the packages. In metallic seals, gas transport occurs through a few nanoscale leak channels (gas conduction) that are produced randomly during the solder reflow process, while gas transport in polymeric seals occurs through the bulk material (gas diffusion). In this review article, the techniques to measure true leak rates of MEMS packages with the two sealing materials are described and discussed: a Helium mass spectrometer based technique for metallic sealing and a gas diffusion based model for polymeric sealing. PMID:22736994

Statistical analysis of vibration in tyres

NASA Astrophysics Data System (ADS)

Le Bot, Alain; Bazari, Zakia; Klein, Philippe; Lelong, Joël

2017-03-01

The vibration in tyres submitted to random forces in the contact zone is investigated with the model of prestressed orthotropic plate on visco-elastic foundation. It is shown that beyond a cut-on frequency a single wave propagates whose speed is directional-dependent. A systematic numerical exploration of the governing equation solutions shows that three regimes may exist in such plates. These are modal field, diffuse field and free field. For actual tyres which present a high level of damping, the passage from low to high frequencies generally explores the modal and free field regimes but not the diffuse field regime.

Physics of ultra-high bioproductivity in algal photobioreactors

NASA Astrophysics Data System (ADS)

Greenwald, Efrat; Gordon, Jeffrey M.; Zarmi, Yair

2012-04-01

Cultivating algae at high densities in thin photobioreactors engenders time scales for random cell motion that approach photosynthetic rate-limiting time scales. This synchronization allows bioproductivity above that achieved with conventional strategies. We show that a diffusion model for cell motion (1) accounts for high bioproductivity at irradiance values previously deemed restricted by photoinhibition, (2) predicts the existence of optimal culture densities and their dependence on irradiance, consistent with available data, (3) accounts for the observed degree to which mixing improves bioproductivity, and (4) provides an estimate of effective cell diffusion coefficients, in accord with independent hydrodynamic estimates.

Self-diffusion in a system of interacting Langevin particles

NASA Astrophysics Data System (ADS)

Dean, D. S.; Lefèvre, A.

2004-06-01

The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature β and the particle density ρ . The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small β and ρβ constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.

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.

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

PubMed Central

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

2011-01-01

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

Efficiency analysis of diffusion on T-fractals in the sense of random walks.

PubMed

Peng, Junhao; Xu, Guoai

2014-04-07

Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results.

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).

Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems

PubMed Central

Yazdani, Alireza; Tartakovsky, Alexandre; Karniadakis, George Em

2015-01-01

We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic dissipative particle dynamics (DPD) framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux and a random flux between tDPD particles, and the advection is implicitly considered by the movements of these Lagrangian particles. An analytical formula is proposed to relate the tDPD parameters to the effective diffusion coefficient. To validate the present tDPD model and the boundary conditions, we perform three tDPD simulations of one-dimensional diffusion with different boundary conditions, and the results show excellent agreement with the theoretical solutions. We also performed two-dimensional simulations of ADR systems and the tDPD simulations agree well with the results obtained by the spectral element method. Finally, we present an application of the tDPD model to the dynamic process of blood coagulation involving 25 reacting species in order to demonstrate the potential of tDPD in simulating biological dynamics at the mesoscale. We find that the tDPD solution of this comprehensive 25-species coagulation model is only twice as computationally expensive as the conventional DPD simulation of the hydrodynamics only, which is a significant advantage over available continuum solvers. PMID:26156459

On the generation of log-Lévy distributions and extreme randomness

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2011-10-01

The log-normal distribution is prevalent across the sciences, as it emerges from the combination of multiplicative processes and the central limit theorem (CLT). The CLT, beyond yielding the normal distribution, also yields the class of Lévy distributions. The log-Lévy distributions are the Lévy counterparts of the log-normal distribution, they appear in the context of ultraslow diffusion processes, and they are categorized by Mandelbrot as belonging to the class of extreme randomness. In this paper, we present a natural stochastic growth model from which both the log-normal distribution and the log-Lévy distributions emerge universally—the former in the case of deterministic underlying setting, and the latter in the case of stochastic underlying setting. In particular, we establish a stochastic growth model which universally generates Mandelbrot’s extreme randomness.

Retention modeling for ultra-thin density of Cu-based conductive bridge random access memory (CBRAM)

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

Aga, Fekadu Gochole; Woo, Jiyong; Lee, Sangheon

We investigate the effect of Cu concentration On-state resistance retention characteristics of W/Cu/Ti/HfO{sub 2}/Pt memory cell. The development of RRAM device for application depends on the understanding of the failure mechanism and the key parameters for device optimization. In this study, we develop analytical expression for cations (Cu{sup +}) diffusion model using Gaussian distribution for detailed analysis of data retention time at high temperature. It is found that the improvement of data retention time depends not only on the conductive filament (CF) size but also on Cu atoms concentration density in the CF. Based on the simulation result, better datamore » retention time is observed for electron wave function associated with Cu{sup +} overlap and an extended state formation. This can be verified by analytical calculation of Cu atom defects inside the filament, based on Cu{sup +} diffusion model. The importance of Cu diffusion for the device reliability and the corresponding local temperature of the filament were analyzed by COMSOL Multiphysics simulation.« less

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.

Product diffusion through on-demand information-seeking behaviour.

PubMed

Riedl, Christoph; Bjelland, Johannes; Canright, Geoffrey; Iqbal, Asif; Engø-Monsen, Kenth; Qureshi, Taimur; Sundsøy, Pål Roe; Lazer, David

2018-02-01

Most models of product adoption predict S-shaped adoption curves. Here we report results from two country-scale experiments in which we find linear adoption curves. We show evidence that the observed linear pattern is the result of active information-seeking behaviour: individuals actively pulling information from several central sources facilitated by modern Internet searches. Thus, a constant baseline rate of interest sustains product diffusion, resulting in a linear diffusion process instead of the S-shaped curve of adoption predicted by many diffusion models. The main experiment seeded 70 000 (48 000 in Experiment 2) unique voucher codes for the same product with randomly sampled nodes in a social network of approximately 43 million individuals with about 567 million ties. We find that the experiment reached over 800 000 individuals with 80% of adopters adopting the same product-a winner-take-all dynamic consistent with search engine driven rankings that would not have emerged had the products spread only through a network of social contacts. We provide evidence for (and characterization of) this diffusion process driven by active information-seeking behaviour through analyses investigating (a) patterns of geographical spreading; (b) the branching process; and (c) diffusion heterogeneity. Using data on adopters' geolocation we show that social spreading is highly localized, while on-demand diffusion is geographically independent. We also show that cascades started by individuals who actively pull information from central sources are more effective at spreading the product among their peers. © 2018 The Authors.

Product diffusion through on-demand information-seeking behaviour

PubMed Central

Bjelland, Johannes; Canright, Geoffrey; Iqbal, Asif; Qureshi, Taimur; Sundsøy, Pål Roe

2018-01-01

Most models of product adoption predict S-shaped adoption curves. Here we report results from two country-scale experiments in which we find linear adoption curves. We show evidence that the observed linear pattern is the result of active information-seeking behaviour: individuals actively pulling information from several central sources facilitated by modern Internet searches. Thus, a constant baseline rate of interest sustains product diffusion, resulting in a linear diffusion process instead of the S-shaped curve of adoption predicted by many diffusion models. The main experiment seeded 70 000 (48 000 in Experiment 2) unique voucher codes for the same product with randomly sampled nodes in a social network of approximately 43 million individuals with about 567 million ties. We find that the experiment reached over 800 000 individuals with 80% of adopters adopting the same product—a winner-take-all dynamic consistent with search engine driven rankings that would not have emerged had the products spread only through a network of social contacts. We provide evidence for (and characterization of) this diffusion process driven by active information-seeking behaviour through analyses investigating (a) patterns of geographical spreading; (b) the branching process; and (c) diffusion heterogeneity. Using data on adopters' geolocation we show that social spreading is highly localized, while on-demand diffusion is geographically independent. We also show that cascades started by individuals who actively pull information from central sources are more effective at spreading the product among their peers. PMID:29467257

Applications of a general random-walk theory for confined diffusion.

PubMed

Calvo-Muñoz, Elisa M; Selvan, Myvizhi Esai; Xiong, Ruichang; Ojha, Madhusudan; Keffer, David J; Nicholson, Donald M; Egami, Takeshi

2011-01-01

A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.

An efficient analytical model for baffled, multi-celled membrane-type acoustic metamaterial panels

NASA Astrophysics Data System (ADS)

Langfeldt, F.; Gleine, W.; von Estorff, O.

2018-03-01

A new analytical model for the oblique incidence sound transmission loss prediction of baffled panels with multiple subwavelength sized membrane-type acoustic metamaterial (MAM) unit cells is proposed. The model employs a novel approach via the concept of the effective surface mass density and approximates the unit cell vibrations in the form of piston-like displacements. This yields a coupled system of linear equations that can be solved efficiently using well-known solution procedures. A comparison with results from finite element model simulations for both normal and diffuse field incidence shows that the analytical model delivers accurate results as long as the edge length of the MAM unit cells is smaller than half the acoustic wavelength. The computation times for the analytical calculations are 100 times smaller than for the numerical simulations. In addition to that, the effect of flexible MAM unit cell edges compared to the fixed edges assumed in the analytical model is studied numerically. It is shown that the compliance of the edges has only a small impact on the transmission loss of the panel, except at very low frequencies in the stiffness-controlled regime. The proposed analytical model is applied to investigate the effect of variations of the membrane prestress, added mass, and mass eccentricity on the diffuse transmission loss of a MAM panel with 120 unit cells. Unlike most previous investigations of MAMs, these results provide a better understanding of the acoustic performance of MAMs under more realistic conditions. For example, it is shown that by varying these parameters deliberately in a checkerboard pattern, a new anti-resonance with large transmission loss values can be introduced. A random variation of these parameters, on the other hand, is shown to have only little influence on the diffuse transmission loss, as long as the standard deviation is not too large. For very large random variations, it is shown that the peak transmission loss value can be greatly diminished.

Stationary moments, diffusion limits, and extinction times for logistic growth with random catastrophes.

PubMed

Schlomann, Brandon H

2018-06-06

A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare, catastrophic events, which are increasingly observed at scales ranging from global fisheries to intestinal microbiota. Due to mathematical challenges, growth processes with random catastrophes are less well characterized and it remains unclear how their consequences differ from those of Gaussian processes. In the face of a changing climate and predicted increases in ecological catastrophes, as well as increased interest in harnessing microbes for therapeutics, these processes have never been more relevant. To better understand them, I revisit here a differential equation model of logistic growth coupled to density-independent catastrophes that arrive as a Poisson process, and derive new analytic results that reveal its statistical structure. First, I derive exact expressions for the model's stationary moments, revealing a single effective catastrophe parameter that largely controls low order statistics. Then, I use weak convergence theorems to construct its Gaussian analog in a limit of frequent, small catastrophes, keeping the stationary population mean constant for normalization. Numerically computing statistics along this limit shows how they transform as the dynamics shifts from catastrophes to diffusions, enabling quantitative comparisons. For example, the mean time to extinction increases monotonically by orders of magnitude, demonstrating significantly higher extinction risk under catastrophes than under diffusions. Together, these results provide insight into a wide range of stochastic dynamical systems important for ecology and conservation. Copyright © 2018 Elsevier Ltd. All rights reserved.

Transport behaviors of locally fractional coupled Brownian motors with fluctuating interactions

NASA Astrophysics Data System (ADS)

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

2018-09-01

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

Cloaks for suppression or enhancement of scattering of diffuse photon density waves

NASA Astrophysics Data System (ADS)

Renthlei, Lalruatfela; Ramakrishna, S. Anantha; Wanare, Harshawardhan

2018-07-01

Enhancement of wave-like characteristics of heavily damped diffuse photon density waves in a random medium by amplification can induce strongly localised resonances. These resonances can be used to either suppress or enhance scattering from an inhomogeneity in the random medium by cloaking the inhomogeneous region by a shell of random medium with the correct levels of absorption or amplification. A spherical core-shell structure consisting of a shell of a random amplifying medium is shown to enhance or suppress specific resonant modes. A shell with an absorbing random medium is also shown to suppress scattering which can also be used for cloaking the core region.

Computer simulation of stochastic processes through model-sampling (Monte Carlo) techniques.

PubMed

Sheppard, C W.

1969-03-01

A simple Monte Carlo simulation program is outlined which can be used for the investigation of random-walk problems, for example in diffusion, or the movement of tracers in the blood circulation. The results given by the simulation are compared with those predicted by well-established theory, and it is shown how the model can be expanded to deal with drift, and with reflexion from or adsorption at a boundary.

Electrochemical Impedance Imaging via the Distribution of Diffusion Times.

PubMed

Song, Juhyun; Bazant, Martin Z

2018-03-16

We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) or Gerischer (reaction-diffusion) circuit elements. A robust DDT inversion method is presented based on complex nonlinear least squares regression with Tikhonov regularization and illustrated for three cases of nanostructured electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow battery. The results demonstrate the feasibility of nondestructive "impedance imaging" to infer microstructural statistics of random, heterogeneous materials.

Diffusion of an Evidence-Based Smoking Cessation Intervention Through Facebook: A Randomized Controlled Trial.

PubMed

Cobb, Nathan K; Jacobs, Megan A; Wileyto, Paul; Valente, Thomas; Graham, Amanda L

2016-06-01

To examine the diffusion of an evidence-based smoking cessation application ("app") through Facebook social networks and identify specific intervention components that accelerate diffusion. Between December 2012 and October 2013, we recruited adult US smokers ("seeds") via Facebook advertising and randomized them to 1 of 12 app variants using a factorial design. App variants targeted components of diffusion: duration of use (t), "contagiousness" (β), and number of contacts (Z). The primary outcome was the reproductive ratio (R), defined as the number of individuals installing the app ("descendants") divided by the number of a seed participant's Facebook friends. We randomized 9042 smokers. App utilization metrics demonstrated between-variant differences in expected directions. The highest level of diffusion (R = 0.087) occurred when we combined active contagion strategies with strategies to increase duration of use (incidence rate ratio = 9.99; 95% confidence interval = 5.58, 17.91; P < .001). Involving nonsmokers did not affect diffusion. The maximal R value (0.087) is sufficient to increase the numbers of individuals receiving treatment if applied on a large scale. Online interventions can be designed a priori to spread through social networks.

The rate constant of a quantum-diffusion-controlled bimolecular reaction

NASA Astrophysics Data System (ADS)

Bondarev, B. V.

1986-04-01

A quantum-mechanical equation is derived in the tight-bond approximation which describes the motion and chemical interaction of a pair of species A and B when their displacement in the matrix is caused by tunnelling. Within the framework of the discrete model of random walks, definitions are given of the probability and rate constant of a reaction A + B → P (products) proceeding in a condensed medium. A method is suggested for calculating the rate constant of a quantum-diffusion-controlled bimolecular reaction. By this method, an expression is obtained for the rate constant in the stationary spherically symmetrical case. An equation for the density matrix is also proposed which describes the motion and chemical interaction of a pair of species when the quantum and classical diffusion are competitive.

Hopping in the Crowd to Unveil Network Topology.

PubMed

Asllani, Malbor; Carletti, Timoteo; Di Patti, Francesca; Fanelli, Duccio; Piazza, Francesco

2018-04-13

We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a constant value for sufficiently large connectivities, at variance with standard diffusion in the absence of excluded-volume effects. Building on this observation, we define and solve an inverse problem, aimed at reconstructing the a priori unknown connectivity distribution. The method gathers all the necessary information by repeating a limited number of independent measurements of the asymptotic density at a single node, which can be chosen randomly. The technique is successfully tested against both synthetic and real data and is also shown to estimate with great accuracy the total number of nodes.

Porous medium acoustics of wave-induced vorticity diffusion

NASA Astrophysics Data System (ADS)

Müller, T. M.; Sahay, P. N.

2011-02-01

A theory for attenuation and dispersion of elastic waves due to wave-induced generation of vorticity at pore-scale heterogeneities in a macroscopically homogeneous porous medium is developed. The diffusive part of the vorticity field associated with a viscous wave in the pore space—the so-called slow shear wave—is linked to the porous medium acoustics through incorporation of the fluid strain rate tensor of a Newtonian fluid in the poroelastic constitutive relations. The method of statistical smoothing is then used to derive dynamic-equivalent elastic wave velocities accounting for the conversion scattering process into the diffusive slow shear wave in the presence of randomly distributed pore-scale heterogeneities. The result is a simple model for wave attenuation and dispersion associated with the transition from viscosity- to inertia-dominated flow regime.

Hopping in the Crowd to Unveil Network Topology

NASA Astrophysics Data System (ADS)

Asllani, Malbor; Carletti, Timoteo; Di Patti, Francesca; Fanelli, Duccio; Piazza, Francesco

2018-04-01

We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a constant value for sufficiently large connectivities, at variance with standard diffusion in the absence of excluded-volume effects. Building on this observation, we define and solve an inverse problem, aimed at reconstructing the a priori unknown connectivity distribution. The method gathers all the necessary information by repeating a limited number of independent measurements of the asymptotic density at a single node, which can be chosen randomly. The technique is successfully tested against both synthetic and real data and is also shown to estimate with great accuracy the total number of nodes.

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

NASA Astrophysics Data System (ADS)

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G.; Hummer, Gerhard

2014-09-01

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

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

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G., E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlapmore » with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.« less

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

PubMed Central

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G.; Hummer, Gerhard

2014-01-01

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space. PMID:25240340

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

Data-driven probability concentration and sampling on manifold

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

Soize, C., E-mail: christian.soize@univ-paris-est.fr; Ghanem, R., E-mail: ghanem@usc.edu

2016-09-15

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation methodmore » for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.« less

Time series analysis of particle tracking data for molecular motion on the cell membrane.

PubMed

Ying, Wenxia; Huerta, Gabriel; Steinberg, Stanly; Zúñiga, Martha

2009-11-01

Biophysicists use single particle tracking (SPT) methods to probe the dynamic behavior of individual proteins and lipids in cell membranes. The mean squared displacement (MSD) has proven to be a powerful tool for analyzing the data and drawing conclusions about membrane organization, including features like lipid rafts, protein islands, and confinement zones defined by cytoskeletal barriers. Here, we implement time series analysis as a new analytic tool to analyze further the motion of membrane proteins. The experimental data track the motion of 40 nm gold particles bound to Class I major histocompatibility complex (MHCI) molecules on the membranes of mouse hepatoma cells. Our first novel result is that the tracks are significantly autocorrelated. Because of this, we developed linear autoregressive models to elucidate the autocorrelations. Estimates of the signal to noise ratio for the models show that the autocorrelated part of the motion is significant. Next, we fit the probability distributions of jump sizes with four different models. The first model is a general Weibull distribution that shows that the motion is characterized by an excess of short jumps as compared to a normal random walk. We also fit the data with a chi distribution which provides a natural estimate of the dimension d of the space in which a random walk is occurring. For the biological data, the estimates satisfy 1 < d < 2, implying that particle motion is not confined to a line, but also does not occur freely in the plane. The dimension gives a quantitative estimate of the amount of nanometer scale obstruction met by a diffusing molecule. We introduce a new distribution and use the generalized extreme value distribution to show that the biological data also have an excess of long jumps as compared to normal diffusion. These fits provide novel estimates of the microscopic diffusion constant. Previous MSD analyses of SPT data have provided evidence for nanometer-scale confinement zones that restrict lateral diffusion, supporting the notion that plasma membrane organization is highly structured. Our demonstration that membrane protein motion is autocorrelated and is characterized by an excess of both short and long jumps reinforces the concept that the membrane environment is heterogeneous and dynamic. Autocorrelation analysis and modeling of the jump distributions are powerful new techniques for the analysis of SPT data and the development of more refined models of membrane organization. The time series analysis also provides several methods of estimating the diffusion constant in addition to the constant provided by the mean squared displacement. The mean squared displacement for most of the biological data shows a power law behavior rather the linear behavior of Brownian motion. In this case, we introduce the notion of an instantaneous diffusion constant. All of the diffusion constants show a strong consistency for most of the biological data.

Diffusely scattered and transmitted elastic waves by random rough solid-solid interfaces using an elastodynamic Kirchhoff approximation

NASA Astrophysics Data System (ADS)

Shi, Fan; Lowe, Mike; Craster, Richard

2017-06-01

Elastic waves scattered by random rough interfaces separating two distinct media play an important role in modeling phonon scattering and impact upon thermal transport models, and are also integral to ultrasonic inspection. We introduce theoretical formulas for the diffuse field of elastic waves scattered by, and transmitted across, random rough solid-solid interfaces using the elastodynamic Kirchhoff approximation. The new formulas are validated by comparison with numerical Monte Carlo simulations, for a wide range of roughness (rms σ ≤λ /3 , correlation length λ0≥ wavelength λ ), demonstrating a significant improvement over the widely used small-perturbation approach, which is valid only for surfaces with small rms values. Physical analysis using the theoretical formulas derived here demonstrates that increasing the rms value leads to a considerable change of the scattering patterns for each mode. The roughness has different effects on the reflection and the transmission, with a strong dependence on the material properties. In the special case of a perfect match of the wave speed of the two solid media, the transmission is the same as the case for a flat interface. We pay particular attention to scattering in the specular direction, often used as an observable quantity, in terms of the roughness parameters, showing a peak at an intermediate value of rms; this rms value coincides with that predicted by the Rayleigh parameter.

Unified underpinning of human mobility in the real world and cyberspace

NASA Astrophysics Data System (ADS)

Zhao, Yi-Ming; Zeng, An; Yan, Xiao-Yong; Wang, Wen-Xu; Lai, Ying-Cheng

2016-05-01

Human movements in the real world and in cyberspace affect not only dynamical processes such as epidemic spreading and information diffusion but also social and economical activities such as urban planning and personalized recommendation in online shopping. Despite recent efforts in characterizing and modeling human behaviors in both the real and cyber worlds, the fundamental dynamics underlying human mobility have not been well understood. We develop a minimal, memory-based random walk model in limited space for reproducing, with a single parameter, the key statistical behaviors characterizing human movements in both cases. The model is validated using relatively big data from mobile phone and online commerce, suggesting memory-based random walk dynamics as the unified underpinning for human mobility, regardless of whether it occurs in the real world or in cyberspace.

A Self-Contained Mapping Closure Approximation for Scalar Mixing

NASA Technical Reports Server (NTRS)

He, Guo-Wei; Zhang, Zi-Fan

2003-01-01

Scalar turbulence exhibits interplays of coherent structures and random fluctuations over a broad range of spatial and temporal scales. This feature necessitates a probabilistic description of the scalar dynamics, which can be achieved comprehensively by using probability density functions (PDFs). Therefore, the challenge is to obtain the scalar PDFs (Lundgren 1967; Dopazo 1979). Generally, the evolution of a scalar is governed by three dynamical processes: advection, diffusion and reaction. In a PDF approach (Pope 1985), the advection and reaction can be treated exactly but the effect of molecular diffusion has to be modeled. It has been shown (Pope 1985) that the effect of molecular diffusion can be expressed as conditional dissipation rates or conditional diffusions. The currently used models for the conditional dissipation rates and conditional diffusions (Pope 1991) have resisted deduction from the fundamental equations and are unable to yield satisfactory results for the basic test cases of decaying scalars in isotropic turbulence, although they have achieved some success in a variety of individual cases. The recently developed mapping closure approach (Pope 1991; Chen, Chen & Kraichnan 1989; Kraichnan 1990; Klimenko & Pope 2003) provides a deductive method for conditional dissipation rates and conditional di usions, and the models obtained can successfully describe the shape relaxation of the scalar PDF from an initial double delta distribution to a Gaussian one. However, the mapping closure approach is not able to provide the rate at which the scalar evolves. The evolution rate has to be modeled. Therefore, the mapping closure approach is not closed. In this letter, we will address this problem.

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

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

A fast random walk algorithm for computing the pulsed-gradient spin-echo signal in multiscale porous media.

PubMed

Grebenkov, Denis S

2011-02-01

A new method for computing the signal attenuation due to restricted diffusion in a linear magnetic field gradient is proposed. A fast random walk (FRW) algorithm for simulating random trajectories of diffusing spin-bearing particles is combined with gradient encoding. As random moves of a FRW are continuously adapted to local geometrical length scales, the method is efficient for simulating pulsed-gradient spin-echo experiments in hierarchical or multiscale porous media such as concrete, sandstones, sedimentary rocks and, potentially, brain or lungs. Copyright © 2010 Elsevier Inc. All rights reserved.

Event-triggered synchronization for reaction-diffusion complex networks via random sampling

NASA Astrophysics Data System (ADS)

Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng

2018-04-01

In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.

Metasurfaced Reverberation Chamber.

PubMed

Sun, Hengyi; Li, Zhuo; Gu, Changqing; Xu, Qian; Chen, Xinlei; Sun, Yunhe; Lu, Shengchen; Martin, Ferran

2018-01-25

The concept of metasurfaced reverberation chamber (RC) is introduced in this paper. It is shown that by coating the chamber wall with a rotating 1-bit random coding metasurface, it is possible to enlarge the test zone of the RC while maintaining the field uniformity as good as that in a traditional RC with mechanical stirrers. A 1-bit random coding diffusion metasurface is designed to obtain all-direction backscattering under normal incidence. Three specific cases are studied for comparisons, including a (traditional) mechanical stirrer RC, a mechanical stirrer RC with a fixed diffusion metasurface, and a RC with a rotating diffusion metasurface. Simulation results show that the compact rotating diffusion metasurface can act as a stirrer with good stirring efficiency. By using such rotating diffusion metasurface, the test region of the RC can be greatly extended.

