Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Abuasad, Salah; Hashim, Ishak

2018-04-01

In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

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

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

PubMed

Stamova, Ivanka; Stamov, Gani

2017-12-01

In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

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.

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

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

Extremely low order time-fractional differential equation and application in combustion process

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Xu, Yufeng

2018-11-01

Fractional blow-up model, especially which is of very low order of fractional derivative, plays a significant role in combustion process. The order of time-fractional derivative in diffusion model essentially distinguishes the super-diffusion and sub-diffusion processes when it is relatively high or low accordingly. In this paper, the blow-up phenomenon and condition of its appearance are theoretically proved. The blow-up moment is estimated by using differential inequalities. To numerically study the behavior around blow-up point, a mixed numerical method based on adaptive finite difference on temporal direction and highly effective discontinuous Galerkin method on spatial direction is proposed. The time of blow-up is calculated accurately. In simulation, we analyze the dynamics of fractional blow-up model under different orders of fractional derivative. It is found that the lower the order, the earlier the blow-up comes, by fixing the other parameters in the model. Our results confirm the physical truth that a combustor for explosion cannot be too small.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

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

A time fractional convection-diffusion equation to model gas transport through heterogeneous soil and gas reservoirs

NASA Astrophysics Data System (ADS)

Chang, Ailian; Sun, HongGuang; Zheng, Chunmiao; Lu, Bingqing; Lu, Chengpeng; Ma, Rui; Zhang, Yong

2018-07-01

Fractional-derivative models have been developed recently to interpret various hydrologic dynamics, such as dissolved contaminant transport in groundwater. However, they have not been applied to quantify other fluid dynamics, such as gas transport through complex geological media. This study reviewed previous gas transport experiments conducted in laboratory columns and real-world oil-gas reservoirs and found that gas dynamics exhibit typical sub-diffusive behavior characterized by heavy late-time tailing in the gas breakthrough curves (BTCs), which cannot be effectively captured by classical transport models. Numerical tests and field applications of the time fractional convection-diffusion equation (fCDE) have shown that the fCDE model can capture the observed gas BTCs including their apparent positive skewness. Sensitivity analysis further revealed that the three parameters used in the fCDE model, including the time index, the convection velocity, and the diffusion coefficient, play different roles in interpreting the delayed gas transport dynamics. In addition, the model comparison and analysis showed that the time fCDE model is efficient in application. Therefore, the time fractional-derivative models can be conveniently extended to quantify gas transport through natural geological media such as complex oil-gas reservoirs.

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

Anomalous Diffusion of Single Particles in Cytoplasm

PubMed Central

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

2013-01-01

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

A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion.

PubMed

Dipierro, Serena; Valdinoci, Enrico

2018-07-01

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.

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

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

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

A Computational Investigation of Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Chao, B. H.; Sunderland, P. B.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2007-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, and residence time. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with residence times longer than 200 ms were found to have temperatures near 1190 K where C/O = 0.6, whereas flames with shorter residence times required increased temperatures. Acetylene was found to be a reasonable surrogate for soot precursor species in these flames, having peak mole fractions of about 0.01.

Bounded diffusion impedance characterization of battery electrodes using fractional modeling

NASA Astrophysics Data System (ADS)

Gabano, Jean-Denis; Poinot, Thierry; Huard, Benoît

2017-06-01

This article deals with the ability of fractional modeling to describe the bounded diffusion behavior encountered in modern thin film and nanoparticles lithium battery electrodes. Indeed, the diffusion impedance of such batteries behaves as a half order integrator characterized by the Warburg impedance at high frequencies and becomes a classical integrator described by a capacitor at low frequencies. The transition between these two behaviors depends on the particles geometry. Three of them will be considered in this paper: planar, cylindrical and spherical ones. The fractional representation proposed is a gray box model able to perfectly fit the low and high frequency diffusive impedance behaviors while optimizing the frequency response transition. Identification results are provided using frequential simulation data considering the three electrochemical diffusion models based on the particles geometry. Furthermore, knowing this geometry allows to estimate the diffusion ionic resistance and time constant using the relationships linking these physical parameters to the structural fractional model parameters. Finally, other simulations using Randles impedance models including the charge transfer impedance and the external resistance demonstrate the interest of fractional modeling in order to identify properly not only the charge transfer impedance but also the diffusion physical parameters whatever the particles geometry.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

NASA Astrophysics Data System (ADS)

Li, Linling; Wang, Xiaoliang; Zhou, Dongshan; Xue, Gi

2013-03-01

We report a diffusion study on the polystyrene/poly(phenylene oxide) (PS/PPO) mixture consisted by the PS and PPO nanoparticles. Diffusion of liquid PS into glassy PPO (l-PS/g-PPO) is promoted by annealing the PS/PPO mixture at several temperatures below Tg of the PPO. By tracing the Tgs of the PS-rich domain behind the diffusion front using DSC, we get the relationships of PS weight fractions and diffusion front advances with the elapsed diffusion times at different diffusion temperatures using the Gordon-Taylor equation and core-shell model. We find that the plots of weight fraction of PS vs. elapsed diffusion times at different temperatures can be converted to a master curve by Time-Temperature superposition, and the shift factors obey the Arrhenius equation. Besides, the diffusion front advances of l-PS into g-PPO show an excellent agreement with the t1/2 scaling law at the beginning of the diffusion process, and the diffusion coefficients of different diffusion temperatures also obey the Arrhenius equation. We believe the diffusion mechanism for l-PS/g-PPO should be the Fickean law rather than the Case II, though there are departures of original linearity at longer diffusion times due to the limited liquid supply system. Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

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

PubMed

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

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Comparative study of the methane and methanol mass transfer in the mesoporous H-ZSM-5/alumina extruded pellet

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-07-01

H-ZSM-5/alumina catalyst pellet was prepared using extrusion method. The as-prepared mesoporous material was characterized using nitrogen adsorption, IR, XRD, and TEM methods. Transport of methane and methanol in the obtained H-ZSM-5/alumina extruded grain was studied. We demonstrate that the methanol transport may be described by the time-fractional diffusion equation in a fairly good manner. The measured value of the fractional order of the time-fractional derivative reveals the fast super-diffusive regime of the methanol transport in the mesoporous solid. Contrary, the methane transport has been found to follow a standard diffusion and described by the second Fick's law. These findings show that mass transfer kinetics is characterized by the order of the temporal derivative. The latter is a unique property of the individual porous media and the diffusing agent.

Comparative study of the methane and methanol mass transfer in the mesoporous H-ZSM-5/alumina extruded pellet

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-01-01

H-ZSM-5/alumina catalyst pellet was prepared using extrusion method. The as-prepared mesoporous material was characterized using nitrogen adsorption, IR, XRD, and TEM methods. Transport of methane and methanol in the obtained H-ZSM-5/alumina extruded grain was studied. We demonstrate that the methanol transport may be described by the time-fractional diffusion equation in a fairly good manner. The measured value of the fractional order of the time-fractional derivative reveals the fast super-diffusive regime of the methanol transport in the mesoporous solid. Contrary, the methane transport has been found to follow a standard diffusion and described by the second Fick's law. These findings show that mass transfer kinetics is characterized by the order of the temporal derivative. The latter is a unique property of the individual porous media and the diffusing agent.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Samiee, Mehdi; Zayernouri, Mohsen

2016-11-01

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

Measurement and modeling of diffusion time dependence of apparent diffusion coefficient and fractional anisotropy in prostate tissue ex vivo.

PubMed

Bourne, Roger; Liang, Sisi; Panagiotaki, Eleftheria; Bongers, Andre; Sved, Paul; Watson, Geoffrey

2017-10-01

The purpose of this study was to measure and model the diffusion time dependence of apparent diffusion coefficient (ADC) and fractional anisotropy (FA) derived from conventional prostate diffusion-weighted imaging methods as used in recommended multiparametric MRI protocols. Diffusion tensor imaging (DTI) was performed at 9.4 T with three radical prostatectomy specimens, with diffusion times in the range 10-120 ms and b-values 0-3000 s/mm 2 . ADC and FA were calculated from DTI measurements at b-values of 800 and 1600 s/mm 2 . Independently, a two-component model (restricted isotropic plus Gaussian anisotropic) was used to synthesize DTI data, from which ADC and FA were predicted and compared with the measured values. Measured ADC and FA exhibited a diffusion time dependence, which was closely predicted by the two-component model. ADC decreased by about 0.10-0.15 μm 2 /ms as diffusion time increased from 10 to 120 ms. FA increased with diffusion time at b-values of 800 and 1600 s/mm 2 but was predicted to be independent of diffusion time at b = 3000 s/mm 2 . Both ADC and FA exhibited diffusion time dependence that could be modeled as two unmixed water pools - one having isotropic restricted dynamics, and the other unrestricted anisotropic dynamics. These results highlight the importance of considering and reporting diffusion times in conventional ADC and FA calculations and protocol recommendations, and inform the development of improved diffusion methods for prostate cancer imaging. Copyright © 2017 John Wiley & Sons, Ltd.

Diffusion in jammed particle packs

NASA Astrophysics Data System (ADS)

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

2015-03-01

Diffusive transport in jammed particle packs is of interest for a number of applications, as well as being a potential indicator of structural properties near the jamming point. To this end, we report stochastic simulations of equilibrium diffusion through monodisperse sphere packs near the jamming point in the limit of a perfectly insulating surrounding medium. The time dependence of various diffusion properties is resolved over several orders of magnitude. Two time regimes of expected Fickian diffusion are observed, separated by an intermediate regime of anomalous diffusion. This intermediate regime grows as the particle volume fraction approaches the critical jamming transition. The diffusion behavior is fully controlled by the extent of the contacts between neighboring particles, which in turn depend on proximity to the jamming point. In particular, the mean first passage time associated with the escape of random walkers between neighboring particles is shown to control both the time to recover Fickian diffusion and the long time diffusivity. Scaling laws are established that relate these quantities to the difference between the actual and critical jamming volume fractions. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's NNSA under Contract DE- AC04-94AL85000.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.

2018-02-01

A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.

Analytical approach for the fractional differential equations by using the extended tanh method

NASA Astrophysics Data System (ADS)

Pandir, Yusuf; Yildirim, Ayse

2018-07-01

In this study, we consider analytical solutions of space-time fractional derivative foam drainage equation, the nonlinear Korteweg-de Vries equation with time and space-fractional derivatives and time-fractional reaction-diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.

Experimental determination of barium isotope fractionation during diffusion and adsorption processes at low temperatures

NASA Astrophysics Data System (ADS)

van Zuilen, Kirsten; Müller, Thomas; Nägler, Thomas F.; Dietzel, Martin; Küsters, Tim

2016-08-01

Variations in barium (Ba) stable isotope abundances measured in low and high temperature environments have recently received increasing attention. The actual processes controlling Ba isotope fractionation, however, remain mostly elusive. In this study, we present the first experimental approach to quantify the contribution of diffusion and adsorption on mass-dependent Ba isotope fractionation during transport of aqueous Ba2+ ions through a porous medium. Experiments have been carried out in which a BaCl2 solution of known isotopic composition diffused through u-shaped glass tubes filled with silica hydrogel at 10 °C and 25 °C for up to 201 days. The diffused Ba was highly fractionated by up to -2.15‰ in δ137/134Ba, despite the low relative difference in atomic mass. The time-dependent isotope fractionation can be successfully reproduced by a diffusive transport model accounting for mass-dependent differences in the effective diffusivities of the Ba isotope species (D137Ba /D134Ba =(m134 /m137) β). Values of β extracted from the transport model were in the range of 0.010-0.011. Independently conducted batch experiments revealed that adsorption of Ba onto the surface of silica hydrogel favoured the heavier Ba isotopes (α = 1.00015 ± 0.00008). The contribution of adsorption on the overall isotope fractionation in the diffusion experiments, however, was found to be small. Our results contribute to the understanding of Ba isotope fractionation processes, which is crucial for interpreting natural isotope variations and the assessment of Ba isotope ratios as geochemical proxies.

Entropy as a measure of diffusion

NASA Astrophysics Data System (ADS)

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

2013-10-01

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

Extracting Diffusion Constants from Echo-Time-Dependent PFG NMR Data Using Relaxation-Time Information

NASA Astrophysics Data System (ADS)

Vandusschoten, D.; Dejager, P. A.; Vanas, H.

Heterogeneous (bio)systems are often characterized by several water-containing compartments that differ in relaxation time values and diffusion constants. Because of the relatively small differences among these diffusion constants, nonoptimal measuring conditions easily lead to the conclusion that a single diffusion constant suffices to describe the water mobility in a heterogeneous (bio)system. This paper demonstrates that the combination of a T2 measurement and diffusion measurements at various echo times (TE), based on the PFG MSE sequence, enables the accurate determination of diffusion constants which are less than a factor of 2 apart. This new method gives errors of the diffusion constant below 10% when two fractions are present, while the standard approach of a biexponential fit to the diffusion data in identical circumstances gives larger (>25%) errors. On application of this approach to water in apple parenchyma tissue, the diffusion constant of water in the vacuole of the cells ( D = 1.7 × 10 -9 m 2/s) can be distinguished from that of the cytoplasm ( D = 1.0 × 10 -9 m 2/s). Also, for mung bean seedlings, the cell size determined by PFG MSE measurements increased from 65 to 100 μm when the echo time increased from 150 to 900 ms, demonstrating that the interpretation of PFG SE data used to investigate cell sizes is strongly dependent on the T2 values of the fractions within the sample. Because relaxation times are used to discriminate the diffusion constants, we propose to name this approach diffusion analysis by relaxation- time- separated (DARTS) PFG NMR.

Isotope fractionation by multicomponent diffusion (Invited)

NASA Astrophysics Data System (ADS)

Watkins, J. M.; Liang, Y.; Richter, F. M.; Ryerson, F. J.; DePaolo, D. J.

2013-12-01

Isotope fractionation by multicomponent diffusion The isotopic composition of mineral phases can be used to probe the temperatures and rates of mineral formation as well as the degree of post-mineralization alteration. The ability to interpret stable isotope variations is limited by our knowledge of three key parameters and their relative importance in determining the composition of a mineral grain and its surroundings: (1) thermodynamic (equilibrium) partitioning, (2) mass-dependent diffusivities, and (3) mass-dependent reaction rate coefficients. Understanding the mechanisms of diffusion and reaction in geological liquids, and how these mass transport processes discriminate between isotopes, represents an important problem that is receiving considerable attention in the geosciences. Our focus in this presentation will be isotope fractionation by chemical diffusion. Previous studies have documented that diffusive isotope effects vary depending on the cation as well as the liquid composition, but the ability to predict diffusive isotope effects from theory is limited; for example, it is unclear whether the magnitude of diffusive isotopic fractionations might also vary with the direction of diffusion in composition space. To test this hypothesis and to further guide the theoretical treatment of isotope diffusion, two chemical diffusion experiments and one self diffusion experiment were conducted at 1250°C and 0.7 GPa. In one experiment (A-B), CaO and Na2O counter-diffuse rapidly in the presence of a small SiO2 gradient. In the other experiment (D-E), CaO and SiO2 counter-diffuse more slowly in a small Na2O gradient. In both chemical diffusion experiments, Ca isotopes become fractionated by chemical diffusion but by different amounts, documenting for the first time that the magnitude of isotope fractionation by diffusion depends on the direction of diffusion in composition space. The magnitude of Ca isotope fractionation that develops is positively correlated with the rate of CaO diffusion; in A-B, the total variation is 2.5‰ whereas in D-E it is only 1.3‰. The diffusion of isotopes in a multicomponent system is modeled using a new expression for the isotope-specific diffusive flux that includes self diffusion terms in addition to the multicomponent chemical diffusion matrix. Kinetic theory predicts a mass dependence on isotopic mobility, i.e., self diffusivity, but it is unknown whether or how the mass dependence on self diffusivity translates into a mass dependence on chemical diffusion coefficients. The new experimental results allow us to assess several empirical expressions relating the self diffusivity and its mass dependence to the elements of the diffusion matrix and their mass dependence. Several plausible theoretical treatments can fit the data equally well. We are currently at the stage where experiments are guiding the theoretical treatment of the isotope fractionation by diffusion problem, underscoring the importance of experiments for aiding interpretations of isotopic variations in nature.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Fractional derivatives in the diffusion process in heterogeneous systems: The case of transdermal patches.

PubMed

Caputo, Michele; Cametti, Cesare

2017-09-01

In this note, we present a simple mathematical model of drug delivery through transdermal patches by introducing a memory formalism in the classical Fick diffusion equation based on the fractional derivative. This approach is developed in the case of a medicated adhesive patch placed on the skin to deliver a time released dose of medication through the skin towards the bloodstream.The main resistance to drug transport across the skin resides in the diffusion through its outermost layer (the stratum corneum). Due to the complicated architecture of this region, a model based on a constant diffusivity in a steady-state condition results in too simplistic assumptions and more refined models are required.The introduction of a memory formalism in the diffusion process, where diffusion parameters depend at a certain time or position on what happens at preceeding times, meets this requirement and allows a significantly better description of the experimental results.The present model may be useful not only for analyzing the rate of skin permeation but also for predicting the drug concentration after transdermal drug delivery depending on the diffusion characteristics of the patch (its thickness and pseudo-diffusion coefficient). Copyright © 2017 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Molecular Dynamics Simulation of the Cage Effect in a Wide Packing Fraction Range

NASA Astrophysics Data System (ADS)

Pestryaev, E. M.

2018-07-01

The self-diffusion coefficient and particle residence time in the first coordination shell of its neighbours were investigated by molecular dynamics simulation with the packing fraction of the model system ranging from 0.1 to 0.8. The residence time distribution spans several orders of magnitude and broadens with the system packing fraction. The distribution exhibits a maximum localized in the short residence time region. The average residence time correlates with the conventionally-used intermolecular correlation time governed by the mutual particle translational diffusion. It was shown that the use of the coordination number as an argument for all searched parameters is the obvious representation of the cage effect onset. The agreement of the self-diffusion coefficient with one of the recent theories is excellent in most of the density range, including the start of the glass transition, with the largest divergence only observed for the rare gas state. The same conclusion is true for the simulated and theoretical values of the caging number, which is nearly five, defining the start of the system liquefaction.

Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

NASA Astrophysics Data System (ADS)

Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

2018-05-01

This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

Trace element diffusion and kinetic fractionation in wet rhyolitic melt

NASA Astrophysics Data System (ADS)

Holycross, Megan E.; Watson, E. Bruce

2018-07-01

Piston-cylinder experiments were run to determine the chemical diffusivities of 21 trace elements (Sc, V, Y, Zr, Nb, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb, Lu, Hf, Th and U) in hydrous rhyolitic melts at 1 GPa pressure and temperatures from 850 to 1250 °C. Diffusion couple glasses were doped with trace elements in low concentrations to characterize the diffusivities of all cations in a single experiment. Laser ablation ICP-MS was used to evaluate the trace element concentration gradients that developed in the silicate glasses. All calculated diffusion coefficients correspond to the temperature dependence D = D0exp(-Ea/RT). Rhyolite liquids contained either ∼4.1 wt% or ∼6.2 wt% dissolved H2O; separate Arrhenius relationships are produced for each melt composition. Trace element diffusivities in the melt with 6.2 wt% H2O are roughly two times higher than those in the less hydrous melt. Calculated trace element diffusion coefficients cover nearly two orders of magnitude at a given temperature. The high field strength elements are the slowest diffusers, followed by the transition metals and heavy rare earth elements. The light rare earth elements have the fastest diffusion rates in hydrous rhyolitic melt. The measured diffusion coefficients range down to values sufficiently low to preclude diffusive homogenization over geochemically realistic time scales in some cases. The substantial differences in the diffusivities of individual cations may result in fractionated trace element signatures in rhyolite melt pockets. A simple model is used to explore the potential for kinetic fractionation of REE during growth of an apatite crystal in a diffusive boundary layer locally saturated in P2O5. The faster-diffusing light REE are more efficiently transported away from the crystal interface than the slower-moving heavy REE. Diffusion effects will enrich the melt boundary layer in slow-moving HREE relative to the faster LREE. The kinetic fractionation of REE in the melt growth medium will result in a precipitated apatite crystal with a disequilibrium trace element composition.

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

NASA Astrophysics Data System (ADS)

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

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

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

PubMed

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

2012-06-01

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

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.

Diffuse colonies of human skin fibroblasts in relation to cellular senescence and proliferation.

PubMed

Zorin, Vadim; Zorina, Alla; Smetanina, Nadezhda; Kopnin, Pavel; Ozerov, Ivan V; Leonov, Sergey; Isaev, Artur; Klokov, Dmitry; Osipov, Andreyan N

2017-05-16

Development of personalized skin treatment in medicine and skin care may benefit from simple and accurate evaluation of the fraction of senescent skin fibroblasts that lost their proliferative capacity. We examined whether enriched analysis of colonies formed by primary human skin fibroblasts, a simple and widely available cellular assay, could reveal correlations with the fraction of senescent cells in heterogenic cell population. We measured fractions of senescence associated β-galactosidase (SA-βgal) positive cells in either mass cultures or colonies of various morphological types (dense, mixed and diffuse) formed by skin fibroblasts from 10 human donors. Although the donors were chosen to be within the same age group (33-54 years), the colony forming efficiency of their fibroblasts (ECO-f) and the percentage of dense, mixed and diffuse colonies varied greatly among the donors. We showed, for the first time, that the SA-βgal positive fraction was the largest in diffuse colonies, confirming that they originated from cells with the least proliferative capacity. The percentage of diffuse colonies was also found to correlate with the SA-βgal positive cells in mass culture. Using Ki67 as a cell proliferation marker, we further demonstrated a strong inverse correlation (r=-0.85, p=0.02) between the percentage of diffuse colonies and the fraction of Ki67+ cells. Moreover, a significant inverse correlation (r=-0.94, p=0.0001) between the percentage of diffuse colonies and ECO-f was found. Our data indicate that quantification of a fraction of diffuse colonies may provide a simple and useful method to evaluate the extent of cellular senescence in human skin fibroblasts.

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.

A diffusion model-free framework with echo time dependence for free-water elimination and brain tissue microstructure characterization.

PubMed

Molina-Romero, Miguel; Gómez, Pedro A; Sperl, Jonathan I; Czisch, Michael; Sämann, Philipp G; Jones, Derek K; Menzel, Marion I; Menze, Bjoern H

2018-03-23

The compartmental nature of brain tissue microstructure is typically studied by diffusion MRI, MR relaxometry or their correlation. Diffusion MRI relies on signal representations or biophysical models, while MR relaxometry and correlation studies are based on regularized inverse Laplace transforms (ILTs). Here we introduce a general framework for characterizing microstructure that does not depend on diffusion modeling and replaces ill-posed ILTs with blind source separation (BSS). This framework yields proton density, relaxation times, volume fractions, and signal disentanglement, allowing for separation of the free-water component. Diffusion experiments repeated for several different echo times, contain entangled diffusion and relaxation compartmental information. These can be disentangled by BSS using a physically constrained nonnegative matrix factorization. Computer simulations, phantom studies, together with repeatability and reproducibility experiments demonstrated that BSS is capable of estimating proton density, compartmental volume fractions and transversal relaxations. In vivo results proved its potential to correct for free-water contamination and to estimate tissue parameters. Formulation of the diffusion-relaxation dependence as a BSS problem introduces a new framework for studying microstructure compartmentalization, and a novel tool for free-water elimination. © 2018 International Society for Magnetic Resonance in Medicine.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Short-time self-diffusion coefficient of a particle in a colloidal suspension bounded by a microchannel: Virial expansions and simulation

NASA Astrophysics Data System (ADS)

Kȩdzierski, Marcin; Wajnryb, Eligiusz

2011-10-01

Self-diffusion of colloidal particles confined to a cylindrical microchannel is considered theoretically and numerically. Virial expansion of the self-diffusion coefficient is performed. Two-body and three-body hydrodynamic interactions are evaluated with high precision using the multipole method. The multipole expansion algorithm is also used to perform numerical simulations of the self-diffusion coefficient, valid for all possible particle packing fractions. Comparison with earlier results shows that the widely used method of reflections is insufficient for calculations of hydrodynamic interactions even for small packing fractions and small particles radii, contrary to the prevalent opinion.

Global uniqueness in an inverse problem for time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Kian, Y.; Oksanen, L.; Soccorsi, E.; Yamamoto, M.

2018-01-01

Given (M , g), a compact connected Riemannian manifold of dimension d ⩾ 2, with boundary ∂M, we consider an initial boundary value problem for a fractional diffusion equation on (0 , T) × M, T > 0, with time-fractional Caputo derivative of order α ∈ (0 , 1) ∪ (1 , 2). We prove uniqueness in the inverse problem of determining the smooth manifold (M , g) (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ∂M at fixed time. In the "flat" case where M is a compact subset of Rd, two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation ρ ∂tα u - div (a∇u) + qu = 0 on (0 , T) × M are recovered simultaneously.

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

Efficient computation of the Grünwald-Letnikov fractional diffusion derivative using adaptive time step memory

NASA Astrophysics Data System (ADS)

MacDonald, Christopher L.; Bhattacharya, Nirupama; Sprouse, Brian P.; Silva, Gabriel A.

2015-09-01

Computing numerical solutions to fractional differential equations can be computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In general, numerical approaches that depend on truncating part of the system history while efficient, can suffer from high degrees of error and inaccuracy. Here we present an adaptive time step memory method for smooth functions applied to the Grünwald-Letnikov fractional diffusion derivative. This method is computationally efficient and results in smaller errors during numerical simulations. Sampled points along the system's history at progressively longer intervals are assumed to reflect the values of neighboring time points. By including progressively fewer points backward in time, a temporally 'weighted' history is computed that includes contributions from the entire past of the system, maintaining accuracy, but with fewer points actually calculated, greatly improving computational efficiency.

Mild hypothermia for treatment of diffuse axonal injury: a quantitative analysis of diffusion tensor imaging

PubMed Central

Jing, Guojie; Yao, Xiaoteng; Li, Yiyi; Xie, Yituan; Li, Wang#x2019;an; Liu, Kejun; Jing, Yingchao; Li, Baisheng; Lv, Yifan; Ma, Baoxin

2014-01-01

Fractional anisotropy values in diffusion tensor imaging can quantitatively reflect the consistency of nerve fibers after brain damage, where higher values generally indicate less damage to nerve fibers. Therefore, we hypothesized that diffusion tensor imaging could be used to evaluate the effect of mild hypothermia on diffuse axonal injury. A total of 102 patients with diffuse axonal injury were randomly divided into two groups: normothermic and mild hypothermic treatment groups. Patient's modified Rankin scale scores 2 months after mild hypothermia were significantly lower than those for the normothermia group. The difference in average fractional anisotropy value for each region of interest before and after mild hypothermia was 1.32-1.36 times higher than the value in the normothermia group. Quantitative assessment of diffusion tensor imaging indicates that mild hypothermia therapy may be beneficial for patients with diffuse axonal injury. PMID:25206800

Multimodal MRI in cerebral small vessel disease: its relationship with cognition and sensitivity to change over time.

PubMed

Nitkunan, Arani; Barrick, Tom R; Charlton, Rebecca A; Clark, Chris A; Markus, Hugh S

2008-07-01

Cerebral small vessel disease is the most common cause of vascular dementia. Interest in using MRI parameters as surrogate markers of disease to assess therapies is increasing. In patients with symptomatic sporadic small vessel disease, we determined which MRI parameters best correlated with cognitive function on cross-sectional analysis and which changed over a period of 1 year. Thirty-five patients with lacunar stroke and leukoaraiosis were recruited. They underwent multimodal MRI (brain volume, fluid-attenuated inversion recovery lesion load, lacunar infarct number, fractional anisotropy, and mean diffusivity from diffusion tensor imaging) and neuropsychological testing. Twenty-seven agreed to reattend for repeat MRI and neuropsychology at 1 year. An executive function score correlated most strongly with diffusion tensor imaging (fractional anisotropy histogram, r=-0.640, P=0.004) and brain volume (r=0.501, P=0.034). Associations with diffusion tensor imaging were stronger than with all other MRI parameters. On multiple regression of all imaging parameters, a model that contained brain volume and fractional anisotropy, together with age, gender, and premorbid IQ, explained 74% of the variance of the executive function score (P=0.0001). Changes in mean diffusivity and fractional anisotropy were detectable over the 1-year follow-up; in contrast, no change in other MRI parameters was detectable over this time period. A multimodal MRI model explains a large proportion of the variation in executive function in cerebral small vessel disease. In particular, diffusion tensor imaging correlates best with executive function and is the most sensitive to change. This supports the use of MRI, in particular diffusion tensor imaging, as a surrogate marker in treatment trials.

Soot Volume Fraction Maps for Normal and Reduced Gravity Laminar Acetylene Jet Diffusion Flames

NASA Technical Reports Server (NTRS)

Greenberg, Paul S.; Ku, Jerry C.

1997-01-01

The study of soot particulate distribution inside gas jet diffusion flames is important to the understanding of fundamental soot particle and thermal radiative transport processes, as well as providing findings relevant to spacecraft fire safety, soot emissions, and radiant heat loads for combustors used in air-breathing propulsion systems. Compared to those under normal gravity (1-g) conditions, the elimination of buoyancy-induced flows is expected to significantly change the flow field in microgravity (O g) flames, resulting in taller and wider flames with longer particle residence times. Work by Bahadori and Edelman demonstrate many previously unreported qualitative and semi-quantitative results, including flame shape and radiation, for sooting laminar zas jet diffusion flames. Work by Ku et al. report soot aggregate size and morphology analyses and data and model predictions of soot volume fraction maps for various gas jet diffusion flames. In this study, we present the first 1-g and 0-g comparisons of soot volume fraction maps for laminar acetylene and nitrogen-diluted acetylene jet diffusion flames. Volume fraction is one of the most useful properties in the study of sooting diffusion flames. The amount of radiation heat transfer depends directly on the volume fraction and this parameter can be measured from line-of-sight extinction measurements. Although most Soot aggregates are submicron in size, the primary particles (20 to 50 nm in diameter) are in the Rayleigh limit, so the extinction absorption) cross section of aggregates can be accurately approximated by the Rayleigh solution as a function of incident wavelength, particles' complex refractive index, and particles' volume fraction.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Diffusion-driven magnesium and iron isotope fractionation in Hawaiian olivine

USGS Publications Warehouse

Teng, F.-Z.; Dauphas, N.; Helz, R.T.; Gao, S.; Huang, S.

2011-01-01

Diffusion plays an important role in Earth sciences to estimate the timescales of geological processes such as erosion, sediment burial, and magma cooling. In igneous systems, these diffusive processes are recorded in the form of crystal zoning. However, meaningful interpretation of these signatures is often hampered by the fact that they cannot be unambiguously ascribed to a single process (e.g., magmatic fractionation, diffusion limited transport in the crystal or in the liquid). Here we show that Mg and Fe isotope fractionations in olivine crystals can be used to trace diffusive processes in magmatic systems. Over sixty olivine fragments from Hawaiian basalts show isotopically fractionated Mg and Fe relative to basalts worldwide, with up to 0.4??? variation in 26Mg/24Mg ratios and 1.6??? variation in 56Fe/54Fe ratios. The linearly and negatively correlated Mg and Fe isotopic compositions [i.e., ??56Fe=(??3.3??0.3)????26Mg], co-variations of Mg and Fe isotopic compositions with Fe/Mg ratios of olivine fragments, and modeling results based on Mg and Fe elemental profiles demonstrate the coupled Mg and Fe isotope fractionation to be a manifestation of Mg-Fe inter-diffusion in zoned olivines during magmatic differentiation. This characteristic can be used to constrain the nature of mineral zoning in igneous and metamorphic rocks, and hence determine the residence times of crystals in magmas, the composition of primary melts, and the duration of metamorphic events. With improvements in methodology, in situ isotope mapping will become an essential tool of petrology to identify diffusion in crystals. ?? 2011 Elsevier B.V.

Equilibrium sorption and diffusion rate studies with halogenated organic chemical and sandy aquifer material

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

Ball, W.P.

1990-01-01

Concepts for rate limitation of sorptive uptake of hydrophobic organic solutes by aquifer solids are reviewed, emphasizing physical diffusion models and in the context of effects on contaminant transport. Data for the sorption of tetrachloroethene (PCE) and 1,2,4,5-tetrachlorobenzene (TeCB) on Borden sand are presented, showing that equilibrium is attained very slowly, requiring equilibration times on the order of tens of days for PCE and hundreds of days for TeCB. The rate of approach to equilibrium decreased with increasing particle size and sorption distribution coefficient, in accordance with retarded intragranular diffusion models. Pulverization of the samples significantly decreased the required timemore » to equilibrium without changing the sorption capacity of the solids. Batch sorption methodology was refined to allow accurate measurement of long-term distribution coefficients, using purified {sup 14}C-labelled solute spikes and sealed glass ampules. Sorption isotherms for PCE and TeCB were conducted with size fractions of Borden sand over four to five orders of magnitude in aqueous concentration, and were found to be slightly nonlinear (Freundlich exponent = 0.8). A concentrated set of data in the low concentration range (<50 ug/L) revealed that sorption in this range could be equally well described by a linear isotherm. Distribution coefficients of the two solutes with seven size fractions of Borden sand, measured at low concentration and at full equilibrium, were between seven and sixty times the value predicted on the basis of recent correlations with organic carbon content. Rate results for coarse size fractions support a simple pore diffusion model, with pore diffusion coefficients estimated to be approximately 3 {times} 10{sup {minus}8} cm{sup 2}/sec, more than 200{times} lower than the aqueous diffusivities.« less

Experimental Evidence for Fast Lithium Diffusion and Isotope Fractionation in Water-bearing Rhyolitic Melts at Magmatic Conditions

NASA Astrophysics Data System (ADS)

Cichy, S. B.; Till, C. B.; Roggensack, K.; Hervig, R. L.; Clarke, A. B.

2015-12-01

The aim of this work is to extend the existing database of experimentally-determined lithium diffusion coefficients to more natural cases of water-bearing melts at the pressure-temperature range of the upper crust. In particular, we are investigating Li intra-melt and melt-vapor diffusion and Li isotope fractionation, which have the potential to record short-lived magmatic processes (seconds to hours) in the shallow crust, especially during decompression-induced magma degassing. Hydrated intra-melt Li diffusion-couple experiments on Los Posos rhyolite glass [1] were performed in a piston cylinder at 300 MPa and 1050 °C. The polished interfaces between the diffusion couples were marked by addition of Pt powder for post-run detection. Secondary ion mass spectrometry analyses indicate that lithium diffuses extremely fast in the presence of water. Re-equilibration of a hydrated ~2.5 mm long diffusion-couple experiment was observed during the heating period from room temperature to the final temperature of 1050 °C at a rate of ~32 °C/min. Fractionation of ~40‰ δ7Li was also detected in this zero-time experiment. The 0.5h and 3h runs show progressively higher degrees of re-equilibration, while the isotope fractionation becomes imperceptible. Li contamination was observed in some experiments when flakes filed off Pt tubing were used to mark the diffusion couple boundary, while the use of high purity Pt powder produced better results and allowed easier detection of the diffusion-couple boundary. The preliminary lithium isotope fractionation results (δ7Li vs. distance) support findings from [2] that 6Li diffuses substantially faster than 7Li. Further experimental sets are in progress, including lower run temperatures (e.g. 900 °C), faster heating procedure (~100 °C/min), shorter run durations and the extension to mafic systems. [1] Stanton (1990) Ph.D. thesis, Arizona State Univ., [2] Richter et al. (2003) GCA 67, 3905-3923.

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).

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

PubMed

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

2017-05-09

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

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Applications and Implications of Fractional Dynamics for Dielectric Relaxation

NASA Astrophysics Data System (ADS)

Hilfer, R.

This article summarizes briefly the presentation given by the author at the NATO Advanced Research Workshop on "Broadband Dielectric Spectroscopy and its Advanced Technological Applications", held in Perpignan, France, in September 2011. The purpose of the invited presentation at the workshop was to review and summarize the basic theory of fractional dynamics (Hilfer, Phys Rev E 48:2466, 1993; Hilfer and Anton, Phys Rev E Rapid Commun 51:R848, 1995; Hilfer, Fractals 3(1):211, 1995; Hilfer, Chaos Solitons Fractals 5:1475, 1995; Hilfer, Fractals 3:549, 1995; Hilfer, Physica A 221:89, 1995; Hilfer, On fractional diffusion and its relation with continuous time random walks. In: Pekalski et al. (eds) Anomalous diffusion: from basis to applications. Springer, Berlin, p 77, 1999; Hilfer, Fractional evolution equations and irreversibility. In: Helbing et al. (eds) Traffic and granular flow'99. Springer, Berlin, p 215, 2000; Hilfer, Fractional time evolution. In: Hilfer (ed) Applications of fractional calculus in physics. World Scientific, Singapore, p 87, 2000; Hilfer, Remarks on fractional time. In: Castell and Ischebeck (eds) Time, quantum and information. Springer, Berlin, p 235, 2003; Hilfer, Physica A 329:35, 2003; Hilfer, Threefold introduction to fractional derivatives. In: Klages et al. (eds) Anomalous transport: foundations and applications. Wiley-VCH, Weinheim, pp 17-74, 2008; Hilfer, Foundations of fractional dynamics: a short account. In: Klafter et al. (eds) Fractional dynamics: recent advances. World Scientific, Singapore, p 207, 2011) and demonstrate its relevance and application to broadband dielectric spectroscopy (Hilfer, J Phys Condens Matter 14:2297, 2002; Hilfer, Chem Phys 284:399, 2002; Hilfer, Fractals 11:251, 2003; Hilfer et al., Fractional Calc Appl Anal 12:299, 2009). It was argued, that broadband dielectric spectroscopy might be useful to test effective field theories based on fractional dynamics.

Fractional Brownian motion with a reflecting wall

NASA Astrophysics Data System (ADS)

Wada, Alexander H. O.; Vojta, Thomas

2018-02-01

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

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Kinetic isotopic fractionation during diffusion of ionic species in water

NASA Astrophysics Data System (ADS)

Richter, Frank M.; Mendybaev, Ruslan A.; Christensen, John N.; Hutcheon, Ian D.; Williams, Ross W.; Sturchio, Neil C.; Beloso, Abelardo D.

2006-01-01

Experiments specifically designed to measure the ratio of the diffusivities of ions dissolved in water were used to determine DLi/DK,D/D,D/D,D/D,andD/D. The measured ratio of the diffusion coefficients for Li and K in water (D Li/D K = 0.6) is in good agreement with published data, providing evidence that the experimental design being used resolves the relative mobility of ions with adequate precision to also be used for determining the fractionation of isotopes by diffusion in water. In the case of Li, we found measurable isotopic fractionation associated with the diffusion of dissolved LiCl (D/D=0.99772±0.00026). This difference in the diffusion coefficient of 7Li compared to 6Li is significantly less than that reported in an earlier study, a difference we attribute to the fact that in the earlier study Li diffused through a membrane separating the water reservoirs. Our experiments involving Mg diffusing in water found no measurable isotopic fractionation (D/D=1.00003±0.00006). Cl isotopes were fractionated during diffusion in water (D/D=0.99857±0.00080) whether or not the co-diffuser (Li or Mg) was isotopically fractionated. The isotopic fractionation associated with the diffusion of ions in water is much smaller than values we found previously for the isotopic fractionation of Li and Ca isotopes by diffusion in molten silicate liquids. A major distinction between water and silicate liquids is that water surrounds dissolved ions with hydration shells, which very likely play an important but still poorly understood role in limiting the isotopic fractionation associated with diffusion.

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Impact of time-of-day on diffusivity measures of brain tissue derived from diffusion tensor imaging.

PubMed

Thomas, Cibu; Sadeghi, Neda; Nayak, Amrita; Trefler, Aaron; Sarlls, Joelle; Baker, Chris I; Pierpaoli, Carlo

2018-06-01

Diurnal fluctuations in MRI measures of structural and functional properties of the brain have been reported recently. These fluctuations may have a physiological origin, since they have been detected using different MRI modalities, and cannot be explained by factors that are typically known to confound MRI measures. While preliminary evidence suggests that measures of structural properties of the brain based on diffusion tensor imaging (DTI) fluctuate as a function of time-of-day (TOD), the underlying mechanism has not been investigated. Here, we used a longitudinal within-subjects design to investigate the impact of time-of-day on DTI measures. In addition to using the conventional monoexponential tensor model to assess TOD-related fluctuations, we used a dual compartment tensor model that allowed us to directly assess if any change in DTI measures is due to an increase in CSF/free-water volume fraction or due to an increase in water diffusivity within the parenchyma. Our results show that Trace or mean diffusivity, as measured using the conventional monoexponential tensor model tends to increase systematically from morning to afternoon scans at the interface of grey matter/CSF, most prominently in the major fissures and the sulci of the brain. Interestingly, in a recent study of the glymphatic system, these same regions were found to show late enhancement after intrathecal injection of a CSF contrast agent. The increase in Trace also impacts DTI measures of diffusivity such as radial and axial diffusivity, but does not affect fractional anisotropy. The dual compartment analysis revealed that the increase in diffusivity measures from PM to AM was driven by an increase in the volume fraction of CSF-like free-water. Taken together, our findings provide important insight into the likely physiological origins of diurnal fluctuations in MRI measurements of structural properties of the brain. Published by Elsevier Inc.

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Modelling nematode movement using time-fractional dynamics.

PubMed

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

2007-09-07

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

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.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

Predicting First Traversal Times for Virions and Nanoparticles in Mucus with Slowed Diffusion

PubMed Central

Erickson, Austen M.; Henry, Bruce I.; Murray, John M.; Klasse, Per Johan; Angstmann, Christopher N.

2015-01-01

Particle-tracking experiments focusing on virions or nanoparticles in mucus have measured mean-square displacements and reported diffusion coefficients that are orders of magnitude smaller than the diffusion coefficients of such particles in water. Accurate description of this subdiffusion is important to properly estimate the likelihood of virions traversing the mucus boundary layer and infecting cells in the epithelium. However, there are several candidate models for diffusion that can fit experimental measurements of mean-square displacements. We show that these models yield very different estimates for the time taken for subdiffusive virions to traverse through a mucus layer. We explain why fits of subdiffusive mean-square displacements to standard diffusion models may be misleading. Relevant to human immunodeficiency virus infection, using computational methods for fractional subdiffusion, we show that subdiffusion in normal acidic mucus provides a more effective barrier against infection than previously thought. By contrast, the neutralization of the mucus by alkaline semen, after sexual intercourse, allows virions to cross the mucus layer and reach the epithelium in a short timeframe. The computed barrier protection from fractional subdiffusion is some orders of magnitude greater than that derived by fitting standard models of diffusion to subdiffusive data. PMID:26153713

Dynamic interactions between a membrane binding protein and lipids induce fluctuating diffusivity

PubMed Central

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

2017-01-01

Pleckstrin homology (PH) domains are membrane-binding lipid recognition proteins that interact with phosphatidylinositol phosphate (PIP) molecules in eukaryotic cell membranes. Diffusion of PH domains plays a critical role in biological reactions on membrane surfaces. Although diffusivity can be estimated by long-time measurements, it lacks information on the short-time diffusive nature. We reveal two diffusive properties of a PH domain bound to the surface of a PIP-containing membrane using molecular dynamics simulations. One is fractional Brownian motion, attributed to the motion of the lipids with which the PH domain interacts. The other is temporally fluctuating diffusivity; that is, the short-time diffusivity of the bound protein changes substantially with time. Moreover, the diffusivity for short-time measurements is intrinsically different from that for long-time measurements. This fluctuating diffusivity results from dynamic changes in interactions between the PH domain and PIP molecules. Our results provide evidence that the complexity of protein-lipid interactions plays a crucial role in the diffusion of proteins on biological membrane surfaces. Changes in the diffusivity of PH domains and related membrane-bound proteins may in turn contribute to the formation/dissolution of protein complexes in membranes. PMID:28116358

Fractional Brownian motion with a reflecting wall.

PubMed

Wada, Alexander H O; Vojta, Thomas

2018-02-01

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

An accurate computational method for the diffusion regime verification

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an accurate computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic analytic solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.

Representation of solution for fully nonlocal diffusion equations with deviation time variable

NASA Astrophysics Data System (ADS)

Drin, I. I.; Drin, S. S.; Drin, Ya. M.

2018-01-01

We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator Dat + a2 (-Δ) γ/2 (0 <= α <= 1, γ ɛ (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.

A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.

2015-07-01

In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.

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

PubMed

Lin, Guoxing

2016-11-21

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

A comparison/validation of a fractional derivative model with an empirical model of non-linear shock waves in swelling shales

NASA Astrophysics Data System (ADS)

Droghei, Riccardo; Salusti, Ettore

2013-04-01

Control of drilling parameters, as fluid pressure, mud weight, salt concentration is essential to avoid instabilities when drilling through shale sections. To investigate shale deformation, fundamental for deep oil drilling and hydraulic fracturing for gas extraction ("fracking"), a non-linear model of mechanic and chemo-poroelastic interactions among fluid, solute and the solid matrix is here discussed. The two equations of this model describe the isothermal evolution of fluid pressure and solute density in a fluid saturated porous rock. Their solutions are quick non-linear Burger's solitary waves, potentially destructive for deep operations. In such analysis the effect of diffusion, that can play a particular role in fracking, is investigated. Then, following Civan (1998), both diffusive and shock waves are applied to fine particles filtration due to such quick transients , their effect on the adjacent rocks and the resulting time-delayed evolution. Notice how time delays in simple porous media dynamics have recently been analyzed using a fractional derivative approach. To make a tentative comparison of these two deeply different methods,in our model we insert fractional time derivatives, i.e. a kind of time-average of the fluid-rocks interactions. Then the delaying effects of fine particles filtration is compared with fractional model time delays. All this can be seen as an empirical check of these fractional models.

Repeated diffusion MRI reveals earliest time point for stratification of radiotherapy response in brain metastases

NASA Astrophysics Data System (ADS)

Mahmood, Faisal; Johannesen, Helle H.; Geertsen, Poul; Hansen, Rasmus H.

2017-04-01

An imaging biomarker for early prediction of treatment response potentially provides a non-invasive tool for better prognostics and individualized management of the disease. Radiotherapy (RT) response is generally related to changes in gross tumor volume manifesting months later. In this prospective study we investigated the apparent diffusion coefficient (ADC), perfusion fraction and pseudo diffusion coefficient derived from diffusion weighted MRI as potential early biomarkers for radiotherapy response of brain metastases. It was a particular aim to assess the optimal time point for acquiring the DW-MRI scan during the course of treatment, since to our knowledge this important question has not been addressed directly in previous studies. Twenty-nine metastases (N  =  29) from twenty-one patients, treated with whole-brain fractionated external beam RT were analyzed. Patients were scanned with a 1 T MRI system to acquire DW-, T2*W-, T2W- and T1W scans, before start of RT, at each fraction and at follow up two to three months after RT. The DW-MRI parameters were derived using regions of interest based on high b-value images (b  =  800 s mm-2). Both volumetric and RECIST criteria were applied for response evaluation. It was found that in non-responding metastases the mean ADC decreased and in responding metastases it increased. The volume based response proved to be far more consistently predictable by the ADC change found at fraction number 7 and later, compared to the linear response (RECIST). The perfusion fraction and pseudo diffusion coefficient did not show sufficient prognostic value with either response assessment criteria. In conclusion this study shows that the ADC derived using high b-values may be a reliable biomarker for early assessment of radiotherapy response for brain metastases patients. The earliest response stratification can be achieved using two DW-MRI scans, one pre-treatment and one at treatment day 7-9 (equivalent to 21 Gy).

Fractional diffusion: recovering the distributed fractional derivative from overposed data

NASA Astrophysics Data System (ADS)

Rundell, W.; Zhang, Z.

2017-03-01

There has been considerable recent study in ‘subdiffusion’ models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one such is to realize that the order of the fractional derivative is related to the time scales of the underlying diffusion process. This raises the question of what order α of derivative should be taken and if a single value actually suffices. This has led to models that combine a finite number of these derivatives each with a different fractional exponent {αk} and different weighting value c k to better model a greater possible range of time scales. Ultimately, one wants to look at a situation that combines derivatives in a continuous way—the so-called distributional model with parameter μ ≤ft(α \\right) . However all of this begs the question of how one determines this ‘order’ of differentiation. Recovering a single fractional value has been an active part of the process from the beginning of fractional diffusion modeling and if this is the only unknown then the markers left by the fractional order derivative are relatively straightforward to determine. In the case of a finite combination of derivatives this becomes much more complex due to the more limited analytic tools available for such equations, but recent progress in this direction has been made, (Li et al 2015 Appl. Math. Comput. 257 381-97, Li and Yamamoto 2015 Appl. Anal. 94 570-9). This paper considers the full distributional model where the order is viewed as a function μ ≤ft(α \\right) on the interval (0, 1]. We show existence, uniqueness and regularity for an initial-boundary value problem including an important representation theorem in the case of a single spatial variable. This is then used in the inverse problem of recovering the distributional coefficient μ ≤ft(α \\right) from a time trace of the solution and a uniqueness result is proven.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

Gusev, Vitalyi; Craig, Walter; Livoti, Roberto; Danworaphong, Sorasak; Diebold, Gerald J.

2005-10-01

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

Experimental investigation on the carbon isotope fractionation of methane during gas migration by diffusion through sedimentary rocks at elevated temperature and pressure

NASA Astrophysics Data System (ADS)

Zhang, Tongwei; Krooss, Bernhard M.

2001-08-01

Molecular transport (diffusion) of methane in water-saturated sedimentary rocks results in carbon isotope fractionation. In order to quantify the diffusive isotope fractionation effect and its dependence on total organic carbon (TOC) content, experimental measurements have been performed on three natural shale samples with TOC values ranging from 0.3 to 5.74%. The experiments were conducted at 90°C and fluid pressures of 9 MPa (90 bar). Based on the instantaneous and cumulative composition of the diffused methane, effective diffusion coefficients of the 12CH4 and 13CH4 species, respectively, have been calculated. Compared with the carbon isotopic composition of the source methane (δ13C1 = -39.1‰), a significant depletion of the heavier carbon isotope (13C) in the diffused methane was observed for all three shales. The degree of depletion is highest during the initial non-steady state of the diffusion process. It then gradually decreases and reaches a constant difference (Δ δ = δ13Cdiff -δ13Csource) when approaching the steady-state. The degree of the isotopic fractionation of methane due to molecular diffusion increases with the TOC content of the shales. The carbon isotope fractionation of methane during molecular migration results practically exclusively from differences in molecular mobility (effective diffusion coefficients) of the 12CH4 and 13CH4 entities. No measurable solubility fractionation was observed. The experimental isotope-specific diffusion data were used in two hypothetical scenarios to illustrate the extent of isotopic fractionation to be expected as a result of molecular transport in geological systems with shales of different TOC contents. The first scenario considers the progression of a diffusion front from a constant source (gas reservoir) into a homogeneous ;semi-infinite; shale caprock over a period of 10 Ma. In the second example, gas diffusion across a 100 m caprock sequence is analyzed in terms of absolute quantities and isotope fractionation effects. The examples demonstrate that methane losses by molecular diffusion are small in comparison with the contents of commercial size gas accumulations. The degree of isotopic fractionation is related inversely to the quantity of diffused gas so that strong fractionation effects are only observed for relatively small portions of gas. The experimental data can be readily used in numerical basin analysis to examine the effects of diffusion-related isotopic fractionation on the composition of natural gas reservoirs.

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

PubMed

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

2014-09-30

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

In Vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules

NASA Astrophysics Data System (ADS)

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

2011-01-01

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

Stimulated echo diffusion tensor imaging (STEAM-DTI) with varying diffusion times as a probe of breast tissue.

PubMed

Teruel, Jose R; Cho, Gene Y; Moccaldi Rt, Melanie; Goa, Pål E; Bathen, Tone F; Feiweier, Thorsten; Kim, Sungheon G; Moy, Linda; Sigmund, Eric E

2017-01-01

To explore the application of diffusion tensor imaging (DTI) for breast tissue and breast pathologies using a stimulated-echo acquisition mode (STEAM) with variable diffusion times. In this Health Insurance Portability and Accountability Act-compliant study, approved by the local institutional review board, eight patients and six healthy volunteers underwent an MRI examination at 3 Tesla including STEAM-DTI with several diffusion times ranging from 68.5 to 902.5 ms. A DTI model was fitted to the data for each diffusion time, and parametric maps of mean diffusivity, fractional anisotropy, axial diffusivity, and radial diffusivity were computed for healthy fibroglandular tissue (FGT) and lesions. The median value of radial diffusivity for FGT was fitted to a linear decay to obtain an estimation of the surface-to-volume ratio, from which the radial diameter was calculated. For healthy FGT, radial diffusivity presented a linear decay with the square root of the diffusion time resulting in a range of estimated radial diameters from 202 to 496 µm, while axial diffusivity presented a nearly time-independent diffusion. Residual fat signal was reduced at longer diffusion times due to the shorter T1 of fat. Residual fat signal to the overall signal in the healthy volunteers' FGT was found to range from 2.39% to 2.55% (shortest mixing time), and from 0.40% to 0.51% (longest mixing time) for the b500 images. The use of variable diffusion times may provide an in vivo noninvasive tool to probe diffusion lengths in breast tissue and breast pathology, and might aid by improving fat suppression at longer diffusion times. 2 J. Magn. Reson. Imaging 2017;45:84-93. © 2016 International Society for Magnetic Resonance in Medicine.

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

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

PubMed

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

2009-12-01

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

Maxwell-Stefan diffusion: a framework for predicting condensed phase diffusion and phase separation in atmospheric aerosol

NASA Astrophysics Data System (ADS)

Fowler, Kathryn; Connolly, Paul J.; Topping, David O.; O'Meara, Simon

2018-02-01

The composition of atmospheric aerosol particles has been found to influence their micro-physical properties and their interaction with water vapour in the atmosphere. Core-shell models have been used to investigate the relationship between composition, viscosity and equilibration timescales. These models have traditionally relied on the Fickian laws of diffusion with no explicit account of non-ideal interactions. We introduce the Maxwell-Stefan diffusion framework as an alternative method, which explicitly accounts for non-ideal interactions through activity coefficients. e-folding time is the time it takes for the difference in surface and bulk concentration to change by an exponential factor and was used to investigate the interplay between viscosity and solubility and the effect this has on equilibration timescales within individual aerosol particles. The e-folding time was estimated after instantaneous increases in relative humidity to binary systems of water and an organic component. At low water mole fractions, viscous effects were found to dominate mixing. However, at high water mole fractions, equilibration times were more sensitive to a range in solubility, shown through the greater variation in e-folding times. This is the first time the Maxwell-Stefan framework has been applied to an atmospheric aerosol core-shell model and shows that there is a complex interplay between the viscous and solubility effects on aerosol composition that requires further investigation.

Brain white matter structure and COMT gene are linked to second-language learning in adults

PubMed Central

Mamiya, Ping C.; Richards, Todd L.; Coe, Bradley P.; Eichler, Evan E.; Kuhl, Patricia K.

2016-01-01

Adult human brains retain the capacity to undergo tissue reorganization during second-language learning. Brain-imaging studies show a relationship between neuroanatomical properties and learning for adults exposed to a second language. However, the role of genetic factors in this relationship has not been investigated. The goal of the current study was twofold: (i) to characterize the relationship between brain white matter fiber-tract properties and second-language immersion using diffusion tensor imaging, and (ii) to determine whether polymorphisms in the catechol-O-methyltransferase (COMT) gene affect the relationship. We recruited incoming Chinese students enrolled in the University of Washington and scanned their brains one time. We measured the diffusion properties of the white matter fiber tracts and correlated them with the number of days each student had been in the immersion program at the time of the brain scan. We found that higher numbers of days in the English immersion program correlated with higher fractional anisotropy and lower radial diffusivity in the right superior longitudinal fasciculus. We show that fractional anisotropy declined once the subjects finished the immersion program. The relationship between brain white matter fiber-tract properties and immersion varied in subjects with different COMT genotypes. Subjects with the Methionine (Met)/Valine (Val) and Val/Val genotypes showed higher fractional anisotropy and lower radial diffusivity during immersion, which reversed immediately after immersion ended, whereas those with the Met/Met genotype did not show these relationships. Statistical modeling revealed that subjects’ grades in the language immersion program were best predicted by fractional anisotropy and COMT genotype. PMID:27298360

Brain white matter structure and COMT gene are linked to second-language learning in adults.

PubMed

Mamiya, Ping C; Richards, Todd L; Coe, Bradley P; Eichler, Evan E; Kuhl, Patricia K

2016-06-28

Adult human brains retain the capacity to undergo tissue reorganization during second-language learning. Brain-imaging studies show a relationship between neuroanatomical properties and learning for adults exposed to a second language. However, the role of genetic factors in this relationship has not been investigated. The goal of the current study was twofold: (i) to characterize the relationship between brain white matter fiber-tract properties and second-language immersion using diffusion tensor imaging, and (ii) to determine whether polymorphisms in the catechol-O-methyltransferase (COMT) gene affect the relationship. We recruited incoming Chinese students enrolled in the University of Washington and scanned their brains one time. We measured the diffusion properties of the white matter fiber tracts and correlated them with the number of days each student had been in the immersion program at the time of the brain scan. We found that higher numbers of days in the English immersion program correlated with higher fractional anisotropy and lower radial diffusivity in the right superior longitudinal fasciculus. We show that fractional anisotropy declined once the subjects finished the immersion program. The relationship between brain white matter fiber-tract properties and immersion varied in subjects with different COMT genotypes. Subjects with the Methionine (Met)/Valine (Val) and Val/Val genotypes showed higher fractional anisotropy and lower radial diffusivity during immersion, which reversed immediately after immersion ended, whereas those with the Met/Met genotype did not show these relationships. Statistical modeling revealed that subjects' grades in the language immersion program were best predicted by fractional anisotropy and COMT genotype.

Negligible fractionation of Kr and Xe isotopes by molecular diffusion in water

NASA Astrophysics Data System (ADS)

Tyroller, Lina; Brennwald, Matthias S.; Busemann, Henner; Maden, Colin; Baur, Heinrich; Kipfer, Rolf

2018-06-01

Molecular diffusion is a key transport process for noble gases in water. Such diffusive transport is often thought to cause a mass-dependent fractionation of noble gas isotopes that is inversely proportional to the square root of the ratio of their atomic mass, referred to as the square root relation. Previous studies, challenged the commonly held assumption that the square root relation adequately describes the behaviour of noble gas isotopes diffusing through water. However, the effect of diffusion on noble gas isotopes has only been determined experimentally for He, Ne and Ar to date, whereas the extent of fractionation of Kr and Xe has not been measured. In the present study the fractionation of Kr and Xe isotopes diffusing through water immobilised by adding agar was quantified through measuring the respective isotope ratio after diffusing through the immobilised water. No fractionation of Kr and Xe isotopes was observed, even using high-precision noble gas analytics. These results complement our current understanding on isotopic fractionation of noble gases diffusing through water. Therefore this complete data set builds a robust basis to describe molecular diffusion of noble gases in water in a physical sound manner which is fundamental to assess the physical aspects of gas dynamics in aquatic systems.

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

PubMed

Hong, Tao; Tang, Zhengming; Zhu, Huacheng

2016-12-28

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

Association between sociability and diffusion tensor imaging in BALB/cJ mice.

PubMed

Kim, Sungheon; Pickup, Stephen; Fairless, Andrew H; Ittyerah, Ranjit; Dow, Holly C; Abel, Ted; Brodkin, Edward S; Poptani, Harish

2012-01-01

The purpose of this study was to use high-resolution diffusion tensor imaging (DTI) to investigate the association between DTI metrics and sociability in BALB/c inbred mice. The sociability of prepubescent (30-day-old) BALB/cJ mice was operationally defined as the time that the mice spent sniffing a stimulus mouse in a social choice test. High-resolution ex vivo DTI data on 12 BALB/cJ mouse brains were acquired using a 9.4-T vertical-bore magnet. Regression analysis was conducted to investigate the association between DTI metrics and sociability. Significant positive regression (p < 0.001) between social sniffing time and fractional anisotropy was found in 10 regions located in the thalamic nuclei, zona incerta/substantia nigra, visual/orbital/somatosensory cortices and entorhinal cortex. In addition, significant negative regression (p < 0.001) between social sniffing time and mean diffusivity was found in five areas located in the sensory cortex, motor cortex, external capsule and amygdaloid region. In all regions showing significant regression with either the mean diffusivity or fractional anisotropy, the tertiary eigenvalue correlated negatively with the social sniffing time. This study demonstrates the feasibility of using DTI to detect brain regions associated with sociability in a mouse model system. Copyright © 2011 John Wiley & Sons, Ltd.

Modelling and formation of spatiotemporal patterns of fractional predation system in subdiffusion and superdiffusion scenarios

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.; Atangana, Abdon

2018-02-01

This paper primarily focused on the question of how population diffusion can affect the formation of the spatial patterns in the spatial fraction predator-prey system by Turing mechanisms. Our numerical findings assert that modeling by fractional reaction-diffusion equations should be considered as an appropriate tool for studying the fundamental mechanisms of complex spatiotemporal dynamics. We observe that pure Hopf instability gives rise to the formation of spiral patterns in 2D and pure Turing instability destroys the spiral pattern and results to the formation of chaotic or spatiotemporal spatial patterns. Existence and permanence of the species is also guaranteed with the 3D simulations at some instances of time for subdiffusive and superdiffusive scenarios.

Asymptotic neutron scattering laws for anomalously diffusing quantum particles

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

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

2016-07-28

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

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

NASA Astrophysics Data System (ADS)

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

2007-05-01

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

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

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

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

Short-time dynamics of monomers and dimers in quasi-two-dimensional colloidal mixtures.

PubMed

Sarmiento-Gómez, Erick; Villanueva-Valencia, José Ramón; Herrera-Velarde, Salvador; Ruiz-Santoyo, José Arturo; Santana-Solano, Jesús; Arauz-Lara, José Luis; Castañeda-Priego, Ramón

2016-07-01

We report on the short-time dynamics in colloidal mixtures made up of monomers and dimers highly confined between two glass plates. At low concentrations, the experimental measurements of colloidal motion agree well with the solution of the Navier-Stokes equation at low Reynolds numbers; the latter takes into account the increase in the drag force on a colloidal particle due to wall-particle hydrodynamic forces. More importantly, we find that the ratio of the short-time diffusion coefficient of the monomer and that of the center of mass of the dimmer is almost independent of both the dimer molar fraction, x_{d}, and the total packing fraction, ϕ, up to ϕ≈0.5. At higher concentrations, this ratio displays a small but systematic increase. A similar physical scenario is observed for the ratio between the parallel and the perpendicular components of the short-time diffusion coefficients of the dimer. This dynamical behavior is corroborated by means of molecular dynamics computer simulations that include explicitly the particle-particle hydrodynamic forces induced by the solvent. Our results suggest that the effects of colloid-colloid hydrodynamic interactions on the short-time diffusion coefficients are almost identical and factorable in both species.

Numerical solution of the time fractional reaction-diffusion equation with a moving boundary

NASA Astrophysics Data System (ADS)

Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J.

2017-06-01

A fractional reaction-diffusion model with a moving boundary is presented in this paper. An efficient numerical method is constructed to solve this moving boundary problem. Our method makes use of a finite difference approximation for the temporal discretization, and spectral approximation for the spatial discretization. The stability and convergence of the method is studied, and the errors of both the semi-discrete and fully-discrete schemes are derived. Numerical examples, motivated by problems from developmental biology, show a good agreement with the theoretical analysis and illustrate the efficiency of our method.

The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain

NASA Astrophysics Data System (ADS)

Pskhu, A. V.

2017-12-01

We solve the first boundary-value problem in a non-cylindrical domain for a diffusion-wave equation with the Dzhrbashyan- Nersesyan operator of fractional differentiation with respect to the time variable. We prove an existence and uniqueness theorem for this problem, and construct a representation of the solution. We show that a sufficient condition for unique solubility is the condition of Hölder smoothness for the lateral boundary of the domain. The corresponding results for equations with Riemann- Liouville and Caputo derivatives are particular cases of results obtained here.