Diffusion of Bevacizumab Across Oncology Practices: An Observational Study.

PubMed

Keating, Nancy L; Huskamp, Haiden A; Schrag, Deborah; McWilliams, John M; McNeil, Barbara J; Landon, Bruce E; Chernew, Michael E; Normand, Sharon-Lise T

2018-01-01

Technological advances can improve care and outcomes but are a primary driver of health care spending growth. Understanding diffusion and use of new oncology therapies is important, given substantial increases in prices and spending on such treatments. Examine diffusion of bevacizumab, a novel (in 2004) and high-priced biologic cancer therapy, among US oncology practices during 2005-2012 and assess variation in use across practices. Population-based observational study. A total of 2329 US practices providing cancer chemotherapy. Random 20% sample of 236,304 Medicare fee-for-service beneficiaries aged above 65 years in 2004-2012 undergoing infused chemotherapy for cancer. Diffusion of bevacizumab (cumulative time to first use and 10% use) in practices, variation in use across practices overall and by higher versus lower-value use. We used hierarchical models with practice random effects to estimate the between-practice variation in the probability of receiving bevacizumab and to identify factors associated with use. We observed relatively rapid diffusion of bevacizumab, particularly in independent practices and larger versus smaller practices. We observed substantial variation in use; the adjusted odds ratio (95% confidence interval) of bevacizumab use was 2.90 higher (2.73-3.08) for practices 1 SD above versus one standard deviation below the mean. Variation was less for higher-value [odds ratio=2.72 (2.56-2.89)] than lower-value uses [odds ratio=3.61 (3.21-4.06)]. Use of bevacizumab varied widely across oncology practices, particularly for lower-value indications. These findings suggest that interventions targeted to practices have potential for decreasing low-value use of high-cost cancer therapies.

Random Walk Simulation of the MRI Apparent Diffusion Coefficient in a Geometrical Model of the Acinar Tree

PubMed Central

Pérez-Sánchez, José M.; Rodríguez, Ignacio; Ruiz-Cabello, Jesús

2009-01-01

Abstract Apparent diffusion coefficient (ADC) measurement in the lung using gas magnetic resonance imaging is a promising technique with potential for reflecting changes in lung microstructure. Despite some recent impressive human applications, full interpretation of ADC measures remains an elusive goal, due to a lack of detailed knowledge about the structure dependency of ADC. In an attempt to fill this gap we have performed random walk simulations in a three-dimensional geometrical model of the lung acinus, the distal alveolated sections of the lung tree accounting for ∼90% of the total lung volume. Simulations were carried out adjusting model parameters after published morphological data for the rat peripheral airway system, which predict an ADC behavior as microstructure changes with lung inflation in partial agreement with measured ADCs at different airway pressures. The approach used to relate experimental ADCs to lung microstructural changes does not make any assumption about the cause of the changes, so it could be applied to other scenarios such as chronic obstructive pulmonary disease, lung development, etc. The work presented here predicts numerically for the first time ADC values measured in the lung from independent morphological measures of lung microstructure taken at different inflation stages during the breath cycle. PMID:19619480

Magnetic Field Line Random Walk in Arbitrarily Stretched Isotropic Turbulence

NASA Astrophysics Data System (ADS)

Wongpan, P.; Ruffolo, D.; Matthaeus, W. H.; Rowlands, G.

2006-12-01

Many types of space and laboratory plasmas involve turbulent fluctuations with an approximately uniform mean magnetic field B_0, and the field line random walk plays an important role in guiding particle motions. Much of the relevant literature concerns isotropic turbulence, and has mostly been perturbative, i.e., for small fluctuations, or based on numerical simulations for specific conditions. On the other hand, solar wind turbulence is apparently anisotropic, and has been modeled as a sum of idealized two-dimensional and one dimensional (slab) components, but with the deficiency of containing no oblique wave vectors. In the present work, we address the above issues with non-perturbative analytic calculations of diffusive field line random walks for unpolarized, arbitrarily stretched isotropic turbulence, including the limits of nearly one-dimensional (highly stretched) and nearly two-dimensional (highly squashed) turbulence. We develop implicit analytic formulae for the diffusion coefficients D_x and D_z, two coupled integral equations in which D_x and D_z appear inside 3-dimensional integrals over all k-space, are solved numerically with the aid of Mathematica routines for specific cases. We can vary the parameters B0 and β, the stretching along z for constant turbulent energy. Furthermore, we obtain analytic closed-form solutions in all extreme cases. We obtain 0.54 < D_z/D_x < 2, indicating an approximately isotropic random walk even for very anisotropic (unpolarized) turbulence, a surprising result. For a given β, the diffusion coefficient vs. B0 can be described by a Padé approximant. We find quasilinear behavior at high B0 and percolative behavior at low B_0. Partially supported by a Sritrangthong Scholarship from the Faculty of Science, Mahidol University; the Thailand Research Fund; NASA Grant NNG05GG83G; and Thailand's Commission for Higher Education.

Cosmic Rays in Intermittent Magnetic Fields

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

Shukurov, Anvar; Seta, Amit; Bushby, Paul J.

The propagation of cosmic rays in turbulent magnetic fields is a diffusive process driven by the scattering of the charged particles by random magnetic fluctuations. Such fields are usually highly intermittent, consisting of intense magnetic filaments and ribbons surrounded by weaker, unstructured fluctuations. Studies of cosmic-ray propagation have largely overlooked intermittency, instead adopting Gaussian random magnetic fields. Using test particle simulations, we calculate cosmic-ray diffusivity in intermittent, dynamo-generated magnetic fields. The results are compared with those obtained from non-intermittent magnetic fields having identical power spectra. The presence of magnetic intermittency significantly enhances cosmic-ray diffusion over a wide range of particlemore » energies. We demonstrate that the results can be interpreted in terms of a correlated random walk.« less

Liquid water breakthrough location distances on a gas diffusion layer of polymer electrolyte membrane fuel cells

NASA Astrophysics Data System (ADS)

Yu, Junliang; Froning, Dieter; Reimer, Uwe; Lehnert, Werner

2018-06-01

The lattice Boltzmann method is adopted to simulate the three dimensional dynamic process of liquid water breaking through the gas diffusion layer (GDL) in the polymer electrolyte membrane fuel cell. 22 micro-structures of Toray GDL are built based on a stochastic geometry model. It is found that more than one breakthrough locations are formed randomly on the GDL surface. Breakthrough location distance (BLD) are analyzed statistically in two ways. The distribution is evaluated statistically by the Lilliefors test. It is concluded that the BLD can be described by the normal distribution with certain statistic characteristics. Information of the shortest neighbor breakthrough location distance can be the input modeling setups on the cell-scale simulations in the field of fuel cell simulation.

A Large-scale Dissemination and Implementation Model for Evidence-based Treatment and Continuing Care

PubMed Central

Garner, Bryan R.; Smith, Jane Ellen; Meyers, Robert J.; Godley, Mark D.

2010-01-01

Multiple evidence-based treatments for adolescents with substance use disorders are available; however, the diffusion of these treatments in practice remains minimal. A dissemination and implementation model incorporating research-based training components for simultaneous implementation across 33 dispersed sites and over 200 clinical staff is described. Key elements for the diffusion of the Adolescent Community Reinforcement Approach and Assertive Continuing Care were: (a) three years of funding to support local implementation; (b) comprehensive training, including a 3.5 day workshop, bi-weekly coaching calls, and ongoing performance feedback facilitated by a web tool; (c) a clinician certification process; (d) a supervisor certification process to promote long-term sustainability; and (e) random fidelity reviews after certification. Process data are summarized for 167 clinicians and 64 supervisors. PMID:21547241

Anomalous subdiffusion in fluorescence photobleaching recovery: a Monte Carlo study.

PubMed Central

Saxton, M J

2001-01-01

Anomalous subdiffusion is hindered diffusion in which the mean-square displacement of a diffusing particle is proportional to some power of time less than one. Anomalous subdiffusion has been observed for a variety of lipids and proteins in the plasma membranes of a variety of cells. Fluorescence photobleaching recovery experiments with anomalous subdiffusion are simulated to see how to analyze the data. It is useful to fit the recovery curve with both the usual recovery equation and the anomalous one, and to judge the goodness of fit on log-log plots. The simulations show that the simplest approximate treatment of anomalous subdiffusion usually gives good results. Three models of anomalous subdiffusion are considered: obstruction, fractional Brownian motion, and the continuous-time random walk. The models differ significantly in their behavior at short times and in their noise level. For obstructed diffusion the approach to the percolation threshold is marked by a large increase in noise, a broadening of the distribution of diffusion coefficients and anomalous subdiffusion exponents, and the expected abrupt decrease in the mobile fraction. The extreme fluctuations in the recovery curves at and near the percolation threshold result from extreme fluctuations in the geometry of the percolation cluster. PMID:11566793

Flexible and polarization-controllable diffusion metasurface with optical transparency

NASA Astrophysics Data System (ADS)

Zhuang, Yaqiang; Wang, Guangming; Liang, Jiangang; Cai, Tong; Guo, Wenlong; Zhang, Qingfeng

2017-11-01

In this paper, a novel coding metasurface is proposed to realize polarization-controllable diffusion scattering. The anisotropic Jerusalem-cross unit cell is employed as the basic coding element due to its polarization-dependent phase response. The isotropic random coding sequence is firstly designed to obtain diffusion scattering, and the anisotropic random coding sequence is subsequently realized by adding different periodic coding sequences to the original isotropic one along different directions. For demonstration, we designed and fabricated a flexible polarization-controllable diffusion metasurface (PCDM) with both chessboard diffusion and hedge diffusion under different polarizations. The specular scattering reduction performance of the anisotropic metasurface is better than the isotropic one because the scattered energies are redirected away from the specular reflection direction. For potential applications, the flexible PCDM wrapped around a cylinder structure is investigated and tested for polarization-controllable diffusion scattering. The numerical and experimental results coincide well, indicating anisotropic low scatterings with comparable performances. This paper provides an alternative approach for designing high-performance, flexible, low-scattering platforms.

Modelling of AlAs/GaAs interfacial structures using high-angle annular dark field (HAADF) image simulations.

PubMed

Robb, Paul D; Finnie, Michael; Craven, Alan J

2012-07-01

High angle annular dark field (HAADF) image simulations were performed on a series of AlAs/GaAs interfacial models using the frozen-phonon multislice method. Three general types of models were considered-perfect, vicinal/sawtooth and diffusion. These were chosen to demonstrate how HAADF image measurements are influenced by different interfacial structures in the technologically important III-V semiconductor system. For each model, interfacial sharpness was calculated as a function of depth and compared to aberration-corrected HAADF experiments of two types of AlAs/GaAs interfaces. The results show that the sharpness measured from HAADF imaging changes in a complicated manner with thickness for complex interfacial structures. For vicinal structures, it was revealed that the type of material that the probe projects through first of all has a significant effect on the measured sharpness. An increase in the vicinal angle was also shown to generate a wider interface in the random step model. The Moison diffusion model produced an increase in the interface width with depth which closely matched the experimental results of the AlAs-on-GaAs interface. In contrast, the interface width decreased as a function of depth in the linear diffusion model. Only in the case of the perfect model was it possible to ascertain the underlying structure directly from HAADF image analysis. Copyright © 2012 Elsevier B.V. All rights reserved.

Diversity of multilayer networks and its impact on collaborating epidemics

NASA Astrophysics Data System (ADS)

Min, Yong; Hu, Jiaren; Wang, Weihong; Ge, Ying; Chang, Jie; Jin, Xiaogang

2014-12-01

Interacting epidemics on diverse multilayer networks are increasingly important in modeling and analyzing the diffusion processes of real complex systems. A viral agent spreading on one layer of a multilayer network can interact with its counterparts by promoting (cooperative interaction), suppressing (competitive interaction), or inducing (collaborating interaction) its diffusion on other layers. Collaborating interaction displays different patterns: (i) random collaboration, where intralayer or interlayer induction has the same probability; (ii) concentrating collaboration, where consecutive intralayer induction is guaranteed with a probability of 1; and (iii) cascading collaboration, where consecutive intralayer induction is banned with a probability of 0. In this paper, we develop a top-bottom framework that uses only two distributions, the overlaid degree distribution and edge-type distribution, to model collaborating epidemics on multilayer networks. We then state the response of three collaborating patterns to structural diversity (evenness and difference of network layers). For viral agents with small transmissibility, we find that random collaboration is more effective in networks with higher diversity (high evenness and difference), while the concentrating pattern is more suitable in uneven networks. Interestingly, the cascading pattern requires a network with moderate difference and high evenness, and the moderately uneven coupling of multiple network layers can effectively increase robustness to resist cascading failure. With large transmissibility, however, we find that all collaborating patterns are more effective in high-diversity networks. Our work provides a systemic analysis of collaborating epidemics on multilayer networks. The results enhance our understanding of biotic and informative diffusion through multiple vectors.

Tempered fractional calculus

NASA Astrophysics Data System (ADS)

Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

2015-07-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS.

PubMed

Meerschaert, Mark M; Sabzikar, Farzad; Chen, Jinghua

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS

PubMed Central

MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA

2014-01-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series. PMID:26085690

Tempered fractional calculus

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

Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu; Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu; Chen, Jinghua, E-mail: cjhdzdz@163.com

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a temperedmore » fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.« less

Nucleation of Organic Molecules via a Hot Precursor State: Pentacene on Amorphous Mica

PubMed Central

2013-01-01

Organic thin films have attracted considerable interest due to their applicability in organic electronics. The classical scenario for thin film nucleation is the diffusion-limited aggregation (DLA). Recently, it has been shown that organic thin film growth is better described by attachment-limited aggregation (ALA). However, in both cases, an unusual relationship between the island density and the substrate temperature was observed. Here, we present an aggregation model that goes beyond the classical DLA or ALA models to explain this behavior. We propose that the (hot) molecules impinging on the surface cannot immediately equilibrate to the substrate temperature but remain in a hot precursor state. In this state, the molecules can migrate considerable distances before attaching to a stable or unstable island. This results in a significantly smaller island density than expected by assuming fast equilibration and random diffusion. We have applied our model to pentacene film growth on amorphous Muscovite mica. PMID:24340130

Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field.

PubMed

Xu, Jia; Li, Chao; Li, Yiran; Lim, Chee Wah; Zhu, Zhiwen

2018-05-04

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of the microstructure is considered based on Eringen’s differential constitutive model. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.

Random Interchange of Magnetic Connectivity

NASA Astrophysics Data System (ADS)

Matthaeus, W. H.; Ruffolo, D. J.; Servidio, S.; Wan, M.; Rappazzo, A. F.

2015-12-01

Magnetic connectivity, the connection between two points along a magnetic field line, has a stochastic character associated with field lines random walking in space due to magnetic fluctuations, but connectivity can also change in time due to dynamical activity [1]. For fluctuations transverse to a strong mean field, this connectivity change be caused by stochastic interchange due to component reconnection. The process may be understood approximately by formulating a diffusion-like Fokker-Planck coefficient [2] that is asymptotically related to standard field line random walk. Quantitative estimates are provided, for transverse magnetic field models and anisotropic models such as reduced magnetohydrodynamics. In heliospheric applications, these estimates may be useful for understanding mixing between open and close field line regions near coronal hole boundaries, and large latitude excursions of connectivity associated with turbulence. [1] A. F. Rappazzo, W. H. Matthaeus, D. Ruffolo, S. Servidio & M. Velli, ApJL, 758, L14 (2012) [2] D. Ruffolo & W. Matthaeus, ApJ, 806, 233 (2015)

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

PubMed

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

2015-01-21

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

Jump-Diffusion models and structural changes for asset forecasting in hydrology

NASA Astrophysics Data System (ADS)

Tranquille Temgoua, André Guy; Martel, Richard; Chang, Philippe J. J.; Rivera, Alfonso

2017-04-01

Impacts of climate change on surface water and groundwater are of concern in many regions of the world since water is an essential natural resource. Jump-Diffusion models are generally used in economics and other related fields but not in hydrology. The potential application could be made for hydrologic data series analysis and forecast. The present study uses Jump-Diffusion models by adding structural changes to detect fluctuations in hydrologic processes in relationship with climate change. The model implicitly assumes that modifications in rivers' flowrates can be divided into three categories: (a) normal changes due to irregular precipitation events especially in tropical regions causing major disturbance in hydrologic processes (this component is modelled by a discrete Brownian motion); (b) abnormal, sudden and non-persistent modifications in hydrologic proceedings are handled by Poisson processes; (c) the persistence of hydrologic fluctuations characterized by structural changes in hydrological data related to climate variability. The objective of this paper is to add structural changes in diffusion models with jumps, in order to capture the persistence of hydrologic fluctuations. Indirectly, the idea is to observe if there are structural changes of discharge/recharge over the study area, and to find an efficient and flexible model able of capturing a wide variety of hydrologic processes. Structural changes in hydrological data are estimated using the method of nonlinear discrete filters via Method of Simulated Moments (MSM). An application is given using sensitive parameters such as baseflow index and recession coefficient to capture discharge/recharge. Historical dataset are examined by the Volume Spread Analysis (VSA) to detect real time and random perturbations in hydrologic processes. The application of the method allows establishing more accurate hydrologic parameters. The impact of this study is perceptible in forecasting floods and groundwater recession. Keywords: hydrologic processes, Jump-Diffusion models, structural changes, forecast, climate change

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.

Wright-Fisher diffusion bridges.

PubMed

Griffiths, Robert C; Jenkins, Paul A; Spanò, Dario

2017-10-06

The trajectory of the frequency of an allele which begins at x at time 0 and is known to have frequency z at time T can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when x=z=0 are particularly interesting because they model the trajectory of the frequency of an allele which appears at a time, then is lost by random drift or mutation after a time T. The coalescent genealogy back in time of a population in a neutral Wright-Fisher diffusion process is well understood. In this paper we obtain a new interpretation of the coalescent genealogy of the population in a bridge from a time t∈(0,T). In a bridge with allele frequencies of 0 at times 0 and T the coalescence structure is that the population coalesces in two directions from t to 0 and t to T such that there is just one lineage of the allele under consideration at times 0 and T. The genealogy in Wright-Fisher diffusion bridges with selection is more complex than in the neutral model, but still with the property of the population branching and coalescing in two directions from time t∈(0,T). The density of the frequency of an allele at time t is expressed in a way that shows coalescence in the two directions. A new algorithm for exact simulation of a neutral Wright-Fisher bridge is derived. This follows from knowing the density of the frequency in a bridge and exact simulation from the Wright-Fisher diffusion. The genealogy of the neutral Wright-Fisher bridge is also modelled by branching Pólya urns, extending a representation in a Wright-Fisher diffusion. This is a new very interesting representation that relates Wright-Fisher bridges to classical urn models in a Bayesian setting. Copyright © 2017 Elsevier Inc. All rights reserved.

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

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

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

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

Diffusion of an Evidence-Based Smoking Cessation Intervention Through Facebook: A Randomized Controlled Trial

PubMed Central

Cobb, Nathan K.; Jacobs, Megan A.; Wileyto, Paul; Valente, Thomas

2016-01-01

Objectives. To examine the diffusion of an evidence-based smoking cessation application (“app”) through Facebook social networks and identify specific intervention components that accelerate diffusion. Methods. Between December 2012 and October 2013, we recruited adult US smokers (“seeds”) via Facebook advertising and randomized them to 1 of 12 app variants using a factorial design. App variants targeted components of diffusion: duration of use (t), “contagiousness” (β), and number of contacts (Z). The primary outcome was the reproductive ratio (R), defined as the number of individuals installing the app (“descendants”) divided by the number of a seed participant’s Facebook friends. Results. We randomized 9042 smokers. App utilization metrics demonstrated between-variant differences in expected directions. The highest level of diffusion (R = 0.087) occurred when we combined active contagion strategies with strategies to increase duration of use (incidence rate ratio = 9.99; 95% confidence interval = 5.58, 17.91; P < .001). Involving nonsmokers did not affect diffusion. Conclusions. The maximal R value (0.087) is sufficient to increase the numbers of individuals receiving treatment if applied on a large scale. Online interventions can be designed a priori to spread through social networks. PMID:27077358

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

Duranty, Edward R.; Baschnagel, Jörg; Dadmun, Mark

Copolymers are commonly used as interface modifiers that allow for the compatibilization of polymer components in a blend. For copolymers to function as a compatibilizer, they must diffuse through the matrix of the blend to the interface between the two blend components. The diffusivity of a copolymer in a blend matrix therefore becomes important in determining good candidates for use as compatibilizers. In this paper, coarse-grained Monte Carlo simulations using the bond fluctuation model modified with an overlap penalty have been developed to study the diffusive behavior of PS/PMMA random copolymers in a PMMA homopolymer blend. The simulations vary themore » connectivity between different monomers, the thermodynamic interactions between the monomers which manifest within a chain, and between copolymer and homopolymer matrix and define the monomer friction coefficient of each component independently, allowing for the determination of the combined effect of these parameters on copolymer chain diffusion. Finally, the results of this work indicate that PS-r-PMMA copolymer diffusion is not linearly dependent on the copolymer composition on a logarithmic scale, but its diffusion is a balance of the kinetics governed by the dominant motion of the faster styrene monomers and thermodynamics, which are governed by the concentration of styrene monomer within a given monomer’s local volume.« less

Can the RNA of the cowpea chlorotic mottle virus be released through a channel by means of free diffusion? A test in silico.

PubMed

Isea, Raul; Aponte, Carlos; Cipriani, Roberto

2004-02-01

Cowpea chlorotic mottle virus (CCMV), a plant virus which is member of the Bromoviridae family, is used as a model for the diffusion of a random, short, single stranded RNA, [5'-R(PGpGpApCpUpUpCpGpGpUpCpC)-3')], through a channel on the pseudo-three-fold axis using molecular dynamic simulations. This proposition is based the fact that CCMV undergoes a dynamic structural transition as a response to changes of pH, temperature and ionic strength. Results indicate that the RNA looses its secondary structure and moves into the capside channel by free diffusion. These results are congruent with the hypothesis suggesting that the CCMV capside does not have to dissolve in order to release the RNA into the host.

Nanoscale diffusive memristor crossbars as physical unclonable functions.

PubMed

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

2018-02-08

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

Repeated-cascade theory of strong turbulence in a magnetized plasma

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1976-01-01

A two-dimensional Navier-Stokes equation of vorticity in fluid turbulence is used to model drift turbulence in a plasma with a strong constant magnetic field and a constant mean density gradient. The nonlinear eddy diffusivity is described by a time-integrated Lagrangian correlation of velocities, and the repeated-cascade method is employed to choose the rank accounting for nearest-neighbor interactions, to calculate the Lagrangian correlation, and to close the correlation hierarchy. As a result, the diffusivity becomes dependent on the plasma's induced diffusion and is represented by a memory chain that is cut off by similarity and inertial randomization. Spectral laws relating the kinetic-energy spectrum to the -5, -5/2, -3, and -11 powers of wavenumber are derived for the velocity subranges of production, approach to inertia, inertia, and dissipation, respectively. It is found that the diffusivity is proportional to some inverse power of the magnetic field, that power being 1, 2/3, 5/6, and 2, respectively, for the four velocity subranges.

Random walk numerical simulation for hopping transport at finite carrier concentrations: diffusion coefficient and transport energy concept.

PubMed

Gonzalez-Vazquez, J P; Anta, Juan A; Bisquert, Juan

2009-11-28

The random walk numerical simulation (RWNS) method is used to compute diffusion coefficients for hopping transport in a fully disordered medium at finite carrier concentrations. We use Miller-Abrahams jumping rates and an exponential distribution of energies to compute the hopping times in the random walk simulation. The computed diffusion coefficient shows an exponential dependence with respect to Fermi-level and Arrhenius behavior with respect to temperature. This result indicates that there is a well-defined transport level implicit to the system dynamics. To establish the origin of this transport level we construct histograms to monitor the energies of the most visited sites. In addition, we construct "corrected" histograms where backward moves are removed. Since these moves do not contribute to transport, these histograms provide a better estimation of the effective transport level energy. The analysis of this concept in connection with the Fermi-level dependence of the diffusion coefficient and the regime of interest for the functioning of dye-sensitised solar cells is thoroughly discussed.

Simulating Pre-Asymptotic, Non-Fickian Transport Although Doing Simple Random Walks - Supported By Empirical Pore-Scale Velocity Distributions and Memory Effects

NASA Astrophysics Data System (ADS)

Most, S.; Jia, N.; Bijeljic, B.; Nowak, W.