ADP Compartmentation Analysis Reveals Coupling between Pyruvate Kinase and ATPases in Heart Muscle

PubMed Central

Sepp, Mervi; Vendelin, Marko; Vija, Heiki; Birkedal, Rikke

2010-01-01

Abstract Cardiomyocytes have intracellular diffusion restrictions, which spatially compartmentalize ADP and ATP. However, the models that predict diffusion restrictions have used data sets generated in rat heart permeabilized fibers, where diffusion distances may be heterogeneous. This is avoided by using isolated, permeabilized cardiomyocytes. The aim of this work was to analyze the intracellular diffusion of ATP and ADP in rat permeabilized cardiomyocytes. To do this, we measured respiration rate, ATPase rate, and ADP concentration in the surrounding solution. The data were analyzed using mathematical models that reflect different levels of cell compartmentalization. In agreement with previous studies, we found significant diffusion restriction by the mitochondrial outer membrane and confirmed a functional coupling between mitochondria and a fraction of ATPases in the cell. In addition, our experimental data show that considerable activity of endogenous pyruvate kinase (PK) remains in the cardiomyocytes after permeabilization. A fraction of ATPases were inactive without ATP feedback by this endogenous PK. When analyzing the data, we were able to reproduce the measurements only with the mathematical models that include a tight coupling between the fraction of endogenous PK and ATPases. To our knowledge, this is the first time such a strong coupling of PK to ATPases has been demonstrated in permeabilized cardiomyocytes. PMID:20550890

Bound Pool Fractions Complement Diffusion Measures to Describe White Matter Micro and Macrostructure

PubMed Central

Stikov, Nikola; Perry, Lee M.; Mezer, Aviv; Rykhlevskaia, Elena; Wandell, Brian A.; Pauly, John M.; Dougherty, Robert F.

2010-01-01

Diffusion imaging and bound pool fraction (BPF) mapping are two quantitative magnetic resonance imaging techniques that measure microstructural features of the white matter of the brain. Diffusion imaging provides a quantitative measure of the diffusivity of water in tissue. BPF mapping is a quantitative magnetization transfer (qMT) technique that estimates the proportion of exchanging protons bound to macromolecules, such as those found in myelin, and is thus a more direct measure of myelin content than diffusion. In this work, we combine BPF estimates of macromolecular content with measurements of diffusivity within human white matter tracts. Within the white matter, the correlation between BPFs and diffusivity measures such as fractional anisotropy and radial diffusivity was modest, suggesting that diffusion tensor imaging and bound pool fractions are complementary techniques. We found that several major tracts have high BPF, suggesting a higher density of myelin in these tracts. We interpret these results in the context of a quantitative tissue model. PMID:20828622

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

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

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

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

Estimation of the Mean Axon Diameter and Intra-axonal Space Volume Fraction of the Human Corpus Callosum: Diffusion q-space Imaging with Low q-values.

PubMed

Suzuki, Yuriko; Hori, Masaaki; Kamiya, Kouhei; Fukunaga, Issei; Aoki, Shigeki; VAN Cauteren, Marc

2016-01-01

Q-space imaging (QSI) is a diffusion-weighted imaging (DWI) technique that enables investigation of tissue microstructure. However, for sufficient displacement resolution to measure the microstructure, QSI requires high q-values that are usually difficult to achieve with a clinical scanner. The recently introduced "low q-value method" fits the echo attenuation to only low q-values to extract the root mean square displacement. We investigated the clinical feasibility of the low q-value method for estimating the microstructure of the human corpus callosum using a 3.0-tesla clinical scanner within a clinically feasible scan time. We performed a simulation to explore the acceptable range of maximum q-values for the low q-value method. We simulated echo attenuations caused by restricted diffusion in the intra-axonal space (IAS) and hindered diffusion in the extra-axonal space (EAS) assuming 100,000 cylinders with various diameters, and we estimated mean axon diameter, IAS volume fraction, and EAS diffusivity by fitting echo attenuations with different maximum q-values. Furthermore, we scanned the corpus callosum of 7 healthy volunteers and estimated the mean axon diameter and IAS volume fraction. Good agreement between estimated and defined values in the simulation study with maximum q-values of 700 and 800 cm(-1) suggested that the maximum q-value used in the in vivo experiment, 737 cm(-1), was reasonable. In the in vivo experiment, the mean axon diameter was larger in the body of the corpus callosum and smaller in the genu and splenium, and this anterior-to-posterior trend is consistent with previously reported histology, although our mean axon diameter seems larger in size. On the other hand, we found an opposite anterior-to-posterior trend, with high IAS volume fraction in the genu and splenium and a lower fraction in the body, which is similar to the fiber density reported in the histology study. The low q-value method may provide insights into tissue microstructure using a 3T clinical scanner within clinically feasible scan time.

Diverging effects of isotopic fractionation upon molecular diffusion of noble gases in water: mechanistic insights through ab initio molecular dynamics simulations.

PubMed

Pinto de Magalhães, Halua; Brennwald, Matthias S; Kipfer, Rolf

2017-03-22

Atmospheric noble gases are routinely used as natural tracers to analyze gas transfer processes in aquatic systems. Their isotopic ratios can be employed to discriminate between different physical transport mechanisms by comparison to the unfractionated atmospheric isotope composition. In many applications of aquatic systems molecular diffusion was thought to cause a mass dependent fractionation of noble gases and their isotopes according to the square root ratio of their masses. However, recent experiments focusing on isotopic fractionation within a single element challenged this broadly accepted assumption. The determined fractionation factors of Ne, Ar, Kr and Xe isotopes revealed that only Ar follows the prediction of the so-called square root relation, whereas within the Ne, Kr and Xe elements no mass-dependence was found. The reason for this unexpected divergence of Ar is not yet understood. The aim of our computational exercise is to establish the molecular-resolved mechanisms behind molecular diffusion of noble gases in water. We make the hypothesis that weak intermolecular interactions are relevant for the dynamical properties of noble gases dissolved in water. Therefore, we used ab initio molecular dynamics to explicitly account for the electronic degrees of freedom. Depending on the size and polarizability of the hydrophobic particles such as noble gases, their motion in dense and polar liquids like water is subject to different diffusive regimes: the inter-cavity hopping mechanism of small particles (He, Ne) breaks down if a critical particle size achieved. For the case of large particles (Kr, Xe), the motion through the water solvent is governed by mass-independent viscous friction leading to hydrodynamical diffusion. Finally, Ar falls in between the two diffusive regimes, where particle dispersion is propagated at the molecular collision time scale of the surrounding water molecules.

The measurement and analysis of normal incidence solar UVB radiation and its application to the photoclimatherapy protocol for psoriasis at the Dead Sea, Israel.

PubMed

Kudish, Avraham I; Harari, Marco; Evseev, Efim G

2011-01-01

The broad-band normal incidence UVB beam radiation has been measured at Neve Zohar, Dead Sea basin, using a prototype tracking instrument composed of a Model 501A UV-Biometer mounted on an Eppley Solar Tracker Model St-1. The diffuse and beam fraction of the solar global UVB radiation have been determined using the concurrently measured solar global UVB radiation. The diffuse fraction was observed to exceed 80% throughout the year. The application of the results of these measurements to the possible revision of the photoclimatherapy protocol for psoriasis patients at the Dead Sea medical spas is now under investigation. The suggested revision would enable the sun-exposure treatment protocol to take advantage of the very high diffuse fraction by allowing the patient to receive the daily dose of UVB radiation without direct exposure to the sun, viz. receive the diffuse UVB radiation under a sunshade. This would require an increase in sun-exposure time intervals, as the UVB radiation intensity beneath a sunshade is less than that on an exposed surface. © 2010 The Authors. Photochemistry and Photobiology © 2010 The American Society of Photobiology.

Improved quantification of microbial CH4 oxidation efficiency in arctic wetland soils using carbon isotope fractionation

NASA Astrophysics Data System (ADS)

Preuss, I.; Knoblauch, C.; Gebert, J.; Pfeiffer, E.-M.

2013-04-01

Permafrost-affected tundra soils are significant sources of the climate-relevant trace gas methane (CH4). The observed accelerated warming of the arctic will cause deeper permafrost thawing, followed by increased carbon mineralization and CH4 formation in water-saturated tundra soils, thus creating a positive feedback to climate change. Aerobic CH4 oxidation is regarded as the key process reducing CH4 emissions from wetlands, but quantification of turnover rates has remained difficult so far. The application of carbon stable isotope fractionation enables the in situ quantification of CH4 oxidation efficiency in arctic wetland soils. The aim of the current study is to quantify CH4 oxidation efficiency in permafrost-affected tundra soils in Russia's Lena River delta based on stable isotope signatures of CH4. Therefore, depth profiles of CH4 concentrations and δ13CH4 signatures were measured and the fractionation factors for the processes of oxidation (αox) and diffusion (αdiff) were determined. Most previous studies employing stable isotope fractionation for the quantification of CH4 oxidation in soils of other habitats (such as landfill cover soils) have assumed a gas transport dominated by advection (αtrans = 1). In tundra soils, however, diffusion is the main gas transport mechanism and diffusive stable isotope fractionation should be considered alongside oxidative fractionation. For the first time, the stable isotope fractionation of CH4 diffusion through water-saturated soils was determined with an αdiff = 1.001 ± 0.000 (n = 3). CH4 stable isotope fractionation during diffusion through air-filled pores of the investigated polygonal tundra soils was αdiff = 1.013 ± 0.003 (n = 18). Furthermore, it was found that αox differs widely between sites and horizons (mean αox = 1.017 ± 0.009) and needs to be determined on a case by case basis. The impact of both fractionation factors on the quantification of CH4 oxidation was analyzed by considering both the potential diffusion rate under saturated and unsaturated conditions and potential oxidation rates. For a submerged, organic-rich soil, the data indicate a CH4 oxidation efficiency of 50% at the anaerobic-aerobic interface in the upper horizon. The improved in situ quantification of CH4 oxidation in wetlands enables a better assessment of current and potential CH4 sources and sinks in permafrost-affected ecosystems and their potential strengths in response to global warming.

A comprehensive diffusion MRI dataset acquired on the MGH Connectome scanner in a biomimetic brain phantom.

PubMed

Fan, Qiuyun; Nummenmaa, Aapo; Wichtmann, Barbara; Witzel, Thomas; Mekkaoui, Choukri; Schneider, Walter; Wald, Lawrence L; Huang, Susie Y

2018-06-01

We provide a comprehensive diffusion MRI dataset acquired with a novel biomimetic phantom mimicking human white matter. The fiber substrates in the diffusion phantom were constructed from hollow textile axons ("taxons") with an inner diameter of 11.8±1.2 µm and outer diameter of 33.5±2.3 µm. Data were acquired on the 3 T CONNECTOM MRI scanner with multiple diffusion times and multiple q-values per diffusion time, which is a dedicated acquisition for validation of microstructural imaging methods, such as compartment size and volume fraction mapping. Minimal preprocessing was performed to correct for susceptibility and eddy current distortions. Data were deposited in the XNAT Central database (project ID: dMRI_Phant_MGH).

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

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

Diffusion of multi-isotopic chemical species in molten silicates

NASA Astrophysics Data System (ADS)

Watkins, James M.; Liang, Yan; Richter, Frank; Ryerson, Frederick J.; DePaolo, Donald J.

2014-08-01

Diffusion experiments in a simplified Na2O-CaO-SiO2 liquid system are used to develop a general formulation for the fractionation of Ca isotopes during liquid-phase diffusion. Although chemical diffusion is a well-studied process, the mathematical description of the effects of diffusion on the separate isotopes of a chemical element is surprisingly underdeveloped and uncertain. Kinetic theory predicts a mass dependence on isotopic mobility, but it is unknown how this translates into a mass dependence on effective binary diffusion coefficients, or more generally, the chemical diffusion coefficients that are housed in a multicomponent diffusion matrix. Our experiments are designed to measure Ca mobility, effective binary diffusion coefficients, the multicomponent diffusion matrix, and the effects of chemical diffusion on Ca isotopes in a liquid of single composition. We carried out two chemical diffusion experiments and one self-diffusion experiment, all at 1250 °C and 0.7 GPa and using a bulk composition for which other information is available from the literature. The self-diffusion experiment is used to determine the mobility of Ca in the absence of diffusive fluxes of other liquid components. The chemical diffusion experiments are designed to determine the effect on Ca isotope fractionation of changing the counter-diffusing component from fast-diffusing Na2O to slow-diffusing SiO2. When Na2O is the main counter-diffusing species, CaO diffusion is fast and larger Ca isotopic effects are generated. When SiO2 is the main counter-diffusing species, CaO diffusion is slow and smaller Ca isotopic effects are observed. In both experiments, the liquid is initially isotopically homogeneous, and during the experiment Ca isotopes become fractionated by diffusion. The results are used as a test of a new general expression for the diffusion of isotopes in a multicomponent liquid system that accounts for both self diffusion and the effects of counter-diffusing species. Our results show that (1) diffusive isotopic fractionations depend on the direction of diffusion in composition space, (2) diffusive isotopic fractionations scale with effective binary diffusion coefficient, as previously noted by Watkins et al. (2011), (3) self-diffusion is not decoupled from chemical diffusion, (4) self diffusion can be faster than or slower than chemical diffusion and (5) off-diagonal terms in the chemical diffusion matrix have isotopic mass-dependence. The results imply that relatively large isotopic fractionations can be generated by multicomponent diffusion even in the absence of large concentration gradients of the diffusing element. The new formulations for isotope diffusion can be tested with further experimentation and provide an improved framework for interpreting mass-dependent isotopic variations in natural liquids.

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.

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.

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier

NASA Technical Reports Server (NTRS)

Bashford, D.; Weaver, D. L.

1986-01-01

A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.

Thermal and ultrasonic evaluation of porosity in composite laminates

NASA Technical Reports Server (NTRS)

Johnston, Patrick H.; Winfree, William P.; Long, Edward R., Jr.; Kullerd, Susan M.; Nathan, N.; Partos, Richard D.

1992-01-01

The effects of porosity on damage incurred by low-velocity impact are investigated. Specimens of graphite/epoxy composite were fabricated with various volume fractions of voids. The void fraction was independently determined using optical examination and acid resin digestion methods. Thermal diffusivity and ultrasonic attenuation were measured, and these results were related to the void volume fraction. The relationship between diffusivity and fiber volume fraction was also considered. The slope of the ultrasonic attenuation coefficient was found to increase linearly with void content, and the diffusivity decreased linearly with void volume fraction, after compensation for an approximately linear dependence on the fiber volume fraction.

Processes and time scales of magmatic evolution as revealed by Fe-Mg chemical and isotopic zoning in natural olivines

NASA Astrophysics Data System (ADS)

Oeser, Martin; Dohmen, Ralf; Horn, Ingo; Schuth, Stephan; Weyer, Stefan

2015-04-01

In this study, we applied high-precision in situ Fe and Mg isotope analyses by femtosecond laser ablation (fs-LA) MC-ICP-MS on chemically zoned olivine xeno- and phenocrysts from intra-plate volcanic regions in order to investigate the magnitude of Fe and Mg isotope fractionation and its suitability to gain information on magma evolution. Our results show that chemical zoning (i.e., Mg#) in magmatic olivines is commonly associated with significant zoning in δ56Fe and δ26Mg (up to 1.7‰ and 0.7‰, respectively). We explored different cases of kinetic fractionation of Fe and Mg isotopes by modeling diffusion in the melt or olivine and simultaneous growth or dissolution. Combining the information of chemical and isotopic zoning in olivine allows to distinguish between various processes that may occur during magma evolution, namely diffusive Fe-Mg exchange between olivine and melt, rapid crystal growth, and Fe-Mg inter-diffusion simultaneous to crystal dissolution or growth. Chemical diffusion in olivine appears to be the dominant process that drives isotope fractionation in magmatic olivine. Simplified modeling of Fe and Mg diffusion is suitable to reproduce both the chemical and the isotopic zoning in most of the investigated olivines and, additionally, provides time information about magmatic processes. For the Massif Central (France), modeling of diffusive re-equilibration of mantle olivines in basanites revealed a short time span (<2 years) between the entrainment of a mantle xenolith in an intra-plate basaltic magma and the eruption of the magma. Furthermore, we determined high cooling rates (on the order of a few tens to hundreds of °C per year) for basanite samples from a single large outcrop in the Massif Central, which probably reflects the cooling of a massive lava flow after eruption. Results from the modeling of Fe and Mg isotope fractionation in olivine point to a systematic difference between βFe and βMg (i.e., βFe/βMg ≈ 2), implying that the diffusivity ratio of 54Fe and 56Fe (i.e., D54Fe/D56Fe) is very similar to that of 24Mg and 26Mg, despite the smaller relative mass difference for the 54Fe-56Fe pair. This study demonstrates that a combined investigation of Fe-Mg chemical and isotopic zoning in olivine provides additional and more reliable information on magma evolution than chemical zoning alone.

CO Diffusion into Amorphous H2O Ices

NASA Astrophysics Data System (ADS)

Lauck, Trish; Karssemeijer, Leendertjan; Shulenberger, Katherine; Rajappan, Mahesh; Öberg, Karin I.; Cuppen, Herma M.

2015-03-01

The mobility of atoms, molecules, and radicals in icy grain mantles regulates ice restructuring, desorption, and chemistry in astrophysical environments. Interstellar ices are dominated by H2O, and diffusion on external and internal (pore) surfaces of H2O-rich ices is therefore a key process to constrain. This study aims to quantify the diffusion kinetics and barrier of the abundant ice constituent CO into H2O-dominated ices at low temperatures (15-23 K), by measuring the mixing rate of initially layered H2O(:CO2)/CO ices. The mixed fraction of CO as a function of time is determined by monitoring the shape of the infrared CO stretching band. Mixing is observed at all investigated temperatures on minute timescales and can be ascribed to CO diffusion in H2O ice pores. The diffusion coefficient and final mixed fraction depend on ice temperature, porosity, thickness, and composition. The experiments are analyzed by applying Fick’s diffusion equation under the assumption that mixing is due to CO diffusion into an immobile H2O ice. The extracted energy barrier for CO diffusion into amorphous H2O ice is ˜160 K. This is effectively a surface diffusion barrier. The derived barrier is low compared to current surface diffusion barriers in use in astrochemical models. Its adoption may significantly change the expected timescales for different ice processes in interstellar environments.

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.

Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen; Magin, Richard L.

2016-07-01

Analytical solutions to the fractional diffusion equation are often obtained by using Laplace and Fourier transforms, which conveniently encode the order of the time and the space derivatives (α and β) as non-integer powers of the conjugate transform variables (s, and k) for the spectral and the spatial frequencies, respectively. This study presents a new solution to the fractional diffusion equation obtained using the Laplace transform and expressed as a Fox's H-function. This result clearly illustrates the kinetics of the underlying stochastic process in terms of the Laplace spectral frequency and entropy. The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss-Kronrod quadrature algorithm. Here, the properties of spectral entropy are investigated for the cases of sub-diffusion and super-diffusion. We find that the overall spectral entropy decreases with the increasing α and β, and that the normal or Gaussian case with α = 1 and β = 2, has the lowest spectral entropy (i.e., less information is needed to describe the state of a Gaussian process). In addition, as the neighborhood over which the entropy is calculated increases, the spectral entropy decreases, which implies a spatial averaging or coarse graining of the material properties. Consequently, the spectral entropy is shown to provide a new way to characterize the temporal correlation of anomalous diffusion. Future studies should be designed to examine changes of spectral entropy in physical, chemical and biological systems undergoing phase changes, chemical reactions and tissue regeneration.

Lithium isotope fractionation by diffusion in minerals Part 2: Olivine

NASA Astrophysics Data System (ADS)

Richter, Frank; Chaussidon, Marc; Bruce Watson, E.; Mendybaev, Ruslan; Homolova, Veronika

2017-12-01

Recent experiments have shown that lithium isotopes can be significantly fractionated by diffusion in silicate liquids and in augite. Here we report new laboratory experiments that document similarly large lithium isotopic fractionation by diffusion in olivine. Two types of experiments were used. A powder-source method where lithium from finely ground spodumene (LiAlSi2O6) diffused into oriented San Carlos olivine, and piston cylinder annealing experiments where Kunlun clinopyroxene (∼30 ppm lithium) and oriented San Carlos olivine (∼2 ppm lithium) were juxtaposed. The lithium concentration along traverses across the run products was measured using both laser ablation as a source for a Varian 820-MS quadrupole mass spectrometer and a CAMECA 1270 secondary ion mass spectrometer. The CAMECA 1270 was also used to measure the lithium isotopic fractionation across olivine grains recovered from the experiments. The lithium isotopes were found to be fractionationed by many tens of permil in the diffusion boundary layer at the grain edges as a result of 6Li diffusing significantly faster than 7Li. The lithium concentration and isotopic fractionation data across the olivine recovered from the different experiments were modeled using calculations in which lithium was assumed to be of two distinct types - one being fast diffusing interstitial lithium, the other much less mobile lithium on a metal site. The two-site diffusion model involves a large number of independent parameters and we found that different choices of the parameters can produce very comparable fits to the lithium concentration profiles and associated isotopic fractionation. Because of this nonuniqueness we are able to determine only a range for the relative diffusivity of 6Li compared to 7Li. When the mass dependence of lithium diffusion is parameterized as D6Li /D7Li =(7 / 6) β , the isotope fractionation for diffusion along the a and c crystallographic direction of olivine can be fit by β = 0.4 ± 0.1 while the fractionation in the b direction appears to be somewhat lower. Model calculations were also used to fit the lithium concentration and isotopic fractionation across a natural olivine grain from a peridotite xenolith from the Eastern North China Craton. The isotopic data were fit using β values (0.3-0.36) similar to that of the laboratory experiments. This, along with the fact that the isotopic fractionation is restricted to that part of the mineral with a gradient in lithium concentration, is strong evidence that the lithium zoning of this mineral grain is the result of lithium loss by diffusion and thus that it can be used, as illustrated, to constrain the cooling history.

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.

Effects of aging on the fraction distribution and bioavailability of selenium in three different soils.

PubMed

Li, Jun; Peng, Qin; Liang, Dongli; Liang, Sijie; Chen, Juan; Sun, Huan; Li, Shuqi; Lei, Penghui

2016-02-01

Aging refers to the processes by which the mobility and bioavailability of metals in soil decline with time. Although long-term aging is a key process that needs to be considered in risk assessment of metals, few investigations has been attempted to determine whether and how residence time influences the selenium (Se) fractions and bioavailability in soil. In this study, the fractions of Se in soils was evaluated, and bioavailability were assessed by measuring Se concentration in pak choi (Brassica chinensis L.). Results showed that the change of soil available Se in all tested soils divided into two phases: rapid decrease at the initial time (42 d) and slow decline thereafter. The second-order equation could describe the decrease processes of available Se in tested soils during the entire incubation time (R(2) > 0.99), while parabolic diffusion equation had less goodness of fit. Those results indicated that Se aging was controlled not only by diffusion process but also by other processes such as nucleation/precipitation, adsorption/desorption with soil component, occlusion by organic matter and reduction reaction. Soil available Se fractions tended to transform to more stable fractions during aging. The changes of Se concentration in pak choi were consistent with the variation in soil available Se content. In addition, 21 d could be reference for the time of Se aging reaching stabilization in krasnozems and fluvo-aquic soil, and 30 d for black soil. Results could provide theoretical basis to formulate environmental quality criterion and choose the equilibrium time before implementing a pot experiment in Se-spiked soils. Copyright © 2015 Elsevier Ltd. All rights reserved.

An Experimental Investigation of the Laminar Flamelet Concept for Soot Properties

NASA Technical Reports Server (NTRS)

Diez, F. J.; Aalburg, C.; Sunderland, P. B.; Urban, D. L.; Yuan, Z.-G.; Faeth, G. M.

2007-01-01

The soot properties of round, nonbuoyant, laminar jet diffusion flames are described, based on experiments at microgravity carried out on orbit during three flights of the Space Shuttle Columbia, (Flights STS-83, 94 and 107). Experimental conditions included ethylene- and propane-fueled flames burning in still air at an ambient temperature of 300 K and ambient pressures of 35-100 kPa. Measurements included soot volume fraction distributions using deconvoluted laser extinction imaging, and soot temperature distributions using deconvoluted multiline emission imaging. Flowfield modeling based on the work of Spalding is presented. The present work explores whether soot properties of these flames are universal functions of mixture fraction, i.e., whether they satisfy soot state relationships. Measurements are presented, including radiative emissions and distributions of soot temperature and soot volume fraction. It is shown that most of the volume of these flames is bounded by the dividing streamline and thus should follow residence time state relationships. Most streamlines from the fuel supply to the surroundings are found to exhibit nearly the same maximum soot volume fraction and temperature. The radiation intensity along internal streamlines also is found to have relatively uniform values. Finally, soot state relationships were observed, i.e., soot volume fraction was found to correlate with estimated mixture fraction for each fuel/pressure selection. These results support the existence of soot property state relationships for steady nonbuoyant laminar diffusion flames, and thus in a large class of practical turbulent diffusion flames through the application of the laminar flamelet concept.

Improved quantification of microbial CH4 oxidation efficiency in Arctic wetland soils using carbon isotope fractionation

NASA Astrophysics Data System (ADS)

Preuss, I.; Knoblauch, C.; Gebert, J.; Pfeiffer, E.-M.

2012-12-01

Permafrost-affected tundra soils are significant sources of the climate-relevant trace gas methane (CH4). The observed accelerated warming of the Arctic will cause a deeper permafrost thawing followed by increased carbon mineralization and CH4 formation in water saturated tundra soils which might cause a positive feedback to climate change. Aerobic CH4 oxidation is regarded as the key process reducing CH4 emissions from wetlands, but quantification of turnover rates has remained difficult so far. The application of carbon stable isotope fractionation enables the in situ quantification of CH4 oxidation efficiency in arctic wetland soils. The aim of the current study is to quantify CH4 oxidation efficiency in permafrost-affected tundra soils in Russia's Lena River Delta based on stable isotope signatures of CH4. Therefore, depth profiles of CH4 concentrations and δ13CH4-signatures were measured and the fractionation factors for the processes of oxidation (αox) and diffusion (αdiff) were determined. Most previous studies employing stable isotope fractionation for the quantification of CH4 oxidation in soils of other habitats (e.g. landfill cover soils) have assumed a gas transport dominated by advection (αtrans = 1). In tundra soils, however, diffusion is the main gas transport mechanism, aside from ebullition. Hence, diffusive stable isotope fractionation has to be considered. For the first time, the stable isotope fractionation of CH4 diffusion through water-saturated soils was determined with an αdiff = 1.001 ± 0.000 (n = 3). CH4 stable isotope fractionation during diffusion through air-filled pores of the investigated polygonal tundra soils was αdiff = 1.013 ± 0.003 (n = 18). Furthermore, it was found that αox differs widely between sites and horizons (mean αox, = 1.017 ± 0.009) and needs to be determined individually. The impact of both fractionation factors on the quantification of CH4 oxidation was analyzed by considering both the potential diffusion rate under saturated and unsaturated conditions and potential oxidation rates. For a submerged organic rich soil, the data indicate a CH4 oxidation efficiency of 50% at the anaerobic-aerobic interface in the upper horizon. The improved in situ quantification of CH4 oxidation in wetlands enables a better assessment of current and potential CH4 sources and sinks in permafrost affected ecosystems and their potential strengths in response to global warming.

Ion Thermal Decoupling and Species Separation in Shock-Driven Implosions

DOE PAGES

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

2015-01-14

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

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.

Effects of carbon on phosphorus diffusion in SiGe:C and the implications on phosphorus diffusion mechanisms

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

Lin, Yiheng; Xia, Guangrui; Yasuda, Hiroshi

2014-10-14

The use of carbon (C) in SiGe base layers is an important approach to control the base layer dopant phosphorus (P) diffusion and thus enhance PNP heterojunction bipolar transistor (HBT) performance. This work quantitatively investigated the carbon impacts on P diffusion in Si₀.₈₂Ge₀.₁₈:C and Si:C under rapid thermal anneal conditions. The carbon molar fraction is up to 0.32%. The results showed that the carbon retardation effect on P diffusion is less effective for Si₀.₈₂Ge₀.₁₈:C than for Si:C. In Si₀.₈₂Ge₀.₁₈:C, there is an optimum carbon content at around 0.05% to 0.1%, beyond which more carbon incorporation does not retard P diffusionmore » any more. This behavior is different from the P diffusion behavior in Si:C and the B in Si:C and low Ge SiGe:C, which can be explained by the decreased interstitial-mediated diffusion fraction f{sub I}{sup P,SiGe} to 95% as Ge content increases to 18%. Empirical models were established to calculate the time-averaged point defect concentrations and effective diffusivities as a function of carbon and was shown to agree with previous studies on boron, phosphorus, arsenic and antimony diffusion with carbon.« less

Diffusive Fractionation of Lithium Isotopes in Olivine Grain Boundaries

NASA Astrophysics Data System (ADS)

Homolova, V.; Watson, E. B.

2012-12-01

Diffusive fractionation of isotopes has been documented in silicate melts, aqueous fluids, and single crystals. In polycrystalline rocks, the meeting place of two grains, or grain boundaries, may also be a site of diffusive fractionation of isotopes. We have undertaken an experimental and modeling approach to investigate diffusive fractionation of lithium (Li) isotopes by grain boundary diffusion. The experimental procedure consists of packing a Ni metal capsule with predominantly ground San Carlos olivine and subjecting the capsule to 1100C and 1GPa for two days in a piston cylinder apparatus to create a nominally dry, 'dunite rock'. After this synthesis step, the capsule is sectioned and polished. One of the polished faces of the 'dunite rock' is then juxtaposed to a source material of spodumene and this diffusion couple is subject to the same experimental conditions as the synthesis step. Li abundances and isotopic profiles (ratios of count rates) were analyzed using LA-ICP-MS. Li concentrations linearly decrease away from the source from 550ppm to the average concentration of the starting olivine (2.5ppm). As a function of distance from the source, the 7Li/6Li ratio decreases to a minimum before increasing to the background ratio of the 'dunite rock'. The 7Li/6Li ratio minimum coincides with the lowest Li concentrations above average 'dunite rock' abundances. The initial decrease in the 7Li/6Li ratio is similar to that seen in other studies of diffusive fractionation of isotopes and is thought to be caused by the higher diffusivity (D) of the lighter isotope relative to the heavier isotope. The relationship between D and mass (m) is given by (D1/D2) =(m2/m1)^β, where β is an empirical fractionation factor; 1 and 2 denote the lighter and heavier isotope, respectively. A fit to the Li isotopic data reveals an effective DLi of ~1.2x10^-12 m/s^2 and a β of 0.1. Numerical modelling was utilized to elucidate the relationship between diffusive fractionation produced in the grain boundaries versus the lattices of the individual grains of the 'dunite rock'. The model assumes a linear grain boundary juxtaposed to the long side of a rectangular crystal lattice. During a simulation, the diffusant may directly enter the lattice or the grain boundary. Once in the grain boundary, the diffusant may then continue to diffuse away from the source until the end of the simulation or, alternatively, it may be incorporated into the lattice at some point during its travels down the grain boundary. The model system is similar to that considered by Whipple-LeClaire (1963) and our model results agree well with their analytical solution. Preliminary modeling results show that the distinctive minimum in the isotopic ratio is only produced when diffusive fractionation occurs in the grain boundary and not when the fractionation occurs only in the lattice. This suggests that the isotopic profile observed in the experiments may be a product of diffusive fractionation in grain boundaries. Implications of these results extend to the longevity of Li isotopic heterogeneities in the mantle, and suggest that the isotopes of other elements, which have a large relative mass difference, may also be diffusively fractionated by grain boundary diffusion.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Multidiffusion mechanisms for noble gases (He, Ne, Ar) in silicate glasses and melts in the transition temperature domain: Implications for glass polymerization

NASA Astrophysics Data System (ADS)

Amalberti, Julien; Burnard, Pete; Laporte, Didier; Tissandier, Laurent; Neuville, Daniel R.

2016-01-01

Noble gases are ideal probes to study the structure of silicate glasses and melts as the modifications of the silicate network induced by the incorporation of noble gases are negligible. In addition, there are systematic variations in noble gas atomic radii and several noble gas isotopes with which the influence of the network itself on diffusion may be investigated. Noble gases are therefore ideally suited to constrain the time scales of magma degassing and cooling. In order to document noble gas diffusion behavior in silicate glass, we measured the diffusivities of three noble gases (4He, 20Ne and 40Ar) and the isotopic diffusivities of two Ar isotopes (36Ar and 40Ar) in two synthetic basaltic glasses (G1 and G2; 20Ne and 36Ar were only measured in sample G1). These new diffusion results are used to re-interpret time scales of the acquisition of fractionated atmospheric noble gas signatures in pumices. The noble gas bearing glasses were synthesized by exposing the liquids to high noble gas partial pressures at high temperature and pressure (1750-1770 K and 1.2 GPa) in a piston-cylinder apparatus. Diffusivities were measured by step heating the glasses between 423 and 1198 K and measuring the fraction of gas released at each temperature step by noble gas mass spectrometry. In addition we measured the viscosity of G1 between 996 and 1072 K in order to determine the precise glass transition temperature and to estimate network relaxation time scales. The results indicate that, to a first order, that the smaller the size of the diffusing atom, the greater its diffusivity at a given temperature: D(He) > D(Ne) > D(Ar) at constant T. Significantly, the diffusivities of the noble gases in the glasses investigated do not display simple Arrhenian behavior: there are well-defined departures from Arrhenian behavior which occur at lower temperatures for He than for Ne or Ar. We propose that the non-Arrhenian behavior of noble gases can be explained by structural modifications of the silicate network itself as the glass transition temperature is approached: as the available free volume (available site for diffusive jumps) is modified, noble gas diffusion is no longer solely temperature-activated but also becomes sensitive to the kinetics of network rearrangements. The non-Arrhenian behavior of noble gas diffusion close to Tg is well described by a modified Vogel-Tammann-Fulcher (VTF) equation: Finally, our step heating diffusion experiments suggest that at T close to Tg, noble gas isotopes may suffer kinetic fractionation at a degree larger than that predicted by Graham's law. In the case of 40Ar and 36Ar, the traditional assumption based on Graham's law is that the ratio D40Ar/D36Ar should be equal to 0.95 (the square root of the ratio of the mass of 36Ar over the mass of 40Ar). In our experiment with glass G1, D40Ar/D36Ar rapidly decreased with decreasing temperature, from near unity (0.98 ± 0.14) at T > 1040 K to 0.76 when close to Tg (T = 1003 K). Replicate experiments are needed to confirm the strong kinetic fractionation of heavy noble gases close to the transition temperature.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Thermal Diffusivity and Thermal Conductivity of Dispersed Glass Sphere Composites Over a Range of Volume Fractions

NASA Astrophysics Data System (ADS)

Carson, James K.

2018-06-01

Glass spheres are often used as filler materials for composites. Comparatively few articles in the literature have been devoted to the measurement or modelling of thermal properties of composites containing glass spheres, and there does not appear to be any reported data on the measurement of thermal diffusivities over a range of filler volume fractions. In this study, the thermal diffusivities of guar-gel/glass sphere composites were measured using a transient comparative method. The addition of the glass beads to the gel increased the thermal diffusivity of the composite, more than doubling the thermal diffusivity of the composite relative to the diffusivity of the gel at the maximum glass volume fraction of approximately 0.57. Thermal conductivities of the composites were derived from the thermal diffusivity measurements, measured densities and estimated specific heat capacities of the composites. Two approaches to modelling the effective thermal diffusivity were considered.

MRI quantification of diffusion and perfusion in bone marrow by intravoxel incoherent motion (IVIM) and non-negative least square (NNLS) analysis.

PubMed

Marchand, A J; Hitti, E; Monge, F; Saint-Jalmes, H; Guillin, R; Duvauferrier, R; Gambarota, G

2014-11-01

To assess the feasibility of measuring diffusion and perfusion fraction in vertebral bone marrow using the intravoxel incoherent motion (IVIM) approach and to compare two fitting methods, i.e., the non-negative least squares (NNLS) algorithm and the more commonly used Levenberg-Marquardt (LM) non-linear least squares algorithm, for the analysis of IVIM data. MRI experiments were performed on fifteen healthy volunteers, with a diffusion-weighted echo-planar imaging (EPI) sequence at five different b-values (0, 50, 100, 200, 600 s/mm2), in combination with an STIR module to suppress the lipid signal. Diffusion signal decays in the first lumbar vertebra (L1) were fitted to a bi-exponential function using the LM algorithm and further analyzed with the NNLS algorithm to calculate the values of the apparent diffusion coefficient (ADC), pseudo-diffusion coefficient (D*) and perfusion fraction. The NNLS analysis revealed two diffusion components only in seven out of fifteen volunteers, with ADC=0.60±0.09 (10(-3) mm(2)/s), D*=28±9 (10(-3) mm2/s) and perfusion fraction=14%±6%. The values obtained by the LM bi-exponential fit were: ADC=0.45±0.27 (10(-3) mm2/s), D*=63±145 (10(-3) mm2/s) and perfusion fraction=27%±17%. Furthermore, the LM algorithm yielded values of perfusion fraction in cases where the decay was not bi-exponential, as assessed by NNLS analysis. The IVIM approach allows for measuring diffusion and perfusion fraction in vertebral bone marrow; its reliability can be improved by using the NNLS, which identifies the diffusion decays that display a bi-exponential behavior. Copyright © 2014 Elsevier Inc. All rights reserved.

Diffusion-driven magnesium and iron isotope fractionation at a gabbro-granite boundary

NASA Astrophysics Data System (ADS)

Wu, Hongjie; He, Yongsheng; Teng, Fang-Zhen; Ke, Shan; Hou, Zhenhui; Li, Shuguang

2018-02-01

Significant magnesium and iron isotope fractionations were observed in an adjacent gabbro and granite profile from the Dabie Orogen, China. Chilled margin and granitic veins at the gabbro side and gabbro xenoliths in the granite indicate the two intrusions were emplaced simultaneously. The δ26Mg decreases from -0.28 ± 0.04‰ to -0.63 ± 0.08‰ and δ56Fe increases from -0.07 ± 0.03‰ to +0.25 ± 0.03‰ along a ∼16 cm traverse from the contact to the granite. Concentrations of major elements such as Al, Na, Ti and most trace elements also systematically change with distance to the contact. All the observations suggest that weathering, magma mixing, fluid exsolution, fractional crystallization and thermal diffusion are not the major processes responsible for the observed elemental and isotopic variations. Rather, the negatively correlated Mg and Fe isotopic compositions as well as co-variations of Mg and Fe isotopes with Mg# reflect Mg-Fe inter-diffusion driven isotope fractionation, with Mg diffusing from the chilled gabbro into the granitic melt and Fe oppositely. The diffusion modeling yields a characteristic diffusive transport distance of ∼6 cm. Consequently, the diffusion duration, during which the granite may have maintained a molten state, can be constrained to ∼2 My. The cooling rate of the granite is calculated to be 52-107 °C/My. Our study suggests diffusion profiles can be a powerful geospeedometry. The observed isotope fractionations also indicate that Mg-Fe inter-diffusion can produce large stable isotope fractionations at least on a decimeter scale, with implications for Mg and Fe isotope study of mantle xenoliths, mafic dikes, and inter-bedded lavas.

Relationship between the anomalous diffusion and the fractal dimension of the environment

NASA Astrophysics Data System (ADS)

Zhokh, Alexey; Trypolskyi, Andrey; Strizhak, Peter

2018-03-01

In this letter, we provide an experimental study highlighting a relation between the anomalous diffusion and the fractal dimension of the environment using the methanol anomalous transport through the porous solid pellets with various pores geometries and different chemical compositions. The anomalous diffusion exponent was derived from the non-integer order of the time-fractional diffusion equation that describes the methanol anomalous transport through the solid media. The surface fractal dimension was estimated from the nitrogen adsorption isotherms using the Frenkel-Halsey-Hill method. Our study shows that decreasing the fractal dimension leads to increasing the anomalous diffusion exponent, whereas the anomalous diffusion constant is independent on the fractal dimension. We show that the obtained results are in a good agreement with the anomalous diffusion model on a fractal mesh.

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.

Quantitative MRI in hypomyelinating disorders: Correlation with motor handicap.

PubMed

Steenweg, Marjan E; Wolf, Nicole I; van Wieringen, Wessel N; Barkhof, Frederik; van der Knaap, Marjo S; Pouwels, Petra J W

2016-08-23

To assess the correlation of tissue parameters estimated by quantitative magnetic resonance (MR) techniques and motor handicap in patients with hypomyelination. Twenty-eight patients with different causes of hypomyelination (12 males, 16 females; mean age 10 years) and 61 controls (33 males, 28 females; mean age 8 years) were prospectively investigated. We quantified T2 relaxation time, magnetization transfer ratio, fractional anisotropy, mean, axial, and radial diffusivities, and brain metabolites. We performed measurements in the splenium, parietal deep white matter, and corticospinal tracts in the centrum semiovale. We further analyzed diffusion measures using tract-based spatial statistics. We estimated severity of motor handicap by the gross motor function classification system. We evaluated correlation of handicap with MR measures by linear regression analyses. Fractional anisotropy, magnetization transfer ratio, choline, and N-acetylaspartate/creatine ratio were lower and diffusivities, T2 values, and inositol were higher in patients than in controls. Tract-based spatial statistics showed that these changes were widespread for fractional anisotropy (96% of the white matter skeleton), radial (93%) and mean (84%) diffusivity, and less so for axial diffusivity (20%). Correlation with handicap yielded radial diffusivity and N-acetylaspartate/creatine ratio as strongest independent explanatory variables. Gross motor function classification system grades are in part explained by MR measures. They indicate that mainly lack of myelin and, to a lesser degree, loss of axonal integrity codetermine the degree of motor handicap in patients with hypomyelinating disorders. These MR measures can be used to evaluate strategies that are aimed at promotion of myelination. © 2016 American Academy of Neurology.

Effects of C/O Ratio and Temperature on Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Sunderland, P. B.; Chao, B. H.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2008-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, residence time and scalar dissipation rate. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with scalar dissipation rate lower than 2/s were found to have temperatures near 1400 K where C/O = 0.51, whereas flames with greater scalar dissipation rate required increased temperatures. This finding was valid across a broad range of fuel and oxidizer compositions and convection directions.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

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

DOE PAGES

Cao, Boqiang; Zhang, Qimin; Ye, Ming

2016-11-29

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

Chemical and isotopic fractionations by evaporation and their cosmochemical implications

NASA Astrophysics Data System (ADS)

Ozawa, Kazuhito; Nagahara, Hiroko

2001-07-01

A kinetic model for evaporation of a multi-component condensed phase with a fixed rate constant of the reaction is developed. A binary system with two isotopes for one of the components undergoing simple thermal histories (e.g., isothermal heating) is investigated in order to evaluate the extent of isotopic and chemical fractionations during evaporation. Diffusion in the condensed phase and the effect of back reaction from ambient gas are taken into consideration. Chemical and isotopic fractionation factors and the Péclet number for evaporation are the three main parameters that control the fractionation. Dust enrichment factor (η), the ratio of the initial dust quantity to that required for attainment of gas-dust equilibrium, is critical when back reactions become significant. Dust does not reach equilibrium with gas at η < 1. Notable chemical and isotopic fractionations usually take place under these conditions. There are two circumstances in which isotopic fractionation of a very volatile element does not accompany chemical fractionation during isothermal heating. One is free evaporation when diffusion in the condensed phase is very slow (η = 0), and the other is evaporation in the presence of ambient gas (η > 0). In the former case, a quasi-steady state in the diffusion boundary layer is maintained for isotopic fractionation but not for chemical fractionation. In the latter case, the back reaction brings the strong isotopic fractionation generated in the earlier stage of evaporation back to a negligibly small value in the later stage before complete evaporation. The model results are applied to cosmochemical fractionation of volatile elements during evaporation from a condensed phase that can be regarded as a binary solution phase. The wide range of potassium depletion without isotopic fractionation in various types of chondrules (Alexander et al., 2000) is explained by instantaneous heating followed by cooling in a closed system with various degrees of dust enrichment (η = 0.001-10) and cooling rates of less than ˜5°C/min. The extent of decoupling between isotopic and chemical fractionations of various elements in chondrules and matrix minerals may constrain the time scale and the conditions of heating and cooling processes in the early solar nebula.

On the diffuse fraction of daily and monthly global radiation for the island of Cyprus

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

Jacovides, C.P.; Hadjioannou, L.; Pashiardis, S.

1996-06-01

Six years of hourly global and diffuse irradiation measurements on a horizontal surface performed at Athalassa, Cyprus, are used to establish a relationship between the daily diffuse fraction and the daily clearness index. Two types of correlations - yearly and seasonal - have been developed. These correlations, of first and third order in the clearness index are compared to the various correlations established by Collares-Pereira and Rabl (1979), Newland (1989), Erbs et al. (1982), Rao et al. (1984), Page (1961), Liu and Jordan (1960) and Lalas et al. (1987). The comparison has been performed in terms of the widely usedmore » statistical indicators (MBE) and (RMSE) errors; and additional statistical indicator, the t-statistic, combining the earlier indicators, is introduced. The results indicate that the proposed yearly correlation matches the earlier correlations quite closely and all correlations examined yield results that are statistically significant. For large K{sub t} > 0.60 values, most of the earlier correlations exhibit a slight tendency to systematically overestimate the diffuse fraction. This marginal disagreement between the earlier correlations and the proposed model is probably significantly affected by the clear sky conditions that prevail over Cyprus for most of the time as well as atmospheric humidity content. It is clear that the standard correlations examined in this analysis appear to be location-independent models for diffuse irradiation predictions, at least for the Cyprus case. 13 refs., 5 figs., 4 tabs.« less

Air-Parcel Residence Times Within Forest Canopies

NASA Astrophysics Data System (ADS)

Gerken, Tobias; Chamecki, Marcelo; Fuentes, Jose D.

2017-10-01

We present a theoretical model, based on a simple model of turbulent diffusion and first-order chemical kinetics, to determine air-parcel residence times and the out-of-canopy export of reactive gases emitted within forest canopies under neutral conditions. Theoretical predictions of the air-parcel residence time are compared to values derived from large-eddy simulation for a range of canopy architectures and turbulence levels under neutral stratification. Median air-parcel residence times range from a few sec in the upper canopy to approximately 30 min near the ground and the distribution of residence times is skewed towards longer times in the lower canopy. While the predicted probability density functions from the theoretical model and large-eddy simulation are in good agreement with each other, the theoretical model requires only information on canopy height and eddy diffusivities inside the canopy. The eddy-diffusivity model developed additionally requires the friction velocity at canopy top and a parametrized profile of the standard deviation of vertical velocity. The theoretical model of air-parcel residence times is extended to include first-order chemical reactions over a range of of Damköhler numbers ( Da) characteristic of plant-emitted hydrocarbons. The resulting out-of-canopy export fractions range from near 1 for Da =10^{-3} to less than 0.3 at Da = 10. These results highlight the necessity for dense and tall forests to include the impacts of air-parcel residence times when calculating the out-of-canopy export fraction for reactive trace gases.

Continuous time anomalous diffusion in a composite medium.

PubMed

Stickler, B A; Schachinger, E

2011-08-01

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

Activated dynamics in dense fluids of attractive nonspherical particles. II. Elasticity, barriers, relaxation, fragility, and self-diffusion

NASA Astrophysics Data System (ADS)

Tripathy, Mukta; Schweizer, Kenneth S.

2011-04-01

In paper II of this series we apply the center-of-mass version of Nonlinear Langevin Equation theory to study how short-range attractive interactions influence the elastic shear modulus, transient localization length, activated dynamics, and kinetic arrest of a variety of nonspherical particle dense fluids (and the spherical analog) as a function of volume fraction and attraction strength. The activation barrier (roughly the natural logarithm of the dimensionless relaxation time) is predicted to be a rich function of particle shape, volume fraction, and attraction strength, and the dynamic fragility varies significantly with particle shape. At fixed volume fraction, the barrier grows in a parabolic manner with inverse temperature nondimensionalized by an onset value, analogous to what has been established for thermal glass-forming liquids. Kinetic arrest boundaries lie at significantly higher volume fractions and attraction strengths relative to their dynamic crossover analogs, but their particle shape dependence remains the same. A limited universality of barrier heights is found based on the concept of an effective mean-square confining force. The mean hopping time and self-diffusion constant in the attractive glass region of the nonequilibrium phase diagram is predicted to vary nonmonotonically with attraction strength or inverse temperature, qualitatively consistent with recent computer simulations and colloid experiments.

The isotope mass effect on chlorine diffusion in dacite melt, with implications for fractionation during bubble growth

NASA Astrophysics Data System (ADS)

Fortin, Marc-Antoine; Watson, E. Bruce; Stern, Richard

2017-12-01

Previous experimental studies have revealed that the difference in diffusivity of two isotopes can be significant in some media and can lead to an observable fractionation effect in silicate melts based on isotope mass. Here, we report the first characterization of the difference in diffusivities of stable isotopes of Cl (35Cl and 37Cl). Using a piston-cylinder apparatus, we generated quenched melts of dacitic composition enriched in Cl; from these we fabricated diffusion couples in which Cl atoms were induced to diffuse in a chemical gradient at 1200 to 1350 °C and 1 GPa. We analyzed the run products by secondary ion mass spectrometry (SIMS) for their isotopic compositions along the diffusion profiles, and we report a diffusivity ratio for 37Cl/35Cl of 0.995 ± 0.001 (β = 0.09 ± 0.02). No significant effect of temperature on the diffusivity ratio was discernable over the 150 °C range covered by our experiments. The observed 0.5% difference in diffusivity of the two isotopes could affect our interpretation of isotopic measurements of Cl isotopes in bubble-bearing or degassed magmas, because bubble growth is regulated in part by the diffusive supply of volatiles to the bubble from the surrounding melt. Through numerical simulations, we constrain the extent of Cl isotopic fractionation between bubble and host melt during this process. Bubble growth rates vary widely in nature-which implies a substantial range in the expected magnitude of isotopic fractionation-but plausible growth scenarios lead to Cl isotopic fractionations up to about 5‰ enrichment of 35Cl relative to 37Cl in the bubble. This effect should be considered when interpreting Cl isotopic measurements of systems that have experienced vapor exsolution.

Soot volume fraction fields in unsteady axis-symmetric flames by continuous laser extinction technique.

PubMed

Kashif, Muhammad; Bonnety, Jérôme; Guibert, Philippe; Morin, Céline; Legros, Guillaume

2012-12-17

A Laser Extinction Method has been set up to provide two-dimensional soot volume fraction field time history at a tunable frequency up to 70 Hz inside an axis-symmetric diffusion flame experiencing slow unsteady phenomena preserving the symmetry. The use of a continuous wave laser as the light source enables this repetition rate, which is an incremental advance in the laser extinction technique. The technique is shown to allow a fine description of the soot volume fraction field in a flickering flame exhibiting a 12.6 Hz flickering phenomenon. Within this range of repetition rate, the technique and its subsequent post-processing require neither any method for time-domain reconstruction nor any correction for energy intrusion. Possibly complemented by such a reconstruction method, the technique should support further soot volume fraction database in oscillating flames that exhibit characteristic times relevant to the current efforts in the validation of soot processes modeling.

First passage times for a tracer particle in single file diffusion and fractional Brownian motion.

PubMed

Sanders, Lloyd P; Ambjörnsson, Tobias

2012-05-07

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-defined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. Extensive stochastic (non-Markovian) SFD and fBm simulations are performed and compared to two analytical Markovian techniques: the method of images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-time power-law exponent, when H ≥ 1/3, as predicted by Molchan [Commun. Math. Phys. 205, 97 (1999)] for fBm. When H < 1/3, which includes homogeneous SFD (H = 1/4), and heterogeneous SFD (H < 1/4), the WFA fails to agree with any temporal scale of the simulations and Molchan's long-time result. SFD systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.

Identify source location and release time for pollutants undergoing super-diffusion and decay: Parameter analysis and model evaluation

NASA Astrophysics Data System (ADS)

Zhang, Yong; Sun, HongGuang; Lu, Bingqing; Garrard, Rhiannon; Neupauer, Roseanna M.

2017-09-01

Backward models have been applied for four decades by hydrologists to identify the source of pollutants undergoing Fickian diffusion, while analytical tools are not available for source identification of super-diffusive pollutants undergoing decay. This technical note evaluates analytical solutions for the source location and release time of a decaying contaminant undergoing super-diffusion using backward probability density functions (PDFs), where the forward model is the space fractional advection-dispersion equation with decay. Revisit of the well-known MADE-2 tracer test using parameter analysis shows that the peak backward location PDF can predict the tritium source location, while the peak backward travel time PDF underestimates the tracer release time due to the early arrival of tracer particles at the detection well in the maximally skewed, super-diffusive transport. In addition, the first-order decay adds additional skewness toward earlier arrival times in backward travel time PDFs, resulting in a younger release time, although this impact is minimized at the MADE-2 site due to tritium's half-life being relatively longer than the monitoring period. The main conclusion is that, while non-trivial backward techniques are required to identify pollutant source location, the pollutant release time can and should be directly estimated given the speed of the peak resident concentration for super-diffusive pollutants with or without decay.

Investigating the capability to resolve complex white matter structures with high b-value diffusion magnetic resonance imaging on the MGH-USC Connectom scanner.

PubMed

Fan, Qiuyun; Nummenmaa, Aapo; Witzel, Thomas; Zanzonico, Roberta; Keil, Boris; Cauley, Stephen; Polimeni, Jonathan R; Tisdall, Dylan; Van Dijk, Koene R A; Buckner, Randy L; Wedeen, Van J; Rosen, Bruce R; Wald, Lawrence L

2014-11-01

One of the major goals of the NIH Blueprint Human Connectome Project was to map and quantify the white matter connections in the brain using diffusion tractography. Given the prevalence of complex white matter structures, the capability of resolving local white matter geometries with multiple crossings in the diffusion magnetic resonance imaging (dMRI) data is critical. Increasing b-value has been suggested for delineation of the finer details of the orientation distribution function (ODF). Although increased gradient strength and duration increase sensitivity to highly restricted intra-axonal water, gradient strength limitations require longer echo times (TE) to accommodate the increased diffusion encoding times needed to achieve a higher b-value, exponentially lowering the signal-to-noise ratio of the acquisition. To mitigate this effect, the MGH-USC Connectom scanner was built with 300 mT/m gradients, which can significantly reduce the TE of high b-value diffusion imaging. Here we report comparisons performed across b-values based on q-ball ODF metrics to investigate whether high b-value diffusion imaging on the Connectom scanner can improve resolving complex white matter structures. The q-ball ODF features became sharper as the b-value increased, with increased power fraction in higher order spherical harmonic series of the ODF and increased peak heights relative to the overall size of the ODF. Crossing structures were detected in an increasingly larger fraction of white matter voxels and the spatial distribution of two-way and three-way crossing structures was largely consistent with known anatomy. Results indicate that dMRI with high diffusion encoding on the Connectom system is a promising tool to better characterize, and ultimately understand, the underlying structural organization and motifs in the human brain.

Structure-specific magnetic field inhomogeneities and its effect on the correlation time.

PubMed

Ziener, Christian H; Bauer, Wolfgang R; Melkus, Gerd; Weber, Thomas; Herold, Volker; Jakob, Peter M

2006-12-01

We describe the relationship between the correlation time and microscopic spatial inhomogeneities in the static magnetic field. The theory takes into account diffusion of nuclear spins in the inhomogeneous field created by magnetized objects. A simple general expression for the correlation time is obtained. It is shown that the correlation time is dependent on a characteristic length, the diffusion coefficient of surrounding medium, the permeability of the surface and the volume fraction of the magnetized objects. For specific geometries (spheres and cylinders), exact analytical expressions for the correlation time are given. The theory can be applied to contrast agents (magnetically labeled cells), capillary network, BOLD effect and so forth.

Density-driven transport of gas phase chemicals in unsaturated soils

NASA Astrophysics Data System (ADS)

Fen, Chiu-Shia; Sun, Yong-tai; Cheng, Yuen; Chen, Yuanchin; Yang, Whaiwan; Pan, Changtai

2018-01-01

Variations of gas phase density are responsible for advective and diffusive transports of organic vapors in unsaturated soils. Laboratory experiments were conducted to explore dense gas transport (sulfur hexafluoride, SF6) from different source densities through a nitrogen gas-dry soil column. Gas pressures and SF6 densities at transient state were measured along the soil column for three transport configurations (horizontal, vertically upward and vertically downward transport). These measurements and others reported in the literature were compared with simulation results obtained from two models based on different diffusion approaches: the dusty gas model (DGM) equations and a Fickian-type molar fraction-based diffusion expression. The results show that the DGM and Fickian-based models predicted similar dense gas density profiles which matched the measured data well for horizontal transport of dense gas at low to high source densities, despite the pressure variations predicted in the soil column were opposite to the measurements. The pressure evolutions predicted by both models were in trend similar to the measured ones for vertical transport of dense gas. However, differences between the dense gas densities predicted by the DGM and Fickian-based models were discernible for vertically upward transport of dense gas even at low source densities, as the DGM-based predictions matched the measured data better than the Fickian results did. For vertically downward transport, the dense gas densities predicted by both models were not greatly different from our experimental measurements, but substantially greater than the observations obtained from the literature, especially at high source densities. Further research will be necessary for exploring factors affecting downward transport of dense gas in soil columns. Use of the measured data to compute flux components of SF6 showed that the magnitudes of diffusive flux component based on the Fickian-type diffusion expressions in terms of molar concentration, molar fraction and mass density fraction gradient were almost the same. However, they were greater than the result computed with the mass fraction gradient for > 24% and the DGM-based result for more than one time. As a consequence, the DGM-based total flux of SF6 was in magnitude greatly less than the Fickian result not only for horizontal transport (diffusion-dominating) but also for vertical transport (advection and diffusion) of dense gas. Particularly, the Fickian-based total flux was more than two times in magnitude as much as the DGM result for vertically upward transport of dense gas.

Brain aging in humans, chimpanzees (Pan troglodytes), and rhesus macaques (Macaca mulatta): magnetic resonance imaging studies of macro- and microstructural changes

PubMed Central

Chen, Xu; Errangi, Bhargav; Li, Longchuan; Glasser, Matthew F.; Westlye, Lars T.; Fjell, Anders M.; Walhovd, Kristine B.; Hu, Xiaoping; Herndon, James G.; Preuss, Todd M.; Rilling, James K.

2013-01-01

Among primates, humans are uniquely vulnerable to many age-related neurodegenerative disorders. We used structural and diffusion magnetic resonance imaging (MRI) to examine the brains of chimpanzees and rhesus monkeys across each species' adult lifespan, and compared these results with published findings in humans. As in humans, gray matter volume decreased with age in chimpanzees and rhesus monkeys. Also like humans, chimpanzees showed a trend for decreased white matter volume with age, but this decrease occurred proportionally later in the chimpanzee lifespan than in humans. Diffusion MRI revealed widespread age-related decreases in fractional anisotropy and increases in radial diffusivity in chimpanzees and macaques. However, both the fractional anisotropy decline and the radial diffusivity increase started at a proportionally earlier age in humans than in chimpanzees. Thus, even though overall patterns of gray and white matter aging are similar in humans and chimpanzees, the longer lifespan of humans provides more time for white matter to deteriorate before death, with the result that some neurological effects of aging may be exacerbated in our species. PMID:23623601

Effect of diffusion annealing regimes on the structure of Nb3Sn layers in ITER-type bronze-processed wires

NASA Astrophysics Data System (ADS)

Valova-Zaharevskaya, E. G.; Popova, E. N.; Deryagina, I. L.; Abdyukhanov, I. M.; Tsapleva, A. S.

2018-03-01

The goal of the present study is to characterize the growth kinetics and structural parameters of the Nb3Sn layers formed under various regimes of the diffusion annealing of bronze-processed Nb/Cu-Sn composites. The structure of the superconducting layers is characterized by their thickness, average size of equiaxed grains and by the ratio of fractions of columnar and equiaxed grains. It was found that at higher diffusion annealing temperatures (above 650°C) thicker superconducting layers are obtained, but the average sizes of equiaxed Nb3Sn grains even under short exposures (10 h) are much larger than after the long low-temperature annealing. At the low-temperature (575 °C) annealing the relative fraction of columnar grains increases with increasing annealing time. Based on the data obtained, optimal regimes of the diffusion annealing can be chosen, which would on the one hand ensure complete transformation of Nb into Nb3Sn of close to the stoichiometric composition, and on the other hand prevent the formation of coarse and columnar grains.

Communication: Probing anomalous diffusion in frequency space

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

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

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

A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-03-01

Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag-Leffler function as the structural function, in which the MSD is a function of inverse Mittag-Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag-Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.

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

NASA Astrophysics Data System (ADS)

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

2011-12-01

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

Isotopic fractionation of gases during its migration: experiments and 2D numerical simulation

NASA Astrophysics Data System (ADS)

Kara, S.; Prinzhofer, A.

2003-04-01

Several works have been developed in the last decade on the experimental isotope fractionation of gases during migration (Prinzhofer et al., 1997 and Zhang &Krooss, 2001 among others). We add to these results new experiments on diffusion of CO_2, which becomes currently a crucial subject for environmental purpose. Our experiments showed that transport by diffusion of CO_2 through a water saturated shale induces a significant and systematic carbon isotopic fractionation with heavier (13C enriched) CO_2 migrating first. In all experiments, significant isotope fractionation was found but still remains without quantitative interpretation. To interpret these data, we developed a 2D numerical model at the pore scale. The general principle of this model is the study of transport by water solubilization/diffusion of gas in a capillary saturated with water with two different media : a mobile zone representing free water and a immobile zone representing bounded water. The model takes also into account solubilization coefficients of gas in water, as well as the migration distance and the volume of upstream and downstream reservoirs. Using our numerical model, we could reproduce the evolution of isotopic fractionations and the velocity of CO_2 migration versus the production factor F (proportion of diffused gas). We determined some physical parameters of the porous medium (bentonite) which are not directly measurable at the present time. Furthermore, we used these parameters to reproduce the curves of isotopic fractionation obtained by Pernaton (1998) on methane migration with the same porous rock. We used also a modified version of this model with infinite reservoirs to reproduce the curves of isotopic fractionation of Zhang &Krooss (2001). Application of this model to geological scale is under progress, in order to implement it into sedimentary basins modelling. REFERENCES: Zhang T. and Krooss M. (2001). Geochim. Cosmochim. Acta, Vol. 65, No.16, pp. 2723-2742. Pernaton E. (1998) PhD. Thesis, Université de Paris VII, 272 pp. Prinzhofer A. and Pernaton E. (1997) Chem. Geol., vol. 142, 193-200.

In vivo quantification of demyelination and recovery using compartment-specific diffusion MRI metrics validated by electron microscopy.

PubMed

Jelescu, Ileana O; Zurek, Magdalena; Winters, Kerryanne V; Veraart, Jelle; Rajaratnam, Anjali; Kim, Nathanael S; Babb, James S; Shepherd, Timothy M; Novikov, Dmitry S; Kim, Sungheon G; Fieremans, Els

2016-05-15

There is a need for accurate quantitative non-invasive biomarkers to monitor myelin pathology in vivo and distinguish myelin changes from other pathological features including inflammation and axonal loss. Conventional MRI metrics such as T2, magnetization transfer ratio and radial diffusivity have proven sensitivity but not specificity. In highly coherent white matter bundles, compartment-specific white matter tract integrity (WMTI) metrics can be directly derived from the diffusion and kurtosis tensors: axonal water fraction, intra-axonal diffusivity, and extra-axonal radial and axial diffusivities. We evaluate the potential of WMTI to quantify demyelination by monitoring the effects of both acute (6weeks) and chronic (12weeks) cuprizone intoxication and subsequent recovery in the mouse corpus callosum, and compare its performance with that of conventional metrics (T2, magnetization transfer, and DTI parameters). The changes observed in vivo correlated with those obtained from quantitative electron microscopy image analysis. A 6-week intoxication produced a significant decrease in axonal water fraction (p<0.001), with only mild changes in extra-axonal radial diffusivity, consistent with patchy demyelination, while a 12-week intoxication caused a more marked decrease in extra-axonal radial diffusivity (p=0.0135), consistent with more severe demyelination and clearance of the extra-axonal space. Results thus revealed increased specificity of the axonal water fraction and extra-axonal radial diffusivity parameters to different degrees and patterns of demyelination. The specificities of these parameters were corroborated by their respective correlations with microstructural features: the axonal water fraction correlated significantly with the electron microscopy derived total axonal water fraction (ρ=0.66; p=0.0014) but not with the g-ratio, while the extra-axonal radial diffusivity correlated with the g-ratio (ρ=0.48; p=0.0342) but not with the electron microscopy derived axonal water fraction. These parameters represent promising candidates as clinically feasible biomarkers of demyelination and remyelination in the white matter. Copyright © 2016 Elsevier Inc. All rights reserved.