2016-12-01

Pre-asymptotic characteristics are almost ubiquitous when analyzing solute transport processes in porous media. These pre-asymptotic aspects are caused by spatial coherence in the velocity field and by its heterogeneity. For the Lagrangian perspective of particle displacements, the causes of pre-asymptotic, non-Fickian transport are skewed velocity distribution, statistical dependencies between subsequent increments of particle positions (memory) and dependence between the x, y and z-components of particle increments. Valid simulation frameworks should account for these factors. We propose a particle tracking random walk (PTRW) simulation technique that can use empirical pore-space velocity distributions as input, enforces memory between subsequent random walk steps, and considers cross dependence. Thus, it is able to simulate pre-asymptotic non-Fickian transport phenomena. Our PTRW framework contains an advection/dispersion term plus a diffusion term. The advection/dispersion term produces time-series of particle increments from the velocity CDFs. These time series are equipped with memory by enforcing that the CDF values of subsequent velocities change only slightly. The latter is achieved through a random walk on the axis of CDF values between 0 and 1. The virtual diffusion coefficient for that random walk is our only fitting parameter. Cross-dependence can be enforced by constraining the random walk to certain combinations of CDF values between the three velocity components in x, y and z. We will show that this modelling framework is capable of simulating non-Fickian transport by comparison with a pore-scale transport simulation and we analyze the approach to asymptotic behavior.

Monte Carlo Modeling of VLWIR HgCdTe Interdigitated Pixel Response

NASA Astrophysics Data System (ADS)

D'Souza, A. I.; Stapelbroek, M. G.; Wijewarnasuriya, P. S.

2010-07-01

Increasing very long-wave infrared (VLWIR, λ c ≈ 15 μm) pixel operability was approached by subdividing each pixel into four interdigitated subpixels. High response is maintained across the pixel, even if one or two interdigitated subpixels are deselected (turned off), because interdigitation provides that the preponderance of minority carriers photogenerated in the pixel are collected by the selected subpixels. Monte Carlo modeling of the photoresponse of the interdigitated subpixel simulates minority-carrier diffusion from carrier creation to recombination. Each carrier generated at an appropriately weighted random location is assigned an exponentially distributed random lifetime τ i, where < τ i> is the bulk minority-carrier lifetime. The minority carrier is allowed to diffuse for a short time d τ, and the fate of the carrier is decided from its present position and the boundary conditions, i.e., whether the carrier is absorbed in a junction, recombined at a surface, reflected from a surface, or recombined in the bulk because it lived for its designated lifetime. If nothing happens, the process is then repeated until one of the boundary conditions is attained. The next step is to go on to the next carrier and repeat the procedure for all the launches of minority carriers. For each minority carrier launched, the original location and boundary condition at fatality are recorded. An example of the results from Monte Carlo modeling is that, for a 20- μm diffusion length, the calculated quantum efficiency (QE) changed from 85% with no subpixels deselected, to 78% with one subpixel deselected, 67% with two subpixels deselected, and 48% with three subpixels deselected. Demonstration of the interdigitated pixel concept and verification of the Monte Carlo modeling utilized λ c(60 K) ≈ 15 μm HgCdTe pixels in a 96 × 96 array format. The measured collection efficiency for one, two, and three subelements selected, divided by the collection efficiency for all four subelements selected, matched that calculated using Monte Carlo modeling.

Diffusion of copolymers composed of monomers with drastically different friction factors in copolymer/homopolymer blends

DOE PAGES

Duranty, Edward R.; Baschnagel, Jörg; Dadmun, Mark

2017-02-07

Copolymers are commonly used as interface modifiers that allow for the compatibilization of polymer components in a blend. For copolymers to function as a compatibilizer, they must diffuse through the matrix of the blend to the interface between the two blend components. The diffusivity of a copolymer in a blend matrix therefore becomes important in determining good candidates for use as compatibilizers. In this paper, coarse-grained Monte Carlo simulations using the bond fluctuation model modified with an overlap penalty have been developed to study the diffusive behavior of PS/PMMA random copolymers in a PMMA homopolymer blend. The simulations vary themore » connectivity between different monomers, the thermodynamic interactions between the monomers which manifest within a chain, and between copolymer and homopolymer matrix and define the monomer friction coefficient of each component independently, allowing for the determination of the combined effect of these parameters on copolymer chain diffusion. Finally, the results of this work indicate that PS-r-PMMA copolymer diffusion is not linearly dependent on the copolymer composition on a logarithmic scale, but its diffusion is a balance of the kinetics governed by the dominant motion of the faster styrene monomers and thermodynamics, which are governed by the concentration of styrene monomer within a given monomer’s local volume.« less

Superdiffusion, large-scale synchronization, and topological defects

NASA Astrophysics Data System (ADS)

Großmann, Robert; Peruani, Fernando; Bär, Markus

2016-04-01

We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby introducing an additional, independent source of fluctuations, thus constituting the intrinsic nonequilibrium nature of the temporal dynamics. We employ this paradigmatic model system to discuss how the emergence of order is affected by the motion of individual entities. In particular, we consider both normal diffusive motion and superdiffusion. A non-Hamiltonian field theory including multiplicative noise terms is derived which describes the nonequilibrium dynamics at the macroscale. This theory reveals a defect-mediated transition from incoherence to quasi-long-range order for normal diffusion of oscillators in two dimensions, implying a power-law dependence of all synchronization properties on system size. In contrast, superdiffusive transport suppresses the emergence of topological defects, thereby inducing a continuous synchronization transition to long-range order in two dimensions. These results are consistent with particle-based simulations.

Does movement behaviour predict population densities? A test with 25 butterfly species.

PubMed

Schultz, Cheryl B; Pe'er, B Guy; Damiani, Christine; Brown, Leone; Crone, Elizabeth E

2017-03-01

Diffusion, which approximates a correlated random walk, has been used by ecologists to describe movement, and forms the basis for many theoretical models. However, it is often criticized as too simple a model to describe animal movement in real populations. We test a key prediction of diffusion models, namely, that animals should be more abundant in land cover classes through which they move more slowly. This relationship between density and diffusion has rarely been tested across multiple species within a given landscape. We estimated diffusion rates and corresponding densities of 25 Israeli butterfly species from flight path data and visual surveys. The data were collected across 19 sites in heterogeneous landscapes with four land cover classes: semi-natural habitat, olive groves, wheat fields and field margins. As expected from theory, species tended to have higher densities in land cover classes through which they moved more slowly and lower densities in land cover classes through which they moved more quickly. Two components of movement (move length and turning angle) were not associated with density, nor was expected net squared displacement. Move time, however, was associated with density, and animals spent more time per move step in areas with higher density. The broad association we document between movement behaviour and density suggests that diffusion is a good first approximation of movement in butterflies. Moreover, our analyses demonstrate that dispersal is not a species-invariant trait, but rather one that depends on landscape context. Thus, land cover classes with high diffusion rates are likely to have low densities and be effective conduits for movement. © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society.

Quantitative phenomenological model of the BOLD contrast mechanism

NASA Astrophysics Data System (ADS)

Dickson, John D.; Ash, Tom W. J.; Williams, Guy B.; Sukstanskii, Alexander L.; Ansorge, Richard E.; Yablonskiy, Dmitriy A.

2011-09-01

Different theoretical models of the BOLD contrast mechanism are used for many applications including BOLD quantification (qBOLD) and vessel size imaging, both in health and disease. Each model simplifies the system under consideration, making approximations about the structure of the blood vessel network and diffusion of water molecules through inhomogeneities in the magnetic field created by deoxyhemoglobin-containing blood vessels. In this study, Monte-Carlo methods are used to simulate the BOLD MR signal generated by diffusing water molecules in the presence of long, cylindrical blood vessels. Using these simulations we introduce a new, phenomenological model that is far more accurate over a range of blood oxygenation levels and blood vessel radii than existing models. This model could be used to extract physiological parameters of the blood vessel network from experimental data in BOLD-based experiments. We use our model to establish ranges of validity for the existing analytical models of Yablonskiy and Haacke, Kiselev and Posse, Sukstanskii and Yablonskiy (extended to the case of arbitrary time in the spin echo sequence) and Bauer et al. (extended to the case of randomly oriented cylinders). Although these models are shown to be accurate in the limits of diffusion under which they were derived, none of them is accurate for the whole physiological range of blood vessels radii and blood oxygenation levels. We also show the extent of systematic errors that are introduced due to the approximations of these models when used for BOLD signal quantification.

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.

A new interpretation of the Keller-Segel model based on multiphase modelling.

PubMed

Byrne, Helen M; Owen, Markus R

2004-12-01

In this paper an alternative derivation and interpretation are presented of the classical Keller-Segel model of cell migration due to random motion and chemotaxis. A multiphase modelling approach is used to describe how a population of cells moves through a fluid containing a diffusible chemical to which the cells are attracted. The cells and fluid are viewed as distinct components of a two-phase mixture. The principles of mass and momentum balance are applied to each phase, and appropriate constitutive laws imposed to close the resulting equations. A key assumption here is that the stress in the cell phase is influenced by the concentration of the diffusible chemical. By restricting attention to one-dimensional cartesian geometry we show how the model reduces to a pair of nonlinear coupled partial differential equations for the cell density and the chemical concentration. These equations may be written in the form of the Patlak-Keller-Segel model, naturally including density-dependent nonlinearities in the cell motility coefficients. There is a direct relationship between the random motility and chemotaxis coefficients, both depending in an inter-related manner on the chemical concentration. We suggest that this may explain why many chemicals appear to stimulate both chemotactic and chemokinetic responses in cell populations. After specialising our model to describe slime mold we then show how the functional form of the chemical potential that drives cell locomotion influences the ability of the system to generate spatial patterns. The paper concludes with a summary of the key results and a discussion of avenues for future research.

Surface flux transport simulations: Effect of inflows toward active regions and random velocities on the evolution of the Sun's large-scale magnetic field

NASA Astrophysics Data System (ADS)

Martin-Belda, D.; Cameron, R. H.

2016-02-01

Aims: We aim to determine the effect of converging flows on the evolution of a bipolar magnetic region (BMR), and to investigate the role of these inflows in the generation of poloidal flux. We also discuss whether the flux dispersal due to turbulent flows can be described as a diffusion process. Methods: We developed a simple surface flux transport model based on point-like magnetic concentrations. We tracked the tilt angle, the magnetic flux and the axial dipole moment of a BMR in simulations with and without inflows and compared the results. To test the diffusion approximation, simulations of random walk dispersal of magnetic features were compared against the predictions of the diffusion treatment. Results: We confirm the validity of the diffusion approximation to describe flux dispersal on large scales. We find that the inflows enhance flux cancellation, but at the same time affect the latitudinal separation of the polarities of the bipolar region. In most cases the latitudinal separation is limited by the inflows, resulting in a reduction of the axial dipole moment of the BMR. However, when the initial tilt angle of the BMR is small, the inflows produce an increase in latitudinal separation that leads to an increase in the axial dipole moment in spite of the enhanced flux destruction. This can give rise to a tilt of the BMR even when the BMR was originally aligned parallel to the equator.

Characterizing individual scattering events by measuring the amplitude and phase of the electric field diffusing through a random medium.

PubMed

Jian, Zhongping; Pearce, Jeremy; Mittleman, Daniel M

2003-07-18

We describe observations of the amplitude and phase of an electric field diffusing through a three-dimensional random medium, using terahertz time-domain spectroscopy. These measurements are spatially resolved with a resolution smaller than the speckle spot size and temporally resolved with a resolution better than one optical cycle. By computing correlation functions between fields measured at different positions and with different temporal delays, it is possible to obtain information about individual scattering events experienced by the diffusing field. This represents a new method for characterizing a multiply scattered wave.

Fractional calculus and morphogen gradient formation

NASA Astrophysics Data System (ADS)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

Bounded fractional diffusion in geological media: Definition and Lagrangian approximation

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

Optimization and universality of Brownian search in a basic model of quenched heterogeneous media

NASA Astrophysics Data System (ADS)

Godec, Aljaž; Metzler, Ralf

2015-05-01

The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time (MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.

Random Walk Particle Tracking For Multiphase Heat Transfer

NASA Astrophysics Data System (ADS)

Lattanzi, Aaron; Yin, Xiaolong; Hrenya, Christine

2017-11-01

As computing capabilities have advanced, direct numerical simulation (DNS) has become a highly effective tool for quantitatively predicting the heat transfer within multiphase flows. Here we utilize a hybrid DNS framework that couples the lattice Boltzmann method (LBM) to the random walk particle tracking (RWPT) algorithm. The main challenge of such a hybrid is that discontinuous fields pose a significant challenge to the RWPT framework and special attention must be given to the handling of interfaces. We derive a method for addressing discontinuities in the diffusivity field, arising at the interface between two phases. Analytical means are utilized to develop an interfacial tracer balance and modify the RWPT algorithm. By expanding the modulus of the stochastic (diffusive) step and only allowing a subset of the tracers within the high diffusivity medium to undergo a diffusive step, the correct equilibrium state can be restored (globally homogeneous tracer distribution). The new RWPT algorithm is implemented within the SUSP3D code and verified against a variety of systems: effective diffusivity of a static gas-solids mixture, hot sphere in unbounded diffusion, cooling sphere in unbounded diffusion, and uniform flow past a hot sphere.

Relative distance between tracers as a measure of diffusivity within moving aggregates

NASA Astrophysics Data System (ADS)

Pönisch, Wolfram; Zaburdaev, Vasily

2018-02-01

Tracking of particles, be it a passive tracer or an actively moving bacterium in the growing bacterial colony, is a powerful technique to probe the physical properties of the environment of the particles. One of the most common measures of particle motion driven by fluctuations and random forces is its diffusivity, which is routinely obtained by measuring the mean squared displacement of the particles. However, often the tracer particles may be moving in a domain or an aggregate which itself experiences some regular or random motion and thus masks the diffusivity of tracers. Here we provide a method for assessing the diffusivity of tracer particles within mobile aggregates by measuring the so-called mean squared relative distance (MSRD) between two tracers. We provide analytical expressions for both the ensemble and time averaged MSRD allowing for direct identification of diffusivities from experimental data.

Analysis of fluctuations in semiconductor devices

NASA Astrophysics Data System (ADS)

Andrei, Petru

The random nature of ion implantation and diffusion processes as well as inevitable tolerances in fabrication result in random fluctuations of doping concentrations and oxide thickness in semiconductor devices. These fluctuations are especially pronounced in ultrasmall (nanoscale) semiconductor devices when the spatial scale of doping and oxide thickness variations become comparable with the geometric dimensions of devices. In the dissertation, the effects of these fluctuations on device characteristics are analyzed by using a new technique for the analysis of random doping and oxide thickness induced fluctuations. This technique is universal in nature in the sense that it is applicable to any transport model (drift-diffusion, semiclassical transport, quantum transport etc.) and it can be naturally extended to take into account random fluctuations of the oxide (trapped) charges and channel length. The technique is based on linearization of the transport equations with respect to the fluctuating quantities. It is computationally much (a few orders of magnitude) more efficient than the traditional Monte-Carlo approach and it yields information on the sensitivity of fluctuations of parameters of interest (e.g. threshold voltage, small-signal parameters, cut-off frequencies, etc.) to the locations of doping and oxide thickness fluctuations. For this reason, it can be very instrumental in the design of fluctuation-resistant structures of semiconductor devices. Quantum mechanical effects are taken into account by using the density-gradient model as well as through self-consistent Poisson-Schrodinger computations. Special attention is paid to the presenting of the technique in a form that is suitable for implementation on commercial device simulators. The numerical implementation of the technique is discussed in detail and numerous computational results are presented and compared with those previously published in literature.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2018-03-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2017-12-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2} ). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3} ) and the level sets of the Gaussian free field ({d≥ 3} ). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Precipitation and Release of Solar Energetic Particles from the Solar Coronal Magnetic Field

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

Zhang, Ming; Zhao, Lulu, E-mail: mzhang@fit.edu

Most solar energetic particles (SEPs) are produced in the corona. They propagate through complex coronal magnetic fields subject to scattering and diffusion across the averaged field lines by turbulence. We examine the behaviors of particle transport using a stochastic 3D focused transport simulation in a potential field source surface model of coronal magnetic field. The model is applied to an SEP event on 2010 February 7. We study three scenarios of particle injection at (i) the compact solar flare site, (ii) the coronal mass ejection (CME) shock, and (iii) the EUV wave near the surface. The majority of particles injectedmore » on open field lines are able to escape the corona. We found that none of our models can explain the observations of wide longitudinal SEP spread without perpendicular diffusion. If the perpendicular diffusion is about 10% of what is derived from the random walk of field lines at the rate of supergranular diffusion, particles injected at the compact solar flare site can spread to a wide range of longitude and latitude, very similar to the behavior of particles injected at a large CME shock. Stronger pitch-angle scattering results in a little more lateral spread by holding the particles in the corona for longer periods of time. Some injected particles eventually end up precipitating onto the solar surface. Even with a very small perpendicular diffusion, the pattern of the particle precipitation can be quite complicated depending on the detailed small-scale coronal magnetic field structures, which could be seen with future sensitive gamma-ray telescopes.« less

Precipitation and Release of Solar Energetic Particles from the Solar Coronal Magnetic Field

NASA Astrophysics Data System (ADS)

Zhang, Ming; Zhao, Lulu

2017-09-01

Most solar energetic particles (SEPs) are produced in the corona. They propagate through complex coronal magnetic fields subject to scattering and diffusion across the averaged field lines by turbulence. We examine the behaviors of particle transport using a stochastic 3D focused transport simulation in a potential field source surface model of coronal magnetic field. The model is applied to an SEP event on 2010 February 7. We study three scenarios of particle injection at (I) the compact solar flare site, (II) the coronal mass ejection (CME) shock, and (III) the EUV wave near the surface. The majority of particles injected on open field lines are able to escape the corona. We found that none of our models can explain the observations of wide longitudinal SEP spread without perpendicular diffusion. If the perpendicular diffusion is about 10% of what is derived from the random walk of field lines at the rate of supergranular diffusion, particles injected at the compact solar flare site can spread to a wide range of longitude and latitude, very similar to the behavior of particles injected at a large CME shock. Stronger pitch-angle scattering results in a little more lateral spread by holding the particles in the corona for longer periods of time. Some injected particles eventually end up precipitating onto the solar surface. Even with a very small perpendicular diffusion, the pattern of the particle precipitation can be quite complicated depending on the detailed small-scale coronal magnetic field structures, which could be seen with future sensitive gamma-ray telescopes.

Emergence of an optimal search strategy from a simple random walk

PubMed Central

Sakiyama, Tomoko; Gunji, Yukio-Pegio

2013-01-01

In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths. PMID:23804445

Emergence of an optimal search strategy from a simple random walk.

PubMed

Sakiyama, Tomoko; Gunji, Yukio-Pegio

2013-09-06

In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths.

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

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

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

2005-08-10

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

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.

Diffusion, subdiffusion, and localization of active colloids in random post lattices

NASA Astrophysics Data System (ADS)

Morin, Alexandre; Lopes Cardozo, David; Chikkadi, Vijayakumar; Bartolo, Denis

2017-10-01

Combining experiments and theory, we address the dynamics of self-propelled particles in crowded environments. We first demonstrate that motile colloids cruising at constant speed through random lattices undergo a smooth transition from diffusive to subdiffusive to localized dynamics upon increasing the obstacle density. We then elucidate the nature of these transitions by performing extensive simulations constructed from a detailed analysis of the colloid-obstacle interactions. We evidence that repulsion at a distance and hard-core interactions both contribute to slowing down the long-time diffusion of the colloids. In contrast, the localization transition stems solely from excluded-volume interactions and occurs at the void-percolation threshold. Within this critical scenario, equivalent to that of the random Lorentz gas, genuine asymptotic subdiffusion is found only at the critical density where the motile particles explore a fractal maze.

Random-walk enzymes.

PubMed

Mak, Chi H; Pham, Phuong; Afif, Samir A; Goodman, Myron F

2015-09-01

Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C→U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.

Random-walk enzymes

PubMed Central

Mak, Chi H.; Pham, Phuong; Afif, Samir A.; Goodman, Myron F.

2015-01-01

Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C → U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics. PMID:26465508

Random-walk enzymes

NASA Astrophysics Data System (ADS)

Mak, Chi H.; Pham, Phuong; Afif, Samir A.; Goodman, Myron F.

2015-09-01

Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C →U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.

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.

Accuracy of RGD approximation for computing light scattering properties of diffusing and motile bacteria. [Rayleigh-Gans-Debye

NASA Technical Reports Server (NTRS)

Kottarchyk, M.; Chen, S.-H.; Asano, S.

1979-01-01

The study tests the accuracy of the Rayleigh-Gans-Debye (RGD) approximation against a rigorous scattering theory calculation for a simplified model of E. coli (about 1 micron in size) - a solid spheroid. A general procedure is formulated whereby the scattered field amplitude correlation function, for both polarized and depolarized contributions, can be computed for a collection of particles. An explicit formula is presented for the scattered intensity, both polarized and depolarized, for a collection of randomly diffusing or moving particles. Two specific cases for the intermediate scattering functions are considered: diffusing particles and freely moving particles with a Maxwellian speed distribution. The formalism is applied to microorganisms suspended in a liquid medium. Sensitivity studies revealed that for values of the relative index of refraction greater than 1.03, RGD could be in serious error in computing the intensity as well as correlation functions.

An investigation of turbulent transport in the extreme lower atmosphere

NASA Technical Reports Server (NTRS)

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

1975-01-01

A model in which the Lagrangian autocorrelation is expressed by a domain integral over a set of usual Eulerian autocorrelations acquired concurrently at all points within a turbulence box is proposed along with a method for ascertaining the statistical stationarity of turbulent velocity by creating an equivalent ensemble to investigate the flow in the extreme lower atmosphere. Simultaneous measurements of turbulent velocity on a turbulence line along the wake axis were carried out utilizing a longitudinal array of five hot-wire anemometers remotely operated. The stationarity test revealed that the turbulent velocity is approximated as a realization of a weakly self-stationary random process. Based on the Lagrangian autocorrelation it is found that: (1) large diffusion time predominated; (2) ratios of Lagrangian to Eulerian time and spatial scales were smaller than unity; and, (3) short and long diffusion time scales and diffusion spatial scales were constrained within their Eulerian counterparts.

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.

Survival probability of diffusion with trapping in cellular neurobiology

NASA Astrophysics Data System (ADS)

Holcman, David; Marchewka, Avi; Schuss, Zeev

2005-09-01

The problem of diffusion with absorption and trapping sites arises in the theory of molecular signaling inside and on the membranes of biological cells. In particular, this problem arises in the case of spine-dendrite communication, where the number of calcium ions, modeled as random particles, is regulated across the spine microstructure by pumps, which play the role of killing sites, while the end of the dendritic shaft is an absorbing boundary. We develop a general mathematical framework for diffusion in the presence of absorption and killing sites and apply it to the computation of the time-dependent survival probability of ions. We also compute the ratio of the number of absorbed particles at a specific location to the number of killed particles. We show that the ratio depends on the distribution of killing sites. The biological consequence is that the position of the pumps regulates the fraction of calcium ions that reach the dendrite.

Bounded fractional diffusion in geological media: Definition and Lagrangian approximation

USGS Publications Warehouse

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

2016-01-01

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

Modeling the diffusion of complex innovations as a process of opinion formation through social networks.

PubMed

Assenova, Valentina A

2018-01-01

Complex innovations- ideas, practices, and technologies that hold uncertain benefits for potential adopters-often vary in their ability to diffuse in different communities over time. To explain why, I develop a model of innovation adoption in which agents engage in naïve (DeGroot) learning about the value of an innovation within their social networks. Using simulations on Bernoulli random graphs, I examine how adoption varies with network properties and with the distribution of initial opinions and adoption thresholds. The results show that: (i) low-density and high-asymmetry networks produce polarization in influence to adopt an innovation over time, (ii) increasing network density and asymmetry promote adoption under a variety of opinion and threshold distributions, and (iii) the optimal levels of density and asymmetry in networks depend on the distribution of thresholds: networks with high density (>0.25) and high asymmetry (>0.50) are optimal for maximizing diffusion when adoption thresholds are right-skewed (i.e., barriers to adoption are low), but networks with low density (<0.01) and low asymmetry (<0.25) are optimal when thresholds are left-skewed. I draw on data from a diffusion field experiment to predict adoption over time and compare the results to observed outcomes.

Diffusion Weighted Magnetic Resonance Imaging Assessment of Blood Flow in the Microvasculature of Abdominal Organs

NASA Astrophysics Data System (ADS)

Truica, Loredana Sorina

In this thesis, water diffusion in human liver and placenta is studied using diffusion weighted magnetic resonance imaging. For short, randomly oriented vascular segments, intravascular water motion is diffusion-like. For tissues with large vascular compartments the diffusion decay is bi-exponential with one component corresponding to diffusing water and the other to water in the microvasculature. This model, known as the intravoxel incoherent motion (IVIM) model, is seldom used with abdominal organs because of motion artifacts. This limitation was overcome for the experiments reported here by introducing: 1) parallel imaging, 2) navigator echo respiratory triggering (NRT), 3) a double echo diffusion sequence that inherently compensates for eddy current effects, 4) SPAIR fat suppression and 5) a superior approach to image analysis. In particular, the use of NRT allowed us to use a free breathing protocol instead of the previously required breath hold protocol. The resulting DWI images were of high quality and motion artifact free. Diffusion decays were measured over a larger portion of the decay than had previously been reported and the results are considerably better than those previously reported. For both studies, reliable measurements of the diffusion coefficient (D), pseudo-diffusion coefficient (D) and perfusion fraction (f), were obtained using a region of interest analysis as well as a pixel-by-pixel approach. To within experimental error, all patients had the same values of D (1.10 mum 2/ms +/- 0.16 mum2/ms), D* (46 mum2/ms +/- 17 mum2/ms) and f (44.0% +/- 6.9%) in liver and D (1.8 mum 2/ms +/- 0.2 mum2/ms), D* (30 mum 2/ms +/- 12 mmu2/ms), and f (40% +/- 6%) in the placenta. No dependence on gestational age was found for the placental study. Parametric maps of f and D* were consistent with blood flow patterns in both systems. The model worked well for both investigated organs even though their anatomical structures are quite different. A method for removing rectified noise bias from low intensity magnitude MR images measured with phased array coils is also presented. This algorithm has significance for diffusion decay measurements since it permits the use of low intensity data points which could, for example, allow the acquisition of high resolution parametric maps.