Backstepping-based boundary control design for a fractional reaction diffusion system with a space-dependent diffusion coefficient.

PubMed

Chen, Juan; Cui, Baotong; Chen, YangQuan

2018-06-11

This paper presents a boundary feedback control design for a fractional reaction diffusion (FRD) system with a space-dependent (non-constant) diffusion coefficient via the backstepping method. The contribution of this paper is to generalize the results of backstepping-based boundary feedback control for a FRD system with a space-independent (constant) diffusion coefficient to the case of space-dependent diffusivity. For the boundary stabilization problem of this case, a designed integral transformation treats it as a problem of solving a hyperbolic partial differential equation (PDE) of transformation's kernel, then the well posedness of the kernel PDE is solved for the plant with non-constant diffusivity. Furthermore, by the fractional Lyapunov stability (Mittag-Leffler stability) theory and the backstepping-based boundary feedback controller, the Mittag-Leffler stability of the closed-loop FRD system with non-constant diffusivity is proved. Finally, an extensive numerical example for this closed-loop FRD system with non-constant diffusivity is presented to verify the effectiveness of our proposed controller. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

Computing diffuse fraction of global horizontal solar radiation: A model comparison.

PubMed

Dervishi, Sokol; Mahdavi, Ardeshir

2012-06-01

For simulation-based prediction of buildings' energy use or expected gains from building-integrated solar energy systems, information on both direct and diffuse component of solar radiation is necessary. Available measured data are, however, typically restricted to global horizontal irradiance. There have been thus many efforts in the past to develop algorithms for the derivation of the diffuse fraction of solar irradiance. In this context, the present paper compares eight models for estimating diffuse fraction of irradiance based on a database of measured irradiance from Vienna, Austria. These models generally involve mathematical formulations with multiple coefficients whose values are typically valid for a specific location. Subsequent to a first comparison of these eight models, three better performing models were selected for a more detailed analysis. Thereby, the coefficients of the models were modified to account for Vienna data. The results suggest that some models can provide relatively reliable estimations of the diffuse fractions of the global irradiance. The calibration procedure could only slightly improve the models' performance.

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

PubMed

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

2017-02-01

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

Comparisons among MRI signs, apparent diffusion coefficient, and fractional anisotropy in dogs with a solitary intracranial meningioma or histiocytic sarcoma.

PubMed

Wada, Masae; Hasegawa, Daisuke; Hamamoto, Yuji; Yu, Yoshihiko; Fujiwara-Igarashi, Aki; Fujita, Michio

2017-07-01

Although MRI has become widely used in small animal practice, little is known about the validity of advanced MRI techniques such as diffusion-weighted imaging and diffusion tensor imaging. The aim of this retrospective analytical observational study was to investigate the characteristics of diffusion parameters, that is the apparent diffusion coefficient and fractional anisotropy, in dogs with a solitary intracranial meningioma or histiocytic sarcoma. Dogs were included based on the performance of diffusion MRI and histological confirmation. Statistical analyses were performed to compare apparent diffusion coefficient and fractional anisotropy for the two types of tumor in the intra- and peritumoral regions. Eleven cases with meningioma and six with histiocytic sarcoma satisfied the inclusion criteria. Significant differences in apparent diffusion coefficient value (× 10 -3 mm 2 /s) between meningioma vs. histiocytic sarcoma were recognized in intratumoral small (1.07 vs. 0.76) and large (1.04 vs. 0.77) regions of interest, in the peritumoral margin (0.93 vs. 1.08), and in the T2 high region (1.21 vs. 1.41). Significant differences in fractional anisotropy values were found in the peritumoral margin (0.29 vs. 0.24) and the T2 high region (0.24 vs. 0.17). The current study identified differences in measurements of apparent diffusion coefficient and fractional anisotropy for meningioma and histiocytic sarcoma in a small sample of dogs. In addition, we observed that all cases of intracranial histiocytic sarcoma showed leptomeningeal enhancement and/or mass formation invading into the sulci in the contrast study. Future studies are needed to determine the sensitivity of these imaging characteristics for differentiating between these tumor types. © 2017 American College of Veterinary Radiology.

Measurement and Modeling of the Optical Scattering Properties of Crop Canopies

NASA Technical Reports Server (NTRS)

Vanderbilt, V. C. (Principal Investigator)

1985-01-01

The specular reflection process is shown to be a key aspect of radiation transfer by plant canopies. Polarization measurements are demonstrated as the tool for determining the specular and diffuse portions of the canopy radiance. The magnitude of the specular fraction of the reflectance is significant compared to the magnitude of the diffuse fraction. Therefore, it is necessary to consider specularly reflected light in developing and evaluating light-canopy interaction models for wheat canopies. Models which assume leaves are diffuse reflectors correctly predict only the diffuse fraction of the canopy reflectance factor. The specular reflectance model, when coupled with a diffuse leaf model, would predict both the specular and diffuse portions of the reflectance factor. The specular model predicts and the data analysis confirms that the single variable, angle of incidence of specularly reflected sunlight on the leaf, explains much of variation in the polarization data as a function of view-illumination directions.

Fractional derivatives in the transport of drugs across biological materials and human skin

NASA Astrophysics Data System (ADS)

Caputo, Michele; Cametti, Cesare

2016-11-01

The diffusion of drugs across a composite structure such as a biological membrane is a rather complex phenomenon, because of its inhomogeneous nature, yielding a diffusion rate and a drug solubility strongly dependent on the local position across the membrane itself. These problems are particularly strengthened in composite structures of a considerable thickness like, for example, the human skin, where the high heterogeneity provokes the transport through different simultaneous pathways. In this note, we propose a generalization of the diffusion model based on Fick's 2nd equation by substituting a diffusion constant by means of the memory formalism approach (diffusion with memory). In particular, we employ two different definitions of the fractional derivative, i.e., the usual Caputo fractional derivative and a new definition recently proposed by Caputo and Fabrizio. The model predictions have been compared to experimental results concerning the permeation of two different compounds through human skin in vivo, such as piroxicam, an anti-inflammatory drug, and 4-cyanophenol, a test chemical model compound. Moreover, we have also considered water penetration across human stratum corneum and the diffusion of an antiviral agent employed as model drugs across the skin of male hairless rats. In all cases, a satisfactory good agreement based on the diffusion with memory has been found. However, the model based on the new definition of fractional derivative gives a better description of the experimental data, on the basis of the residuals analysis. The use of the new definition widens the applicability of the fractional derivative to diffusion processes in highly heterogeneous systems.

Multidetector thermal field-flow fractionation as a novel tool for the microstructure separation of polyisoprene and polybutadiene.

PubMed

Greyling, Guilaume; Pasch, Harald

2014-11-01

For the first time, it is demonstrated that thermal field-flow fractionation (ThFFF) is an efficient tool for the fractionation of polyisoprene (PI) and polybutadiene (PB) with regard to molecular microstructure. ThFFF analysis of 1,4- and 3,4-PI as well as 1,4- and 1,2-PB samples in tetrahydrofuran (THF), THF/cyclohexane, and cyclohexane reveals that isomers of the same polymer family having similar molar masses exhibit different Soret coefficients depending on microstructure for each solvent. The separation according to microstructure is found to be based on the cooperative influence of the normal and the thermal diffusion coefficient. Of the three solvents, cyclohexane has the greatest influence on the fractionation of the isomers. In order to determine the distribution of isomeric structures in the PI and PB samples, the samples are fractionated by ThFFF in cyclohexane and subsequently analyzed by (1) H NMR. The isomeric distributions determined from NMR data correlate well with ThFFF retention data of the samples and thus further highlight the unique fractionating capabilities of ThFFF. The interplay of the normal and thermal diffusion coefficients that are influenced by temperature and the mobile phase opens the way to highly selective fractionations without the drawbacks of column-based separation methods. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Diffusion in inhomogeneous polymer membranes

NASA Astrophysics Data System (ADS)

Kasargod, Sameer S.; Adib, Farhad; Neogi, P.

1995-10-01

The dual mode sorption solubility isotherms assume, and in instances Zimm-Lundberg analysis of the solubilities show, that glassy polymers are heterogeneous and that the distribution of the solute in the polymer is also inhomogeneous. Under some conditions, the heterogeneities cannot be represented as holes. A mathematical model describing diffusion in inhomogeneous polymer membranes is presented using Cahn and Hilliard's gradient theory. The fractional mass uptake is found to be proportional to the fourth root of time rather than the square root, predicted by Fickian diffusion. This type of diffusion is classified as pseudo-Fickian. The model is compared with one experimental result available. A negative value of the persistence factor is obtained and the results are interpreted.

Characterizing Microstructural Tissue Properties in Multiple Sclerosis with Diffusion MRI at 7 T and 3 T: The Impact of the Experimental Design.

PubMed

De Santis, Silvia; Bastiani, Matteo; Droby, Amgad; Kolber, Pierre; Zipp, Frauke; Pracht, Eberhard; Stoecker, Tony; Groppa, Sergiu; Roebroeck, Alard

2018-04-07

The recent introduction of advanced magnetic resonance (MR) imaging techniques to characterize focal and global degeneration in multiple sclerosis (MS), like the Composite Hindered and Restricted Model of Diffusion, or CHARMED, diffusional kurtosis imaging (DKI) and Neurite Orientation Dispersion and Density Imaging (NODDI) made available new tools to image axonal pathology non-invasively in vivo. These methods already showed greater sensitivity and specificity compared to conventional diffusion tensor-based metrics (e.g., fractional anisotropy), overcoming some of its limitations. While previous studies uncovered global and focal axonal degeneration in MS patients compared to healthy controls, here our aim is to investigate and compare different diffusion MRI acquisition protocols in their ability to highlight microstructural differences between MS and control tissue over several much used models. For comparison, we contrasted the ability of fractional anisotropy measurements to uncover differences between lesion, normal-appearing white matter (WM), gray matter and healthy tissue under the same imaging protocols. We show that: (1) focal and diffuse differences in several microstructural parameters are observed under clinical settings; (2) advanced models (CHARMED, DKI and NODDI) have increased specificity and sensitivity to neurodegeneration when compared to fractional anisotropy measurements; and (3) both high (3 T) and ultra-high fields (7 T) are viable options for imaging tissue change in MS lesions and normal appearing WM, while higher b-values are less beneficial under the tested short-time (10 min acquisition) conditions. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.

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

PubMed Central

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

2013-01-01

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

Ergodicity convergence test suggests telomere motion obeys fractional dynamics

NASA Astrophysics Data System (ADS)

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

2011-04-01

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

Grading of Gliomas by Using Monoexponential, Biexponential, and Stretched Exponential Diffusion-weighted MR Imaging and Diffusion Kurtosis MR Imaging

PubMed Central

Bai, Yan; Lin, Yusong; Tian, Jie; Shi, Dapeng; Cheng, Jingliang; Haacke, E. Mark; Hong, Xiaohua; Ma, Bo; Zhou, Jinyuan

2016-01-01

Purpose To quantitatively compare the potential of various diffusion parameters obtained from monoexponential, biexponential, and stretched exponential diffusion-weighted imaging models and diffusion kurtosis imaging in the grading of gliomas. Materials and Methods This study was approved by the local ethics committee, and written informed consent was obtained from all subjects. Both diffusion-weighted imaging and diffusion kurtosis imaging were performed in 69 patients with pathologically proven gliomas by using a 3-T magnetic resonance (MR) imaging unit. An isotropic apparent diffusion coefficient (ADC), true ADC, pseudo-ADC, and perfusion fraction were calculated from diffusion-weighted images by using a biexponential model. A water molecular diffusion heterogeneity index and distributed diffusion coefficient were calculated from diffusion-weighted images by using a stretched exponential model. Mean diffusivity, fractional anisotropy, and mean kurtosis were calculated from diffusion kurtosis images. All values were compared between high-grade and low-grade gliomas by using a Mann-Whitney U test. Receiver operating characteristic and Spearman rank correlation analysis were used for statistical evaluations. Results ADC, true ADC, perfusion fraction, water molecular diffusion heterogeneity index, distributed diffusion coefficient, and mean diffusivity values were significantly lower in high-grade gliomas than in low-grade gliomas (U = 109, 56, 129, 6, 206, and 229, respectively; P < .05). Pseudo-ADC and mean kurtosis values were significantly higher in high-grade gliomas than in low-grade gliomas (U = 98 and 8, respectively; P < .05). Both water molecular diffusion heterogeneity index (area under the receiver operating characteristic curve [AUC] = 0.993) and mean kurtosis (AUC = 0.991) had significantly greater AUC values than ADC (AUC = 0.866), mean diffusivity (AUC = 0.722), and fractional anisotropy (AUC = 0.500) in the differentiation of low-grade and high-grade gliomas (P < .05). Conclusion Water molecular diffusion heterogeneity index and mean kurtosis values may provide additional information and improve the grading of gliomas compared with conventional diffusion parameters. © RSNA, 2015 Online supplemental material is available for this article. PMID:26230975

Effect of hydrodynamic interactions on the diffusion of integral membrane proteins: diffusion in plasma membranes.

PubMed Central

Bussell, S J; Koch, D L; Hammer, D A

1995-01-01

Tracer diffusion coefficients of integral membrane proteins (IMPs) in intact plasma membranes are often much lower than those found in blebbed, organelle, and reconstituted membranes. We calculate the contribution of hydrodynamic interactions to the tracer, gradient, and rotational diffusion of IMPs in plasma membranes. Because of the presence of immobile IMPs, Brinkman's equation governs the hydrodynamics in plasma membranes. Solutions of Brinkman's equation enable the calculation of short-time diffusion coefficients of IMPs. There is a large reduction in particle mobilities when a fraction of them is immobile, and as the fraction increases, the mobilities of the mobile particles continue to decrease. Combination of the hydrodynamic mobilities with Monte Carlo simulation results, which incorporate excluded area effects, enable the calculation of long-time diffusion coefficients. We use our calculations to analyze results for tracer diffusivities in several different systems. In erythrocytes, we find that the hydrodynamic theory, when combined with excluded area effects, closes the gap between existing theory and experiment for the mobility of band 3, with the remaining discrepancy likely due to direct obstruction of band 3 lateral mobility by the spectrin network. In lymphocytes, the combined hydrodynamic-excluded area theory provides a plausible explanation for the reduced mobility of sIg molecules induced by binding concanavalin A-coated platelets. However, the theory does not explain all reported cases of "anchorage modulation" in all cell types in which receptor mobilities are reduced after binding by concanavalin A-coated platelets. The hydrodynamic theory provides an explanation of why protein lateral mobilities are restricted in plasma membranes and why, in many systems, deletion of the cytoplasmic tail of a receptor has little effect on diffusion rates. However, much more data are needed to test the theory definitively. We also predict that gradient and tracer diffusivities are the same to leading order. Finally, we have calculated rotational diffusion coefficients in plasma membranes. They decrease less rapidly than translational diffusion coefficients with increasing protein immobilization, and the results agree qualitatively with the limited experimental data available. PMID:7612825

Void formation in INCONEL MA-754 by high temperature oxidation

NASA Astrophysics Data System (ADS)

Rosenstein, Alan H.; Tien, John K.; Nix, William D.

1986-01-01

Subsurface void formation in oxide dispersion strengthened MA-754 caused by high temperature oxidation was investigated at temperatures of 1100, 1150, and 1200 °C for times of 1, 10, 50, and 100 hours. Material exposed at 1200 °C was examined using microprobe, SEM, and optical microscopy techniques. After exposure in air at 1200 °C for 100 hours, chromium depletion by as much as 10 wt pct was observed near the surface, and voids of various sizes up to 15 µm in diameter were found to depths of 300 µm. The fraction of voids increases with exposure time and, with the exception of anomalous values near the surface, decreases with depth. The maximum area fraction of voids observed was approximately 8 pct. Correlation of the void area fraction profile with the measured chromium depletion through a diffusion analysis shows that void formation is due to vacancy injection. Similar void formation in Ni-Cr alloys without oxide dispersions suggests that void formation is not dependent upon the presence of oxide dispersions. The diffusion coefficient for chromium in MA-754 at 1200 °C was computed from microprobe data to be 4 × 10-10 cm2 per second.

Shear-induced reversibility of 2D colloidal suspensions in the presence of minimal thermal noise.

PubMed

Farhadi, Somayeh; Arratia, Paulo E

2017-06-14

The effects of minimal thermal noise on particle rearrangements in cyclically sheared colloidal suspensions are experimentally investigated using particle tracking methods. Our experimental model system consists of polystyrene microspheres adsorbed at an oil-water interface, in which the particles exhibit small but non-negligible Brownian motion. Experiments are performed on bidisperse (1.0 and 1.2 μm in diameter) systems, which form area fractions of 0.20 and 0.32 at the interface. We first characterize the thermal (Brownian) noise using particle diffusivities at quiescent states, and show that under our experimental flow conditions both systems (0.20 and 0.32 area fraction) behave as athermal, in the sense that the particle diffusion time scale is larger than the flow time scale. We then characterize particle rearrangements as a function of strain amplitude, and show that small but finite levels of thermal noise affect the reversibility dynamics, even in effectively athermal systems. Our data indicate that as thermal noise is slightly increased in a cyclically sheared athermal system, the fraction of reversible rearrangements is reduced, the reversible cycles become unstable, and the rearrangement hysteresis is significantly hindered.

Desorption modeling of hydrophobic organic chemicals from plastic sheets using experimentally determined diffusion coefficients in plastics.

PubMed

Lee, Hwang; Byun, Da-Eun; Kim, Ju Min; Kwon, Jung-Hwan

2018-01-01

To evaluate rate of migration from plastic debris, desorption of model hydrophobic organic chemicals (HOCs) from polyethylene (PE)/polypropylene (PP) films to water was measured using PE/PP films homogeneously loaded with the HOCs. The HOCs fractions remaining in the PE/PP films were compared with those predicted using a model characterized by the mass transfer Biot number. The experimental data agreed with the model simulation, indicating that HOCs desorption from plastic particles can generally be described by the model. For hexachlorocyclohexanes with lower plastic-water partition coefficients, desorption was dominated by diffusion in the plastic film, whereas desorption of chlorinated benzenes with higher partition coefficients was determined by diffusion in the aqueous boundary layer. Evaluation of the fraction of HOCs remaining in plastic films with respect to film thickness and desorption time showed that the partition coefficient between plastic and water is the most important parameter influencing the desorption half-life. Copyright © 2017 Elsevier Ltd. All rights reserved.

Characterizing the microstructural basis of "unidentified bright objects" in neurofibromatosis type 1: A combined in vivo multicomponent T2 relaxation and multi-shell diffusion MRI analysis.

PubMed

Billiet, Thibo; Mädler, Burkhard; D'Arco, Felice; Peeters, Ronald; Deprez, Sabine; Plasschaert, Ellen; Leemans, Alexander; Zhang, Hui; den Bergh, Bea Van; Vandenbulcke, Mathieu; Legius, Eric; Sunaert, Stefan; Emsell, Louise

2014-01-01

The histopathological basis of "unidentified bright objects" (UBOs) (hyperintense regions seen on T2-weighted magnetic resonance (MR) brain scans in neurofibromatosis-1 (NF1)) remains unclear. New in vivo MRI-based techniques (multi-exponential T2 relaxation (MET2) and diffusion MR imaging (dMRI)) provide measures relating to microstructural change. We combined these methods and present previously unreported data on in vivo UBO microstructure in NF1. 3-Tesla dMRI data were acquired on 17 NF1 patients, covering 30 white matter UBOs. Diffusion tensor, kurtosis and neurite orientation and dispersion density imaging parameters were calculated within UBO sites and in contralateral normal appearing white matter (cNAWM). Analysis of MET2 parameters was performed on 24 UBO-cNAWM pairs. No significant alterations in the myelin water fraction and intra- and extracellular (IE) water fraction were found. Mean T2 time of IE water was significantly higher in UBOs. UBOs furthermore showed increased axial, radial and mean diffusivity, and decreased fractional anisotropy, mean kurtosis and neurite density index compared to cNAWM. Neurite orientation dispersion and isotropic fluid fraction were unaltered. Our results suggest that demyelination and axonal degeneration are unlikely to be present in UBOs, which appear to be mainly caused by a shift towards a higher T2-value of the intra- and extracellular water pool. This may arise from altered microstructural compartmentalization, and an increase in 'extracellular-like', intracellular water, possibly due to intramyelinic edema. These findings confirm the added value of combining dMRI and MET2 to characterize the microstructural basis of T2 hyperintensities in vivo.

Conformable derivative approach to anomalous diffusion

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

State Relationships of Laminar Permanently-Blue Opposed-Jet Hydrocarbon-Fueled Diffusion Flames. Appendix D

NASA Technical Reports Server (NTRS)

Lin, K.-C.; Faeth, G. M.; Urban, D. L. (Technical Monitor)

2000-01-01

The structure and state relationships of laminar soot-free (permanently-blue) diffusion flames at various strain rates were studied experimentally using an opposed-jet configuration, motivated by the importance of soot-free hydrocarbon-fueled diffusion flames for many practical applications. Measurements of gas velocities, temperatures and compositions were carried out along the stagnation stream line. Flame conditions studied included propylene- and 1,3-butadiene-fueled opposed-jet diffusion flames having a stoichiometric mixture fractions of 0.7 and strain rates of 60-240 s (exp -1) at normal temperature and pressure. It was found that oxygen leakage to fuel-rich conditions and carbon monoxide leakage to fuel-lean conditions both increased as strain rates increased. Furthermore, increased strain rates caused increased fuel concentrations near the flame sheet, decreased peak gas temperatures, and decreased concentrations of carbon dioxide and water vapor throughout the flames. State relationships for major gas species and gas temperatures for these flames were found to exist over broad ranges of strain rates. In addition, current measurements, as well as previous measurements and predictions of ethylene-fueled permanently-blue diffusion flames, all having a stoichiometric mixture fraction of 0.7, were combined to establish generalized state relationships for permanently-blue diffusion flames for this stoichiometric mixture fraction. The combined measurements and predictions support relatively universal generalized state relationships for N2, CO2, H2O and fuel over a broad range of strain rates and fuel types. State relationships for O2 in the fuel-rich region, and for CO in the fuel-lean region, however, are functions of strain rate and fuel type. State relationships for H2 and temperature exhibit less universality, mainly due to the increased experimental uncertainties for these variables. The existence of state relationships for soot-free hydrocarbon-fueled diffusion flames provides potential for significant computational simplifications for modeling purposes in many instances, allowing for effects of finite-rate chemistry while avoiding time-consuming computations of Arrhenius expressions.

A Fractional Differential Kinetic Equation and Applications to Modelling Bursts in Turbulent Nonlinear Space Plasmas

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Rosenberg, S.; Sanchez, R.; Chapman, S. C.; Credgington, D.

2008-12-01

Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototype) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold. This problem relates to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [PRE, 2000] on solar wind Poynting flux near L1. We test how expressions derived by other authors generalise to the non-Gaussian, constant threshold problem. Ongoing work on extension of these LFSM results to multifractals will also be discussed.

Loss or Mislocalization of Aquaporin-4 Affects Diffusion Properties and Intermediary Metabolism in Gray Matter of Mice.

PubMed

Pavlin, T; Nagelhus, E A; Brekken, C; Eyjolfsson, E M; Thoren, A; Haraldseth, O; Sonnewald, U; Ottersen, O P; Håberg, A K

2017-01-01

The first aim of this study was to determine how complete or perivascular loss of aquaporin-4 (AQP4) water channels affects membrane permeability for water in the mouse brain grey matter in the steady state. Time-dependent diffusion magnetic resonance imaging was performed on global Aqp4 knock out (KO) and α-syntrophin (α-syn) KO mice, in the latter perivascular AQP4 are mislocalized, but still functioning. Control animals were corresponding wild type (WT) mice. By combining in vivo diffusion measurements with the effective medium theory and previously measured extra-cellular volume fractions, the effects of membrane permeability and extracellular volume fraction were uncoupled for Aqp4 and α-syn KO. The second aim was to assess the effect of α-syn KO on cortical intermediary metabolism combining in vivo [1- 13 C]glucose and [1,2- 13 C]acetate injection with ex vivo 13 C MR spectroscopy. Aqp4 KO increased the effective diffusion coefficient at long diffusion times by 5%, and a 14% decrease in membrane water permeability was estimated for Aqp4 KO compared with WT mice. α-syn KO did not affect the measured diffusion parameters. In the metabolic analyses, significantly lower amounts of [4- 13 C]glutamate and [4- 13 C]glutamine, and percent enrichment in [4- 13 C]glutamate were detected in the α-syn KO mice. [1,2- 13 C]acetate metabolism was unaffected in α-syn KO, but the contribution of astrocyte derived metabolites to GABA synthesis was significantly increased. Taken together, α-syn KO mice appeared to have decreased neuronal glucose metabolism, partly compensated for by utilization of astrocyte derived metabolites.

Isotopic fractionation of volatile species during bubble growth in magmas

NASA Astrophysics Data System (ADS)

Watson, E. B.

2016-12-01

Bubbles grow in decompressing magmas by simple expansion and also by diffusive supply of volatiles to the bubble/melt interface. The latter phenomenon is of significant geochemical interest because diffusion can fractionate isotopes, raising the possibility that the isotopic character of volatile components in bubbles may not reflect that of volatiles dissolved in the host melt over the lifetime of a bubble—even in the complete absence of equilibrium vapor/melt isotopic fractionation. None of the foregoing is conceptually new, but recent experimental studies have established the existence of isotope mass effects on diffusion in silicate melts for several elements (Li, Mg, Ca, Fe), and this finding has now been extended to the volatile (anionic) element chlorine (Fortin et al. 2016; this meeting). Knowledge of isotope mass effects on diffusion of volatile species opens the way for quantitative models of diffusive fractionation during bubble growth. Significantly different effects are anticipated for "passive" volatiles (e.g., noble gases and Cl) that are partitioned into existing bubbles but play little role in nucleation and growth, as opposed to "active" volatiles whose limited solubilities lead to bubble nucleation during magma decompression. Numerical solution of the appropriate diffusion/mass-conservation equations reveals that the isotope effect on passive volatiles partitioned into bubbles growing at a constant rate in a static system depends (predictably) upon R/D, Kd and D1/D2 (R = growth rate; D = diffusivity; Kd = bubble/melt partition coefficient; D1/D2 = diffusivity ratio of the isotopes of interest). Constant R is unrealistic, but other scenarios can be explored by including the solubility and EOS of an "active" volatile (e.g., CO2) in numerical simulations of bubble growth. For plausible decompression paths, R increases exponentially with time—leading, potentially, to larger isotopic fractionation of species partitioned into the growing bubble.

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

NASA Astrophysics Data System (ADS)

Yin, Deshun; Qu, Pengfei

2018-02-01

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

Fractionation of Poly(butyl methacrylate) by Molecular Topology Using Multidetector Thermal Field-Flow Fractionation.

PubMed

Greyling, Guilaume; Pasch, Harald

2015-12-01

Thermal field-flow fractionation (ThFFF) is an interesting alternative to column-based fractionation being able to address different molecular parameters including size and composition. Until today it has not been shown to be able to fractionate polymers of similar molar masses and chemical compositions by molecular topology. The present study demonstrates that poly(butyl methacrylates) with identical molar masses can be fractionated by ThFFF according to the topology of the butyl group. The influence of the solvent polarity on the thermal diffusion behavior of these polymers is presented and it is shown to have a significant influence on the fractionation of poly(n-butyl methacrylate) and poly(t-butyl methacrylate). Fractionation improves with increasing solvent polarity and solvent polarity may have a greater influence on fractionation than solvent viscosity. It is found that the thermal diffusion coefficient, D(T), as well as the hydrodynamic diameter, D(h), exhibit increasing trends with increasing solvent polarity. The solvent quality has a significant influence on the fractionation. It is found that cyclohexane, being a theta solvent for poly(t-butyl methacrylate) but not for poly(n-butyl methacrylate), significantly improves the fractionation of the samples by decreasing the diffusion rate of the former but not the latter. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Simulations of normal and inverse laminar diffusion flames under oxygen enhancement and gravity variation

NASA Astrophysics Data System (ADS)

Bhatia, P.; Katta, V. R.; Krishnan, S. S.; Zheng, Y.; Sunderland, P. B.; Gore, J. P.

2012-10-01

Steady-state global chemistry calculations for 20 different flames were carried out using an axisymmetric Computational Fluid Dynamics (CFD) code. Computational results for 16 flames were compared with flame images obtained at the NASA Glenn Research Center. The experimental flame data for these 16 flames were taken from Sunderland et al. [4] which included normal and inverse diffusion flames of ethane with varying oxidiser compositions (21, 30, 50, 100% O2 mole fraction in N2) stabilised on a 5.5 mm diameter burner. The test conditions of this reference resulted in highly convective inverse diffusion flames (Froude numbers of the order of 10) and buoyant normal diffusion flames (Froude numbers ∼0.1). Additionally, six flames were simulated to study the effect of oxygen enhancement on normal diffusion flames. The enhancement in oxygen resulted in increased flame temperatures and the presence of gravity led to increased gas velocities. The effect of gravity-variation and oxygen enhancement on flame shape and size of normal diffusion flames was far more pronounced than for inverse diffusion flames. For normal-diffusion flames, their flame-lengths decreased (1 to 2 times) and flames-widths increased (2 to 3 times) when going from earth-gravity to microgravity, and flame height decreased by five times when going from air to a pure oxygen environment.

Study on laser-assisted drug delivery with optical coherence tomography

NASA Astrophysics Data System (ADS)

Tsai, Wen-Guei; Tsai, Ting-Yen; Yang, Chih-Hsun; Tsai, Meng-Tsan

2017-04-01

The nail provides a functional protection to the fingertips and surrounding tissue from external injuries. Nail plate divided into three layers including dorsal, intermediate, and ventral layers. The dorsal layer consists of compact, hard keratins, limiting topical drug delivery through the nail. In this study, we investigate the application of fractional CO2 laser that produces arrays of microthermal ablation zones (MAZs) to facilitate drug delivery in the nails. Moreover, optical coherence tomography (OCT) is implemented for real-time monitoring of the laser-skin tissue interaction, sparing the patient from invasive surgical sampling procedure. Observations of drug diffusion through the induced MAZ array are achieved by evaluating the time-dependent OCT intensity variance. Subsequently, nails are treated with cream and liquid topical drugs to investigate the feasibility and diffusion efficacy of laser-assisted drug delivery. Our results show that fractional CO2 laser improves the efficacy of topical drug delivery in the nail plate, and that OCT could potentially be used for in vivo monitoring of the depth of laser penetration as well as real-time observations of drug delivery.

Age-related differences in the response of leg muscle cross-sectional area and water diffusivity measures to a period of supine rest.

PubMed

Lorbergs, Amanda L; Noseworthy, Michael D; MacIntyre, Norma J

2015-06-01

The object was to assess whether cross-sectional area (CSA) and water diffusion properties of leg muscles in young and older women change with increased time spent in supine rest. Healthy young (n = 9, aged 20-30 years) and older (n = 9, aged 65-75 years) women underwent MRI scanning of the right leg at baseline, 30 and 60 min of supine rest. Muscle CSA was derived from proton density images. Water diffusion properties [apparent diffusion coefficient (ADC) and fractional anisotropy (FA)] of the tibialis anterior and posterior, soleus, and medial and lateral heads of the gastrocnemius were derived from diffusion tensor imaging (DTI). Repeated measures ANOVAs and Bonferroni post hoc tests determined the effects of time and group on each muscle outcome. In both groups, muscle CSA and FA did not significantly change over time, whereas ADC significantly decreased. A greater decline at 30 min for young women was only observed for ADC in the medial gastrocnemius. Regardless of age, ADC values decreased with fluid shift associated with time spent supine, whereas CSA and FA were not affected. For leg muscle assessment in young and older women, DTI scanning protocols should consider the amount of time spent in a recumbent position.

Passivity analysis for uncertain BAM neural networks with time delays and reaction-diffusions

NASA Astrophysics Data System (ADS)

Zhou, Jianping; Xu, Shengyuan; Shen, Hao; Zhang, Baoyong

2013-08-01

This article deals with the problem of passivity analysis for delayed reaction-diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results.

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 parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.

PubMed

Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie

2014-01-01

It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.

Brain aging in humans, chimpanzees (Pan troglodytes), and rhesus macaques (Macaca mulatta): magnetic resonance imaging studies of macro- and microstructural changes.

PubMed

Chen, Xu; Errangi, Bhargav; Li, Longchuan; Glasser, Matthew F; Westlye, Lars T; Fjell, Anders M; Walhovd, Kristine B; Hu, Xiaoping; Herndon, James G; Preuss, Todd M; Rilling, James K

2013-10-01

Among primates, humans are uniquely vulnerable to many age-related neurodegenerative disorders. We used structural and diffusion magnetic resonance imaging (MRI) to examine the brains of chimpanzees and rhesus monkeys across each species' adult lifespan, and compared these results with published findings in humans. As in humans, gray matter volume decreased with age in chimpanzees and rhesus monkeys. Also like humans, chimpanzees showed a trend for decreased white matter volume with age, but this decrease occurred proportionally later in the chimpanzee lifespan than in humans. Diffusion MRI revealed widespread age-related decreases in fractional anisotropy and increases in radial diffusivity in chimpanzees and macaques. However, both the fractional anisotropy decline and the radial diffusivity increase started at a proportionally earlier age in humans than in chimpanzees. Thus, even though overall patterns of gray and white matter aging are similar in humans and chimpanzees, the longer lifespan of humans provides more time for white matter to deteriorate before death, with the result that some neurological effects of aging may be exacerbated in our species. Copyright © 2013 Elsevier Inc. All rights reserved.

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

PubMed

Carasso, Alfred S; Vladár, András E

2012-01-01

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

Design of broadband time-domain impedance boundary conditions using the oscillatory-diffusive representation of acoustical models.

PubMed

Monteghetti, Florian; Matignon, Denis; Piot, Estelle; Pascal, Lucas

2016-09-01

A methodology to design broadband time-domain impedance boundary conditions (TDIBCs) from the analysis of acoustical models is presented. The derived TDIBCs are recast exclusively as first-order differential equations, well-suited for high-order numerical simulations. Broadband approximations are yielded from an elementary linear least squares optimization that is, for most models, independent of the absorbing material geometry. This methodology relies on a mathematical technique referred to as the oscillatory-diffusive (or poles and cuts) representation, and is applied to a wide range of acoustical models, drawn from duct acoustics and outdoor sound propagation, which covers perforates, semi-infinite ground layers, as well as cavities filled with a porous medium. It is shown that each of these impedance models leads to a different TDIBC. Comparison with existing numerical models, such as multi-pole or extended Helmholtz resonator, provides insights into their suitability. Additionally, the broadly-applicable fractional polynomial impedance models are analyzed using fractional calculus.

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

PubMed

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

2010-02-01

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

Meta-analysis of diffusion metrics for the prediction of tumor grade in gliomas.

PubMed

Miloushev, V Z; Chow, D S; Filippi, C G

2015-02-01

Diffusion tensor metrics are potential in vivo quantitative neuroimaging biomarkers for the characterization of brain tumor subtype. This meta-analysis analyzes the ability of mean diffusivity and fractional anisotropy to distinguish low-grade from high-grade gliomas in the identifiable tumor core and the region of peripheral edema. A meta-analysis of articles with mean diffusivity and fractional anisotropy data for World Health Organization low-grade (I, II) and high-grade (III, IV) gliomas, between 2000 and 2013, was performed. Pooled data were analyzed by using the odds ratio and mean difference. Receiver operating characteristic analysis was performed for patient-level data. The minimum mean diffusivity of high-grade gliomas was decreased compared with low-grade gliomas. High-grade gliomas had decreased average mean diffusivity values compared with low-grade gliomas in the tumor core and increased average mean diffusivity values in the peripheral region. High-grade gliomas had increased FA values compared with low-grade gliomas in the tumor core, decreased values in the peripheral region, and a decreased fractional anisotropy difference between the tumor core and peripheral region. The minimum mean diffusivity differs significantly with respect to the World Health Organization grade of gliomas. Statistically significant effects of tumor grade on average mean diffusivity and fractional anisotropy were observed, supporting the concept that high-grade tumors are more destructive and infiltrative than low-grade tumors. Considerable heterogeneity within the literature may be due to systematic factors in addition to underlying lesion heterogeneity. © 2015 by American Journal of Neuroradiology.

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

PubMed

Chen, Duan

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

Martelloni, Gianluca; Bagnoli, Franco

2016-04-01

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

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

NASA Astrophysics Data System (ADS)

Buonocore, Salvatore; Semperlotti, Fabio

2018-06-01

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

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

Janssens, Geert O.R.J.; Gidding, Corrie E.M.; Lindert, Erik J. van

Purpose: Most children with a diffuse intrinsic brainstem glioma will die within 1 year after diagnosis. To reduce patient burden, we investigated the feasibility of a radical hypofractionation radiotherapy schedule, given over 3 weeks, as an alternative to the standard regimen (30 fractions over 6 weeks). Methods and Materials: Nine children, ages 3-13, were treated by 13 fractions of 3 Gy (n = 8) or 6 fractions of 5.5 Gy (n = 1) given over 3 weeks. All patients had symptoms for {<=}3 months and {>=}2 signs of the neurologic triad (long tract signs, ataxia, cranial nerve deficit). Bilateral involvementmore » of the pons (n = 8), encasement of the basilar artery (n = 7) and extension into the cerebellar peduncle (n = 6) was visible on magnetic resonance imaging. Results: Symptom improvement occurred in all patients within 2 weeks after start of radiotherapy. At a mean follow-up time of 15 months, 7 patients have died. Median time to progression and overall survival was 4.9 and 8.6 months, respectively. Median time to death after progression was 3.6 months. No Grade 3 or 4 toxicity was observed. In a recently published review of clinical trials, median time to progression, overall survival, and time between progression and death ranged from 5.0-8.8, 7.0-16, and 1.0-4.5 months, respectively, with more aggressive regimens. Conclusion: This radical hypofractionation radiotherapy regimen for children with diffuse intrinsic brainstem glioma is feasible and associated with no Grade 3 or 4 toxicities. With a minimal overall treatment time, it offers quick symptom relief and outcome results within the range of published data.« less

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

PubMed

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

2013-11-05

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

An experimental and modeling study of grain-scale uranium desorption from field-contaminated sediments and the potential influence of microporosity on mass-transfer

NASA Astrophysics Data System (ADS)

Stoliker, D.; Liu, C.; Kent, D. B.; Zachara, J. M.

2012-12-01

The aquifer below the 300-Area of the Hanford site (Richland, WA, USA) is plagued by a persistent plume of dissolved uranium (U(VI)) in excess of the Environmental Protection Agency drinking water maximum contamination level even after the removal of highly contaminated sediments. The aquifer sediments in the seasonally saturated lower vadose zone act as both a source and sink for uranium during stage changes in the nearby Columbia River. Diffusion limitation of uranium mass-transfer within these sediments has been cited as a potential cause of the plume's persistence. Equilibrium U(VI) sorption is a strong function of variable chemical conditions, especially carbonate, hydrogen, and uranyl ion activities. Field-contaminated sediments from the site require up to 1,000 hours to reach equilibrium in static batch reactors. Increases in U(VI) concentrations over longer time-scales result from changes in chemical conditions, which drive reactions with sediments that favor U(VI) desorption. Grain-scale U(VI) sorption/desorption rates are slow, likely owing to diffusion of U(VI) and other solutes through intra-granular pore domains. In order to improve understanding of the impact of intra-granular diffusion and chemical reactions controlling grain-scale U(VI) release, experiments were conducted on individual particle size fractions of a <8 mm composite of field-contaminated, lower vadose zone sediments. For each size fraction, equilibrium U(VI) sorption/desorption in static batch reactors was well-described by surface complexation models over a range of chemical conditions applicable to the field site. Desorption rates from individual size fractions in flow-through batch reactors, examined under a single set of constant chemical conditions with multiple stop-flow events, were similar for all size fractions <2 mm. Kinetic U(VI) desorption in flow-through batch reactors was modeled using a multi-rate surface complexation approach, where sorption/desorption rates were assumed to be proportional to the displacement from equilibrium and multiple diffusion domains were described with a two-parameter lognormal distribution of mass-transfer rate coefficients. Parameters describing mass transfer were the same for all size fractions <2 mm but differed for the largest (2-8 mm) size fraction. The evolution of pH, along with dissolved cation and carbonate concentrations, was modeled using equilibrium cation exchange, rate-limited calcite dissolution, aerobic respiration, and silica dissolution. Desorption and chemical reaction models calibrated with individual size fractions predicted U(VI) and chemical composition as a function of time for the bulk sediment sample. Volumes of pores less than 2.4 nm, quantified using nitrogen adsorption-desorption isotherms, were the same for all size fractions < 2 mm, nearly double that of the 2-8 mm size fraction. Similarity in the observed pore volumes and multi-rate mass-transfer parameters across all size fractions <2 mm suggest the importance of pores in this size class in controlling slow grain-scale U(VI) desorption rates. Models like these provide a means for testing the influence of grain-scale mass-transfer on the persistence of U(VI) plume at the site.

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.

Fractional Dynamics of Single File Diffusion in Dusty Plasma Ring

NASA Astrophysics Data System (ADS)

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

2011-11-01

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

Diffusion method of seperating gaseous mixtures

DOEpatents

Pontius, Rex B.

1976-01-01

A method of effecting a relatively large change in the relative concentrations of the components of a gaseous mixture by diffusion which comprises separating the mixture into heavier and lighter portions according to major fraction mass recycle procedure, further separating the heavier portions into still heavier subportions according to a major fraction mass recycle procedure, and further separating the lighter portions into still lighter subportions according to a major fraction equilibrium recycle procedure.

Variance change point detection for fractional Brownian motion based on the likelihood ratio test

NASA Astrophysics Data System (ADS)

Kucharczyk, Daniel; Wyłomańska, Agnieszka; Sikora, Grzegorz

2018-01-01

Fractional Brownian motion is one of the main stochastic processes used for describing the long-range dependence phenomenon for self-similar processes. It appears that for many real time series, characteristics of the data change significantly over time. Such behaviour one can observe in many applications, including physical and biological experiments. In this paper, we present a new technique for the critical change point detection for cases where the data under consideration are driven by fractional Brownian motion with a time-changed diffusion coefficient. The proposed methodology is based on the likelihood ratio approach and represents an extension of a similar methodology used for Brownian motion, the process with independent increments. Here, we also propose a statistical test for testing the significance of the estimated critical point. In addition to that, an extensive simulation study is provided to test the performance of the proposed method.

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.

Diffusive and rotational dynamics of condensed n-H2 confined in MCM-41

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

Prisk, Timothy R; Bryan, Matthew; Sokol, Paul E

2014-01-01

In this paper, we report an inelastic neutron scattering study of liquid and solid n-H2 confined within MCM-41. This is a high surface area, mesoporous silica glass with a narrow pore size distribution centered at 3.5 nm. The scattering data provides information about the diffusive and rotational dynamics of the adsorbed n-H2 at low temperatures. In the liquid state, the neutron scattering data demonstrates that only a fraction of the adsorbed o-H2 is mobile on the picosecond time scale. This mobile fraction undergoes liquid-like jump diffusion, and values for the residence time t and effective mean-squared displacement hu2i are reportedmore » as a function of pore filling. In the solid state, the rotational energy levels of adsorbed H2 are strongly perturbed from their free quantum rotor behavior in the bulk solid. The underlying orientational potential of the hindered rotors is due to the surface roughness and heterogeneity of the MCM-41 pore walls. This potential is compared to the hindering potential of other porous silicas, such as Vycor. Strong selective adsorption makes the interfacial layer rich in o-H2, leaving the inner core volume consisting of a depleted mixture of o-H2 and p-H2.« less

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

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

PubMed

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

2007-06-16

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

Microscopic diffusion and hydrodynamic interactions of hemoglobin in red blood cells.

PubMed

Doster, Wolfgang; Longeville, Stéphane

2007-08-15

The cytoplasm of red blood cells is congested with the oxygen storage protein hemoglobin occupying a quarter of the cell volume. The high protein concentration leads to a reduced mobility; the self-diffusion coefficient of hemoglobin in blood cells is six times lower than in dilute solution. This effect is generally assigned to excluded volume effects in crowded media. However, the collective or gradient diffusion coefficient of hemoglobin is only weakly dependent on concentration, suggesting the compensation of osmotic and friction forces. This would exclude hydrodynamic interactions, which are of dynamic origin and do not contribute to the osmotic pressure. Hydrodynamic coupling between protein molecules is dominant at short time- and length scales before direct interactions are fully established. Employing neutron spin-echo-spectroscopy, we study hemoglobin diffusion on a nanosecond timescale and protein displacements on the scale of a few nanometers. A time- and wave-vector dependent diffusion coefficient is found, suggesting the crossover of self- and collective diffusion. Moreover, a wave-vector dependent friction function is derived, which is a characteristic feature of hydrodynamic interactions. The wave-vector and concentration dependence of the long-time self-diffusion coefficient of hemoglobin agree qualitatively with theoretical results on hydrodynamics in hard spheres suspensions. Quantitative agreement requires us to adjust the volume fraction by including part of the hydration shell: Proteins exhibit a larger surface/volume ratio compared to standard colloids of much larger size. It is concluded that hydrodynamic and not direct interactions dominate long-range molecular transport at high concentration.

Multi-site study of diffusion metric variability: effects of site, vendor, field strength, and echo time on regions-of-interest and histogram-bin analyses.

PubMed

Helmer, K G; Chou, M-C; Preciado, R I; Gimi, B; Rollins, N K; Song, A; Turner, J; Mori, S

2016-02-27

It is now common for magnetic-resonance-imaging (MRI) based multi-site trials to include diffusion-weighted imaging (DWI) as part of the protocol. It is also common for these sites to possess MR scanners of different manufacturers, different software and hardware, and different software licenses. These differences mean that scanners may not be able to acquire data with the same number of gradient amplitude values and number of available gradient directions. Variability can also occur in achievable b-values and minimum echo times. The challenge of a multi-site study then, is to create a common protocol by understanding and then minimizing the effects of scanner variability and identifying reliable and accurate diffusion metrics. This study describes the effect of site, scanner vendor, field strength, and TE on two diffusion metrics: the first moment of the diffusion tensor field (mean diffusivity, MD), and the fractional anisotropy (FA) using two common analyses (region-of-interest and mean-bin value of whole brain histograms). The goal of the study was to identify sources of variability in diffusion-sensitized imaging and their influence on commonly reported metrics. The results demonstrate that the site, vendor, field strength, and echo time all contribute to variability in FA and MD, though to different extent. We conclude that characterization of the variability of DTI metrics due to site, vendor, field strength, and echo time is a worthwhile step in the construction of multi-center trials.

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

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.

How multiple social networks affect user awareness: The information diffusion process in multiplex networks

NASA Astrophysics Data System (ADS)

Li, Weihua; Tang, Shaoting; Fang, Wenyi; Guo, Quantong; Zhang, Xiao; Zheng, Zhiming

2015-10-01

The information diffusion process in single complex networks has been extensively studied, especially for modeling the spreading activities in online social networks. However, individuals usually use multiple social networks at the same time, and can share the information they have learned from one social network to another. This phenomenon gives rise to a new diffusion process on multiplex networks with more than one network layer. In this paper we account for this multiplex network spreading by proposing a model of information diffusion in two-layer multiplex networks. We develop a theoretical framework using bond percolation and cascading failure to describe the intralayer and interlayer diffusion. This allows us to obtain analytical solutions for the fraction of informed individuals as a function of transmissibility T and the interlayer transmission rate θ . Simulation results show that interaction between layers can greatly enhance the information diffusion process. And explosive diffusion can occur even if the transmissibility of the focal layer is under the critical threshold, due to interlayer transmission.

Diffusion in Brain Extracellular Space

PubMed Central

Syková, Eva; Nicholson, Charles

2009-01-01

Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecules in the brain. Deviations from the equation reveal loss of molecules across the blood-brain barrier, through cellular uptake, binding or other mechanisms. Early diffusion measurements used radiolabeled sucrose and other tracers. Presently, the real-time iontophoresis (RTI) method is employed for small ions and the integrative optical imaging (IOI) method for fluorescent macromolecules, including dextrans or proteins. Theoretical models and simulations of the ECS have explored the influence of ECS geometry, effects of dead-space microdomains, extracellular matrix and interaction of macromolecules with ECS channels. Extensive experimental studies with the RTI method employing the cation tetramethylammonium (TMA) in normal brain tissue show that the volume fraction of the ECS typically is about 20% and the tortuosity about 1.6 (i.e. free diffusion coefficient of TMA is reduced by 2.6), although there are regional variations. These parameters change during development and aging. Diffusion properties have been characterized in several interventions, including brain stimulation, osmotic challenge and knockout of extracellular matrix components. Measurements have also been made during ischemia, in models of Alzheimer's and Parkinson's diseases and in human gliomas. Overall, these studies improve our conception of ECS structure and the roles of glia and extracellular matrix in modulating the ECS microenvironment. Knowledge of ECS diffusion properties are valuable in contexts ranging from understanding extrasynaptic volume transmission to the development of paradigms for drug delivery to the brain. PMID:18923183

GC-MS profile of antimicrobial and antioxidant fractions from Cordia rothii roots.

PubMed

Khan, Kehkashan; Firdous, Sadiqa; Ahmad, Aqeel; Fayyaz, Nida; Nadir, Muhammad; Rasheed, Munawwer; Faizi, Shaheen

2016-11-01

An ethnobotanical survey of Cordia rothii Roem. & Schult. (Boraginaceae) reveals it as a medicinal plant. Antimicrobial and antioxidant potential evaluation and identification of chemical constituents via GC-MS of C. rothii roots fractions. To the best of our knowledge, this is the first systematic investigation of the roots exploiting GC-MS. Extraction and fractionation of C. rothii roots furnished various fractions using solvents of varying polarity, i.e., n-hexane, chloroform, ethyl acetate, acetone and methanol. In vitro antimicrobial and antioxidant screening was performed using disk diffusion and DPPH methods, respectively. MIC of active fractions was also determined using disk diffusion method. GC-MS was used to identify constituents which may be responsible for these activities. Among various fractions from C. rothii roots, fraction KA-C showed strong antibacterial activity against 17 microorganisms tested, with MIC ranging from 250-31.25 μg/mL. Fractions KA-A, KM and KM-A exhibited significant antioxidant potential with EC 50 46.875 μg/mL, while fractions KEA-PE, KM-PE and KM-M were good with EC 50 93.750 μg/mL. Forty-five phytochemicals were identified in GC-MS studies including eight hydrocarbons, six free fatty acids, 11 fatty acids esters, two phenylpropanoids, four aromatics, four terpenoid quinones/hydroquinones, three triterpenes, four phytosterols, two hexose metabolites and a DNA base. Of these, 32 constituents have been reported for the first time from C. rothii, 24 from genus Cordia and 15 from Boraginaceae. Strong antibacterial and antioxidant potential of C. rothii roots may be due to the contribution of phytoconstituents identified through GC-MS studies.

Experimental investigation of concentration and stable isotopes signals during organic contaminants back diffusion

NASA Astrophysics Data System (ADS)

Jin, Biao; Nika, Chrysanthi-Elisabeth; Rolle, Massimo

2017-04-01

Back diffusion of organic contaminants is often the cause of groundwater plumes' persistence and can significantly hinder cleanup interventions [1, 2]. In this study we perform a high-resolution investigation of back diffusion in a well-controlled flow-through laboratory setup. We considered cis-dichloroethene (cis-DCE) as model contaminant and we investigated its back diffusion from an impermeable source into a permeable saturated layer, in which advection-dominated flow conditions were established. We used concentration and stable chlorine isotope measurements to investigate the plumes originated by cis-DCE back diffusion in a series of flow-through experiments, performed in porous media with different hydraulic conductivity and at different seepage velocities (i.e., 0.4, 0.8 and 1.2 m/day). A two-centimeter thick agarose gel layer was placed at the bottom of the setup to simulate the source of cis-DCE back diffusion from an impervious layer. Intensive sampling (>1000 measurements) was carried out, including the withdrawal of aqueous samples at closely spaced (1 cm) outlet ports, as well as the high-resolution sampling of the source zone (agarose gel) at the end of each experiment. The transient behavior of the plumes originated by back diffusion was investigated by sampling the outlet ports at regular intervals in the experiments, each run for a total time corresponding to 15 pore volumes. The high-resolution sampling allowed us to resolve the spatial and temporal evolution of concentration and stable isotope gradients in the flow-through setup. In particular, steep concentration and stable isotope gradients were observed at the outlet. Lateral isotope gradients corresponding to chlorine isotope fractionation up to 20‰ were induced by cis-DCE back diffusion and subsequent advection-dominated transport in all flow-through experiments. A numerical modeling approach, tracking individually all chlorine isotopologues, based on the accurate parameterization of local dispersion, as well as on the values of aqueous diffusion coefficients and diffusion-induced isotope fractionation from a previous study [3], provided a good agreement with the experimental data. References [1] Mackay, D. M.; Cherry, J. A. Groundwater contamination: Pumpand-treat remediation. Environ. Sci. Technol. 1989, 23, 630-636. [2] Parker, B. L.; Chapman, S. W.; Guilbeault, M. A. Plume persistence caused by back diffusion from thin clay layers in a sand aquifer following TCE source-zone hydraulic isolation. J. Contam. Hydrol. 2008, 102, 19-19. [3] Jin, B., Rolle, M., Li, T., Haderlein, S.B., 2014. Diffusive fractionation of BTEX and chlorinated ethenes in aqueous solution: quantification of spatial isotope gradients. Environ. Sci. Technol. 48, 6141-6150.

X-ray Diffuse Scattering from Ultrafast Laser Excited Solids

NASA Astrophysics Data System (ADS)

Trigo, Mariano; Sheu, Yu-Miin; Chen, Jian; Reis, David; Fahy, Stephen; Murray, Eamonn; Graber, Timothy; Henning, Robert

2009-03-01

Intense, ultrashort laser pulses can be used to excite and detect coherent phonons in solids. However, optical experiments can only probe a reduced fraction of the Brillouin zone and hence most of the decay channels of such coherent phonons become invisible. In contrast, time-resolved x-ray diffuse scattering (TRXDS) has the potential to be the ultimate tool to study these phonon decay processes throughout the Brillouin-zone of the crystal. In our work, performed at the BioCARS beamline at the Advanced Photon Source, we use synchrotron time-resolved diffuse x-ray scattering to study Si and Bi under intense laser excitation with 100 ps resolution. We show that reasonable signal levels can be achieved with incident flux of 10^12 photons comparable to the flux that will be available at future 4th generation sources such as the LCLS in a single pulse. These sources will also provide three orders of magnitude shorter pulses; thus, this experiment serves as a test of the feasibility of time-resolved X-ray diffuse scattering as a tool for studying nonequilibrium phonon dynamics in solids.

Some analyses of the chemistry and diffusion of SST exhaust materials during phase 3 of the wake period. [in lower stratosphere

NASA Technical Reports Server (NTRS)

Hilst, G. R.; Donaldson, C. D.; Contiliano, R. M.

1973-01-01

In the generally stably stratified lower stratosphere, SST exhaust plumes could spend a significant length of time in a relatively undispersed state. This effort has utilized invariant modeling techniques to simulate the separate and combined effects of atmospheric turbulence, turbulent diffusion, and chemical reactions of SST exhaust materials in the lower stratosphere. The primary results to date are: (1) The combination of relatively slow diffusive mixing and rapid chemical reactions during the Phase III wake period minimizes the effect of SST exhausts on O3 depletion by the so-called NOx catalytic cycle. While the SST-produced NO is substantially above background concentrations, it appears diffusive mixing of NO and O3 is simply too slow to produce the O3 depletions originally proposed. (2) The time required to dilute the SST exhaust plume may be a significant fraction of the total time these materials are resident in the lower stratosphere. If this is the case, then prior estimates of the environmental impact of these materials must be revised significantly downward.

Diffuse gamma-ray emission from pulsars in the Large Magellanic Cloud

NASA Technical Reports Server (NTRS)

Hartmann, Dieter H.; Brown, Lawrence E.; Schnepf, Neil

1993-01-01

We investigate the contribution of pulsars to the diffuse gamma-ray emission from the LMC. The pulsar birth rate in the LMC is a factor of about 10 lower than that of the Galaxy and the distance to pulsars in the LMC is about 5-10 times larger than to Galactic pulsars. The resulting total integrated photon flux from LMC pulsars is thus reduced by a factor of about 100 to 1000. However, the surface brightness is not reduced by the same amount because of the much smaller angular extent of the LMC in comparison to the diffuse glow from the Galactic plane. We show that gamma-ray emission due to pulsars born in the LMC could produce gamma-ray fluxes that are larger than the inverse Compton component from relativistic cosmic-ray electrons and a significant fraction of the extragalactic isotropic background or the diffuse Galactic background in that direction. The diffuse pulsar glow above 100 MeV should therefore be included in models of high-energy emission from the LMC. For a gamma-ray beaming fraction of order unity the detected emissions from the LMC constrain the pulsar birth rate to less than one per 50 yr. This limit is about one order of magnitude above the supernova rate inferred from the historic record or from the star-formation rate.

Diffusion anisotropy in fresh and fixed prostate tissue ex vivo.

PubMed

Bourne, Roger M; Bongers, Andre; Chatterjee, Aritrick; Sved, Paul; Watson, Geoffrey

2016-08-01

To investigate diffusion anisotropy in whole human prostate specimens Seven whole radical prostatectomy specimens were obtained with informed patient consent and institutional ethics approval. Diffusion tensor imaging was performed at 9.4 Tesla. Diffusion tensors were calculated from the native acquired data and after progressive downsampling Fractional anisotropy (FA) decreased as voxel volume increased, and differed widely between prostates. Fixation decreased mean FA by ∼0.05-0.08 at all voxel volumes but did not alter principle eigenvector orientation. In unfixed tissue high FA (> 0.6) was found only in voxels of volume <0.5 mm(3) , and then only in a small fraction of all voxels. At typical clinical voxel volumes (4-16 mm(3) ) less than 50% of voxels had FA > 0.25. FA decreased at longer diffusion times (Δ = 60 or 80 ms compared with 20 ms), but only by ∼0.02 at typical clinical voxel volume. Peripheral zone FA was significantly lower than transition zone FA in five of the seven prostates FA varies widely between prostates. The very small proportion of clinical size voxels with high FA suggests that in clinical DWI studies ADC based on three-direction measurements will be minimally affected by anisotropy. Magn Reson Med 76:626-634, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Sign Crossover in All Maxwell-Stefan Diffusivities for Molten Salt LiF-BeF2: A Molecular Dynamics Study.

PubMed

Chakraborty, Brahmananda

2015-08-20

Applying Green-Kubo formalism and equilibrium molecular dynamics (MD) simulations, we have studied for the first time the dynamic correlation, Onsager coefficients, and Maxwell-Stefan (MS) diffusivities of molten salt LiF-BeF2, which is a potential candidate for a coolant in a high temperature reactor. We observe an unusual composition dependence and strikingly a crossover in sign for all the MS diffusivities at a composition of around 7% of LiF where the MS diffusivity between cation-anion pair (Đ(BeF) and Đ(LiF)) jumps from positive to negative value while the MS diffusivity between cation-cation pair (Đ(LiBe)) becomes positive from a negative value. Even though the negative MS diffusivities have been observed for electrolyte solutions between cation-cation pair, here we report negative MS diffusivity between cation-anion pair where Đ(BeF) shows a sharp rise around 66% of BeF2, reaches maximum value at 70% of BeF2, and then decreases almost exponentially with a sign change for BeF2 around 93%. For low mole fraction of LiF, Đ(BeF) follows the Debye-Huckel theory and rises with the square root of LiF mole fraction similar to the MS diffusivity between cation-anion pair in aqueous solution of electrolyte salt. Negative MS diffusivities while unusual are, however, shown to satisfy the non-negative entropy constraints at all thermodynamic states as required by the second law of thermodynamics. We have established a strong correlation between the structure and dynamics and predict that the formation of flouride polyanion network between Be and F ions and coulomb interaction is responsible for sharp variation of the MS diffusivities which controls the multicomponent diffusion phenomenon in LiF-BeF2 which has a strong impact on the performance of the reactor.

Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

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

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

2017-05-20

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

Fractional phenomenology of cosmic ray anomalous diffusion

NASA Astrophysics Data System (ADS)

Uchaikin, V. V.

2013-11-01

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

Regional Microstructural and Volumetric Magnetic Resonance Imaging (MRI) Abnormalities in the Corpus Callosum of Neonates With Congenital Heart Defect Undergoing Cardiac Surgery.

PubMed

Hagmann, Cornelia; Singer, Jitka; Latal, Beatrice; Knirsch, Walter; Makki, Malek

2016-03-01

The purpose of the study is to investigate the structural development of the corpus callosum in term neonates with congenital heart defect before and after surgery using diffusion tensor imaging and 3-dimensional T1-weighted magnetic resonance imaging (MRI). We compared parallel and radial diffusions, apparent diffusion coefficient (ADC), fractional anisotropy, and volume of 5 substructures of the corpus callosum: genu, rostral body, body, isthmus, and splenium. Compared to healthy controls, we found a significantly lower volume of the splenium and total corpus callosum and a higher radial diffusion and lower fractional anisotropy in the splenium of patients presurgery; a lower volume in all substructures in the postsurgery group; higher radial diffusion in the rostral body, body, and splenium; and a higher apparent diffusion coefficient in the splenium of postsurgery patients. Similar fractional anisotropy changes in congenital heart defect patients were reported in preterm infants. Our findings in apparent diffusion coefficient in the splenium of these patients (pre and postsurgery) are comparable to findings in preterm neonates with psychomotor delay. Delayed maturation of the isthmus was also reported in preterm infants. © The Author(s) 2015.

White matter microstructure throughout the brain correlates with visual imagery in grapheme-color synesthesia.

PubMed

Whitaker, Kirstie J; Kang, Xiaojian; Herron, Timothy J; Woods, David L; Robertson, Lynn C; Alvarez, Bryan D

2014-04-15

In this study we show, for the first time, a correlation between the neuroanatomy of the synesthetic brain and a metric that measures behavior not exclusive to the synesthetic experience. Grapheme-color synesthetes (n=20), who experience colors triggered by viewing or thinking of specific letters or numbers, showed altered white matter microstructure, as measured using diffusion tensor imaging, compared with carefully matched non-synesthetic controls. Synesthetes had lower fractional anisotropy and higher perpendicular diffusivity when compared to non-synesthetic controls. An analysis of the mode of anisotropy suggested that these differences were likely due to the presence of more crossing pathways in the brains of synesthetes. Additionally, these differences in white matter microstructure correlated negatively, and only for synesthetes, with a measure of the vividness of their visual imagery. Synesthetes who reported the most vivid visual imagery had the lowest fractional anisotropy and highest perpendicular diffusivity. We conclude that synesthetes as a population vary along a continuum while showing categorical differences in neuroanatomy and behavior compared to non-synesthetes. Copyright © 2013 Elsevier Inc. All rights reserved.

A novel bicomponent hemolysin from Bacillus cereus.