Diffusion amid random overlapping obstacles: Similarities, invariants, approximations

PubMed Central

Novak, Igor L.; Gao, Fei; Kraikivski, Pavel; Slepchenko, Boris M.

2011-01-01

Efficient and accurate numerical techniques are used to examine similarities of effective diffusion in a void between random overlapping obstacles: essential invariance of effective diffusion coefficients (Deff) with respect to obstacle shapes and applicability of a two-parameter power law over nearly entire range of excluded volume fractions (ϕ), except for a small vicinity of a percolation threshold. It is shown that while neither of the properties is exact, deviations from them are remarkably small. This allows for quick estimation of void percolation thresholds and approximate reconstruction of Deff (ϕ) for obstacles of any given shape. In 3D, the similarities of effective diffusion yield a simple multiplication “rule” that provides a fast means of estimating Deff for a mixture of overlapping obstacles of different shapes with comparable sizes. PMID:21513372

Mean-cluster approach indicates cell sorting time scales are determined by collective dynamics

NASA Astrophysics Data System (ADS)

Beatrici, Carine P.; de Almeida, Rita M. C.; Brunnet, Leonardo G.

2017-03-01

Cell migration is essential to cell segregation, playing a central role in tissue formation, wound healing, and tumor evolution. Considering random mixtures of two cell types, it is still not clear which cell characteristics define clustering time scales. The mass of diffusing clusters merging with one another is expected to grow as td /d +2 when the diffusion constant scales with the inverse of the cluster mass. Cell segregation experiments deviate from that behavior. Explanations for that could arise from specific microscopic mechanisms or from collective effects, typical of active matter. Here we consider a power law connecting diffusion constant and cluster mass to propose an analytic approach to model cell segregation where we explicitly take into account finite-size corrections. The results are compared with active matter model simulations and experiments available in the literature. To investigate the role played by different mechanisms we considered different hypotheses describing cell-cell interaction: differential adhesion hypothesis and different velocities hypothesis. We find that the simulations yield normal diffusion for long time intervals. Analytic and simulation results show that (i) cluster evolution clearly tends to a scaling regime, disrupted only at finite-size limits; (ii) cluster diffusion is greatly enhanced by cell collective behavior, such that for high enough tendency to follow the neighbors, cluster diffusion may become independent of cluster size; (iii) the scaling exponent for cluster growth depends only on the mass-diffusion relation, not on the detailed local segregation mechanism. These results apply for active matter systems in general and, in particular, the mechanisms found underlying the increase in cell sorting speed certainly have deep implications in biological evolution as a selection mechanism.

Obstructed metabolite diffusion within skeletal muscle cells in silico.

PubMed

Aliev, Mayis K; Tikhonov, Alexander N

2011-12-01

Using a Monte Carlo simulation technique, we have modeled 3D diffusion of low molecular weight metabolites inside a skeletal muscle cell. The following structural elements are considered: (i) a regular lattice of actin and myosin filaments inside a myofibril, (ii) the membranes of sarcoplasmic reticulum and mitochondria surrounding the myofibrils, (iii) a set of myofibrils inside a skeletal muscle cell encircled by the outer cell membrane, and (iv) an additional set of regular intracellular structures ("macrocompartments") embedded into the cell interior. The macrocompartments are considered to simulate diffusion restrictions because of hypothetical cylindrical structures (16-22 μm in diameter) suggested earlier (de Graaf et al. Biophys J 78: 1657-1664, 2000). This model allowed us to calculate the apparent coefficients of particle diffusion in the radial and axial directions, D(app)(⊥) and D(app)(II), respectively. Particle movements in the axial direction are considered, at first approximation, as unrestricted diffusion (D(app)(II) = const). The apparent coefficient of radial diffusion, D(app)(⊥), decreases with time because of particle collisions with myofilaments and other rigid obstacles. Results of our random walk simulations are in fairly good agreement with experimental data on NMR measurements of restricted radial diffusion of phosphocreatine in white and red skeletal muscles of goldfish (Kinsey et al. NMR Biomed 12:1-7, 1999). Particle reflections from the low-permeable borders of macrocompartments (efficient diameter, D(eff)(MC) ≈ 9.2-10.4 μm) are the prerequisite for agreeing theoretical and experimental data. The low-permeable coverage of hypothetical macrocompartments (99.8% of coverage) provides the main contribution to time-dependent decrease in D(app)(⊥).

Analysis of speckle and material properties in laider tracer

NASA Astrophysics Data System (ADS)

Ross, Jacob W.; Rigling, Brian D.; Watson, Edward A.

2017-04-01

The SAL simulation tool Laider Tracer models speckle: the random variation in intensity of an incident light beam across a rough surface. Within Laider Tracer, the speckle field is modeled as a 2-D array of jointly Gaussian random variables projected via ray tracing onto the scene of interest. Originally, all materials in Laider Tracer were treated as ideal diffuse scatterers, for which the far-field return computed uses the Lambertian Bidirectional Reflectance Distribution Function (BRDF). As presented here, we implement material properties into Laider Tracer via the Non-conventional Exploitation Factors Data System: a database of properties for thousands of different materials sampled at various wavelengths and incident angles. We verify the intensity behavior as a function of incident angle after material properties are added to the simulation.

Use of Analogies in the Study of Diffusion

ERIC Educational Resources Information Center

Letic, Milorad

2014-01-01

Emergent processes, such as diffusion, are considered more difficult to understand than direct processes. In physiology, most processes are presented as direct processes, so emergent processes, when encountered, are even more difficult to understand. It has been suggested that, when studying diffusion, misconceptions about random processes are the…

Geometrical effects on the electron residence time in semiconductor nano-particles.

PubMed

Koochi, Hakimeh; Ebrahimi, Fatemeh

2014-09-07

We have used random walk (RW) numerical simulations to investigate the influence of the geometry on the statistics of the electron residence time τ(r) in a trap-limited diffusion process through semiconductor nano-particles. This is an important parameter in coarse-grained modeling of charge carrier transport in nano-structured semiconductor films. The traps have been distributed randomly on the surface (r(2) model) or through the whole particle (r(3) model) with a specified density. The trap energies have been taken from an exponential distribution and the traps release time is assumed to be a stochastic variable. We have carried out (RW) simulations to study the effect of coordination number, the spatial arrangement of the neighbors and the size of nano-particles on the statistics of τ(r). It has been observed that by increasing the coordination number n, the average value of electron residence time, τ̅(r) rapidly decreases to an asymptotic value. For a fixed coordination number n, the electron's mean residence time does not depend on the neighbors' spatial arrangement. In other words, τ̅(r) is a porosity-dependence, local parameter which generally varies remarkably from site to site, unless we are dealing with highly ordered structures. We have also examined the effect of nano-particle size d on the statistical behavior of τ̅(r). Our simulations indicate that for volume distribution of traps, τ̅(r) scales as d(2). For a surface distribution of traps τ(r) increases almost linearly with d. This leads to the prediction of a linear dependence of the diffusion coefficient D on the particle size d in ordered structures or random structures above the critical concentration which is in accordance with experimental observations.

Turbulent transport with intermittency: Expectation of a scalar concentration.

PubMed

Rast, Mark Peter; Pinton, Jean-François; Mininni, Pablo D

2016-04-01

Scalar transport by turbulent flows is best described in terms of Lagrangian parcel motions. Here we measure the Eulerian distance travel along Lagrangian trajectories in a simple point vortex flow to determine the probabilistic impulse response function for scalar transport in the absence of molecular diffusion. As expected, the mean squared Eulerian displacement scales ballistically at very short times and diffusively for very long times, with the displacement distribution at any given time approximating that of a random walk. However, significant deviations in the displacement distributions from Rayleigh are found. The probability of long distance transport is reduced over inertial range time scales due to spatial and temporal intermittency. This can be modeled as a series of trapping events with durations uniformly distributed below the Eulerian integral time scale. The probability of long distance transport is, on the other hand, enhanced beyond that of the random walk for both times shorter than the Lagrangian integral time and times longer than the Eulerian integral time. The very short-time enhancement reflects the underlying Lagrangian velocity distribution, while that at very long times results from the spatial and temporal variation of the flow at the largest scales. The probabilistic impulse response function, and with it the expectation value of the scalar concentration at any point in space and time, can be modeled using only the evolution of the lowest spatial wave number modes (the mean and the lowest harmonic) and an eddy based constrained random walk that captures the essential velocity phase relations associated with advection by vortex motions. Preliminary examination of Lagrangian tracers in three-dimensional homogeneous isotropic turbulence suggests that transport in that setting can be similarly modeled.

Operator Spreading in Random Unitary Circuits

NASA Astrophysics Data System (ADS)

Nahum, Adam; Vijay, Sagar; Haah, Jeongwan

2018-04-01

Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries. We study both 1 +1 D and higher dimensions and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems. In 1 +1 D , we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC and determines the butterfly speed vB. We find that in 1 +1 D , the "front" of the OTOC broadens diffusively, with a width scaling in time as t1 /2. We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front within a realization. Turning to higher dimensions, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a purely classical droplet growth problem. This implies that the width of the front of the averaged OTOC scales as t1 /3 in 2 +1 D and as t0.240 in 3 +1 D (exponents of the Kardar-Parisi-Zhang universality class). We support our analytic argument with simulations in 2 +1 D . We point out that, in two or higher spatial dimensions, the shape of the spreading operator at late times is affected by underlying lattice symmetries and, in general, is not spherical. However, when full spatial rotational symmetry is present in 2 +1 D , our mapping implies an exact asymptotic form for the OTOC, in terms of the Tracy-Widom distribution. For an alternative perspective on the OTOC in 1 +1 D , we map it to the partition function of an Ising-like statistical mechanics model. As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be performed exactly. We also use this mapping to give exact results for entanglement growth in 1 +1 D circuits.

Optoenergy storage and random walks assisted broadband amplification in Er3+-doped (Pb,La)(Zr,Ti)O3 disordered ceramics.

PubMed

Xu, Long; Zhao, Hua; Xu, Caixia; Zhang, Siqi; Zou, Yingyin K; Zhang, Jingwen

2014-02-01

A broadband optical amplification was observed and investigated in Er3+-doped electrostrictive ceramics of lanthanum-modified lead zirconate titanate under a corona atmosphere. The ceramic structure change caused by UV light, electric field, and random walks originated from the diffusive process in intrinsically disordered materials may all contribute to the optical amplification and the associated energy storage. Discussion based on optical energy storage and diffusive equations was given to explain the findings. Those experiments performed made it possible to study random walks and optical amplification in transparent ceramics materials.

Random-walk approach to the d -dimensional disordered Lorentz gas

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2008-02-01

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3 . Extensive numerical simulations were also performed to elucidate the role of the approximations involved.

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media

NASA Technical Reports Server (NTRS)

Mair, R. W.; Sen, P. N.; Hurlimann, M. D.; Patz, S.; Cory, D. G.; Walsworth, R. L.

2002-01-01

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Pade approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Pade interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Pade length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter. c. 2002 Elsevier Sciences (USA).

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media.

PubMed

Mair, R W; Sen, P N; Hürlimann, M D; Patz, S; Cory, D G; Walsworth, R L

2002-06-01

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Padé approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Padé interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Padé length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter. c. 2002 Elsevier Sciences (USA).

Silicon solar cell process development, fabrication and analysis

NASA Technical Reports Server (NTRS)

Iles, P. A.; Leung, D. C.

1982-01-01

For UCP Si, randomly selected wafers and wafers cut from two specific ingots were studied. For the randomly selected wafers, a moderate gettering diffusion had little effect. Moreover, an efficiency up to 14% AMI was achieved with advanced processes. For the two specific UCP ingots, ingot #5848-13C displayed severe impurity effects as shown by lower 3sc in the middle of the ingot and low CFF in the top of the ingot. Also the middle portions of this ingot responded to a series of progressively more severe gettering diffusion. Unexplained was the fact that severely gettered samples of this ingot displayed a negative light biased effect on the minority carrier diffusion length while the nongettered or moderately gettered ones had the more conventional positive light biased effect on diffusion length. On the other hand, ingot C-4-21A did not have the problem of ingot 5848-13C and behaved like to the randomly selected wafers. The top half of the ingot was shown to be slightly superior to the bottom half, but moderate gettering helped to narrow the gap.

A General Model for Estimating Macroevolutionary Landscapes.

PubMed

Boucher, Florian C; Démery, Vincent; Conti, Elena; Harmon, Luke J; Uyeda, Josef

2018-03-01

The evolution of quantitative characters over long timescales is often studied using stochastic diffusion models. The current toolbox available to students of macroevolution is however limited to two main models: Brownian motion and the Ornstein-Uhlenbeck process, plus some of their extensions. Here, we present a very general model for inferring the dynamics of quantitative characters evolving under both random diffusion and deterministic forces of any possible shape and strength, which can accommodate interesting evolutionary scenarios like directional trends, disruptive selection, or macroevolutionary landscapes with multiple peaks. This model is based on a general partial differential equation widely used in statistical mechanics: the Fokker-Planck equation, also known in population genetics as the Kolmogorov forward equation. We thus call the model FPK, for Fokker-Planck-Kolmogorov. We first explain how this model can be used to describe macroevolutionary landscapes over which quantitative traits evolve and, more importantly, we detail how it can be fitted to empirical data. Using simulations, we show that the model has good behavior both in terms of discrimination from alternative models and in terms of parameter inference. We provide R code to fit the model to empirical data using either maximum-likelihood or Bayesian estimation, and illustrate the use of this code with two empirical examples of body mass evolution in mammals. FPK should greatly expand the set of macroevolutionary scenarios that can be studied since it opens the way to estimating macroevolutionary landscapes of any conceivable shape. [Adaptation; bounds; diffusion; FPK model; macroevolution; maximum-likelihood estimation; MCMC methods; phylogenetic comparative data; selection.].

Diffusion of strongly magnetized cosmic ray particles in a turbulent medium

NASA Technical Reports Server (NTRS)

Ptuskin, V. S.

1985-01-01

Cosmic ray (CR) propagation in a turbulent medium is usually considered in the diffusion approximation. Here, the diffusion equation is obtained for strongly magnetized particles in the general form. The influence of a large-scale random magnetic field on CR propagation in interstellar medium is discussed. Cosmic rays are assumed to propagate in a medium with a regular field H and an ensemble of random MHD waves. The energy density of waves on scales smaller than the free path 1 of CR particles is small. The collision integral of the general form which describes interaction between relativistic particles and waves in the quasilinear approximation is used.

Comparing three knowledge communication strategies - Diffusion, Dissemination and Translation - through randomized controlled studies.

PubMed

Lane, Joseph P; Stone, Vathsala I

2015-01-01

This paper describes a series of three randomized controlled case studies comparing the effectiveness of three strategies for communicating new research-based knowledge (Diffusion, Dissemination, Translation), to different Assistive Technology (AT) stakeholder groups. Pre and post intervention measures for level of knowledge use (unaware, aware, interested, using) via the LOKUS instrument, assessed the relative effectiveness of the three strategies. The latter two approaches were both more effective than diffusion but also equally effective. The results question the value added by tailoring research findings to specific audiences, and instead supports the critical yet neglected role for relevance in determining knowledge use by stakeholders.

Upscaling transport of a reacting solute through a peridocially converging-diverging channel at pre-asymptotic times

NASA Astrophysics Data System (ADS)

Sund, Nicole L.; Bolster, Diogo; Dawson, Clint

2015-11-01

In this study we extend the Spatial Markov model, which has been successfully used to upscale conservative transport across a diverse range of porous media flows, to test if it can accurately upscale reactive transport, defined by a spatially heterogeneous first order degradation rate. We test the model in a well known highly simplified geometry, commonly considered as an idealized pore or fracture structure, a periodic channel with wavy boundaries. The edges of the flow domain have a layer through which there is no flow, but in which diffusion of a solute still occurs. Reactions are confined to this region. We demonstrate that the Spatial Markov model, an upscaled random walk model that enforces correlation between successive jumps, can reproduce breakthrough curves measured from microscale simulations that explicitly resolve all pertinent processes. We also demonstrate that a similar random walk model that does not enforce successive correlations is unable to reproduce all features of the measured breakthrough curves.

Modeling of mechanical properties of II-VI materials

NASA Technical Reports Server (NTRS)

Sher, A.; Berding, M. A.; Van Schilfgaarde, M.; Chen, A.-B.; Patrick, R.

1988-01-01

This paper reviews some new developments in the theory of alloy correlations, order-disorder transitions, and solidus phase-transition curves. It is argued that semiconductor alloys are never truly random, and the various phenomena that drive deviations from random arrangements are introduced. Likely consequences of correlations on the ability to fine-tune the lattice match of epitaxial layers to substrates, on vacancy formation, on diffusion, and on vapor-phase crystal growth are discussed. Examples are chosen for the alloys Hg(1-x)Cd(x)Te, Hg(1-x)Zn(x)Te, Cd(1-y)Zn(y)Te, and CdSe(1-y)Te(y).

The impact of network characteristics on the diffusion of innovations

NASA Astrophysics Data System (ADS)

Peres, Renana

2014-05-01

This paper studies the influence of network topology on the speed and reach of new product diffusion. While previous research has focused on comparing network types, this paper explores explicitly the relationship between topology and measurements of diffusion effectiveness. We study simultaneously the effect of three network metrics: the average degree, the relative degree of social hubs (i.e., the ratio of the average degree of highly-connected individuals to the average degree of the entire population), and the clustering coefficient. A novel network-generation procedure based on random graphs with a planted partition is used to generate 160 networks with a wide range of values for these topological metrics. Using an agent-based model, we simulate diffusion on these networks and check the dependence of the net present value (NPV) of the number of adopters over time on the network metrics. We find that the average degree and the relative degree of social hubs have a positive influence on diffusion. This result emphasizes the importance of high network connectivity and strong hubs. The clustering coefficient has a negative impact on diffusion, a finding that contributes to the ongoing controversy on the benefits and disadvantages of transitivity. These results hold for both monopolistic and duopolistic markets, and were also tested on a sample of 12 real networks.

Exact PDF equations and closure approximations for advective-reactive transport

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

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

A proposal for the experimental detection of CSL induced random walk

PubMed Central

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

2015-01-01

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

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

Effect of field-aligned-beam in parallel diffusion of energetic particles in the Earth's foreshock

NASA Astrophysics Data System (ADS)

Matsukiyo, S.; Nakanishi, K.; Otsuka, F.; Kis, A.; Lemperger, I.; Hada, T.

2016-12-01

Diffusive shock acceleration (DSA) is one of the plausible acceleration mechanisms of cosmic rays. In the standard DSA model the partial density of the accelerated particles, diffused into upstream, exponentially decreases as the distance to the shock increases. Kis et al. (GRL, 31, L20801, 2004) examined the density gradients of energetic ions upstream of the bow shock with high accuracy by using Cluster data. They estimated the diffusion coefficients of energetic ions for the event in February 18, 2003 and showed that the obtained diffusion coefficients are significantly smaller than those estimated in the past statistical study. This implies that particle acceleration at the bow shock can be more efficient than considered before. Here, we focus on the effect of the field-aligned-beam (FAB) which is often observed in the foreshock, and examine how the FAB affects the efficiency of diffusion of the energetic ions by performing test particle simulations. The upstream turbulence is given by the superposition of parallel Alfven waves with power-law energy spectrum with random phase approximation. In the spectrum we further add a peak corresponding to the waves resonantly generated by the FAB. The dependence of the diffusion coefficient on the presence of the FAB as well as total energy of the turbulence, power-law index of the turbulence, and intensity of FAB oriented waves are discussed.

Multimodal brain-tumor segmentation based on Dirichlet process mixture model with anisotropic diffusion and Markov random field prior.

PubMed

Lu, Yisu; Jiang, Jun; Yang, Wei; Feng, Qianjin; Chen, Wufan

2014-01-01

Brain-tumor segmentation is an important clinical requirement for brain-tumor diagnosis and radiotherapy planning. It is well-known that the number of clusters is one of the most important parameters for automatic segmentation. However, it is difficult to define owing to the high diversity in appearance of tumor tissue among different patients and the ambiguous boundaries of lesions. In this study, a nonparametric mixture of Dirichlet process (MDP) model is applied to segment the tumor images, and the MDP segmentation can be performed without the initialization of the number of clusters. Because the classical MDP segmentation cannot be applied for real-time diagnosis, a new nonparametric segmentation algorithm combined with anisotropic diffusion and a Markov random field (MRF) smooth constraint is proposed in this study. Besides the segmentation of single modal brain-tumor images, we developed the algorithm to segment multimodal brain-tumor images by the magnetic resonance (MR) multimodal features and obtain the active tumor and edema in the same time. The proposed algorithm is evaluated using 32 multimodal MR glioma image sequences, and the segmentation results are compared with other approaches. The accuracy and computation time of our algorithm demonstrates very impressive performance and has a great potential for practical real-time clinical use.

Multimodal Brain-Tumor Segmentation Based on Dirichlet Process Mixture Model with Anisotropic Diffusion and Markov Random Field Prior

PubMed Central

Lu, Yisu; Jiang, Jun; Chen, Wufan

2014-01-01

Brain-tumor segmentation is an important clinical requirement for brain-tumor diagnosis and radiotherapy planning. It is well-known that the number of clusters is one of the most important parameters for automatic segmentation. However, it is difficult to define owing to the high diversity in appearance of tumor tissue among different patients and the ambiguous boundaries of lesions. In this study, a nonparametric mixture of Dirichlet process (MDP) model is applied to segment the tumor images, and the MDP segmentation can be performed without the initialization of the number of clusters. Because the classical MDP segmentation cannot be applied for real-time diagnosis, a new nonparametric segmentation algorithm combined with anisotropic diffusion and a Markov random field (MRF) smooth constraint is proposed in this study. Besides the segmentation of single modal brain-tumor images, we developed the algorithm to segment multimodal brain-tumor images by the magnetic resonance (MR) multimodal features and obtain the active tumor and edema in the same time. The proposed algorithm is evaluated using 32 multimodal MR glioma image sequences, and the segmentation results are compared with other approaches. The accuracy and computation time of our algorithm demonstrates very impressive performance and has a great potential for practical real-time clinical use. PMID:25254064

Stock market context of the Lévy walks with varying velocity

NASA Astrophysics Data System (ADS)

Kutner, Ryszard

2002-11-01

We developed the most general Lévy walks with varying velocity, shorter called the Weierstrass walks (WW) model, by which one can describe both stationary and non-stationary stochastic time series. We considered a non-Brownian random walk where the walker moves, in general, with a velocity that assumes a different constant value between the successive turning points, i.e., the velocity is a piecewise constant function. This model is a kind of Lévy walks where we assume a hierarchical, self-similar in a stochastic sense, spatio-temporal representation of the main quantities such as waiting-time distribution and sojourn probability density (which are principal quantities in the continuous-time random walk formalism). The WW model makes possible to analyze both the structure of the Hurst exponent and the power-law behavior of kurtosis. This structure results from the hierarchical, spatio-temporal coupling between the walker displacement and the corresponding time of the walks. The analysis uses both the fractional diffusion and the super Burnett coefficients. We constructed the diffusion phase diagram which distinguishes regions occupied by classes of different universality. We study only such classes which are characteristic for stationary situations. We thus have a model ready for describing the data presented, e.g., in the form of moving averages; the operation is often used for stochastic time series, especially financial ones. The model was inspired by properties of financial time series and tested for empirical data extracted from the Warsaw stock exchange since it offers an opportunity to study in an unbiased way several features of stock exchange in its early stage.

Modeling non-Fickian dispersion by use of the velocity PDF on the pore scale

NASA Astrophysics Data System (ADS)

Kooshapur, Sheema; Manhart, Michael

2015-04-01

For obtaining a description of reactive flows in porous media, apart from the geometrical complications of resolving the velocities and scalar values, one has to deal with the additional reactive term in the transport equation. An accurate description of the interface of the reacting fluids - which is strongly influenced by dispersion- is essential for resolving this term. In REV-based simulations the reactive term needs to be modeled taking sub-REV fluctuations and possibly non-Fickian dispersion into account. Non-Fickian dispersion has been observed in strongly heterogeneous domains and in early phases of transport. A fully resolved solution of the Navier-Stokes and transport equations which yields a detailed description of the flow properties, dispersion, interfaces of fluids, etc. however, is not practical for domains containing more than a few thousand grains, due to the huge computational effort required. Through Probability Density Function (PDF) based methods, the velocity distribution in the pore space can facilitate the understanding and modelling of non-Fickian dispersion [1,2]. Our aim is to model the transition between non-Fickian and Fickian dispersion in a random sphere pack within the framework of a PDF based transport model proposed by Meyer and Tchelepi [1,3]. They proposed a stochastic transport model where velocity components of tracer particles are represented by a continuous Markovian stochastic process. In addition to [3], we consider the effects of pore scale diffusion and formulate a different stochastic equation for the increments in velocity space from first principles. To assess the terms in this equation, we performed Direct Numerical Simulations (DNS) for solving the Navier-Stokes equation on a random sphere pack. We extracted the PDFs and statistical moments (up to the 4th moment) of the stream-wise velocity, u, and first and second order velocity derivatives both independent and conditioned on velocity. By using this data and combining the Taylor expansion of velocity increments, du, and the Langevin equation for point particles we obtained the components of velocity fluxes which point to a drift and diffusion behavior in the velocity space. Thus a partial differential equation for the velocity PDF has been formulated that constitutes an advection-diffusion equation in velocity space (a Fokker-Planck equation) in which the drift and diffusion coefficients are obtained using the velocity conditioned statistics of the derivatives of the pore scale velocity field. This has been solved by both a Random Walk (RW) model and a Finite Volume method. We conclude that both, these methods are able to simulate the velocity PDF obtained by DNS. References [1] D. W. Meyer, P. Jenny, H.A.Tschelepi, A joint velocity-concentration PDF method for traqcer flow in heterogeneous porous media, Water Resour.Res., 46, W12522, (2010). [2] Nowak, W., R. L. Schwede, O. A. Cirpka, and I. Neuweiler, Probability density functions of hydraulic head and velocity in three-dimensional heterogeneous porous media, Water Resour.Res., 44, W08452, (2008) [3] D. W. Meyer, H. A. Tchelepi, Particle-based transport model with Markovian velocity processes for tracer dispersion in highly heterogeneous porous media, Water Resour. Res., 46, W11552, (2010)

Interstellar Pickup Ion Acceleration in the Turbulent Magnetic Field at the Solar Wind Termination Shock Using a Focused Transport Approach

NASA Astrophysics Data System (ADS)

Ye, Junye; le Roux, Jakobus A.; Arthur, Aaron D.

2016-08-01

We study the physics of locally born interstellar pickup proton acceleration at the nearly perpendicular solar wind termination shock (SWTS) in the presence of a random magnetic field spiral angle using a focused transport model. Guided by Voyager 2 observations, the spiral angle is modeled with a q-Gaussian distribution. The spiral angle fluctuations, which are used to generate the perpendicular diffusion of pickup protons across the SWTS, play a key role in enabling efficient injection and rapid diffusive shock acceleration (DSA) when these particles follow field lines. Our simulations suggest that variation of both the shape (q-value) and the standard deviation (σ-value) of the q-Gaussian distribution significantly affect the injection speed, pitch-angle anisotropy, radial distribution, and the efficiency of the DSA of pickup protons at the SWTS. For example, increasing q and especially reducing σ enhances the DSA rate.

Chromatin organization regulates viral egress dynamics

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

Aho, Vesa; Myllys, Markko; Ruokolainen, Visa

Various types of DNA viruses are known to elicit the formation of a large nuclear viral replication compartment and marginalization of the cell chromatin. We used three-dimensional soft x-ray tomography, confocal and electron microscopy, combined with numerical modelling of capsid diffusion to analyse the molecular organization of chromatin in herpes simplex virus 1 infection and its effect on the transport of progeny viral capsids to the nuclear envelope. Our data showed that the formation of the viral replication compartment at late infection resulted in the enrichment of heterochromatin in the nuclear periphery accompanied by the compaction of chromatin. Random walkmore » modelling of herpes simplex virus 1–sized particles in a three-dimensional soft x-ray tomography reconstruction of an infected cell nucleus demonstrated that the peripheral, compacted chromatin restricts viral capsid diffusion, but due to interchromatin channels capsids are able to reach the nuclear envelope, the site of their nuclear egress.« less

Chromatin organization regulates viral egress dynamics

DOE PAGES

Aho, Vesa; Myllys, Markko; Ruokolainen, Visa; ...

2017-06-16

Various types of DNA viruses are known to elicit the formation of a large nuclear viral replication compartment and marginalization of the cell chromatin. We used three-dimensional soft x-ray tomography, confocal and electron microscopy, combined with numerical modelling of capsid diffusion to analyse the molecular organization of chromatin in herpes simplex virus 1 infection and its effect on the transport of progeny viral capsids to the nuclear envelope. Our data showed that the formation of the viral replication compartment at late infection resulted in the enrichment of heterochromatin in the nuclear periphery accompanied by the compaction of chromatin. Random walkmore » modelling of herpes simplex virus 1–sized particles in a three-dimensional soft x-ray tomography reconstruction of an infected cell nucleus demonstrated that the peripheral, compacted chromatin restricts viral capsid diffusion, but due to interchromatin channels capsids are able to reach the nuclear envelope, the site of their nuclear egress.« less

Motion of kinesin in a viscoelastic medium

NASA Astrophysics Data System (ADS)

Knoops, Gert; Vanderzande, Carlo

2018-05-01

Kinesin is a molecular motor that transports cargo along microtubules. The results of many in vitro experiments on kinesin-1 are described by kinetic models in which one transition corresponds to the forward motion and subsequent binding of the tethered motor head. We argue that in a viscoelastic medium like the cytosol of a cell this step is not Markov and has to be described by a nonexponential waiting time distribution. We introduce a semi-Markov kinetic model for kinesin that takes this effect into account. We calculate, for arbitrary waiting time distributions, the moment generating function of the number of steps made, and determine from this the average velocity and the diffusion constant of the motor. We illustrate our results for the case of a waiting time distribution that is Weibull. We find that for realistic parameter values, viscoelasticity decreases the velocity and the diffusion constant, but increases the randomness (or Fano factor).

Effects of various boundary conditions on the response of Poisson-Nernst-Planck impedance spectroscopy analysis models and comparison with a continuous-time random-walk model.

PubMed

Macdonald, J Ross

2011-11-24

Various electrode reaction rate boundary conditions suitable for mean-field Poisson-Nernst-Planck (PNP) mobile charge frequency response continuum models are defined and incorporated in the resulting Chang-Jaffe (CJ) CJPNP model, the ohmic OHPNP one, and a simplified GPNP one in order to generalize from full to partial blocking of mobile charges at the two plane parallel electrodes. Model responses using exact synthetic PNP data involving only mobile negative charges are discussed and compared for a wide range of CJ dimensionless reaction rate values. The CJPNP and OHPNP ones are shown to be fully equivalent, except possibly for the analysis of nanomaterial structures. The dielectric strengths associated with the CJPNP diffuse double layers at the electrodes were found to decrease toward 0 as the reaction rate increased, consistent with fewer blocked charges and more reacting ones. Parameter estimates from GPNP fits of CJPNP data were shown to lead to accurate calculated values of the CJ reaction rate and of some other CJPNP parameters. Best fits of CaCu(3)Ti(4)O(12) (CCTO) single-crystal data, an electronic conductor, at 80 and 140 K, required the anomalous diffusion model, CJPNPA, and led to medium-size rate estimates of about 0.12 and 0.03, respectively, as well as good estimates of the values of other important CJPNPA parameters such as the independently verified concentration of neutral dissociable centers. These continuum-fit results were found to be only somewhat comparable to those obtained from a composite continuous-time random-walk hopping/trapping semiuniversal UN model.

The fractional diffusion limit of a kinetic model with biochemical pathway

NASA Astrophysics Data System (ADS)

Perthame, Benoît; Sun, Weiran; Tang, Min

2018-06-01

Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.

Probabilistic transport models for plasma transport in the presence of critical thresholds: Beyond the diffusive paradigma)

NASA Astrophysics Data System (ADS)

Sánchez, R.; van Milligen, B. Ph.; Carreras, B. A.

2005-05-01

It is argued that the modeling of plasma transport in tokamaks may benefit greatly from extending the usual local paradigm to accommodate scale-free transport mechanisms. This can be done by combining Lévy distributions and a nonlinear threshold condition within the continuous time random walk concept. The advantages of this nonlocal, nonlinear extension are illustrated by constructing a simple particle density transport model that, as a result of these ideas, spontaneously exhibits much of nondiffusive phenomenology routinely observed in tokamaks. The fluid limit of the system shows that the kind of equations that are appropriate to capture these dynamics are based on fractional differential operators. In them, effective diffusivities and pinch velocities are found that are dynamically set by the system in response to the specific characteristics of the fueling source and external perturbations. This fact suggests some dramatic consequences for the extrapolation of these transport properties to larger size systems.

A CTRW-based model of time-resolved fluorescence lifetime imaging in a turbid medium

NASA Astrophysics Data System (ADS)

Chernomordik, Victor; Gandjbakhche, Amir H.; Hassan, Moinuddin; Pajevic, Sinisa; Weiss, George H.

2010-12-01

We develop an analytic model of time-resolved fluorescent imaging of photons migrating through a semi-infinite turbid medium bounded by an infinite plane in the presence of a single stationary point fluorophore embedded in the medium. In contrast to earlier models of fluorescent imaging in which photon motion is assumed to be some form of continuous diffusion process, the present analysis is based on a continuous-time random walk (CTRW) on a simple cubic lattice, the objective being to estimate the position and lifetime of the fluorophore. This can provide information related to local variations in pH and temperature with potential medical significance. Aspects of the theory were tested using time-resolved measurements of the fluorescence from small inclusions inside tissue-like phantoms. The experimental results were found to be in good agreement with theoretical predictions provided that the fluorophore was not located too close to the planar boundary, a common problem in many diffusive systems.

Particle dynamics in a viscously decaying cat's eye: The effect of finite Schmidt numbers

NASA Astrophysics Data System (ADS)

Newton, P. K.; Meiburg, Eckart

1991-05-01

The dynamics and mixing of passive marker particles for the model problem of a decaying cat's eye flow is studied. The flow field corresponds to Stuart's one-parameter family of solutions [J. Fluid Mech. 29, 417 (1967)]. It is time dependent as a result of viscosity, which is modeled by allowing the free parameter to depend on time according to the self-similar solution of the Navier-Stokes equations for an isolated point vortex. Particle diffusion is numerically simulated by a random walk model. While earlier work had shown that, for small values of time over Reynolds number t/Re≪1, the interval length characterizing the formation of lobes of fluid escaping from the cat's eye scales as Re-1/2, the present study shows that, for the case of diffusive effects and t/Pe≪1, the scaling follows Pe-1/4. A simple argument, taking into account streamline convergence and divergence in different parts of the flow field, explains the Pe-1/4 scaling.

Probability distribution of haplotype frequencies under the two-locus Wright-Fisher model by diffusion approximation.

PubMed

Boitard, Simon; Loisel, Patrice

2007-05-01

The probability distribution of haplotype frequencies in a population, and the way it is influenced by genetical forces such as recombination, selection, random drift ...is a question of fundamental interest in population genetics. For large populations, the distribution of haplotype frequencies for two linked loci under the classical Wright-Fisher model is almost impossible to compute because of numerical reasons. However the Wright-Fisher process can in such cases be approximated by a diffusion process and the transition density can then be deduced from the Kolmogorov equations. As no exact solution has been found for these equations, we developed a numerical method based on finite differences to solve them. It applies to transient states and models including selection or mutations. We show by several tests that this method is accurate for computing the conditional joint density of haplotype frequencies given that no haplotype has been lost. We also prove that it is far less time consuming than other methods such as Monte Carlo simulations.

Diffusion with social reinforcement: The role of individual preferences

NASA Astrophysics Data System (ADS)

Tur, Elena M.; Zeppini, Paolo; Frenken, Koen

2018-02-01

The debate on diffusion in social networks has traditionally focused on the structure of the network to understand the efficiency of a network in terms of diffusion. Recently, the role of social reinforcement has been added to the debate, as it has been proposed that simple contagions diffuse better in random networks and complex contagions diffuse better in regular networks. In this paper, we show that individual preferences cannot be overlooked: complex contagions diffuse better in regular networks only if the large majority of the population is biased against adoption.

Normalized sensitivities and parameter identifiability of in situ diffusion experiments on Callovo Oxfordian clay at Bure site

NASA Astrophysics Data System (ADS)

Samper, J.; Dewonck, S.; Zheng, L.; Yang, Q.; Naves, A.

Diffusion of inert and reactive tracers (DIR) is an experimental program performed by ANDRA at Bure underground research laboratory in Meuse/Haute Marne (France) to characterize diffusion and retention of radionuclides in Callovo-Oxfordian (C-Ox) argillite. In situ diffusion experiments were performed in vertical boreholes to determine diffusion and retention parameters of selected radionuclides. C-Ox clay exhibits a mild diffusion anisotropy due to stratification. Interpretation of in situ diffusion experiments is complicated by several non-ideal effects caused by the presence of a sintered filter, a gap between the filter and borehole wall and an excavation disturbed zone (EdZ). The relevance of such non-ideal effects and their impact on estimated clay parameters have been evaluated with numerical sensitivity analyses and synthetic experiments having similar parameters and geometric characteristics as real DIR experiments. Normalized dimensionless sensitivities of tracer concentrations at the test interval have been computed numerically. Tracer concentrations are found to be sensitive to all key parameters. Sensitivities are tracer dependent and vary with time. These sensitivities are useful to identify which are the parameters that can be estimated with less uncertainty and find the times at which tracer concentrations begin to be sensitive to each parameter. Synthetic experiments generated with prescribed known parameters have been interpreted automatically with INVERSE-CORE 2D and used to evaluate the relevance of non-ideal effects and ascertain parameter identifiability in the presence of random measurement errors. Identifiability analysis of synthetic experiments reveals that data noise makes difficult the estimation of clay parameters. Parameters of clay and EdZ cannot be estimated simultaneously from noisy data. Models without an EdZ fail to reproduce synthetic data. Proper interpretation of in situ diffusion experiments requires accounting for filter, gap and EdZ. Estimates of the effective diffusion coefficient and the porosity of clay are highly correlated, indicating that these parameters cannot be estimated simultaneously. Accurate estimation of De and porosities of clay and EdZ is only possible when the standard deviation of random noise is less than 0.01. Small errors in the volume of the circulation system do not affect clay parameter estimates. Normalized sensitivities as well as the identifiability analysis of synthetic experiments provide additional insight on inverse estimation of in situ diffusion experiments and will be of great benefit for the interpretation of real DIR in situ diffusion experiments.

Colony patterning and collective hyphal growth of filamentous fungi

NASA Astrophysics Data System (ADS)

Matsuura, Shu

2002-11-01

Colony morphology of wild and mutant strains of Aspergillus nidulans at various nutrient and agar levels was investigated. Two types of colony patterning were found for these strains. One type produced uniform colonies at all nutrient and agar levels tested, and the other exhibited morphological change into disordered ramified colonies at low nutrient levels. Both types showed highly condensed compact colonies at high nutrient levels on low agar media that was highly diffusive. Disordered colonies were found to develop with low hyphal extension rates at low nutrient levels. To understand basic pattern selection rules, a colony model with three parameters, i.e., the initial nutrient level and the step length of nutrient random walk as the external parameters, and the frequency of nutrient uptake as an internal parameter, was constructed. At low nutrient levels, with decreasing nutrient uptake frequency under diffusive conditions, the model colony exhibited onsets of disordered ramification. Further, in the growth process of A. nidulans, reduction of hyphal extension rate due to a population effect of hyphae was found when hyphae form three-dimensional dense colonies, as compared to the case in which hyphal growth was restricted into two-dimensional space. A hyphal population effect was introduced in the colony model. Thickening of colony periphery due to the population effect became distinctive as the nutrient diffusion effect was raised at high nutrient levels with low hyphal growth rate. It was considered that colony patterning and onset of disorder were strongly governed by the combination of nutrient diffusion and hyphal growth rate.

Transport of volatile organic compounds across the capillary fringe

USGS Publications Warehouse

McCarthy, Kathleen A.; Johnson, Richard L.

1993-01-01

Physical experiments were conducted to investigate the transport of a dissolved volatile organic compound (trichloroethylene, TCE) from shallow groundwater to the unsaturated zone under a variety of conditions including changes in the soil moisture profile and water table position. Experimental data indicated that at moderate groundwater velocities (0.1 m/d), vertical mechanical dispersion was negligible and molecular diffusion was the dominant vertical transport mechanism. Under these conditions, TCE concentrations decreased nearly 3 orders of magnitude across the capillary fringe and soil gas concentrations remained low relative to those of underlying groundwater. Data collected during a water table drop showed a short-term increase in concentrations throughout most of the unsaturated zone, but these concentrations quickly declined and approached initial values after the water table was returned to its original level. In the deep part of the unsaturated zone, the water table drop resulted in a long-term decrease in concentrations, illustrating the effects of hysteresis in the soil moisture profile. A two-dimensional random walk advection-diffusion model was developed to simulate the experimental conditions, and numerical simulations agreed well with experimental data. A simpler, one-dimensional finite-difference diffusion-dispersion model was also developed. One-dimensional simulations based on molecular diffusion also agreed well with experimental data. Simulations which incorporated mechanical dispersion tended to overestimate flux across the capillary fringe. Good agreement between the one- and two-dimensional models suggested that a simple, one-dimensional approximation of vertical transport across the capillary fringe can be useful when conditions are appropriate.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

A dynamic spatio-temporal model for spatial data

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Hanks, Ephraim M.; Russell, Robin; Walsh, Daniel P.

2017-01-01

Analyzing spatial data often requires modeling dependencies created by a dynamic spatio-temporal data generating process. In many applications, a generalized linear mixed model (GLMM) is used with a random effect to account for spatial dependence and to provide optimal spatial predictions. Location-specific covariates are often included as fixed effects in a GLMM and may be collinear with the spatial random effect, which can negatively affect inference. We propose a dynamic approach to account for spatial dependence that incorporates scientific knowledge of the spatio-temporal data generating process. Our approach relies on a dynamic spatio-temporal model that explicitly incorporates location-specific covariates. We illustrate our approach with a spatially varying ecological diffusion model implemented using a computationally efficient homogenization technique. We apply our model to understand individual-level and location-specific risk factors associated with chronic wasting disease in white-tailed deer from Wisconsin, USA and estimate the location the disease was first introduced. We compare our approach to several existing methods that are commonly used in spatial statistics. Our spatio-temporal approach resulted in a higher predictive accuracy when compared to methods based on optimal spatial prediction, obviated confounding among the spatially indexed covariates and the spatial random effect, and provided additional information that will be important for containing disease outbreaks.

Generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains

NASA Astrophysics Data System (ADS)

Angstmann, C. N.; Henry, B. I.; McGann, A. V.

2017-10-01

The ubiquity of subdiffusive transport in physical and biological systems has led to intensive efforts to provide robust theoretical models for this phenomena. These models often involve fractional derivatives. The important physical extension of this work to processes occurring in growing materials has proven highly nontrivial. Here we derive evolution equations for modeling subdiffusive transport in a growing medium. The derivation is based on a continuous-time random walk. The concise formulation of these evolution equations requires the introduction of a new, comoving, fractional derivative. The implementation of the evolution equation is illustrated with a simple model of subdiffusing proteins in a growing membrane.

Parameterization of large-scale turbulent diffusion in the presence of both well-mixed and weakly mixed patchy layers

NASA Astrophysics Data System (ADS)

Osman, M. K.; Hocking, W. K.; Tarasick, D. W.

2016-06-01

Vertical diffusion and mixing of tracers in the upper troposphere and lower stratosphere (UTLS) are not uniform, but primarily occur due to patches of turbulence that are intermittent in time and space. The effective diffusivity of regions of patchy turbulence is related to statistical parameters describing the morphology of turbulent events, such as lifetime, number, width, depth and local diffusivity (i.e., diffusivity within the turbulent patch) of the patches. While this has been recognized in the literature, the primary focus has been on well-mixed layers, with few exceptions. In such cases the local diffusivity is irrelevant, but this is not true for weakly and partially mixed layers. Here, we use both theory and numerical simulations to consider the impact of intermediate and weakly mixed layers, in addition to well-mixed layers. Previous approaches have considered only one dimension (vertical), and only a small number of layers (often one at each time step), and have examined mixing of constituents. We consider a two-dimensional case, with multiple layers (10 and more, up to hundreds and even thousands), having well-defined, non-infinite, lengths and depths. We then provide new formulas to describe cases involving well-mixed layers which supersede earlier expressions. In addition, we look in detail at layers that are not well mixed, and, as an interesting variation on previous models, our procedure is based on tracking the dispersion of individual particles, which is quite different to the earlier approaches which looked at mixing of constituents. We develop an expression which allows determination of the degree of mixing, and show that layers used in some previous models were in fact not well mixed and so produced erroneous results. We then develop a generalized model based on two dimensional random-walk theory employing Rayleigh distributions which allows us to develop a universal formula for diffusion rates for multiple two-dimensional layers with general degrees of mixing. We show that it is the largest, most vigorous and less common turbulent layers that make the major contribution to global diffusion. Finally, we make estimates of global-scale diffusion coefficients in the lower stratosphere and upper troposphere. For the lower stratosphere, κeff ≈ 2x10-2 m2 s-1, assuming no other processes contribute to large-scale diffusion.

Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.

PubMed

Potdar, Alka A; Jeon, Junhwan; Weaver, Alissa M; Quaranta, Vito; Cummings, Peter T

2010-03-10

Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW). Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases) each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation). Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.

Estimation of the Thermal Process in the Honeycomb Panel by a Monte Carlo Method

NASA Astrophysics Data System (ADS)

Gusev, S. A.; Nikolaev, V. N.

2018-01-01

A new Monte Carlo method for estimating the thermal state of the heat insulation containing honeycomb panels is proposed in the paper. The heat transfer in the honeycomb panel is described by a boundary value problem for a parabolic equation with discontinuous diffusion coefficient and boundary conditions of the third kind. To obtain an approximate solution, it is proposed to use the smoothing of the diffusion coefficient. After that, the obtained problem is solved on the basis of the probability representation. The probability representation is the expectation of the functional of the diffusion process corresponding to the boundary value problem. The process of solving the problem is reduced to numerical statistical modelling of a large number of trajectories of the diffusion process corresponding to the parabolic problem. It was used earlier the Euler method for this object, but that requires a large computational effort. In this paper the method is modified by using combination of the Euler and the random walk on moving spheres methods. The new approach allows us to significantly reduce the computation costs.

Galactic civilizations - Population dynamics and interstellar diffusion

NASA Technical Reports Server (NTRS)

Newman, W. I.; Sagan, C.

1981-01-01

A model is developed of the interstellar diffusion of galactic civilizations which takes into account the population dynamics of such civilizations. The problem is formulated in terms of potential theory, with a family of nonlinear partial differential and difference equations specifying population growth and diffusion for an organism with advantageous genes that undergoes random dispersal while increasing in population locally, and a population at zero population growth. In the case of nonlinear diffusion with growth and saturation, it is found that the colonization wavefront from the nearest independently arisen galactic civilization can have reached the earth only if its lifetime exceeds 2.6 million years, or 20 million years if discretization can be neglected. For zero population growth, the corresponding lifetime is 13 billion years. It is concluded that the earth is uncolonized not because interstellar spacefaring civilizations are rare, but because there are too many worlds to be colonized in the plausible colonization lifetime of nearby civilizations, and that there exist no very old galactic civilizations with a consistent policy of the conquest of inhabited worlds.

Exploring a potential energy surface by machine learning for characterizing atomic transport

NASA Astrophysics Data System (ADS)

Kanamori, Kenta; Toyoura, Kazuaki; Honda, Junya; Hattori, Kazuki; Seko, Atsuto; Karasuyama, Masayuki; Shitara, Kazuki; Shiga, Motoki; Kuwabara, Akihide; Takeuchi, Ichiro

2018-03-01

We propose a machine-learning method for evaluating the potential barrier governing atomic transport based on the preferential selection of dominant points for atomic transport. The proposed method generates numerous random samples of the entire potential energy surface (PES) from a probabilistic Gaussian process model of the PES, which enables defining the likelihood of the dominant points. The robustness and efficiency of the method are demonstrated on a dozen model cases for proton diffusion in oxides, in comparison with a conventional nudge elastic band method.

Semiconductor technology program. Progress briefs

NASA Technical Reports Server (NTRS)

Bullis, W. M. (Editor)

1979-01-01

The current status of NBS work on measurement technology for semiconductor materials, process control, and devices is reported. Results of both in-house and contract research are covered. Highlighted activities include modeling of diffusion processes, analysis of model spreading resistance data, and studies of resonance ionization spectroscopy, resistivity-dopant density relationships in p-type silicon, deep level measurements, photoresist sensitometry, random fault measurements, power MOSFET thermal characteristics, power transistor switching characteristics, and gross leak testing. New and selected on-going projects are described. Compilations of recent publications and publications in press are included.

Self-diffusion in dense granular shear flows.

PubMed

Utter, Brian; Behringer, R P

2004-03-01

Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear flows in a two-dimensional Couette geometry. We find that self-diffusivities D are proportional to the local shear rate gamma; with diffusivities along the direction of the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D approximately gamma;a(2), where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and strong drag at the moving boundary lead to particle displacements that can appear subdiffusive or superdiffusive. In particular, diffusion appears to be superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems and has no obvious analog in rapid flows. Specifically, the diffusivity is suppressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean velocity field, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Lévy flights are also observed. Although correlated motion creates velocity fields which are qualitatively different from collisional Brownian motion and can introduce nondiffusive effects, on average the system appears simply diffusive.