PubMed Central

Beecher, D J; MacMillan, J D

1990-01-01

A procedure combining isoelectric focusing (Sephadex IEF) and fast protein liquid chromatography (Superose 12; Mono-Q) removed hemolytic activity (presumably a contaminant) from partially purified preparations of the multicomponent diarrheal enterotoxin produced by Bacillus cereus. However, when the separated fractions were recombined, hemolytic activity was restored, suggesting that hemolysis is a property of the enterotoxin components. Combined fractions exhibited a unique ring pattern in gel diffusion assays in blood agar. During diffusion of the hemolysin from an agar well, the erythrocytes closest to the well were not lysed initially. After diffusion, hemolysis was observed as a sharp ring beginning several millimeters away from the edge of the well. With time the cells closer to the well were also lysed. This novel hemolysin consists of a protein (component B) which binds to or alters cells, allowing subsequent lysis by a second protein (component L). Sodium dodecyl sulfate-polyacrylamide gel electrophoresis, isoelectric focusing, and Western blot analysis showed that hemolysin BL has properties similar to those described previously for the enterotoxin and that both components are distinct from cereolysin and cereolysin AB. Images PMID:2114359

Characterization of the atrazine sorption process on Andisol and Ultisol volcanic ash-derived soils: kinetic parameters and the contribution of humic fractions.

PubMed

Báez, María E; Fuentes, Edwar; Espinoza, Jeannette

2013-07-03

Atrazine sorption was studied in six Andisol and Ultisol soils. Humic and fulvic acids and humin contributions were established. Sorption on soils was well described by the Freundlich model. Kf values ranged from 2.2-15.6 μg(1-1/n)mL(1/n)g⁻¹. The relevance of humic acid and humin was deduced from isotherm and kinetics experiments. KOC values varied between 221 and 679 mLg⁻¹ for these fractions. Fulvic acid presented low binding capacity. Sorption was controlled by instantaneous equilibrium followed by a time-dependent phase. The Elovich equation, intraparticle diffusion model, and a two-site nonequilibrium model allowed us to conclude that (i) there are two rate-limited phases in Andisols related to intrasorbent diffusion in organic matter and retarded intraparticle diffusion in the organo-mineral complex and that (ii) there is one rate-limited phase in Ultisols attributed to the mineral composition. The lower organic matter content of Ultisols and the slower sorption rate and mechanisms involved must be considered to assess the leaching behavior of atrazine.

In vivo free-breathing DTI and IVIM of the whole human heart using a real-time slice-followed SE-EPI navigator-based sequence: A reproducibility study in healthy volunteers.

PubMed

Moulin, Kevin; Croisille, Pierre; Feiweier, Thorsten; Delattre, Benedicte M A; Wei, Hongjiang; Robert, Benjamin; Beuf, Olivier; Viallon, Magalie

2016-07-01

In this study, we proposed an efficient free-breathing strategy for rapid and improved cardiac diffusion-weighted imaging (DWI) acquisition using a single-shot spin-echo echo planar imaging (SE-EPI) sequence. A real-time slice-following technique during free-breathing was combined with a sliding acquisition-window strategy prior Principal Component Analysis temporal Maximum Intensity Projection (PCAtMIP) postprocessing of in-plane co-registered diffusion-weighted images. This methodology was applied to 10 volunteers to quantify the performance of the motion correction technique and the reproducibility of diffusion parameters. The slice-following technique offers a powerful head-foot respiratory motion management solution for SE-EPI cDWI with the advantage of a 100% duty cycle scanning efficiency. The level of co-registration was further improved using nonrigid motion corrections and was evaluated with a co-registration index. Vascular fraction f and the diffusion coefficients D and D* were determined to be 0.122 ± 0.013, 1.41 ± 0.09 × 10(-3) mm(2) /s and 43.6 ± 9.2 × 10(-3) mm(2) /s, respectively. From the multidirectional dataset, the measured mean diffusivity was 1.72 ± 0.09 × 10(-3) mm(2) /s and the fractional anisotropy was 0.36 ± 0.02. The slice-following DWI SE-EPI sequence is a promising solution for clinical implementation, offering a robust improved workflow for further evaluation of DWI in cardiology. Magn Reson Med 76:70-82, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Microstructural effects in drug release by solid and cellular polymeric dosage forms: A comparative study.

PubMed

Blaesi, Aron H; Saka, Nannaji

2017-11-01

In recent studies, we have introduced melt-processed polymeric cellular dosage forms to achieve both immediate drug release and predictable manufacture. Dosage forms ranging from minimally-porous solids to highly porous, open-cell and thin-walled structures were prepared, and the drug release characteristics investigated as the volume fraction of cells and the excipient molecular weight were varied. In the present study, both minimally-porous solid and cellular dosage forms consisting of various weight fractions of Acetaminophen drug and polyethylene glycol (PEG) excipient are prepared and analyzed. Microstructures of the solid forms and the cell walls range from single-phase solid solutions of the excipient and a small amount of drug molecules to two-phase composites of the excipient and tightly packed drug particles. Results of dissolution experiments show that the minimally-porous solid forms disintegrate and release drug by slow surface erosion. The erosion rate decreases as the drug weight fraction is increased. By contrast, the open-cell structures disintegrate rapidly by viscous exfoliation, and the disintegration time is independent of drug weight fraction. Drug release models suggest that the solid forms erode by convective mass transfer of the faster-eroding excipient if the drug volume fraction is small. At larger drug volume fractions, however, the slower-eroding drug particles hinder access of the free-flowing fluid to the excipient, thus slowing down erosion of the composite. Conversely, the disintegration rate of the cellular forms is limited by diffusion of the dissolution fluid into the excipient phase of the thin cell walls. Because the wall thickness is of the order of the drug particle size, and the particles are enveloped by the excipient during melt-processing, the drug particles cannot hinder diffusion through the excipient across the walls. Thus the disintegration time of the cellular forms is mostly unaffected by the volume fraction of drug in the walls. Copyright © 2017 Elsevier B.V. All rights reserved.

Evenly spaced Detrended Fluctuation Analysis: Selecting the number of points for the diffusion plot

NASA Astrophysics Data System (ADS)

Liddy, Joshua J.; Haddad, Jeffrey M.

2018-02-01

Detrended Fluctuation Analysis (DFA) has become a widely-used tool to examine the correlation structure of a time series and provided insights into neuromuscular health and disease states. As the popularity of utilizing DFA in the human behavioral sciences has grown, understanding its limitations and how to properly determine parameters is becoming increasingly important. DFA examines the correlation structure of variability in a time series by computing α, the slope of the log SD- log n diffusion plot. When using the traditional DFA algorithm, the timescales, n, are often selected as a set of integers between a minimum and maximum length based on the number of data points in the time series. This produces non-uniformly distributed values of n in logarithmic scale, which influences the estimation of α due to a disproportionate weighting of the long-timescale regions of the diffusion plot. Recently, the evenly spaced DFA and evenly spaced average DFA algorithms were introduced. Both algorithms compute α by selecting k points for the diffusion plot based on the minimum and maximum timescales of interest and improve the consistency of α estimates for simulated fractional Gaussian noise and fractional Brownian motion time series. Two issues that remain unaddressed are (1) how to select k and (2) whether the evenly-spaced DFA algorithms show similar benefits when assessing human behavioral data. We manipulated k and examined its effects on the accuracy, consistency, and confidence limits of α in simulated and experimental time series. We demonstrate that the accuracy and consistency of α are relatively unaffected by the selection of k. However, the confidence limits of α narrow as k increases, dramatically reducing measurement uncertainty for single trials. We provide guidelines for selecting k and discuss potential uses of the evenly spaced DFA algorithms when assessing human behavioral data.

Molecular dynamics simulation of three plastic additives' diffusion in polyethylene terephthalate.

PubMed

Li, Bo; Wang, Zhi-Wei; Lin, Qin-Bao; Hu, Chang-Ying

2017-06-01

Accurate diffusion coefficient data of additives in a polymer are of paramount importance for estimating the migration of the additives over time. This paper shows how this diffusion coefficient can be estimated for three plastic additives [2-(2'-hydroxy-5'-methylphenyl) (UV-P), 2,6-di-tert-butyl-4-methylphenol (BHT) and di-(2-ethylhexyl) phthalate (DEHP)] in polyethylene terephthalate (PET) using the molecular dynamics (MD) simulation method. MD simulations were performed at temperatures of 293-433 K. The diffusion coefficient was calculated through the Einstein relationship connecting the data of mean-square displacement at different times. Comparison of the diffusion coefficients simulated by the MD simulation technique, predicted by the Piringer model and experiments, showed that, except for a few samples, the MD-simulated values were in agreement with the experimental values within one order of magnitude. Furthermore, the diffusion process for additives is discussed in detail, and four factors - the interaction energy between additive molecules and PET, fractional free volume, molecular shape and size, and self-diffusion of the polymer - are proposed to illustrate the microscopic diffusion mechanism. The movement trajectories of additives in PET cell models suggested that the additive molecules oscillate slowly rather than hopping for a long time. Occasionally, when a sufficiently large hole was created adjacently, the molecule could undergo spatial motion by jumping into the free-volume hole and consequently start a continuous oscillation and hop. The results indicate that MD simulation is a useful approach for predicting the microstructure and diffusion coefficient of plastic additives, and help to estimate the migration level of additives from PET packaging.

Is Solute Rotation in an Ionic Liquid Influenced by the Addition of Glucose?

PubMed

Maurya, Rajan; Naithani, Sudhanshu; Bandyopadhyay, Dibyendu; Choudhury, Niharendu; Dutt, G B

2017-12-07

Fluorescence anisotropy measurements and molecular dynamics (MD) simulations have been performed to understand the specific interactions of two structurally similar nondipolar solutes, 2,5-dimethyl-1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole (DMDPP) and 1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole (DPP), with neat 1-butyl-3-methylimidazolium dicyanamide ([BMIM][N(CN) 2 ]) and also in the presence of glucose. It has been observed that the measured reorientation times of DMDPP in neat [BMIM][N(CN) 2 ] follow the predictions of the Stokes-Einstein-Debye hydrodynamic theory with slip boundary condition. Addition of glucose (0.075 and 0.15 mole fraction) has no bearing on the rotational diffusion of the solute apart from the viscosity related effects. In contrast, the reorientation times of DPP in neat [BMIM][N(CN) 2 ] obey stick boundary condition as the hydrogen bond donating solute experiences specific interactions with the dicyanamide anion. No influence of the additive can be noticed on the rotational diffusion of DPP at 0.075 mole fraction of glucose. However, at 0.15 mole fraction of glucose, the reorientation times of the solute at a given viscosity and temperature decrease by 15-40% compared to those obtained in the neat ionic liquid. MD simulations indicate that each DPP molecule hydrogen bonds with two dicyanamide anions in neat ionic liquid. The simulations also reveal that, at 0.15 mole fraction of glucose, the concentration of anions hydrogen bonded to glucose increases significantly; therefore, the percentage of solute molecules that can form hydrogen bonds with two dicyanamide anions decreases to 84, which leads to faster rotation of DPP.

Fractal Model of Fission Product Release in Nuclear Fuel

NASA Astrophysics Data System (ADS)

Stankunas, Gediminas

2012-09-01

A model of fission gas migration in nuclear fuel pellet is proposed. Diffusion process of fission gas in granular structure of nuclear fuel with presence of inter-granular bubbles in the fuel matrix is simulated by fractional diffusion model. The Grunwald-Letnikov derivative parameter characterizes the influence of porous fuel matrix on the diffusion process of fission gas. A finite-difference method for solving fractional diffusion equations is considered. Numerical solution of diffusion equation shows correlation of fission gas release and Grunwald-Letnikov derivative parameter. Calculated profile of fission gas concentration distribution is similar to that obtained in the experimental studies. Diffusion of fission gas is modeled for real RBMK-1500 fuel operation conditions. A functional dependence of Grunwald-Letnikov derivative parameter with fuel burn-up is established.

Anomalous Diffusion of Water in Lamellar Membranes Formed by Pluronic Polymers

NASA Astrophysics Data System (ADS)

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

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

A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Chen, Hao; Lv, Wen; Zhang, Tongtong

2018-05-01

We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

Radiative Extinction of Gaseous Spherical Diffusion Flames in Microgravity

NASA Technical Reports Server (NTRS)

Santa, K. J.; Chao, B. H.; Sunderland, P. B.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2007-01-01

Radiative extinction of spherical diffusion flames was investigated experimentally and numerically. The experiments involved microgravity spherical diffusion flames burning ethylene and propane at 0.98 bar. Both normal (fuel flowing into oxidizer) and inverse (oxidizer flowing into fuel) flames were studied, with nitrogen supplied to either the fuel or the oxygen. Flame conditions were chosen to ensure that the flames extinguished within the 2.2 s of available test time; thus extinction occurred during unsteady flame conditions. Diagnostics included color video and thin-filament pyrometry. The computations, which simulated flow from a porous sphere into a quiescent environment, included detailed chemistry, transport and radiation, and yielded transient results. Radiative extinction was observed experimentally and simulated numerically. Extinction time, peak temperature, and radiative loss fraction were found to be independent of flow rate except at very low flow rates. Radiative heat loss was dominated by the combustion products downstream of the flame and was found to scale with flame surface area, not volume. For large transient flames the heat release rate also scaled with surface area and thus the radiative loss fraction was largely independent of flow rate. Peak temperatures at extinction onset were about 1100 K, which is significantly lower than for kinetic extinction. One observation of this work is that while radiative heat losses can drive transient extinction, this is not because radiative losses are increasing with time (flame size) but rather because the heat release rate is falling off as the temperature drops.

Longitudinal diffusion MRI for treatment response assessment: Preliminary experience using an MRI-guided tri-cobalt 60 radiotherapy system.

PubMed

Yang, Yingli; Cao, Minsong; Sheng, Ke; Gao, Yu; Chen, Allen; Kamrava, Mitch; Lee, Percy; Agazaryan, Nzhde; Lamb, James; Thomas, David; Low, Daniel; Hu, Peng

2016-03-01

To demonstrate the preliminary feasibility of a longitudinal diffusion magnetic resonance imaging (MRI) strategy for assessing patient response to radiotherapy at 0.35 T using an MRI-guided radiotherapy system (ViewRay). Six patients (three head and neck cancer, three sarcoma) who underwent fractionated radiotherapy were enrolled in this study. A 2D multislice spin echo single-shot echo planar imaging diffusion pulse sequence was implemented on the ViewRay system and tested in phantom studies. The same pulse sequence was used to acquire longitudinal diffusion data (every 2-5 fractions) on the six patients throughout the entire course of radiotherapy. The reproducibility of the apparent diffusion coefficient (ADC) measurements was assessed using reference regions and the temporal variations of the tumor ADC values were evaluated. In diffusion phantom studies, the ADC values measured on the ViewRay system matched well with reference ADC values with <5% error for a range of ground truth diffusion coefficients of 0.4-1.1 × 10(-3) mm(2)/s. The remote reference regions (i.e., brainstem in head and neck patients) had consistent ADC values throughout the therapy for all three head and neck patients, indicating acceptable reproducibility of the diffusion imaging sequence. The tumor ADC values changed throughout therapy, with the change differing between patients, ranging from a 40% drop in ADC within the first week of therapy to gradually increasing throughout therapy. For larger tumors, intratumoral heterogeneity was observed. For one sarcoma patient, postradiotherapy biopsy showed less than 10% necrosis score, which correlated with the observed 40% decrease in ADC from the fifth fraction to the eighth treatment fraction. This pilot study demonstrated that longitudinal diffusion MRI is feasible using the 0.35 T ViewRay MRI. Larger patient cohort studies are warranted to correlate the longitudinal diffusion measurements to patient outcomes. Such an approach may enable response-guided adaptive radiotherapy.

Continuum model for hydrogen pickup in zirconium alloys of LWR fuel cladding

NASA Astrophysics Data System (ADS)

Wang, Xing; Zheng, Ming-Jie; Szlufarska, Izabela; Morgan, Dane

2017-04-01

A continuum model for calculating the time-dependent hydrogen pickup fractions in various Zirconium alloys under steam and pressured water oxidation has been developed in this study. Using only one fitting parameter, the effective hydrogen gas partial pressure at the oxide surface, a qualitative agreement is obtained between the predicted and previously measured hydrogen pickup fractions. The calculation results therefore demonstrate that H diffusion through the dense oxide layer plays an important role in the hydrogen pickup process. The limitations and possible improvement of the model are also discussed.

Observation of interspecies ion separation in inertial-confinement-fusion implosions

DOE PAGES

Hsu, Scott C.; Joshi, Tirtha Raj; Hakel, Peter; ...

2016-10-24

Here we report direct experimental evidence of interspecies ion separation in direct-drive, inertial-confinement-fusion experiments on the OMEGA laser facility. These experiments, which used plastic capsules with D 2/Ar gas fill (1% Ar by atom), were designed specifically to reveal interspecies ion separation by exploiting the predicted, strong ion thermo-diffusion between ion species of large mass and charge difference. Via detailed analyses of imaging x-ray-spectroscopy data, we extract Ar-atom-fraction radial profiles at different times, and observe both enhancement and depletion compared to the initial 1%-Ar gas fill. The experimental results are interpreted with radiation-hydrodynamic simulations that include recently implemented, first-principles modelsmore » of interspecies ion diffusion. Finally, the experimentally inferred Ar-atom-fraction profiles agree reasonably, but not exactly, with calculated profiles associated with the incoming and rebounding first shock.« less

Simulating Isotope Enrichment by Gaseous Diffusion

NASA Astrophysics Data System (ADS)

Reed, Cameron

2015-04-01

A desktop-computer simulation of isotope enrichment by gaseous diffusion has been developed. The simulation incorporates two non-interacting point-mass species whose members pass through a cascade of cells containing porous membranes and retain constant speeds as they reflect off the walls of the cells and the spaces between holes in the membranes. A particular feature is periodic forward recycling of enriched material to cells further along the cascade along with simultaneous return of depleted material to preceding cells. The number of particles, the mass ratio, the initial fractional abundance of the lighter species, and the time between recycling operations can be chosen by the user. The simulation is simple enough to be understood on the basis of two-dimensional kinematics, and demonstrates that the fractional abundance of the lighter-isotope species increases along the cascade. The logic of the simulation will be described and results of some typical runs will be presented and discussed.

Modeling the erythemal surface diffuse irradiance fraction for Badajoz, Spain

NASA Astrophysics Data System (ADS)

Sanchez, Guadalupe; Serrano, Antonio; Cancillo, María Luisa

2017-10-01

Despite its important role on the human health and numerous biological processes, the diffuse component of the erythemal ultraviolet irradiance (UVER) is scarcely measured at standard radiometric stations and therefore needs to be estimated. This study proposes and compares 10 empirical models to estimate the UVER diffuse fraction. These models are inspired from mathematical expressions originally used to estimate total diffuse fraction, but, in this study, they are applied to the UVER case and tested against experimental measurements. In addition to adapting to the UVER range the various independent variables involved in these models, the total ozone column has been added in order to account for its strong impact on the attenuation of ultraviolet radiation. The proposed models are fitted to experimental measurements and validated against an independent subset. The best-performing model (RAU3) is based on a model proposed by Ruiz-Arias et al. (2010) and shows values of r2 equal to 0.91 and relative root-mean-square error (rRMSE) equal to 6.1 %. The performance achieved by this entirely empirical model is better than those obtained by previous semi-empirical approaches and therefore needs no additional information from other physically based models. This study expands on previous research to the ultraviolet range and provides reliable empirical models to accurately estimate the UVER diffuse fraction.

Longitudinal brain white matter alterations in minimal hepatic encephalopathy before and after liver transplantation.

PubMed

Lin, Wei-Che; Chou, Kun-Hsien; Chen, Chao-Long; Chen, Hsiu-Ling; Lu, Cheng-Hsien; Li, Shau-Hsuan; Huang, Chu-Chung; Lin, Ching-Po; Cheng, Yu-Fan

2014-01-01

Cerebral edema is the common pathogenic mechanism for cognitive impairment in minimal hepatic encephalopathy. Whether complete reversibility of brain edema, cognitive deficits, and their associated imaging can be achieved after liver transplantation remains an open question. To characterize white matter integrity before and after liver transplantation in patients with minimal hepatic encephalopathy, multiple diffusivity indices acquired via diffusion tensor imaging was applied. Twenty-eight patients and thirty age- and sex-matched healthy volunteers were included. Multiple diffusivity indices were obtained from diffusion tensor images, including mean diffusivity, fractional anisotropy, axial diffusivity and radial diffusivity. The assessment was repeated 6-12 month after transplantation. Differences in white matter integrity between groups, as well as longitudinal changes, were evaluated using tract-based spatial statistical analysis. Correlation analyses were performed to identify first scan before transplantation and interval changes among the neuropsychiatric tests, clinical laboratory tests, and diffusion tensor imaging indices. After transplantation, decreased water diffusivity without fractional anisotropy change indicating reversible cerebral edema was found in the left anterior cingulate, claustrum, postcentral gyrus, and right corpus callosum. However, a progressive decrease in fractional anisotropy and an increase in radial diffusivity suggesting demyelination were noted in temporal lobe. Improved pre-transplantation albumin levels and interval changes were associated with better recoveries of diffusion tensor imaging indices. Improvements in interval diffusion tensor imaging indices in the right postcentral gyrus were correlated with visuospatial function score correction. In conclusion, longitudinal voxel-wise analysis of multiple diffusion tensor imaging indices demonstrated different white matter changes in minimal hepatic encephalopathy patients. Transplantation improved extracellular cerebral edema and the results of associated cognition tests. However, white matter demyelination may advance in temporal lobe.

A model for shrinkage strain in photo polymerization of dental composites.

PubMed

Petrovic, Ljubomir M; Atanackovic, Teodor M

2008-04-01

We formulate a new model for the shrinkage strain developed during photo polymerization in dental composites. The model is based on the diffusion type fractional order equation, since it has been proved that polymerization reaction is diffusion controlled (Atai M, Watts DC. A new kinetic model for the photo polymerization shrinkage-strain of dental composites and resin-monomers. Dent Mater 2006;22:785-91). Our model strongly confirms the observation by Atai and Watts (see reference details above) and their experimental results. The shrinkage strain is modeled by a nonlinear differential equation in (see reference details above) and that equation must be solved numerically. In our approach, we use the linear fractional order differential equation to describe the strain rate due to photo polymerization. This equation is solved exactly. As shrinkage is a consequence of the polymerization reaction and polymerization reaction is diffusion controlled, we postulate that shrinkage strain rate is described by a diffusion type equation. We find explicit form of solution to this equation and determine the strain in the resin monomers. Also by using equations of linear viscoelasticity, we determine stresses in the polymer due to the shrinkage. The time evolution of stresses implies that the maximal stresses are developed at the very beginning of the polymerization process. The stress in a dental composite that is light treated has the largest value short time after the treatment starts. The strain settles at the constant value in the time of about 100s (for the cases treated in Atai and Watts). From the model developed here, the shrinkage strain of dental composites and resin monomers is analytically determined. The maximal value of stresses is important, since this value must be smaller than the adhesive bond strength at cavo-restoration interface. The maximum stress determined here depends on the diffusivity coefficient. Since diffusivity coefficient increases as polymerization proceeds, it follows that the periods of light treatments should be shorter at the beginning of the treatment and longer at the end of the treatment, with dark interval between the initial low intensity and following high intensity curing. This is because at the end of polymerization the stress relaxation cannot take place.

Computational Investigation of Soot and Radiation in Turbulent Reacting Flows

NASA Astrophysics Data System (ADS)

Lalit, Harshad

This study delves into computational modeling of soot and infrared radiation for turbulent reacting flows, detailed understanding of both of which is paramount in the design of cleaner engines and pollution control. In the first part of the study, the concept of Stochastic Time and Space Series Analysis (STASS) as a numerical tool to compute time dependent statistics of radiation intensity is introduced for a turbulent premixed flame. In the absence of high fidelity codes for large eddy simulation or direct numerical simulation of turbulent flames, the utility of STASS for radiation imaging of reacting flows to understand the flame structure is assessed by generating images of infrared radiation in spectral bands dominated by radiation from gas phase carbon dioxide and water vapor using an assumed PDF method. The study elucidates the need for time dependent computation of radiation intensity for validation with experiments and the need for accounting for turbulence radiation interactions for correctly predicting radiation intensity and consequently the flame temperature and NOx in a reacting fluid flow. Comparison of single point statistics of infrared radiation intensity with measurements show that STASS can not only predict the flame structure but also estimate the dynamics of thermochemical scalars in the flame with reasonable accuracy. While a time series is used to generate realizations of thermochemical scalars in the first part of the study, in the second part, instantaneous realizations of resolved scale temperature, CO2 and H2O mole fractions and soot volume fractions are extracted from a large eddy simulation (LES) to carry out quantitative imaging of radiation intensity (QIRI) for a turbulent soot generating ethylene diffusion flame. A primary motivation of the study is to establish QIRI as a computational tool for validation of soot models, especially in the absence of conventional flow field and measured scalar data for sooting flames. Realizations of scalars from the LES are used in conjunction with the radiation heat transfer equation and a narrow band radiation model to compute time dependent and time averaged images of infrared radiation intensity in spectral bands corresponding to molecular radiation from gas phase carbon dioxide and soot particles exclusively. While qualitative and quantitative comparisons with measured images in the CO2 radiation band show that the flame structure is correctly computed, images computed in the soot radiation band illustrate that the soot volume fraction is under predicted by the computations. The effect of the soot model and cause of under prediction is investigated further by correcting the soot volume fraction using an empirical state relationship. By comparing default simulations with computations using the state relation, it is shown that while the soot model under-estimates the soot concentration, it correctly computes the intermittency of soot in the flame. The study of sooting flames is extended further by performing a parametric analysis of physical and numerical parameters that affect soot formation and transport in two laboratory scale turbulent sooting flames, one fueled by natural gas and the other by ethylene. The study is focused on investigating the effect of molecular diffusion of species, dilution of fuel with hydrogen gas and the effect of chemical reaction mechanism on the soot concentration in the flame. The effect of species Lewis numbers on soot evolution and transport is investigated by carrying out simulations, first with the default equal diffusivity (ED) assumption and then by incorporating a differential diffusion (DD) model. Computations using the DD model over-estimate the concentration of the soot precursor and soot oxidizer species, leading to inconsistencies in the estimate of the soot concentration. The linear differential diffusion (LDD) model, reported previously to consistently model differential diffusion effects is implemented to correct the over prediction effect of the DD model. It is shown that the effect of species Lewis number on soot evolution is a secondary phenomenon and that soot is primarily transported by advection of the fluid in a turbulent flame. The effect of hydrogen dilution on the soot formation and transport process is also studied. It is noted that the decay of soot volume fraction and flame length with hydrogen addition follows trends observed in laminar sooting flame measurements. While hydrogen enhances mixing shown by the laminar flamelet solutions, the mixing effect does not significantly contribute to differential molecular diffusion effects in the soot nucleation regions downstream of the flame and has a negligible effect on soot transport. The sensitivity of computations of soot volume fraction towards the chemical reaction mechanism is shown. It is concluded that modeling reaction pathways of C3 and C4 species that lead up to Polycyclic Aromatic Hydrocarbon (PAH) molecule formation is paramount for accurate predictions of soot in the flame. (Abstract shortened by ProQuest.).

Best dispersal strategies in spatially heterogeneous environments: optimization of the principal eigenvalue for indefinite fractional Neumann problems.

PubMed

Pellacci, Benedetta; Verzini, Gianmaria

2018-05-01

We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the investigation of the survival threshold in population dynamics. Our main result concerns the optimization of such threshold with respect to the fractional order [Formula: see text], the case [Formula: see text] corresponding to the standard Neumann Laplacian: when the habitat is not too fragmented, the principal positive eigenvalue can not have local minima for [Formula: see text]. As a consequence, the best strategy for survival is either following the diffusion with [Formula: see text] (i.e. Brownian diffusion), or with the lowest possible s (i.e. diffusion allowing long jumps), depending on the size of the domain. In addition, we show that analogous results hold for the standard fractional Laplacian in [Formula: see text], in periodic environments.

Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering

NASA Astrophysics Data System (ADS)

Jeong, Seungwon; Lee, Ye-Ryoung; Choi, Wonjun; Kang, Sungsam; Hong, Jin Hee; Park, Jin-Sung; Lim, Yong-Sik; Park, Hong-Gyu; Choi, Wonshik

2018-05-01

The efficient delivery of light energy is a prerequisite for the non-invasive imaging and stimulating of target objects embedded deep within a scattering medium. However, the injected waves experience random diffusion by multiple light scattering, and only a small fraction reaches the target object. Here, we present a method to counteract wave diffusion and to focus multiple-scattered waves at the deeply embedded target. To realize this, we experimentally inject light into the reflection eigenchannels of a specific flight time to preferably enhance the intensity of those multiple-scattered waves that have interacted with the target object. For targets that are too deep to be visible by optical imaging, we demonstrate a more than tenfold enhancement in light energy delivery in comparison with ordinary wave diffusion cases. This work will lay a foundation to enhance the working depth of imaging, sensing and light stimulation.

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.

Diffuse radiation increases global ecosystem-level water-use efficiency

NASA Astrophysics Data System (ADS)

Moffat, A. M.; Reichstein, M.; Cescatti, A.; Knohl, A.; Zaehle, S.

2012-12-01

Current environmental changes lead not only to rising atmospheric CO2 levels and air temperature but also to changes in air pollution and thus the light quality of the solar radiation reaching the land-surface. While rising CO2 levels are thought to enhance photosynthesis and closure of stomata, thus leading to relative water savings, the effect of diffuse radiation on transpiration by plants is less clear. It has been speculated that the stimulation of photosynthesis by increased levels of diffuse light may be counteracted by higher transpiration and consequently water depletion and drought stress. Ultimately, in water co-limited systems, the overall effect of diffuse radiation will depend on the sensitivity of canopy transpiration versus photosynthesis to diffuse light, i.e. whether water-use efficiency changes with relative levels of diffuse light. Our study shows that water-use efficiency increases significantly with higher fractions of diffuse light. It uses the ecosystem-atmosphere gas-exchange observations obtained with the eddy covariance method at 29 flux tower sites. In contrast to previous global studies, the analysis is based directly on measurements of diffuse radiation. Its effect on water-use efficiency was derived by analyzing the multivariate response of carbon and water fluxes to radiation and air humidity using a purely empirical approach based on artificial neural networks. We infer that per unit change of diffuse fraction the water-use efficiency increases up to 40% depending on diffuse fraction levels and ecosystem type. Hence, in regions with increasing diffuse radiation positive effects on primary production are expected even under conditions where water is co-limiting productivity.

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

PubMed Central

2011-01-01

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

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

PubMed

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

2011-05-01

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

The physical and biological basis of quantitative parameters derived from diffusion MRI

PubMed Central

2012-01-01

Diffusion magnetic resonance imaging is a quantitative imaging technique that measures the underlying molecular diffusion of protons. Diffusion-weighted imaging (DWI) quantifies the apparent diffusion coefficient (ADC) which was first used to detect early ischemic stroke. However this does not take account of the directional dependence of diffusion seen in biological systems (anisotropy). Diffusion tensor imaging (DTI) provides a mathematical model of diffusion anisotropy and is widely used. Parameters, including fractional anisotropy (FA), mean diffusivity (MD), parallel and perpendicular diffusivity can be derived to provide sensitive, but non-specific, measures of altered tissue structure. They are typically assessed in clinical studies by voxel-based or region-of-interest based analyses. The increasing recognition of the limitations of the diffusion tensor model has led to more complex multi-compartment models such as CHARMED, AxCaliber or NODDI being developed to estimate microstructural parameters including axonal diameter, axonal density and fiber orientations. However these are not yet in routine clinical use due to lengthy acquisition times. In this review, I discuss how molecular diffusion may be measured using diffusion MRI, the biological and physical bases for the parameters derived from DWI and DTI, how these are used in clinical studies and the prospect of more complex tissue models providing helpful micro-structural information. PMID:23289085

Molecular modeling of diffusion coefficient and ionic conductivity of CO2 in aqueous ionic solutions.