Quasi-analytical treatment of spatially averaged radiation transfer in complex terrain

NASA Astrophysics Data System (ADS)

Löwe, H.; Helbig, N.

2012-04-01

We provide a new quasi-analytical method to compute the topographic influence on the effective albedo of complex topography as required for meteorological, land-surface or climate models. We investigate radiative transfer in complex terrain via the radiosity equation on isotropic Gaussian random fields. Under controlled approximations we derive expressions for domain averages of direct, diffuse and terrain radiation and the sky view factor. Domain averaged quantities are related to a type of level-crossing probability of the random field which is approximated by longstanding results developed for acoustic scattering at ocean boundaries. This allows us to express all non-local horizon effects in terms of a local terrain parameter, namely the mean squared slope. Emerging integrals are computed numerically and fit formulas are given for practical purposes. As an implication of our approach we provide an expression for the effective albedo of complex terrain in terms of the sun elevation angle, mean squared slope, the area averaged surface albedo, and the direct-to-diffuse ratio of solar radiation. As an application, we compute the effective albedo for the Swiss Alps and discuss possible generalizations of the method.

Reduction of Poisson noise in measured time-resolved data for time-domain diffuse optical tomography.

PubMed

Okawa, S; Endo, Y; Hoshi, Y; Yamada, Y

2012-01-01

A method to reduce noise for time-domain diffuse optical tomography (DOT) is proposed. Poisson noise which contaminates time-resolved photon counting data is reduced by use of maximum a posteriori estimation. The noise-free data are modeled as a Markov random process, and the measured time-resolved data are assumed as Poisson distributed random variables. The posterior probability of the occurrence of the noise-free data is formulated. By maximizing the probability, the noise-free data are estimated, and the Poisson noise is reduced as a result. The performances of the Poisson noise reduction are demonstrated in some experiments of the image reconstruction of time-domain DOT. In simulations, the proposed method reduces the relative error between the noise-free and noisy data to about one thirtieth, and the reconstructed DOT image was smoothed by the proposed noise reduction. The variance of the reconstructed absorption coefficients decreased by 22% in a phantom experiment. The quality of DOT, which can be applied to breast cancer screening etc., is improved by the proposed noise reduction.

Sorption reaction mechanism of some hazardous radionuclides from mixed waste by impregnated crown ether onto polymeric resin.

PubMed

Shehata, F A; Attallah, M F; Borai, E H; Hilal, M A; Abo-Aly, M M

2010-02-01

A novel impregnated polymeric resin was practically tested as adsorbent material for removal of some hazardous radionuclides from radioactive liquid waste. The applicability for the treatment of low-level liquid radioactive waste was investigated. The material was prepared by loading 4,4'(5')di-t-butylbenzo 18 crown 6 (DtBB18C6) onto poly(acrylamide-acrylic acid-acrylonitril)-N, N'-methylenediacrylamide (P(AM-AA-AN)-DAM). The removal of (134)Cs, (60)Co, (65)Zn , and ((152+154))Eu onto P(AM-AA-AN)-DAM/DtBB18C6 was investigated using a batch equilibrium technique with respect to the pH, contact time, and temperature. Kinetic models are used to determine the rate of sorption and to investigate the mechanism of sorption process. Five kinetics models, pseudo-first-order, pseudo-second-order, intra-particle diffusion, homogeneous particle diffusion (HPDM), and Elovich models, were used to investigate the sorption process. The obtained results of kinetic models predicted that, pseudo-second-order is applicable; the sorption is controlled by particle diffusion mechanism and the process is chemisorption. The obtained values of thermodynamics parameters, DeltaH degrees , DeltaS degrees , and DeltaG degrees indicated that the endothermic nature, increased randomness at the solid/solution interface and the spontaneous nature of the sorption processes. Copyright (c) 2009 Elsevier Ltd. All rights reserved.

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.

The topomer-sampling model of protein folding

PubMed Central

Debe, Derek A.; Carlson, Matt J.; Goddard, William A.

1999-01-01

Clearly, a protein cannot sample all of its conformations (e.g., ≈3100 ≈ 1048 for a 100 residue protein) on an in vivo folding timescale (<1 s). To investigate how the conformational dynamics of a protein can accommodate subsecond folding time scales, we introduce the concept of the native topomer, which is the set of all structures similar to the native structure (obtainable from the native structure through local backbone coordinate transformations that do not disrupt the covalent bonding of the peptide backbone). We have developed a computational procedure for estimating the number of distinct topomers required to span all conformations (compact and semicompact) for a polypeptide of a given length. For 100 residues, we find ≈3 × 107 distinct topomers. Based on the distance calculated between different topomers, we estimate that a 100-residue polypeptide diffusively samples one topomer every ≈3 ns. Hence, a 100-residue protein can find its native topomer by random sampling in just ≈100 ms. These results suggest that subsecond folding of modest-sized, single-domain proteins can be accomplished by a two-stage process of (i) topomer diffusion: random, diffusive sampling of the 3 × 107 distinct topomers to find the native topomer (≈0.1 s), followed by (ii) intratopomer ordering: nonrandom, local conformational rearrangements within the native topomer to settle into the precise native state. PMID:10077555

Fluorescence imaging of single-molecule retention trajectories in reversed-phase chromatographic particles.

PubMed

Cooper, Justin T; Peterson, Eric M; Harris, Joel M

2013-10-01

Due to its high specific surface area and chemical stability, porous silica is used as a support structure in numerous applications, including heterogeneous catalysis, biomolecule immobilization, sensors, and liquid chromatography. Reversed-phase liquid chromatography (RPLC), which uses porous silica support particles, has become an indispensable separations tool in quality control, pharmaceutics, and environmental analysis requiring identification of compounds in mixtures. For complex samples, the need for higher resolution separations requires an understanding of the time scale of processes responsible for analyte retention in the stationary phase. In the present work, single-molecule fluorescence imaging is used to observe transport of individual molecules within RPLC porous silica particles. This technique allows direct measurement of intraparticle molecular residence times, intraparticle diffusion rates, and the spatial distribution of molecules within the particle. On the basis of the localization uncertainty and characteristic measured diffusion rates, statistical criteria were developed to resolve the frame-to-frame behavior of molecules into moving and stuck events. The measured diffusion coefficient of moving molecules was used in a Monte Carlo simulation of a random-walk model within the cylindrical geometry of the particle diameter and microscope depth-of-field. The simulated molecular transport is in good agreement with the experimental data, indicating transport of moving molecules in the porous particle is described by a random-walk. Histograms of stuck-molecule event times, locations, and their contributions to intraparticle residence times were also characterized.

Anderson transition in a three-dimensional kicked rotor

NASA Astrophysics Data System (ADS)

Wang, Jiao; García-García, Antonio M.

2009-03-01

We investigate Anderson localization in a three-dimensional (3D) kicked rotor. By a finite-size scaling analysis we identify a mobility edge for a certain value of the kicking strength k=kc . For k>kc dynamical localization does not occur, all eigenstates are delocalized and the spectral correlations are well described by Wigner-Dyson statistics. This can be understood by mapping the kicked rotor problem onto a 3D Anderson model (AM) where a band of metallic states exists for sufficiently weak disorder. Around the critical region k≈kc we carry out a detailed study of the level statistics and quantum diffusion. In agreement with the predictions of the one parameter scaling theory (OPT) and with previous numerical simulations, the number variance is linear, level repulsion is still observed, and quantum diffusion is anomalous with ⟨p2⟩∝t2/3 . We note that in the 3D kicked rotor the dynamics is not random but deterministic. In order to estimate the differences between these two situations we have studied a 3D kicked rotor in which the kinetic term of the associated evolution matrix is random. A detailed numerical comparison shows that the differences between the two cases are relatively small. However in the deterministic case only a small set of irrational periods was used. A qualitative analysis of a much larger set suggests that deviations between the random and the deterministic kicked rotor can be important for certain choices of periods. Heuristically it is expected that localization effects will be weaker in a nonrandom potential since destructive interference will be less effective to arrest quantum diffusion. However we have found that certain choices of irrational periods enhance Anderson localization effects.

MAGNETIC FIELD LINE RANDOM WALK FOR DISTURBED FLUX SURFACES: TRAPPING EFFECTS AND MULTIPLE ROUTES TO BOHM DIFFUSION

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

Ghilea, M. C.; Ruffolo, D.; Sonsrettee, W.

2011-11-01

The magnetic field line random walk (FLRW) is important for the transport of energetic particles in many astrophysical situations. While all authors agree on the quasilinear diffusion of field lines for fluctuations that mainly vary parallel to a large-scale field, for the opposite case of fluctuations that mainly vary in the perpendicular directions, there has been an apparent conflict between concepts of Bohm diffusion and percolation/trapping effects. Here computer simulation and non-perturbative analytic techniques are used to re-examine the FLRW in magnetic turbulence with slab and two-dimensional (2D) components, in which 2D flux surfaces are disturbed by the slab fluctuations.more » Previous non-perturbative theories for D{sub perpendicular}, based on Corrsin's hypothesis, have identified a slab contribution with quasilinear behavior and a 2D contribution due to Bohm diffusion with diffusive decorrelation (DD), combined in a quadratic formula. Here we present analytic theories for other routes to Bohm diffusion, with random ballistic decorrelation (RBD) either due to the 2D component itself (for a weak slab contribution) or the total fluctuation field (for a strong slab contribution), combined in a direct sum with the slab contribution. Computer simulations confirm the applicability of RBD routes for weak or strong slab contributions, while the DD route applies for a moderate slab contribution. For a very low slab contribution, interesting trapping effects are found, including a depressed diffusion coefficient and subdiffusive behavior. Thus quasilinear, Bohm, and trapping behaviors are all found in the same system, together with an overall viewpoint to explain these behaviors.« less

Membrane Diffusion Occurs by Continuous-Time Random Walk Sustained by Vesicular Trafficking.

PubMed

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

2018-06-19

Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein and interlipid interactions, interactions with membrane microdomains, interactions with the underlying cytoskeleton, and cellular processes that result in net membrane movement. The complex, non-Brownian diffusion that results from these processes has been difficult to characterize, and moreover, the impact of factors such as membrane recycling on membrane diffusion remains largely unexplored. We have used a careful statistical analysis of single-particle tracking data of the single-pass plasma membrane protein CD93 to show that the diffusion of this protein is well described by a continuous-time random walk in parallel with an aging process mediated by membrane corrals. The overall result is an evolution in the diffusion of CD93: proteins initially diffuse freely on the cell surface but over time become increasingly trapped within diffusion-limiting membrane corrals. Stable populations of freely diffusing and corralled CD93 are maintained by an endocytic/exocytic process in which corralled CD93 is selectively endocytosed, whereas freely diffusing CD93 is replenished by exocytosis of newly synthesized and recycled CD93. This trafficking not only maintained CD93 diffusivity but also maintained the heterogeneous distribution of CD93 in the plasma membrane. These results provide insight into the nature of the biological and biophysical processes that can lead to significantly non-Brownian diffusion of membrane proteins and demonstrate that ongoing membrane recycling is critical to maintaining steady-state diffusion and distribution of proteins in the plasma membrane. Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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.

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.

Multiscale diffusion of a molecular probe in a crowded environment: a concept

NASA Astrophysics Data System (ADS)

Currie, Megan; Thao, Chang; Timerman, Randi; Welty, Robb; Berry, Brenden; Sheets, Erin D.; Heikal, Ahmed A.

2015-08-01

Living cells are crowded with macromolecules and organelles. Yet, it is not fully understood how macromolecular crowding affects the myriad of biochemical reactions, transport and the structural stability of biomolecules that are essential to cellular function and survival. These molecular processes, with or without electrostatic interactions, in living cells are therefore expected to be distinct from those carried out in test tube in dilute solutions where excluded volumes are absent. Thus there is an urgent need to understand the macromolecular crowding effects on cellular and molecular biophysics towards quantitative cell biology. In this report, we investigated how biomimetic crowding affects both the rotational and translation diffusion of a small probe (rhodamine green, RhG). For biomimetic crowding agents, we used Ficoll-70 (synthetic polymer), bovine serum albumin and ovalbumin (proteins) at various concentrations in a buffer at room temperature. As a control, we carried out similar measurements on glycerolenriched buffer as an environment with homogeneous viscosity as a function of glycerol concentration. The corresponding bulk viscosity was measured independently to test the validity of the Stokes-Einstein model of a diffusing species undergoing a random walk. For rotational diffusion (ps-ns time scale), we used time-resolved anisotropy measurements to examine potential binding of RhG as a function of the crowding agents (surface structure and size). For translational diffusion (μs-s time scale), we used fluorescence correlation spectroscopy for single-molecule fluctuation analysis. Our results allow us to examine the diffusion model of a molecular probe in crowded environments as a function of concentration, length scale, homogeneous versus heterogeneous viscosity, size and surface structures. These biomimetic crowding studies, using non-invasive fluorescence spectroscopy methods, represent an important step towards understanding cellular biophysics and quantitative cell biology.

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.

Structure Elucidation of Mixed-Linker Zeolitic Imidazolate Frameworks by Solid-State (1)H CRAMPS NMR Spectroscopy and Computational Modeling.

PubMed

Jayachandrababu, Krishna C; Verploegh, Ross J; Leisen, Johannes; Nieuwendaal, Ryan C; Sholl, David S; Nair, Sankar

2016-06-15

Mixed-linker zeolitic imidazolate frameworks (ZIFs) are nanoporous materials that exhibit continuous and controllable tunability of properties like effective pore size, hydrophobicity, and organophilicity. The structure of mixed-linker ZIFs has been studied on macroscopic scales using gravimetric and spectroscopic techniques. However, it has so far not been possible to obtain information on unit-cell-level linker distribution, an understanding of which is key to predicting and controlling their adsorption and diffusion properties. We demonstrate the use of (1)H combined rotation and multiple pulse spectroscopy (CRAMPS) NMR spin exchange measurements in combination with computational modeling to elucidate potential structures of mixed-linker ZIFs, particularly the ZIF 8-90 series. All of the compositions studied have structures that have linkers mixed at a unit-cell-level as opposed to separated or highly clustered phases within the same crystal. Direct experimental observations of linker mixing were accomplished by measuring the proton spin exchange behavior between functional groups on the linkers. The data were then fitted to a kinetic spin exchange model using proton positions from candidate mixed-linker ZIF structures that were generated computationally using the short-range order (SRO) parameter as a measure of the ordering, clustering, or randomization of the linkers. The present method offers the advantages of sensitivity without requiring isotope enrichment, a straightforward NMR pulse sequence, and an analysis framework that allows one to relate spin diffusion behavior to proposed atomic positions. We find that structures close to equimolar composition of the two linkers show a greater tendency for linker clustering than what would be predicted based on random models. Using computational modeling we have also shown how the window-type distribution in experimentally synthesized mixed-linker ZIF-8-90 materials varies as a function of their composition. The structural information thus obtained can be further used for predicting, screening, or understanding the tunable adsorption and diffusion behavior of mixed-linker ZIFs, for which the knowledge of linker distributions in the framework is expected to be important.

Diffusion Coefficients of Endogenous Cytosolic Proteins from Rabbit Skinned Muscle Fibers

PubMed Central

Carlson, Brian E.; Vigoreaux, Jim O.; Maughan, David W.

2014-01-01

Efflux time courses of endogenous cytosolic proteins were obtained from rabbit psoas muscle fibers skinned in oil and transferred to physiological salt solution. Proteins were separated by gel electrophoresis and compared to load-matched standards for quantitative analysis. A radial diffusion model incorporating the dissociation and dissipation of supramolecular complexes accounts for an initial lag and subsequent efflux of glycolytic and glycogenolytic enzymes. The model includes terms representing protein crowding, myofilament lattice hindrance, and binding to the cytomatrix. Optimization algorithms returned estimates of the apparent diffusion coefficients, D(r,t), that were very low at the onset of diffusion (∼10−10 cm2 s−1) but increased with time as cytosolic protein density, which was initially high, decreased. D(r,t) at later times ranged from 2.11 × 10−7 cm2 s−1 (parvalbumin) to 0.20 × 10−7 cm2 s−1 (phosphofructose kinase), values that are 3.6- to 12.3-fold lower than those predicted in bulk water. The low initial values are consistent with the presence of complexes in situ; the higher later values are consistent with molecular sieving and transient binding of dissociated proteins. Channeling of metabolic intermediates via enzyme complexes may enhance production of adenosine triphosphate at rates beyond that possible with randomly and/or sparsely distributed enzymes, thereby matching supply with demand. PMID:24559981

Statistical properties of fluctuations of time series representing appearances of words in nationwide blog data and their applications: An example of modeling fluctuation scalings of nonstationary time series.

PubMed

Watanabe, Hayafumi; Sano, Yukie; Takayasu, Hideki; Takayasu, Misako

2016-11-01

To elucidate the nontrivial empirical statistical properties of fluctuations of a typical nonsteady time series representing the appearance of words in blogs, we investigated approximately 3×10^{9} Japanese blog articles over a period of six years and analyze some corresponding mathematical models. First, we introduce a solvable nonsteady extension of the random diffusion model, which can be deduced by modeling the behavior of heterogeneous random bloggers. Next, we deduce theoretical expressions for both the temporal and ensemble fluctuation scalings of this model, and demonstrate that these expressions can reproduce all empirical scalings over eight orders of magnitude. Furthermore, we show that the model can reproduce other statistical properties of time series representing the appearance of words in blogs, such as functional forms of the probability density and correlations in the total number of blogs. As an application, we quantify the abnormality of special nationwide events by measuring the fluctuation scalings of 1771 basic adjectives.

Fuzzy Markov random fields versus chains for multispectral image segmentation.

PubMed

Salzenstein, Fabien; Collet, Christophe

2006-11-01

This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data.

Classification of nanoparticle diffusion processes in vital cells by a multifeature random forests approach: application to simulated data, darkfield, and confocal laser scanning microscopy

NASA Astrophysics Data System (ADS)

Wagner, Thorsten; Kroll, Alexandra; Wiemann, Martin; Lipinski, Hans-Gerd

2016-04-01

Darkfield and confocal laser scanning microscopy both allow for a simultaneous observation of live cells and single nanoparticles. Accordingly, a characterization of nanoparticle uptake and intracellular mobility appears possible within living cells. Single particle tracking makes it possible to characterize the particle and the surrounding cell. In case of free diffusion, the mean squared displacement for each trajectory of a nanoparticle can be measured which allows computing the corresponding diffusion coefficient and, if desired, converting it into the hydrodynamic diameter using the Stokes-Einstein equation and the viscosity of the fluid. However, within the more complex system of a cell's cytoplasm unrestrained diffusion is scarce and several other types of movements may occur. Thus, confined or anomalous diffusion (e.g. diffusion in porous media), active transport, and combinations thereof were described by several authors. To distinguish between these types of particle movement we developed an appropriate classification method, and simulated three types of particle motion in a 2D plane using a Monte Carlo approach: (1) normal diffusion, using random direction and step-length, (2) subdiffusion, using confinements like a reflective boundary with defined radius or reflective objects in the closer vicinity, and (3) superdiffusion, using a directed flow added to the normal diffusion. To simulate subdiffusion we devised a new method based on tracks of different length combined with equally probable obstacle interaction. Next we estimated the fractal dimension, elongation and the ratio of long-time / short-time diffusion coefficients. These features were used to train a random forests classification algorithm. The accuracy for simulated trajectories with 180 steps was 97% (95%-CI: 0.9481-0.9884). The balanced accuracy was 94%, 99% and 98% for normal-, sub- and superdiffusion, respectively. Nanoparticle tracking analysis was used with 100 nm polystyrene particles to get trajectories for normal diffusion. As a next step we identified diffusion types of nanoparticles in vital cells and incubated V79 fibroblasts with 50 nm gold nanoparticles, which appeared as intensely bright objects due to their surface plasmon resonance. The movement of particles in both the extracellular and intracellular space was observed by dark field and confocal laser scanning microscopy. After reducing background noise from the video it became possible to identify individual particle spots by a maximum detection algorithm and trace them using the robust single-particle tracking algorithm proposed by Jaqaman, which is able to handle motion heterogeneity and particle disappearance. The particle trajectories inside cells indicated active transport (superdiffusion) as well as subdiffusion. Eventually, the random forest classification algorithm, after being trained by the above simulations, successfully classified the trajectories observed in live cells.

Matrix models for size-structured populations: unrealistic fast growth or simply diffusion?

PubMed

Picard, Nicolas; Liang, Jingjing

2014-01-01

Matrix population models are widely used to study population dynamics but have been criticized because their outputs are sensitive to the dimension of the matrix (or, equivalently, to the class width). This sensitivity is concerning for the population growth rate (λ) because this is an intrinsic characteristic of the population that should not depend on the model specification. It has been suggested that the sensitivity of λ to matrix dimension was linked to the existence of fast pathways (i.e. the fraction of individuals that systematically move up a class), whose proportion increases when class width increases. We showed that for matrix population models with growth transition only from class i to class i + 1, λ was independent of the class width when the mortality and the recruitment rates were constant, irrespective of the growth rate. We also showed that if there were indeed fast pathways, there were also in about the same proportion slow pathways (i.e. the fraction of individuals that systematically remained in the same class), and that they jointly act as a diffusion process (where diffusion here is the movement in size of an individual whose size increments are random according to a normal distribution with mean zero). For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic. Yet, the sensitivity of λ to matrix dimension for a class width in the range 1-10 cm was small, much smaller than the sampling uncertainty on the value of λ. Moreover, λ could either increase or decrease when class width increased depending on the species. Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of λ for tree species.

A study of sound absorption by street canyon boundaries and asphalt rubber concrete pavement

NASA Astrophysics Data System (ADS)

Drysdale, Graeme Robert

A sound field model, based on a classical diffusion equation, is extended to account for sound absorption in a diffusion parameter used to model sound energy in a narrow street canyon. The model accounts for a single sound absorption coefficient, separate accommodation coefficients and a combination of separate absorption and accommodation coefficients from parallel canyon walls. The new expressions are compared to the original formula through numerical simulations to reveal the effect of absorption on sound diffusion. The newly established analytical formulae demonstrate satisfactory agreement with their predecessor under perfect reflection. As well, the influence of the extended diffusion parameter on normalized sound pressure levels in a narrow street canyon is in agreement with experimental data. The diffusion parameters are used to model sound energy density in a street canyon as a function of the sound absorption coefficient of the street canyon walls. The acoustic and material properties of conventional and asphalt rubber concrete (ARC) pavement are also studied to assess how the crumb rubber content influences sound absorption in street canyons. The porosity and absolute permeability of compacted specimens of asphalt rubber concrete are measured and compared to their normal and random incidence sound absorption coefficients as a function of crumb rubber content in the modified binder. Nonlinear trends are found between the sound absorption coefficients, porosity and absolute permeability of the compacted specimens and the percentage of crumb rubber in the modified binders. The cross-sectional areas of the air voids on the surfaces of the compacted specimens are measured using digital image processing techniques and a linear relationship is obtained between the average void area and crumb rubber content. The measured material properties are used to construct an empirical formula relating the average porosity, normal incidence noise reduction coefficients and percentage of crumb rubber in the modified binder of the compacted specimens.

Spatially-Distributed Cost–Effectiveness Analysis Framework to Control Phosphorus from Agricultural Diffuse Pollution

PubMed Central

Geng, Runzhe; Wang, Xiaoyan; Sharpley, Andrew N.; Meng, Fande

2015-01-01

Best management practices (BMPs) for agricultural diffuse pollution control are implemented at the field or small-watershed scale. However, the benefits of BMP implementation on receiving water quality at multiple spatial is an ongoing challenge. In this paper, we introduce an integrated approach that combines risk assessment (i.e., Phosphorus (P) index), model simulation techniques (Hydrological Simulation Program–FORTRAN), and a BMP placement tool at various scales to identify the optimal location for implementing multiple BMPs and estimate BMP effectiveness after implementation. A statistically significant decrease in nutrient discharge from watersheds is proposed to evaluate the effectiveness of BMPs, strategically targeted within watersheds. Specifically, we estimate two types of cost-effectiveness curves (total pollution reduction and proportion of watersheds improved) for four allocation approaches. Selection of a ‘‘best approach” depends on the relative importance of the two types of effectiveness, which involves a value judgment based on the random/aggregated degree of BMP distribution among and within sub-watersheds. A statistical optimization framework is developed and evaluated in Chaohe River Watershed located in the northern mountain area of Beijing. Results show that BMP implementation significantly (p >0.001) decrease P loss from the watershed. Remedial strategies where BMPs were targeted to areas of high risk of P loss, deceased P loads compared with strategies where BMPs were randomly located across watersheds. Sensitivity analysis indicated that aggregated BMP placement in particular watershed is the most cost-effective scenario to decrease P loss. The optimization approach outlined in this paper is a spatially hierarchical method for targeting nonpoint source controls across a range of scales from field to farm, to watersheds, to regions. Further, model estimates showed targeting at multiple scales is necessary to optimize program efficiency. The integrated model approach described that selects and places BMPs at varying levels of implementation, provides a new theoretical basis and technical guidance for diffuse pollution management in agricultural watersheds. PMID:26313561

Spatially-Distributed Cost-Effectiveness Analysis Framework to Control Phosphorus from Agricultural Diffuse Pollution.

PubMed

Geng, Runzhe; Wang, Xiaoyan; Sharpley, Andrew N; Meng, Fande

2015-01-01

Best management practices (BMPs) for agricultural diffuse pollution control are implemented at the field or small-watershed scale. However, the benefits of BMP implementation on receiving water quality at multiple spatial is an ongoing challenge. In this paper, we introduce an integrated approach that combines risk assessment (i.e., Phosphorus (P) index), model simulation techniques (Hydrological Simulation Program-FORTRAN), and a BMP placement tool at various scales to identify the optimal location for implementing multiple BMPs and estimate BMP effectiveness after implementation. A statistically significant decrease in nutrient discharge from watersheds is proposed to evaluate the effectiveness of BMPs, strategically targeted within watersheds. Specifically, we estimate two types of cost-effectiveness curves (total pollution reduction and proportion of watersheds improved) for four allocation approaches. Selection of a ''best approach" depends on the relative importance of the two types of effectiveness, which involves a value judgment based on the random/aggregated degree of BMP distribution among and within sub-watersheds. A statistical optimization framework is developed and evaluated in Chaohe River Watershed located in the northern mountain area of Beijing. Results show that BMP implementation significantly (p >0.001) decrease P loss from the watershed. Remedial strategies where BMPs were targeted to areas of high risk of P loss, deceased P loads compared with strategies where BMPs were randomly located across watersheds. Sensitivity analysis indicated that aggregated BMP placement in particular watershed is the most cost-effective scenario to decrease P loss. The optimization approach outlined in this paper is a spatially hierarchical method for targeting nonpoint source controls across a range of scales from field to farm, to watersheds, to regions. Further, model estimates showed targeting at multiple scales is necessary to optimize program efficiency. The integrated model approach described that selects and places BMPs at varying levels of implementation, provides a new theoretical basis and technical guidance for diffuse pollution management in agricultural watersheds.

Modeling of synchronization behavior of bursting neurons at nonlinearly coupled dynamical networks.

PubMed

Çakir, Yüksel

2016-01-01

Synchronization behaviors of bursting neurons coupled through electrical and dynamic chemical synapses are investigated. The Izhikevich model is used with random and small world network of bursting neurons. Various currents which consist of diffusive electrical and time-delayed dynamic chemical synapses are used in the simulations to investigate the influences of synaptic currents and couplings on synchronization behavior of bursting neurons. The effects of parameters, such as time delay, inhibitory synaptic strengths, and decay time on synchronization behavior are investigated. It is observed that in random networks with no delay, bursting synchrony is established with the electrical synapse alone, single spiking synchrony is observed with hybrid coupling. In small world network with no delay, periodic bursting behavior with multiple spikes is observed when only chemical and only electrical synapse exist. Single-spike and multiple-spike bursting are established with hybrid couplings. A decrease in the synchronization measure is observed with zero time delay, as the decay time is increased in random network. For synaptic delays which are above active phase period, synchronization measure increases with an increase in synaptic strength and time delay in small world network. However, in random network, it increases with only an increase in synaptic strength.

Essential energy space random walk via energy space metadynamics method to accelerate molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Li, Hongzhi; Min, Donghong; Liu, Yusong; Yang, Wei

2007-09-01

To overcome the possible pseudoergodicity problem, molecular dynamic simulation can be accelerated via the realization of an energy space random walk. To achieve this, a biased free energy function (BFEF) needs to be priori obtained. Although the quality of BFEF is essential for sampling efficiency, its generation is usually tedious and nontrivial. In this work, we present an energy space metadynamics algorithm to efficiently and robustly obtain BFEFs. Moreover, in order to deal with the associated diffusion sampling problem caused by the random walk in the total energy space, the idea in the original umbrella sampling method is generalized to be the random walk in the essential energy space, which only includes the energy terms determining the conformation of a region of interest. This essential energy space generalization allows the realization of efficient localized enhanced sampling and also offers the possibility of further sampling efficiency improvement when high frequency energy terms irrelevant to the target events are free of activation. The energy space metadynamics method and its generalization in the essential energy space for the molecular dynamics acceleration are demonstrated in the simulation of a pentanelike system, the blocked alanine dipeptide model, and the leucine model.

Factors influencing pharmacists’ adoption of prescribing: qualitative application of the diffusion of innovations theory

PubMed Central

2013-01-01

Background In 2007, Alberta became the first Canadian jurisdiction to grant pharmacists a wide range of prescribing privileges. Our objective was to understand what factors influence pharmacists’ adoption of prescribing using a model for the Diffusion of Innovations in healthcare services. Methods Pharmacists participated in semi-structured telephone interviews to discuss their prescribing practices and explore the facilitators and barriers to implementation. Pharmacists working in community, hospital, PCN, or other settings were selected using a mix of random and purposive sampling. Two investigators independently analyzed each transcript using an Interpretive Description approach to identify themes. Analyses were informed by a model explaining the Diffusion of Innovations in health service organizations. Results Thirty-eight participants were interviewed. Prescribing behaviours varied from non-adoption through to product, disease, and patient focused use of prescribing. Pharmacists’ adoption of prescribing was dependent on the innovation itself, adopter, system readiness, and communication and influence. Adopting pharmacists viewed prescribing as a legitimization of previous practice and advantageous to instrumental daily tasks. The complexity of knowledge required for prescribing increased respectively in product, disease and patient focused prescribing scenarios. Individual adopters had higher levels of self-efficacy toward prescribing skills. At a system level, pharmacists who were in practice settings that were patient focused were more likely to adopt advanced prescribing practices, over those in product-focused settings. All pharmacists stated that physician relationships impacted their prescribing behaviours and individual pharmacists’ decisions to apply for independent prescribing privileges. Conclusions Diffusion of Innovations theory was helpful in understanding the multifaceted nature of pharmacists’ adoption of prescribing. The characteristics of the prescribing model itself which legitimized prior practices, the model of practice in a pharmacy setting, and relationships with physicians were prominent influences on pharmacists’ prescribing behaviours. PMID:24034176

Factors influencing pharmacists' adoption of prescribing: qualitative application of the diffusion of innovations theory.

PubMed

Makowsky, Mark J; Guirguis, Lisa M; Hughes, Christine A; Sadowski, Cheryl A; Yuksel, Nese

2013-09-14

In 2007, Alberta became the first Canadian jurisdiction to grant pharmacists a wide range of prescribing privileges. Our objective was to understand what factors influence pharmacists' adoption of prescribing using a model for the Diffusion of Innovations in healthcare services. Pharmacists participated in semi-structured telephone interviews to discuss their prescribing practices and explore the facilitators and barriers to implementation. Pharmacists working in community, hospital, PCN, or other settings were selected using a mix of random and purposive sampling. Two investigators independently analyzed each transcript using an Interpretive Description approach to identify themes. Analyses were informed by a model explaining the Diffusion of Innovations in health service organizations. Thirty-eight participants were interviewed. Prescribing behaviours varied from non-adoption through to product, disease, and patient focused use of prescribing. Pharmacists' adoption of prescribing was dependent on the innovation itself, adopter, system readiness, and communication and influence. Adopting pharmacists viewed prescribing as a legitimization of previous practice and advantageous to instrumental daily tasks. The complexity of knowledge required for prescribing increased respectively in product, disease and patient focused prescribing scenarios. Individual adopters had higher levels of self-efficacy toward prescribing skills. At a system level, pharmacists who were in practice settings that were patient focused were more likely to adopt advanced prescribing practices, over those in product-focused settings. All pharmacists stated that physician relationships impacted their prescribing behaviours and individual pharmacists' decisions to apply for independent prescribing privileges. Diffusion of Innovations theory was helpful in understanding the multifaceted nature of pharmacists' adoption of prescribing. The characteristics of the prescribing model itself which legitimized prior practices, the model of practice in a pharmacy setting, and relationships with physicians were prominent influences on pharmacists' prescribing behaviours.

Joint min-max distribution and Edwards-Anderson's order parameter of the circular 1/f-noise model

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Le Doussal, Pierre

2016-05-01

We calculate the joint min-max distribution and the Edwards-Anderson's order parameter for the circular model of 1/f-noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial techniques. Numerical checks come with significantly improved control of finite-size effects in the glassy phase, and the results convincingly validate the freezing-duality conjecture. Application to diffusive dynamics is discussed. We also provide a formula for the pre-factor ratio of the joint/marginal Carpentier-Le Doussal tail for minimum/maximum which applies to any logarithmic random energy model.

Diffusion pseudotime robustly reconstructs lineage branching.

PubMed

Haghverdi, Laleh; Büttner, Maren; Wolf, F Alexander; Buettner, Florian; Theis, Fabian J

2016-10-01

The temporal order of differentiating cells is intrinsically encoded in their single-cell expression profiles. We describe an efficient way to robustly estimate this order according to diffusion pseudotime (DPT), which measures transitions between cells using diffusion-like random walks. Our DPT software implementations make it possible to reconstruct the developmental progression of cells and identify transient or metastable states, branching decisions and differentiation endpoints.

Scaling laws of passive-scalar diffusion in the interstellar medium

NASA Astrophysics Data System (ADS)

Colbrook, Matthew J.; Ma, Xiangcheng; Hopkins, Philip F.; Squire, Jonathan

2017-05-01

Passive-scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the fundamental scaling laws remain poorly understood in the highly supersonic, magnetized, shearing regime relevant for the ISM. We therefore study the full scaling laws governing passive-scalar transport in idealized simulations of supersonic turbulence. Using simple phenomenological arguments for the variation of diffusivity with scale based on Richardson diffusion, we propose a simple fractional diffusion equation to describe the turbulent advection of an initial passive scalar distribution. These predictions agree well with the measurements from simulations, and vary with turbulent Mach number in the expected manner, remaining valid even in the presence of a large-scale shear flow (e.g. rotation in a galactic disc). The evolution of the scalar distribution is not the same as obtained using simple, constant 'effective diffusivity' as in Smagorinsky models, because the scale dependence of turbulent transport means an initially Gaussian distribution quickly develops highly non-Gaussian tails. We also emphasize that these are mean scalings that apply only to ensemble behaviours (assuming many different, random scalar injection sites): individual Lagrangian 'patches' remain coherent (poorly mixed) and simply advect for a large number of turbulent flow-crossing times.

Investigation of LRS dependence on the retention of HRS in CBRAM

NASA Astrophysics Data System (ADS)

Xu, Xiaoxin; Lv, Hangbing; Liu, Hongtao; Luo, Qing; Gong, Tiancheng; Wang, Ming; Wang, Guoming; Zhang, Meiyun; Li, Yang; Liu, Qi; Long, Shibing; Liu, Ming

2015-02-01

The insufficient retention prevents the resistive random access memory from intended application, such as code storage, FPGA, encryption, and others. The retention characteristics of high resistance state (HRS) switching from different low resistance state (LRS) were investigated in a 1-kb array with one transistor and one resistor configuration. The HRS degradation was found strongly dependent on the LRS: the lower the resistance of the LRS ( R LRS) is, the worse HRS retention will be. According to the quantum point contact model, the HRS corresponds to a tiny tunnel gap or neck bridge with atomic size in the filament. The degradation of HRS is due to the filling or widening of the neck point by the diffusion of copper species from the residual filament. As the residual filament is stronger in case of the lower R LRS, the active area around the neck point for copper species diffusion is larger, resulting in higher diffusion probability and faster degradation of HRS during the temperature-accelerated retention measurement.

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.

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.

Single-Nanoparticle Photoelectrochemistry at a Nanoparticulate TiO2 -Filmed Ultramicroelectrode.

PubMed

Peng, Yue-Yi; Ma, Hui; Ma, Wei; Long, Yi-Tao; Tian, He

2018-03-26

An ultrasensitive photoelectrochemical method for achieving real-time detection of single nanoparticle collision events is presented. Using a micrometer-thick nanoparticulate TiO 2 -filmed Au ultra-microelectrode (TiO 2 @Au UME), a sub-millisecond photocurrent transient was observed for an individual N719-tagged TiO 2 (N719@TiO 2 ) nanoparticle and is due to the instantaneous collision process. Owing to a trap-limited electron diffusion process as the rate-limiting step, a random three-dimensional diffusion model was developed to simulate electron transport dynamics in TiO 2 film. The combination of theoretical simulation and high-resolution photocurrent measurement allow electron-transfer information of a single N719@TiO 2 nanoparticle to be quantified at single-molecule accuracy and the electron diffusivity and the electron-collection efficiency of TiO 2 @Au UME to be estimated. This method provides a test for studies of photoinduced electron transfer at the single-nanoparticle level. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

Acid diffusion, standing waves, and information theory: a molecular-scale model of chemically amplified resist

NASA Astrophysics Data System (ADS)

Trefonas, Peter, III; Allen, Mary T.

1992-06-01

Shannon's information theory is adapted to analyze the photolithographic process, defining the mask pattern as the prior state. Definitions and constraints to the general theory are developed so that the information content at various stages of the lithographic process can be described. Its application is illustrated by exploring the information content within projected aerial images and resultant latent images. Next, a 3-dimensional molecular scale model of exposure, acid diffusion, and catalytic crosslinking in acid-hardened resists (AHR) is presented. In this model, initial positions of photogenerated acids are determined by probability functions generated from the aerial images and the local light intensity in the film. In order to simulate post-exposure baking processes, acids are diffused in a random walk manner, for which the catalytic chain length and the average distance between crosslinks can be set. Crosslink locations are defined in terms of the topologically minimized number required to link different chains. The size and location of polymer chains involved in a larger scale crosslinked network is established and related to polymer solubility. In this manner, the nature of the crosslinked latent image can be established. Good correlation with experimental data is found for the calculated percent insolubilization as a function of dose when the rms acid diffusion length is about 500 angstroms. Information analysis is applied in detail to the specific example of AHR chemistry. The information contained within the 3-D crosslinked latent image is explored as a function of exposure dose, catalytic chain length, average distance between crosslinks. Eopt (the exposure dose which optimizes the information contained within the latent image) was found to vary with catalytic chain length in a manner similar to that observed experimentally in a plot of E90 versus post-exposure bake time. Surprisingly, the information content of the crosslinked latent image remains high even when rms diffusion lengths are as long as 1500 angstroms. The information content of a standing wave is shown to decrease with increasing diffusion length, with essentially all standing wave information being lost at diffusion lengths greater than 450 angstroms. A unique mechanism for self-contrast enhancement and high resolution in AHR resist is proposed.

Optimizing the models for rapid determination of chlorogenic acid, scopoletin and rutin in plant samples by near-infrared diffuse reflectance spectroscopy

NASA Astrophysics Data System (ADS)

Mao, Zhiyi; Shan, Ruifeng; Wang, Jiajun; Cai, Wensheng; Shao, Xueguang

2014-07-01

Polyphenols in plant samples have been extensively studied because phenolic compounds are ubiquitous in plants and can be used as antioxidants in promoting human health. A method for rapid determination of three phenolic compounds (chlorogenic acid, scopoletin and rutin) in plant samples using near-infrared diffuse reflectance spectroscopy (NIRDRS) is studied in this work. Partial least squares (PLS) regression was used for building the calibration models, and the effects of spectral preprocessing and variable selection on the models are investigated for optimization of the models. The results show that individual spectral preprocessing and variable selection has no or slight influence on the models, but the combination of the techniques can significantly improve the models. The combination of continuous wavelet transform (CWT) for removing the variant background, multiplicative scatter correction (MSC) for correcting the scattering effect and randomization test (RT) for selecting the informative variables was found to be the best way for building the optimal models. For validation of the models, the polyphenol contents in an independent sample set were predicted. The correlation coefficients between the predicted values and the contents determined by high performance liquid chromatography (HPLC) analysis are as high as 0.964, 0.948 and 0.934 for chlorogenic acid, scopoletin and rutin, respectively.

Provider-related barriers to rapid HIV testing in U.S. urban non-profit community clinics, community-based organizations (CBOs) and hospitals.

PubMed

Bogart, Laura M; Howerton, Devery; Lange, James; Setodji, Claude Messan; Becker, Kirsten; Klein, David J; Asch, Steven M

2010-06-01

We examined provider-reported barriers to rapid HIV testing in U.S. urban non-profit community clinics, community-based organizations (CBOs), and hospitals. 12 primary metropolitan statistical areas (PMSAs; three per region) were sampled randomly, with sampling weights proportional to AIDS case reports. Across PMSAs, all 671 hospitals and a random sample of 738 clinics/CBOs were telephoned for a survey on rapid HIV test availability. Of the 671 hospitals, 172 hospitals were randomly selected for barriers questions, for which 158 laboratory and 136 department staff were eligible and interviewed in 2005. Of the 738 clinics/CBOs, 276 were randomly selected for barriers questions, 206 were reached, and 118 were eligible and interviewed in 2005-2006. In multivariate models, barriers regarding translation of administrative/quality assurance policies into practice were significantly associated with rapid HIV testing availability. For greater rapid testing diffusion, policies are needed to reduce administrative barriers and provide quality assurance training to non-laboratory staff.

Note: On the relation between Lifson-Jackson and Derrida formulas for effective diffusion coefficient

NASA Astrophysics Data System (ADS)

Kalnin, Juris R.; Berezhkovskii, Alexander M.

2013-11-01

The Lifson-Jackson formula provides the effective free diffusion coefficient for a particle diffusing in an arbitrary one-dimensional periodic potential. Its counterpart, when the underlying dynamics is described in terms of an unbiased nearest-neighbor Markovian random walk on a one-dimensional periodic lattice is given by the formula obtained by Derrida. It is shown that the latter formula can be considered as a discretized version of the Lifson-Jackson formula with correctly chosen position-dependent diffusion coefficient.

A theoretical model describing the one-dimensional growth of single crystals on free sustained substrates

NASA Astrophysics Data System (ADS)

Ye, Ziran; Wang, Ke; Lu, Chenxi; Jin, Ying; Sui, Chenghua; Yan, Bo; Gao, Fan; Cai, Pinggen; Lv, Bin; Li, Yun; Chen, Naibo; Sun, Guofang; Xu, Fengyun; Ye, Gaoxiang

2018-03-01

We develop a theoretical model that interprets the growth mechanism of zinc (Zn) crystal nanorods on a liquid substrate by thermal evaporation. During deposition, Zn atoms diffuse randomly on an isotropic and quasi-free sustained substrate, the nucleation of the atoms results in the primary nanorod (or seed crystal) growth. Subsequently, a characteristic one-dimensional atomic aggregation is proposed, which leads to the accelerating growth of the crystal nanorod along its preferential growth direction until the growth terminates. The theoretical results are in good agreement with the experimental findings.

The effects of intermittency on statistical characteristics of turbulence and scale similarity of breakdown coefficients

NASA Astrophysics Data System (ADS)

Novikov, E. A.

1990-05-01

The influence of intermittency on turbulent diffusion is expressed in terms of the statistics of the dissipation field. The high-order moments of relative diffusion are obtained by using the concept of scale similarity of the breakdown coefficients (bdc). The method of bdc is useful for obtaining new models and general results, which then can be expressed in terms of multifractals. In particular, the concavity and other properties of spectral codimension are proved. Special attention is paid to the logarithmically periodic modulations. The parametrization of small-scale intermittent turbulence, which can be used for large-eddy simulation, is presented. The effect of molecular viscosity is taken into account in the spirit of the renorm group, but without spectral series, ɛ expansion, and fictitious random forces.

Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

We present a cumulative density function (CDF) method for the probabilistic analysis of $d$-dimensional advection-dominated reactive transport in heterogeneous media. We employ a probabilistic approach in which epistemic uncertainty on the spatial heterogeneity of Darcy-scale transport coefficients is modeled in terms of random fields with given correlation structures. Our proposed CDF method employs a modified Large-Eddy-Diffusivity (LED) approach to close and localize the nonlocal equations governing the one-point PDF and CDF of the concentration field, resulting in a $(d + 1)$ dimensional PDE. Compared to the classsical LED localization, the proposed modified LED localization explicitly accounts for the mean-field advectivemore » dynamics over the phase space of the PDF and CDF. To illustrate the accuracy of the proposed closure, we apply our CDF method to one-dimensional single-species reactive transport with uncertain, heterogeneous advection velocities and reaction rates modeled as random fields.« less

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

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

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

Kinetic Models for Topological Nearest-Neighbor Interactions

NASA Astrophysics Data System (ADS)

Blanchet, Adrien; Degond, Pierre

2017-12-01

We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal and human behavior. Precisely, the system consists of a finite number of particles characterized by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of its closest neighbor, the leader. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit kinetic equation is a non-standard spatial diffusion equation for the particle distribution function. We also study the case wherein the particles interact with their K closest neighbors and show that the corresponding kinetic equation is the same. Finally, we prove that these models can be seen as a singular limit of the smooth rank-based model previously studied in Blanchet and Degond (J Stat Phys 163:41-60, 2016). The proofs are based on a combinatorial interpretation of the rank as well as some concentration of measure arguments.

Examination of various turbulence models for application in liquid rocket thrust chambers

NASA Technical Reports Server (NTRS)

Hung, R. J.

1991-01-01

There is a large variety of turbulence models available. These models include direct numerical simulation, large eddy simulation, Reynolds stress/flux model, zero equation model, one equation model, two equation k-epsilon model, multiple-scale model, etc. Each turbulence model contains different physical assumptions and requirements. The natures of turbulence are randomness, irregularity, diffusivity and dissipation. The capabilities of the turbulence models, including physical strength, weakness, limitations, as well as numerical and computational considerations, are reviewed. Recommendations are made for the potential application of a turbulence model in thrust chamber and performance prediction programs. The full Reynolds stress model is recommended. In a workshop, specifically called for the assessment of turbulence models for applications in liquid rocket thrust chambers, most of the experts present were also in favor of the recommendation of the Reynolds stress model.

Fluid Physics in a Fluctuating Acceleration Environment

NASA Technical Reports Server (NTRS)

Thomson, J. Ross; Drolet, Francois; Vinals, Jorge

1996-01-01

We summarize several aspects of an ongoing investigation of the effects that stochastic residual accelerations (g-jitter) onboard spacecraft can have on experiments conducted in a microgravity environment. The residual acceleration field is modeled as a narrow band noise, characterized by three independent parameters: intensity (g(exp 2)), dominant angular frequency Omega, and characteristic correlation time tau. Realistic values for these parameters are obtained from an analysis of acceleration data corresponding to the SL-J mission, as recorded by the SAMS instruments. We then use the model to address the random motion of a solid particle suspended in an incompressible fluid subjected to such random accelerations. As an extension, the effect of jitter on coarsening of a solid-liquid mixture is briefly discussed, and corrections to diffusion controlled coarsening evaluated. We conclude that jitter will not be significant in the experiment 'Coarsening of solid-liquid mixtures' to be conducted in microgravity. Finally, modifications to the location of onset of instability in systems driven by a random force are discussed by extending the standard reduction to the center manifold to the stochastic case. Results pertaining to time-modulated oscillatory convection are briefly discussed.

A Probabilistic Atlas of Diffuse WHO Grade II Glioma Locations in the Brain

PubMed Central

Baumann, Cédric; Zouaoui, Sonia; Yordanova, Yordanka; Blonski, Marie; Rigau, Valérie; Chemouny, Stéphane; Taillandier, Luc; Bauchet, Luc; Duffau, Hugues; Paragios, Nikos

2016-01-01

Diffuse WHO grade II gliomas are diffusively infiltrative brain tumors characterized by an unavoidable anaplastic transformation. Their management is strongly dependent on their location in the brain due to interactions with functional regions and potential differences in molecular biology. In this paper, we present the construction of a probabilistic atlas mapping the preferential locations of diffuse WHO grade II gliomas in the brain. This is carried out through a sparse graph whose nodes correspond to clusters of tumors clustered together based on their spatial proximity. The interest of such an atlas is illustrated via two applications. The first one correlates tumor location with the patient’s age via a statistical analysis, highlighting the interest of the atlas for studying the origins and behavior of the tumors. The second exploits the fact that the tumors have preferential locations for automatic segmentation. Through a coupled decomposed Markov Random Field model, the atlas guides the segmentation process, and characterizes which preferential location the tumor belongs to and consequently which behavior it could be associated to. Leave-one-out cross validation experiments on a large database highlight the robustness of the graph, and yield promising segmentation results. PMID:26751577

Diffusion MRI noise mapping using random matrix theory

PubMed Central

Veraart, Jelle; Fieremans, Els; Novikov, Dmitry S.

2016-01-01

Purpose To estimate the spatially varying noise map using a redundant magnitude MR series. Methods We exploit redundancy in non-Gaussian multi-directional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices. The bulk of PCA eigenvalues, arising due to noise, is described by the universal Marchenko-Pastur distribution, parameterized by the noise level. This allows us to estimate noise level in a local neighborhood based on the singular value decomposition of a matrix combining neighborhood voxels and diffusion directions. Results We present a model-independent local noise mapping method capable of estimating noise level down to about 1% error. In contrast to current state-of-the art techniques, the resultant noise maps do not show artifactual anatomical features that often reflect physiological noise, the presence of sharp edges, or a lack of adequate a priori knowledge of the expected form of MR signal. Conclusions Simulations and experiments show that typical diffusion MRI data exhibit sufficient redundancy that enables accurate, precise, and robust estimation of the local noise level by interpreting the PCA eigenspectrum in terms of the Marchenko-Pastur distribution. PMID:26599599

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Englander, Arnold C.

2014-01-01

Trajectory optimization methods using monotonic basin hopping (MBH) have become well developed during the past decade [1, 2, 3, 4, 5, 6]. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing random variable (RV)s from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by J. Englander [3, 6]) significantly improves monotonic basin hopping (MBH) performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness. Efficiency is finding better solutions in less time. Robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive random walks (RWs) originally developed in the field of statistical physics.

New insights in dehydration stress behavior of two maize hybrids using advanced distributed reactivity model (DRM). Responses to the impact of 24-epibrassinolide

PubMed Central

Janković, Bojan; Janković, Marija; Nikolić, Bogdan; Dimkić, Ivica; Lalević, Blažo; Raičević, Vera

2017-01-01

Proposed distributed reactivity model of dehydration for seedling parts of two various maize hybrids (ZP434, ZP704) was established. Dehydration stresses were induced thermally, which is also accompanied by response of hybrids to heat stress. It was found that an increased value of activation energy counterparts within radicle dehydration of ZP434, with a high concentration of 24-epibrassinolide (24-EBL) at elevated operating temperatures, probably causes activation of diffusion mechanisms in cutin network and may increases likelihood of formation of free volumes, large enough to accommodate diffusing molecule. Many small random effects were detected and can be correlated with micro-disturbing in a space filled with water caused by thermal gradients, increasing capillary phenomena, and which can induce thermo-capillary migration. The influence of seedling content of various sugars and minerals on dehydration was also examined. Estimated distributed reactivity models indicate a dependence of reactivity on structural arrangements, due to present interactions between water molecules and chemical species within the plant. PMID:28644899

New insights in dehydration stress behavior of two maize hybrids using advanced distributed reactivity model (DRM). Responses to the impact of 24-epibrassinolide.

PubMed

Waisi, Hadi; Janković, Bojan; Janković, Marija; Nikolić, Bogdan; Dimkić, Ivica; Lalević, Blažo; Raičević, Vera

2017-01-01

Proposed distributed reactivity model of dehydration for seedling parts of two various maize hybrids (ZP434, ZP704) was established. Dehydration stresses were induced thermally, which is also accompanied by response of hybrids to heat stress. It was found that an increased value of activation energy counterparts within radicle dehydration of ZP434, with a high concentration of 24-epibrassinolide (24-EBL) at elevated operating temperatures, probably causes activation of diffusion mechanisms in cutin network and may increases likelihood of formation of free volumes, large enough to accommodate diffusing molecule. Many small random effects were detected and can be correlated with micro-disturbing in a space filled with water caused by thermal gradients, increasing capillary phenomena, and which can induce thermo-capillary migration. The influence of seedling content of various sugars and minerals on dehydration was also examined. Estimated distributed reactivity models indicate a dependence of reactivity on structural arrangements, due to present interactions between water molecules and chemical species within the plant.

Conduction Channel Formation and Dissolution Due to Oxygen Thermophoresis/Diffusion in Hafnium Oxide Memristors

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

Kumar, Suhas; Wang, Ziwen; Huang, Xiaopeng

Due to the favorable operating power, endurance, speed, and density., transition-metal-oxide memristors, or resistive random-access memory (RRAM) switches, are under intense development for storage-class memory. Their commercial deployment critically depends on predictive compact models based on understanding nanoscale physiocochemical forces, which remains elusive and controversial owing to the difficulties in directly observing atomic motions during resistive switching, Here, using scanning transmission synchrotron X-ray spectromicroscopy to study in situ switching of hafnium oxide memristors, we directly observed the formation of a localized oxygen-deficiency-derived conductive channel surrounded by a low-conductivity ring of excess oxygen. Subsequent thermal annealing homogenized the segregated oxygen, resettingmore » the cells toward their as-grown resistance state. We show that the formation and dissolution of the conduction channel are successfully modeled by radial thermophoresis and Fick diffusion of oxygen atoms driven by Joule heating. This confirmation and quantification of two opposing nanoscale radial forces that affect bipolar memristor switching are important components for any future physics-based compact model for the electronic switching of these devices.« less

Multispecies diffusion models: A study of uranyl species diffusion

NASA Astrophysics Data System (ADS)

Liu, Chongxuan; Shang, Jianying; Zachara, John M.

2011-12-01

Rigorous numerical description of multispecies diffusion requires coupling of species, charge, and aqueous and surface complexation reactions that collectively affect diffusive fluxes. The applicability of a fully coupled diffusion model is, however, often constrained by the availability of species self-diffusion coefficients, as well as by computational complication in imposing charge conservation. In this study, several diffusion models with variable complexity in charge and species coupling were formulated and compared to describe reactive multispecies diffusion in groundwater. Diffusion of uranyl [U(VI)] species was used as an example in demonstrating the effectiveness of the models in describing multispecies diffusion. Numerical simulations found that a diffusion model with a single, common diffusion coefficient for all species was sufficient to describe multispecies U(VI) diffusion under a steady state condition of major chemical composition, but not under transient chemical conditions. Simulations revealed that for multispecies U(VI) diffusion under transient chemical conditions, a fully coupled diffusion model could be well approximated by a component-based diffusion model when the diffusion coefficient for each chemical component was properly selected. The component-based diffusion model considers the difference in diffusion coefficients between chemical components, but not between the species within each chemical component. This treatment significantly enhanced computational efficiency at the expense of minor charge conservation. The charge balance in the component-based diffusion model can be enforced, if necessary, by adding a secondary migration term resulting from model simplification. The effect of ion activity coefficient gradients on multispecies diffusion is also discussed. The diffusion models were applied to describe U(VI) diffusive mass transfer in intragranular domains in two sediments collected from U.S. Department of Energy's Hanford 300A, where intragranular diffusion is a rate-limiting process controlling U(VI) adsorption and desorption. The grain-scale reactive diffusion model was able to describe U(VI) adsorption/desorption kinetics that had been previously described using a semiempirical, multirate model. Compared with the multirate model, the diffusion models have the advantage to provide spatiotemporal speciation evolution within the diffusion domains.

18,000 displacement vectors and 44 positions surveys of RFID tracers show a normal diffusion of the bedload in a proglacial stream (Bossons glacier, France)

NASA Astrophysics Data System (ADS)

Guillon, Hervé; Mugnier, Jean-Louis; Buoncristiani, Jean-François

2016-04-01

Bedload transport is a stochastic process during which each particle hops for a random length then rests for a random duration. In recent years, this probabilistic approach was investigated by theoretical models, numerical simulations and laboratory experiments. These experiments are generally carried out on short time scales with sand, but underline the diffusive behaviour of the bedload. Conversely, marked pebbles in natural streams have mainly be used to infer about transport processes and transport time of the bedload. In this study, the stochastic characteristics of bedload transport are inferred from the radio-frequency identification (RFID) of pebbles. In particular, we provide insights for answering the following question : is the bedload transport sub-diffusive, normally diffusive or super-diffusive at the long time scale (i.e. global range)? Experiments designed to investigate the phenomenology of bedload transport have been carried out in the proglacial area of Bossons glacier. This 350 m long alluvial plain exhibits daily flood from the glacial system and is still redistributing material from catastrophic events pre-dating our investigations. From 2011 to 2014, the position of the ˜ 1000 RFID tracers have been measured by a mobile antenna and a differential GPS during 44 surveys providing ˜ 2500 tracer positions. Additionnaly, in 2014, 650 new tracers were seeded upstream from a static RFID antenna located at the outlet of the study area. For the 1 to 32 cm fraction surveyed, both mobile and static antenna results show no evidence for a significant export outside of the surveyed zone. Initial data have been maximized by using each possible campaign pairs leading to ˜700 campaign pairs and more than 18,000 displacement vectors. To our knowledge, this is one of the most extensive dataset of tracers positions measured in a natural stream using the RFID methodology. Using 152 campaigns pairs with at least 20 retrieved tracers,r standard probability distributions were tested against the observed travel distances. Regardless of the time scale, heavy- and light-tailed distributions provide a convincing statistical description of measured data. No single distribution is significantly better than the others. Conversely, the distribution of tracers positions in the system and its time evolution is best described by the normal distribution. Its standard deviation scales with time as σ ∝ t0.45±0.12 which suggests a nearly normal diffusive behaviour. The measured virtual velocities and a simple probabilistic model using the time evolution of the mean (i.e. drift) and standard deviation (i.e diffusion) show that the mean bedload transfer time is greater than 5 years. RFID tracers appear as a promising tool to investigate stochastic characteristics of bedload transport.

Similarities between principal components of protein dynamics and random diffusion

NASA Astrophysics Data System (ADS)

Hess, Berk

2000-12-01

Principal component analysis, also called essential dynamics, is a powerful tool for finding global, correlated motions in atomic simulations of macromolecules. It has become an established technique for analyzing molecular dynamics simulations of proteins. The first few principal components of simulations of large proteins often resemble cosines. We derive the principal components for high-dimensional random diffusion, which are almost perfect cosines. This resemblance between protein simulations and noise implies that for many proteins the time scales of current simulations are too short to obtain convergence of collective motions.

Radon detection in conical diffusion chambers: Monte Carlo calculations and experiment

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

Rickards, J.; Golzarri, J. I.; Espinosa, G., E-mail: espinosa@fisica.unam.mx

2015-07-23

The operation of radon detection diffusion chambers of truncated conical shape was studied using Monte Carlo calculations. The efficiency was studied for alpha particles generated randomly in the volume of the chamber, and progeny generated randomly on the interior surface, which reach track detectors placed in different positions within the chamber. Incidence angular distributions, incidence energy spectra and path length distributions are calculated. Cases studied include different positions of the detector within the chamber, varying atmospheric pressure, and introducing a cutoff incidence angle and energy.

Validation of optical codes based on 3D nanostructures

NASA Astrophysics Data System (ADS)

Carnicer, Artur; Javidi, Bahram

2017-05-01

Image information encoding using random phase masks produce speckle-like noise distributions when the sample is propagated in the Fresnel domain. As a result, information cannot be accessed by simple visual inspection. Phase masks can be easily implemented in practice by attaching cello-tape to the plain-text message. Conventional 2D-phase masks can be generalized to 3D by combining glass and diffusers resulting in a more complex, physical unclonable function. In this communication, we model the behavior of a 3D phase mask using a simple approach: light is propagated trough glass using the angular spectrum of plane waves whereas the diffusor is described as a random phase mask and a blurring effect on the amplitude of the propagated wave. Using different designs for the 3D phase mask and multiple samples, we demonstrate that classification is possible using the k-nearest neighbors and random forests machine learning algorithms.

From Random Walks to Brownian Motion, from Diffusion to Entropy: Statistical Principles in Introductory Physics

NASA Astrophysics Data System (ADS)

Reeves, Mark

2014-03-01

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk will present a number of these exercises, with particular focus on the hands-on experiments done by the students, and will give examples of the tangible material that our students work with throughout the two-semester sequence of their course on introductory physics with a bio focus. Supported by NSF DUE.

Observations of O VI Emission from the Diffuse Interstellar Medium

NASA Technical Reports Server (NTRS)

Shelton, R. L.; Kruk, J. W.; Murphy, E. M.; Andersson, B. G.; Blair, W. P.; Dixon, W. V.; Edelstein, J.; Fullerton, A. W.; Gry, C.; Howk, J. C.;

Master stability functions reveal diffusion-driven pattern formation in networks

NASA Astrophysics Data System (ADS)

Brechtel, Andreas; Gramlich, Philipp; Ritterskamp, Daniel; Drossel, Barbara; Gross, Thilo

2018-03-01

We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

Development of self-healing polymers via amine-epoxy chemistry: I. Properties of healing agent carriers and the modelling of a two-part self-healing system

NASA Astrophysics Data System (ADS)

Zhang, He; Yang, Jinglei

2014-06-01

Two types of healing agent carriers (microcapsules containing epoxy solution, referred to as EP-capsules, and etched hollow glass bubbles (HGBs) loaded with amine solution, referred to as AM-HGBs) used in self-healing epoxy systems were prepared and characterized in this study. The core percentages were measured at about 80 wt% and 33 wt% for EP-capsules and AM-HGBs, respectively. The loaded amine in AM-HGB, after incorporation into the epoxy matrix, showed high stability at ambient temperature, but diffused out gradually during heat treatment at 80 °C. The amount and the mass ratio of the two released healants at the crack plane were correlated with the size, concentration, and core percentage of the healing agent carriers. A simplified cubic array model for randomly distributed healing agent carriers was adopted to depict the longest diffusion distance of the released healants, which is inversely proportional to the cubic root of the carrier concentration.

The Limitation of Species Range: A Consequence of Searching Along Resource Gradients

PubMed Central

Rowell, Jonathan T.

2009-01-01

Ecological modelers have long puzzled over the spatial distribution of species. The random walk or diffusive approach to dispersal has yielded important results for biology and mathematics, yet it has been inadequate in explaining all phenomenological features. Ranges can terminate non-smoothly absent a complementary shift in the characteristics of the environment. Also unexplained is the absence of a species from nearby areas of adequate, or even abundant, resources. In this paper, I show how local searching behavior - keyed to a density-dependent fitness - can limit the speed and extent of a species’ spread. In contrast to standard diffusive processes, pseudo-rational movement facilitates the clustering of populations. It also can be used to estimate the speed of an expanding population range, explain expansion stall, and provides a mechanism by which a population can colonize seemingly removed regions - biogeographic islands in a continental framework. Finally, I discuss the effect of resource degradation and different resource impact/utilization curves on the model. PMID:19303032

Dynamic properties of molecular motors in burnt-bridge models

NASA Astrophysics Data System (ADS)

Artyomov, Maxim N.; Morozov, Alexander Yu; Pronina, Ekaterina; Kolomeisky, Anatoly B.

2007-08-01

Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic 'burnt-bridge' models. The transport of the particles is viewed as an effective diffusion along one-dimensional lattices with periodically distributed weak links. When an unbiased random walker passes the weak link it can be destroyed ('burned') with probability p, providing a bias in the motion of the molecular motor. We present a theoretical approach that allows one to calculate exactly all dynamic properties of motor proteins, such as velocity and dispersion, under general conditions. It is found that dispersion is a decreasing function of the concentration of bridges, while the dependence of dispersion on the burning probability is more complex. Our calculations also show a gap in dispersion for very low concentrations of weak links or for very low burning probabilities which indicates a dynamic phase transition between unbiased and biased diffusion regimes. Theoretical findings are supported by Monte Carlo computer simulations.

Tortuosity Computations of Porous Materials using the Direct Simulation Monte Carlo

NASA Technical Reports Server (NTRS)

Borner, A.; Ferguson, C.; Panerai, F.; Mansour, Nagi N.

2017-01-01

Low-density carbon fiber preforms, used as thermal protection systems (TPS) materials for planetary entry systems, have permeable, highly porous microstructures consisting of interlaced fibers. Internal gas transport in TPS is important in modeling the penetration of hot boundary-layer gases and the in-depth transport of pyrolysis and ablation products. The gas effective diffusion coefficient of a porous material must be known before the gas transport can be modeled in material response solvers; however, there are very little available data for rigid fibrous insulators used in heritage TPS.The tortuosity factor, which reflects the efficiency of the percolation paths, can be computed from the effective diffusion coefficient of a gas inside a porous material and is based on the micro-structure of the material. It is well known, that the tortuosity factor is a strong function of the Knudsen number. Due to the small characteristic scales of porous media used in TPS applications (typical pore size of the order of 50 micron), the transport of gases can occur in the rarefied and transitional regimes, at Knudsen numbers above 1. A proper way to model the gas dynamics at these conditions consists in solving the Boltzmann equation using particle-based methods that account for movement and collisions of atoms and molecules.In this work we adopt, for the first time, the Direct Simulation Monte Carlo (DSMC) method to compute the tortuosity factor of fibrous media in the rarefied regime. To enable realistic simulations of the actual transport of gases in the porous medium, digitized computational grids are obtained from X-ray micro-tomography imaging of real TPS materials. The SPARTA DSMC solver is used for simulations. Effective diffusion coefficients and tortuosity factors are obtained by computing the mean-square displacement of diffusing particles.We first apply the method to compute the tortuosity factors as a function of the Knudsen number for computationally designed materials such as random cylindrical fibers and packed bed of spheres with prescribed porosity. Results are compared to literature values obtained using random walk methods in the rarefied and transitional regime and a finite-volume method for the continuum regime. We then compute tortuosity factors for a real carbon fiber material with a transverse isotropic structure (FiberForm), quantifying differences between through-thickness and in-plain tortuosities at various Knudsen regimes.

Simulating intrafraction prostate motion with a random walk model.

PubMed

Pommer, Tobias; Oh, Jung Hun; Munck Af Rosenschöld, Per; Deasy, Joseph O

2017-01-01

Prostate motion during radiation therapy (ie, intrafraction motion) can cause unwanted loss of radiation dose to the prostate and increased dose to the surrounding organs at risk. A compact but general statistical description of this motion could be useful for simulation of radiation therapy delivery or margin calculations. We investigated whether prostate motion could be modeled with a random walk model. Prostate motion recorded during 548 radiation therapy fractions in 17 patients was analyzed and used for input in a random walk prostate motion model. The recorded motion was categorized on the basis of whether any transient excursions (ie, rapid prostate motion in the anterior and superior direction followed by a return) occurred in the trace and transient motion. This was separately modeled as a large step in the anterior/superior direction followed by a returning large step. Random walk simulations were conducted with and without added artificial transient motion using either motion data from all observed traces or only traces without transient excursions as model input, respectively. A general estimate of motion was derived with reasonable agreement between simulated and observed traces, especially during the first 5 minutes of the excursion-free simulations. Simulated and observed diffusion coefficients agreed within 0.03, 0.2 and 0.3 mm 2 /min in the left/right, superior/inferior, and anterior/posterior directions, respectively. A rapid increase in variance at the start of observed traces was difficult to reproduce and seemed to represent the patient's need to adjust before treatment. This could be estimated somewhat using artificial transient motion. Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during delivery of radiation therapy.

Monthly plasmapheresis for systemic lupus erythematosus with diffuse proliferative glomerulonephritis: a pilot study

PubMed Central

Clark, William F.; Lindsay, Robert M.; Cattran, Daniel C.; Chodirker, William B.; Barnes, Colin C.; Linton, Adam L.

1981-01-01

Twelve patients with systemic lupus erythematosus and biopsy-proved diffuse proliferative glomerulonephritis were randomly allocated to a control group (to continue receiving conventional therapy only) or to a plasmapheresis group (to receive conventional therapy along with one 4-I plasma exchange a month). The six patients treated with plasmapheresis had better preservation of renal function, reduced disease activity, fewer admissions to hospital and less need for steroid and immunosuppressive therapy than the six control patients. The patients treated with plasmapheresis also showed evidence of reduced immunologic activity and had no side effects attributable to the plasma exchange. These results suggest that monthly plasma exchange should be assessed in a controlled randomized trial as a possible therapeutic adjunct in patients with systemic lupus erythematosus and diffuse proliferative glomerulonephritis. PMID:7272867

Geometrical effects on the electron residence time in semiconductor nano-particles

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

Koochi, Hakimeh; Ebrahimi, Fatemeh, E-mail: f-ebrahimi@birjand.ac.ir; Solar Energy Research Group, University of Birjand, Birjand

2014-09-07

We have used random walk (RW) numerical simulations to investigate the influence of the geometry on the statistics of the electron residence time τ{sub r} in a trap-limited diffusion process through semiconductor nano-particles. This is an important parameter in coarse-grained modeling of charge carrier transport in nano-structured semiconductor films. The traps have been distributed randomly on the surface (r{sup 2} model) or through the whole particle (r{sup 3} model) with a specified density. The trap energies have been taken from an exponential distribution and the traps release time is assumed to be a stochastic variable. We have carried out (RW)more » simulations to study the effect of coordination number, the spatial arrangement of the neighbors and the size of nano-particles on the statistics of τ{sub r}. It has been observed that by increasing the coordination number n, the average value of electron residence time, τ{sup ¯}{sub r} rapidly decreases to an asymptotic value. For a fixed coordination number n, the electron's mean residence time does not depend on the neighbors' spatial arrangement. In other words, τ{sup ¯}{sub r} is a porosity-dependence, local parameter which generally varies remarkably from site to site, unless we are dealing with highly ordered structures. We have also examined the effect of nano-particle size d on the statistical behavior of τ{sup ¯}{sub r}. Our simulations indicate that for volume distribution of traps, τ{sup ¯}{sub r} scales as d{sup 2}. For a surface distribution of traps τ{sup ¯}{sub r} increases almost linearly with d. This leads to the prediction of a linear dependence of the diffusion coefficient D on the particle size d in ordered structures or random structures above the critical concentration which is in accordance with experimental observations.« less

Noise reduction of a composite cylinder subjected to random acoustic excitation

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Beyer, T.

1989-01-01

Interior and exterior noise measurements were conducted on a stiffened composite floor-equipped cylinder, with and without an interior trim installed. Noise reduction was obtained for the case of random acoustic excitation in a diffuse field; the frequency range of interest was 100-800-Hz one-third octave bands. The measured data were compared with noise reduction predictions from the Propeller Aircraft Interior Noise (PAIN) program and from a statistical energy analysis. Structural model parameters were not predicted well by the PAIN program for the given input parameters; this resulted in incorrect noise reduction predictions for the lower one-third octave bands where the power flow into the interior of the cylinder was predicted on a mode-per-mode basis.

Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution

PubMed Central

Zhang, Yin; Liang, Lanju; Yang, Jing; Feng, Yijun; Zhu, Bo; Zhao, Junming; Jiang, Tian; Jin, Biaobing; Liu, Weiwei

2016-01-01

Suppressing specular electromagnetic wave reflection or backward radar cross section is important and of broad interests in practical electromagnetic engineering. Here, we present a scheme to achieve broadband backward scattering reduction through diffuse terahertz wave reflection by a flexible metasurface. The diffuse scattering of terahertz wave is caused by the randomized reflection phase distribution on the metasurface, which consists of meta-particles of differently sized metallic patches arranged on top of a grounded polyimide substrate simply through a certain computer generated pseudorandom sequence. Both numerical simulations and experimental results demonstrate the ultralow specular reflection over a broad frequency band and wide angle of incidence due to the re-distribution of the incident energy into various directions. The diffuse scattering property is also polarization insensitive and can be well preserved when the flexible metasurface is conformably wrapped on a curved reflective object. The proposed design opens up a new route for specular reflection suppression, and may be applicable in stealth and other technology in the terahertz spectrum. PMID:27225031

Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution.

PubMed

Zhang, Yin; Liang, Lanju; Yang, Jing; Feng, Yijun; Zhu, Bo; Zhao, Junming; Jiang, Tian; Jin, Biaobing; Liu, Weiwei

2016-05-26

Suppressing specular electromagnetic wave reflection or backward radar cross section is important and of broad interests in practical electromagnetic engineering. Here, we present a scheme to achieve broadband backward scattering reduction through diffuse terahertz wave reflection by a flexible metasurface. The diffuse scattering of terahertz wave is caused by the randomized reflection phase distribution on the metasurface, which consists of meta-particles of differently sized metallic patches arranged on top of a grounded polyimide substrate simply through a certain computer generated pseudorandom sequence. Both numerical simulations and experimental results demonstrate the ultralow specular reflection over a broad frequency band and wide angle of incidence due to the re-distribution of the incident energy into various directions. The diffuse scattering property is also polarization insensitive and can be well preserved when the flexible metasurface is conformably wrapped on a curved reflective object. The proposed design opens up a new route for specular reflection suppression, and may be applicable in stealth and other technology in the terahertz spectrum.

Electronic shot noise in fractal conductors.

PubMed

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

2008-05-02

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

Probabilistic migration modelling focused on functional barrier efficiency and low migration concepts in support of risk assessment.

PubMed

Brandsch, Rainer

2017-10-01

Migration modelling provides reliable migration estimates from food-contact materials (FCM) to food or food simulants based on mass-transfer parameters like diffusion and partition coefficients related to individual materials. In most cases, mass-transfer parameters are not readily available from the literature and for this reason are estimated with a given uncertainty. Historically, uncertainty was accounted for by introducing upper limit concepts first, turning out to be of limited applicability due to highly overestimated migration results. Probabilistic migration modelling gives the possibility to consider uncertainty of the mass-transfer parameters as well as other model inputs. With respect to a functional barrier, the most important parameters among others are the diffusion properties of the functional barrier and its thickness. A software tool that accepts distribution as inputs and is capable of applying Monte Carlo methods, i.e., random sampling from the input distributions of the relevant parameters (i.e., diffusion coefficient and layer thickness), predicts migration results with related uncertainty and confidence intervals. The capabilities of probabilistic migration modelling are presented in the view of three case studies (1) sensitivity analysis, (2) functional barrier efficiency and (3) validation by experimental testing. Based on the predicted migration by probabilistic migration modelling and related exposure estimates, safety evaluation of new materials in the context of existing or new packaging concepts is possible. Identifying associated migration risk and potential safety concerns in the early stage of packaging development is possible. Furthermore, dedicated material selection exhibiting required functional barrier efficiency under application conditions becomes feasible. Validation of the migration risk assessment by probabilistic migration modelling through a minimum of dedicated experimental testing is strongly recommended.