PubMed

Garcia-Ratés, Miquel; de Hemptinne, Jean-Charles; Bonet Avalos, Josep; Nieto-Draghi, Carlos

2012-03-08

Mass diffusion coefficients of CO(2)/brine mixtures under thermodynamic conditions of deep saline aquifers have been investigated by molecular simulation. The objective of this work is to provide estimates of the diffusion coefficient of CO(2) in salty water to compensate the lack of experimental data on this property. We analyzed the influence of temperature, CO(2) concentration,and salinity on the diffusion coefficient, the rotational diffusion, as well as the electrical conductivity. We observe an increase of the mass diffusion coefficient with the temperature, but no clear dependence is identified with the salinity or with the CO(2) mole fraction, if the system is overall dilute. In this case, we notice an important dispersion on the values of the diffusion coefficient which impairs any conclusive statement about the effect of the gas concentration on the mobility of CO(2) molecules. Rotational relaxation times for water and CO(2) increase by decreasing temperature or increasing the salt concentration. We propose a correlation for the self-diffusion coefficient of CO(2) in terms of the rotational relaxation time which can ultimately be used to estimate the mutual diffusion coefficient of CO(2) in brine. The electrical conductivity of the CO(2)-brine mixtures was also calculated under different thermodynamic conditions. Electrical conductivity tends to increase with the temperature and salt concentration. However, we do not observe any influence of this property with the CO(2) concentration at the studied regimes. Our results give a first evaluation of the variation of the CO(2)-brine mass diffusion coefficient, rotational relaxation times, and electrical conductivity under the thermodynamic conditions typically encountered in deep saline aquifers.

Isotope Fractionation by Diffusion in Liquids (Final Technical Report)

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

Richter, Frank

The overall objective of the DOE-funded research by grant DE-FG02-01ER15254 was document and quantify kinetic isotope fractionations during chemical and thermal (i.e., Soret) diffusion in liquids (silicate melts and water) and in the later years to include alloys and major minerals such as olivine and pyroxene. The research involved both laboratory experiments and applications to natural settings. The key idea is that major element zoning on natural geologic materials is common and can arise for either changes in melt composition during cooling and crystallization or from diffusion. The isotope effects associated with diffusion that we have documented are the keymore » for determining whether or not the zoning observed in a natural system was the result of diffusion. Only in those cases were the zoning is demonstrably due to diffusion can use independently measured rates of diffusion to constrain the thermal evolution of the system.« less

Selective Adsorption and Selective Transport Diffusion of CO2-CH4 Binary Mixture in Coal Ultramicropores.

PubMed

Zhao, Yongliang; Feng, Yanhui; Zhang, Xinxin

2016-09-06

The adsorption and diffusion of the CO2-CH4 mixture in coal and the underlying mechanisms significantly affect the design and operation of any CO2-enhanced coal-bed methane recovery (CO2-ECBM) project. In this study, bituminous coal was fabricated based on the Wiser molecular model and its ultramicroporous parameters were evaluated; molecular simulations were established through Grand Canonical Monte Carlo (GCMC) and Molecular Dynamic (MD) methods to study the effects of temperature, pressure, and species bulk mole fraction on the adsorption isotherms, adsorption selectivity, three distinct diffusion coefficients, and diffusivity selectivity of the binary mixture in the coal ultramicropores. It turns out that the absolute adsorption amount of each species in the mixture decreases as temperature increases, but increases as its own bulk mole fraction increases. The self-, corrected, and transport diffusion coefficients of pure CO2 and pure CH4 all increase as temperature or/and their own bulk mole fractions increase. Compared to CH4, the adsorption and diffusion of CO2 are preferential in the coal ultramicropores. Adsorption selectivity and diffusivity selectivity were simultaneously employed to reveal that the optimal injection depth for CO2-ECBM is 800-1000 m at 308-323 K temperature and 8.0-10.0 MPa.

Two-dimensional single-shot diffusion-weighted stimulated EPI with reduced FOV for ultrahigh-b radial diffusion-weighted imaging of spinal cord.

PubMed

Sapkota, Nabraj; Shi, Xianfeng; Shah, Lubdha M; Bisson, Erica F; Rose, John W; Jeong, Eun-Kee

2017-06-01

High-resolution diffusion-weighted imaging (DWI) of the spinal cord (SC) is problematic because of the small cross-section of the SC and the large field inhomogeneity. Obtaining the ultrahigh-b DWI poses a further challenge. The purpose of the study was to design and validate two-dimensional (2D) single-shot diffusion-weighted stimulated echo planar imaging with reduced field of view (2D ss-DWSTEPI-rFOV) for ultrahigh-b radial DWI (UHB-rDWI) of the SC. A novel time-efficient 2D ss-DWSTEPI-rFOV sequence was developed based on the stimulated echo sequence. Reduced-phase field of view was obtained by using two slice-selective 90 ° radiofrequency pulses in the presence of the orthogonal slice selection gradients. The sequence was validated on a cylindrical phantom and demonstrated on SC imaging. Ultrahigh-b radial diffusion-weighted ( bmax = 7300 s/mm2) images of the SC with greatly reduced distortion were obtained. The exponential plus constant fitting of the diffusion-decay curve estimated the constant fraction (restricted water fraction) as 0.36 ± 0.05 in the SC white matter. A novel 2D ss-DWSTEPI-rFOV sequence has been designed and demonstrated for high-resolution UHB-rDWI of localized anatomic structures with significantly reduced distortion induced by nonlinear static field inhomogeneity. Magn Reson Med 77:2167-2173, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Improvement of Mechanical Properties of Spheroidized 1045 Steel by Induction Heat Treatment

NASA Astrophysics Data System (ADS)

Kim, Minwook; Shin, Jung-Ho; Choi, Young; Lee, Seok-Jae

2016-04-01

The effects of induction heat treatment on the formation of carbide particles and mechanical properties of spheroidized 1045 steel were investigated by means of microstructural analysis and tensile testing. The induction spheroidization accelerated the formation of spherical cementite particles and effectively softened the steel. The volume fraction of cementite was found to be a key factor that affected the mechanical properties of spheroidized steels. Further tests showed that sequential spheroidization by induction and furnace heat treatments enhanced elongation within a short spheroidization time, resulting in better mechanical properties. This was due to the higher volume fraction of spherical cementite particles that had less diffusion time for particle coarsening.

Calculation of the fractional interstitial component of boron diffusion and segregation coefficient of boron in Si0.8Ge0.2

NASA Astrophysics Data System (ADS)

Fang, Tilden T.; Fang, Wingra T. C.; Griffin, Peter B.; Plummer, James D.

1996-02-01

Investigation of boron diffusion in strained silicon germanium buried layers reveals a fractional interstitial component of boron diffusion (fBI) in Se0.8Ge0.2 approximately equal to the fBI value in silicon. In conjunction with computer-simulated boron profiles, the results yield an absolute lower-bound of fBI in Si0.8Ge0.2 of ˜0.8. In addition, the experimental methodology provides a unique vehicle for measuring the segregation coefficient; oxidation-enhanced diffusion is used instead of an extended, inert anneal to rapidly diffuse the dopant to equilibrium levels across the interface, allowing the segregation coefficient to be measured more quickly.

Multi-site Study of Diffusion Metric Variability: Characterizing the Effects of Site, Vendor, Field Strength, and Echo Time using the Histogram Distance.

PubMed

Helmer, K G; Chou, M-C; Preciado, R I; Gimi, B; Rollins, N K; Song, A; Turner, J; Mori, S

2016-02-27

MRI-based multi-site trials now routinely include some form of diffusion-weighted imaging (DWI) in their protocol. These studies can include data originating from scanners built by different vendors, each with their own set of unique protocol restrictions, including restrictions on the number of available gradient directions, whether an externally-generated list of gradient directions can be used, and restrictions on the echo time (TE). One challenge of multi-site studies is to create a common imaging protocol that will result in a reliable and accurate set of diffusion metrics. The present study describes the effect of site, scanner vendor, field strength, and TE on two common metrics: the first moment of the diffusion tensor field (mean diffusivity, MD), and the fractional anisotropy (FA). We have shown in earlier work that ROI metrics and the mean of MD and FA histograms are not sufficiently sensitive for use in site characterization. Here we use the distance between whole brain histograms of FA and MD to investigate within- and between-site effects. We concluded that the variability of DTI metrics due to site, vendor, field strength, and echo time could influence the results in multi-center trials and that histogram distance is sensitive metrics for each of these variables.

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.

Taming stochastic bifurcations in fractional-order systems via noise and delayed feedback

NASA Astrophysics Data System (ADS)

Sun, Zhongkui; Zhang, Jintian; Yang, Xiaoli; Xu, Wei

2017-08-01

The dynamics in fractional-order systems have been widely studied during the past decade due to the potential applications in new materials and anomalous diffusions, but the investigations have been so far restricted to a fractional-order system without time delay(s). In this paper, we report the first study of random responses of fractional-order system coupled with noise and delayed feedback. Stochastic averaging method has been utilized to determine the stationary probability density functions (PDFs) by means of the principle of minimum mean-square error, based on which stochastic bifurcations could be identified through recognizing the shape of the PDFs. It has been found that by changing the fractional order the shape of the PDFs can switch from unimodal distribution to bimodal one, or from bimodal distribution to unimodal one, thus announcing the onset of stochastic bifurcation. Further, we have demonstrated that by merely modulating the time delay, the feedback strengths, or the noise intensity, the shapes of PDFs can transit between a single peak and a double peak. Therefore, it provides an efficient candidate to control, say, induce or suppress, the stochastic bifurcations in fractional-order systems.

Use of Inert Gases and Carbon Monoxide to Study the Possible Influence of Countercurrent Exchange on Passive Absorption from the Small Bowel

PubMed Central

Bond, John H.; Levitt, David G.; Levitt, Michael D.

1974-01-01

The purpose of the present study was to quantitate the influence of countercurrent exchange on passive absorption of highly diffusible substances from the small intestine of the rabbit. The absorption of carbon monoxide, which is tightly bound to hemoglobin and therefore cannot exchange, was compared to the absorption of four unbound gases (H2, He, CH4, and 133Xe), which should exchange freely. The degree to which the observed absorption of the unbound gases falls below that predicted from CO absorption should provide a quantitative measure of countercurrent exchange. CO uptake at high luminal Pco is flow-limited and, assuming that villus and central hemoglobin concentrations are equal, the flow that equilibrates with CO (Fco) was calculated to equal 7.24 ml/min/100 g. The observed absorption rate of the unbound gases was from two to four times greater than would have been predicted had their entire uptake been accounted for by equilibration with Fco. This is the opposite of what would occur if countercurrent exchange retarded absorption of the unbound gases. The unbound gases have both flow- and diffusion-limited components, and Fco should account for only the fraction of absorption that is flow limited. A simple model of perfusion and diffusion made it possible to calculate the fraction of the total uptake of unbound gases that was flow limited. This fraction of the total observed absorption rate was still about 1.8 times greater than predicted by CO absorption. A possible explanation for this discrepancy is that plasma skimming reduces the hemoglobin of villus blood to about 60% of that of central blood. Thus, Fco is actually about 1.7 times greater than initially calculated, and with this correction, there is close agreement between the predicted and observed rates of absorption of each of the unbound gases. We conclude that countercurrent exchange does not influence passive absorption under the conditions of this study. PMID:4436431

First passage times and asymmetry of DNA translocation

NASA Astrophysics Data System (ADS)

Lua, Rhonald C.; Grosberg, Alexander Y.

2005-12-01

Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional Brownian motion in an asymmetric sawtooth potential, to exit one of the boundaries. We consider the first passage times for the case of classical diffusion, characterized by a mean-square displacement of the form ⟨(Δx)2⟩˜t , and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form ⟨(Δx)2⟩˜tγ with 0<γ<1 . In the context of classical diffusion, we obtain an expression for the mean first passage time and show that this quantity changes when the direction of the sawtooth is reversed or, equivalently, when the reflecting and absorbing boundaries are exchanged. We discuss at which numbers of “teeth” N (or number of DNA nucleotides) and at which heights of the sawtooth potential this difference becomes significant. For large N , it is well known that the mean first passage time scales as N2 . In the context of subdiffusion, the mean first passage time does not exist. Therefore, we obtain instead the distribution of first passage times in the limit of long times. We show that the prefactor in the power relation for this distribution is simply the expression for the mean first passage time in classical diffusion. We also describe a hypothetical experiment to calculate the average of the first passage times for a fraction of passage events that each end within some time t* . We show that this average first passage time scales as N2/γ in subdiffusion.

Assessing White Matter Microstructure in Brain Regions with Different Myelin Architecture Using MRI.

PubMed

Groeschel, Samuel; Hagberg, Gisela E; Schultz, Thomas; Balla, Dávid Z; Klose, Uwe; Hauser, Till-Karsten; Nägele, Thomas; Bieri, Oliver; Prasloski, Thomas; MacKay, Alex L; Krägeloh-Mann, Ingeborg; Scheffler, Klaus

2016-01-01

We investigate how known differences in myelin architecture between regions along the cortico-spinal tract and frontal white matter (WM) in 19 healthy adolescents are reflected in several quantitative MRI parameters that have been proposed to non-invasively probe WM microstructure. In a clinically feasible scan time, both conventional imaging sequences as well as microstructural MRI parameters were assessed in order to quantitatively characterise WM regions that are known to differ in the thickness of their myelin sheaths, and in the presence of crossing or parallel fibre organisation. We found that diffusion imaging, MR spectroscopy (MRS), myelin water fraction (MWF), Magnetization Transfer Imaging, and Quantitative Susceptibility Mapping were myelin-sensitive in different ways, giving complementary information for characterising WM microstructure with different underlying fibre architecture. From the diffusion parameters, neurite density (NODDI) was found to be more sensitive than fractional anisotropy (FA), underlining the limitation of FA in WM crossing fibre regions. In terms of sensitivity to different myelin content, we found that MWF, the mean diffusivity and chemical-shift imaging based MRS yielded the best discrimination between areas. Multimodal assessment of WM microstructure was possible within clinically feasible scan times using a broad combination of quantitative microstructural MRI sequences. By assessing new microstructural WM parameters we were able to provide normative data and discuss their interpretation in regions with different myelin architecture, as well as their possible application as biomarker for WM disorders.

Perilesional and contralateral white matter evolution and integrity in patients with periventricular nodular heterotopia and epilepsy: a longitudinal diffusion tensor imaging study.

PubMed

Liu, W; Yan, B; An, D; Niu, R; Tang, Y; Tong, X; Gong, Q; Zhou, D

2017-12-01

This study aimed to assess the evolution of perinodular and contralateral white matter abnormalities in patients with periventricular nodular heterotopia (PNH) and epilepsy. Diffusion tensor imaging (DTI) (64 directions) and 3 T structural magnetic resonance imaging were performed in 29 PNH patients (mean age 27.3 years), and 16 patients underwent a second scan (average time between the two scans 1.1 years). Fractional anisotropy and mean diffusivity were measured within the perilesional and contralateral white matter. Longitudinal analysis showed that white matter located 10 mm from the focal nodule displayed characteristics intermediate to tissue 5 mm away, and normal-appearing white matter (NAWM) also established evolution profiles of perinodular white matter in different cortical lobes. Compared to 29 age- and sex-matched healthy controls, significant decreased fractional anisotropy and elevated mean diffusivity values were observed in regions 5 and 10 mm from nodules (P < 0.01), whilst DTI metrics of the remaining NAWM did not differ significantly from controls. Additionally, normal DTI metrics were shown in the contralateral region in patients with unilateral PNH. Periventricular nodular heterotopia is associated with microstructural abnormalities within the perilesional white matter and the extent decreases with increasing distance from the nodule. In the homologous contralateral region, white matter diffusion metrics were unchanged in unilateral PNH. These findings have clinical implications with respect to the medical and surgical interventions of PNH-related epilepsy. © 2017 EAN.

Diffuse spreading of inhomogeneities in the ionospheric dusty plasma

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

Shalimov, S. L., E-mail: pmsk7@mail.ru; Kozlovsky, A.

2015-08-15

According to results of sounding of the lower ionosphere at altitudes of about 100 km, the duration of radio reflections from sufficiently dense ionized meteor trails, which characterizes their lifetime, can reach a few tens of seconds to several tens of minutes. This is much longer than the characteristic spreading time (on the order of fractions of a second to several seconds) typical in meteor radar measurements. The presence of dust in the lower ionosphere is shown to affect the ambipolar diffusion coefficient, which determines the spreading of plasma inhomogeneities. It is found that the diffusion coefficient depends substantially onmore » the charge and size of dust grains, which allows one to explain the results of ionospheric sounding.« less

Fluorescence correlation spectroscopy: the case of subdiffusion.

PubMed

Lubelski, Ariel; Klafter, Joseph

2009-03-18

The theory of fluorescence correlation spectroscopy is revisited here for the case of subdiffusing molecules. Subdiffusion is assumed to stem from a continuous-time random walk process with a fat-tailed distribution of waiting times and can therefore be formulated in terms of a fractional diffusion equation (FDE). The FDE plays the central role in developing the fluorescence correlation spectroscopy expressions, analogous to the role played by the simple diffusion equation for regular systems. Due to the nonstationary nature of the continuous-time random walk/FDE, some interesting properties emerge that are amenable to experimental verification and may help in discriminating among subdiffusion mechanisms. In particular, the current approach predicts 1), a strong dependence of correlation functions on the initial time (aging); 2), sensitivity of correlation functions to the averaging procedure, ensemble versus time averaging (ergodicity breaking); and 3), that the basic mean-squared displacement observable depends on how the mean is taken.

High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

NASA Astrophysics Data System (ADS)

Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

2018-06-01

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.

Subdiffusion in Membrane Permeation of Small Molecules.

PubMed

Chipot, Christophe; Comer, Jeffrey

2016-11-02

Within the solubility-diffusion model of passive membrane permeation of small molecules, translocation of the permeant across the biological membrane is traditionally assumed to obey the Smoluchowski diffusion equation, which is germane for classical diffusion on an inhomogeneous free-energy and diffusivity landscape. This equation, however, cannot accommodate subdiffusive regimes, which have long been recognized in lipid bilayer dynamics, notably in the lateral diffusion of individual lipids. Through extensive biased and unbiased molecular dynamics simulations, we show that one-dimensional translocation of methanol across a pure lipid membrane remains subdiffusive on timescales approaching typical permeation times. Analysis of permeant motion within the lipid bilayer reveals that, in the absence of a net force, the mean squared displacement depends on time as t 0.7 , in stark contrast with the conventional model, which assumes a strictly linear dependence. We further show that an alternate model using a fractional-derivative generalization of the Smoluchowski equation provides a rigorous framework for describing the motion of the permeant molecule on the pico- to nanosecond timescale. The observed subdiffusive behavior appears to emerge from a crossover between small-scale rattling of the permeant around its present position in the membrane and larger-scale displacements precipitated by the formation of transient voids.

A simple reaction-rate model for turbulent diffusion flames

NASA Technical Reports Server (NTRS)

Bangert, L. H.

1975-01-01

A simple reaction rate model is proposed for turbulent diffusion flames in which the reaction rate is proportional to the turbulence mixing rate. The reaction rate is also dependent on the mean mass fraction and the mean square fluctuation of mass fraction of each reactant. Calculations are compared with experimental data and are generally successful in predicting the measured quantities.

Progression of White Matter Hyperintensities Preceded by Heterogeneous Decline of Microstructural Integrity.

PubMed

van Leijsen, Esther M C; Bergkamp, Mayra I; van Uden, Ingeborg W M; Ghafoorian, Mohsen; van der Holst, Helena M; Norris, David G; Platel, Bram; Tuladhar, Anil M; de Leeuw, Frank-Erik

2018-05-03

White matter hyperintensities (WMH) are frequently seen on neuroimaging of elderly and are associated with cognitive decline and the development of dementia. Yet, the temporal dynamics of conversion of normal-appearing white matter (NAWM) into WMH remains unknown. We examined whether and when progression of WMH was preceded by changes in fluid-attenuated inversion recovery and diffusion tensor imaging values, thereby taking into account differences between participants with mild versus severe baseline WMH. From 266 participants of the RUN DMC study (Radboud University Nijmegen Diffusion Tensor and Magnetic Resonance Imaging Cohort), we semiautomatically segmented WMH at 3 time points for 9 years. Images were registered to standard space through a subject template. We analyzed differences in baseline fluid-attenuated inversion recovery, fractional anisotropy, and mean diffusivity (MD) values and changes in MD values over time between 4 regions: (1) remaining NAWM, (2) NAWM converting into WMH in the second follow-up period, (3) NAWM converting into WMH in the first follow-up period, and (4) WMH. NAWM converting into WMH in the first or second time interval showed higher fluid-attenuated inversion recovery and MD values than remaining NAWM. MD values in NAWM converting into WMH in the first time interval were similar to MD values in WMH. When stratified by baseline WMH severity, participants with severe WMH had higher fluid-attenuated inversion recovery and MD and lower fractional anisotropy values than participants with mild WMH, in all areas including the NAWM. MD values in WMH and in NAWM that converted into WMH continuously increased over time. Impaired microstructural integrity preceded conversion into WMH and continuously declined over time, suggesting a continuous disease process of white matter integrity loss that can be detected using diffusion tensor imaging even years before WMH become visible on conventional neuroimaging. Differences in microstructural integrity between participants with mild versus severe WMH suggest heterogeneity of both NAWM and WMH, which might explain the clinical variability observed in patients with similar small vessel disease severity. © 2018 American Heart Association, Inc.

A Herschel [C ii] Galactic plane survey. II. CO-dark H2 in clouds

NASA Astrophysics Data System (ADS)

Langer, W. D.; Velusamy, T.; Pineda, J. L.; Willacy, K.; Goldsmith, P. F.

2014-01-01

Context. H i and CO large scale surveys of the Milky Way trace the diffuse atomic clouds and the dense shielded regions of molecular hydrogen clouds, respectively. However, until recently, we have not had spectrally resolved C+ surveys in sufficient lines of sight to characterize the ionized and photon dominated components of the interstellar medium, in particular, the H2 gas without CO, referred to as CO-dark H2, in a large sample of interstellar clouds. Aims: We use a sparse Galactic plane survey of the 1.9 THz (158 μm) [C ii] spectral line from the Herschel open time key programme, Galactic Observations of Terahertz C+ (GOT C+), to characterize the H2 gas without CO in a statistically significant sample of interstellar clouds. Methods: We identify individual clouds in the inner Galaxy by fitting the [C ii] and CO isotopologue spectra along each line of sight. We then combine these spectra with those of H i and use them along with excitation models and cloud models of C+ to determine the column densities and fractional mass of CO-dark H2 clouds. Results: We identify1804 narrow velocity [C ii] components corresponding to interstellar clouds in different categories and evolutionary states. About 840 are diffuse molecular clouds with no CO, ~510 are transition clouds containing [C ii] and 12CO, but no 13CO, and the remainder are dense molecular clouds containing 13CO emission. The CO-dark H2 clouds are concentrated between Galactic radii of ~3.5 to 7.5 kpc and the column density of the CO-dark H2 layer varies significantly from cloud to cloud with a global average of 9 × 1020 cm-2. These clouds contain a significant fraction by mass of CO-dark H2, that varies from ~75% for diffuse molecular clouds to ~20% for dense molecular clouds. Conclusions: We find a significant fraction of the warm molecular ISM gas is invisible in H i and CO, but is detected in [C ii]. The fraction of CO-dark H2 is greatest in the diffuse clouds and decreases with increasing total column density, and is lowest in the massive clouds. The column densities and mass fraction of CO-dark H2 are less than predicted by models of diffuse molecular clouds using solar metallicity, which is not surprising as most of our detections are in Galactic regions where the metallicity is larger and shielding more effective. There is an overall trend towards a higher fraction of CO-dark H2 in clouds with increasing Galactic radius, consistent with lower metallicity there. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

Molecular dynamics at low time resolution.

PubMed

Faccioli, P

2010-10-28

The internal dynamics of macromolecular systems is characterized by widely separated time scales, ranging from fraction of picoseconds to nanoseconds. In ordinary molecular dynamics simulations, the elementary time step Δt used to integrate the equation of motion needs to be chosen much smaller of the shortest time scale in order not to cut-off physical effects. We show that in systems obeying the overdamped Langevin equation, it is possible to systematically correct for such discretization errors. This is done by analytically averaging out the fast molecular dynamics which occurs at time scales smaller than Δt, using a renormalization group based technique. Such a procedure gives raise to a time-dependent calculable correction to the diffusion coefficient. The resulting effective Langevin equation describes by construction the same long-time dynamics, but has a lower time resolution power, hence it can be integrated using larger time steps Δt. We illustrate and validate this method by studying the diffusion of a point-particle in a one-dimensional toy model and the denaturation of a protein.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Experimental characterization and modelization of ion exchange kinetics for a carboxylic resin in infinite solution volume conditions. Application to monovalent-trivalent cations exchange.

PubMed

Picart, Sébastien; Ramière, Isabelle; Mokhtari, Hamid; Jobelin, Isabelle

2010-09-02

This study is devoted to the characterization of ion exchange inside a microsphere of carboxylic resin. It aims at describing the kinetics of this exchange reaction which is known to be controlled by interdiffusion in the particle. The fractional attainment of equilibrium function of time depends on the concentration of the cations in the resin which can be modelized by the Nernst-Planck equation. A powerful approach for the numerical resolution of this equation is introduced in this paper. This modeling is based on the work of Helfferich but involves an implicit numerical scheme which reduces the computational cost. Knowing the diffusion coefficients of the cations in the resin and the radius of the spherical exchanger, the kinetics can be hence completely determined. When those diffusion parameters are missing, they can be deduced by fitting experimental data of fractional attainment of equilibrium. An efficient optimization tool coupled with the implicit resolution has been developed for this purpose. A monovalent/trivalent cation exchange had been experimentally characterized for a carboxylic resin. Diffusion coefficients and concentration profiles in the resin were then deduced through this new model.

Lateral mobility of plasma membrane proteins in dividing eggs of the loach (Misgurnus fossilis): Regional differences and changes during the cell cycle.

PubMed

Bozhkova, V P; Budayova, M; Kvasnicka, P; Cigankova, N; Chorvat, D

1994-12-01

Regional differences in lateral diffusion rates of fluorescence-labeled proteins have been studied in the plasma membrane of dividing eggs of the loach (Misgurnus fossilis) by fluorescence recovery after photobleaching (FRAP). Apparent animal-vegetal differences in fluorescence intensity, lateral diffusion coefficients, and fractions of mobile proteins have been found, with all these quantities being higher in the animal pole region than in the yolk region. Cyclic changes in protein diffusion coefficients and mobile fractions during the first few cell cycles have also been recorded. Soon after the end of a cleavage, the diffusion coefficient reaches its minimal value and increases rapidly before the next cleavage.

Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.

PubMed

Bendahmane, Mostafa; Ruiz-Baier, Ricardo; Tian, Canrong

2016-05-01

In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis.

Multimodal Imaging Evidence for Axonal and Myelin Deterioration in Amnestic Mild Cognitive Impairment

PubMed Central

Gold, Brian T.; Jiang, Yang; Powell, David K.; Smith, Charles D.

2012-01-01

White matter (WM) microstructural declines have been demonstrated in Alzheimer’s disease and amnestic mild cognitive impairment (aMCI). However, the pattern of WM microstructural changes in aMCI after controlling for WM atrophy is unknown. Here, we address this issue through joint consideration of aMCI alterations in fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity, as well as macrostructural volume in WM and gray matter compartments. Participants were 18 individuals with aMCI and 24 healthy seniors. Voxelwise analyses of diffusion tensor imaging data was carried out using tract-based spatial statistics (TBSS) and voxelwise analyses of high-resolution structural data was conducted using voxel based morphometry. After controlling for WM atrophy, the main pattern of TBSS findings indicated reduced fractional anisotropy with only small alterations in mean diffusivity/radial diffusivity/axial diffusivity. These WM microstructural declines bordered and/or were connected to gray matter structures showing volumetric declines. However, none of the potential relationships between WM integrity and volume in connected gray matter structures was significant, and adding fractional anisotropy information improved the classificatory accuracy of aMCI compared to the use of hippocampal atrophy alone. These results suggest that WM microstructural declines provide unique information not captured by atrophy measures that may aid the magnetic resonance imaging contribution to aMCI detection. PMID:22460327

The effects of complex chemistry on triple flames

NASA Technical Reports Server (NTRS)

Echekki, T.; Chen, J. H.

1996-01-01

The structure, ignition, and stabilization mechanisms for a methanol (CH3OH)-air triple flame are studied using Direct Numerical Simulations (DNS). The methanol (CH3OH)-air triple flame is found to burn with an asymmetric shape due to the different chemical and transport processes characterizing the mixture. The excess fuel, methanol (CH3OH), on the rich premixed flame branch is replaced by more stable fuels CO and H2, which burn at the diffusion flame. On the lean premixed flame side, a higher concentration of O2 leaks through to the diffusion flame. The general structure of the triple point features the contribution of both differential diffusion of radicals and heat. A mixture fraction-temperature phase plane description of the triple flame structure is proposed to highlight some interesting features in partially premixed combustion. The effects of differential diffusion at the triple point add to the contribution of hydrodynamic effects in the stabilization of the triple flame. Differential diffusion effects are measured using two methods: a direct computation using diffusion velocities and an indirect computation based on the difference between the normalized mixture fractions of C and H. The mixture fraction approach does not clearly identify the effects of differential diffusion, in particular at the curved triple point, because of ambiguities in the contribution of carbon and hydrogen atoms' carrying species.

Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

2017-12-01

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

Self-diffusion Coefficient and Structure of Binary n-Alkane Mixtures at the Liquid-Vapor Interfaces.

PubMed

Chilukoti, Hari Krishna; Kikugawa, Gota; Ohara, Taku

2015-10-15

The self-diffusion coefficient and molecular-scale structure of several binary n-alkane liquid mixtures in the liquid-vapor interface regions have been examined using molecular dynamics simulations. It was observed that in hexane-tetracosane mixture hexane molecules are accumulated in the liquid-vapor interface region and the accumulation intensity decreases with increase in a molar fraction of hexane in the examined range. Molecular alignment and configuration in the interface region of the liquid mixture change with a molar fraction of hexane. The self-diffusion coefficient in the direction parallel to the interface of both tetracosane and hexane in their binary mixture increases in the interface region. It was found that the self-diffusion coefficient of both tetracosane and hexane in their binary mixture is considerably higher in the vapor side of the interface region as the molar fraction of hexane goes lower, which is mostly due to the increase in local free volume caused by the local structure of the liquid in the interface region.

Kinetics of Diffusional Droplet Growth in a Liquid/Liquid Two-Phase System

NASA Technical Reports Server (NTRS)

Glicksman, M. E.; Fradkov, V. E.

1996-01-01

We address the problem of diffusional interactions in a finite sized cluster of spherical particles for volume fractions, V(sub v) in the range 0-0.01. We determined the quasi-static monopole diffusion solution for n particles distributed at random in a continuous matrix. A global mass conservation condition is employed, obviating the need for any external boundary condition. The numerical results provide the instantaneous (snapshot) growth or shrinkage rate of each particle, precluding the need for extensive time-dependent computations. The close connection between these snapshot results and the coarsegrained kinetic constants are discussed. A square-root dependence of the deviations of the rate constants from their zero volume fraction value is found for the higher V(sub v) investigated. This behavior is consistent with predictions from diffusion Debye-Huckel screening theory. By contrast, a cube-root dependence, reported in earlier numerical studies, is found for the lower V(sub v) investigated. The roll-over region of the volume fraction where the two asymptotics merge depends on the number of particles, n, alone. A theoretical estimate for the roll-over point predicts that the corresponding V(sub v) varies as n(sup -2), in good agreement with the numerical results.

Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusion

PubMed Central

Ning, Lipeng; Özarslan, Evren; Westin, Carl-Fredrik; Rathi, Yogesh

2017-01-01

Inferring the microstructure of complex media from the diffusive motion of molecules is a challenging problem in diffusion physics. In this paper, we introduce a novel representation of diffusion MRI (dMRI) signal from tissue with spatially-varying diffusivity using a diffusion disturbance function. This disturbance function contains information about the (intra-voxel) spatial fluctuations in diffusivity due to restrictions, hindrances and tissue heterogeneity of the underlying tissue substrate. We derive the short- and long-range disturbance coefficients from this disturbance function to characterize the tissue structure and organization. Moreover, we provide an exact relation between the disturbance coefficients and the time-varying moments of the diffusion propagator, as well as their relation to specific tissue microstructural information such as the intra-axonal volume fraction and the apparent axon radius. The proposed approach is quite general and can model dMRI signal for any type of gradient sequence (rectangular, oscillating, etc.) without using the Gaussian phase approximation. The relevance of the proposed PICASO model is explored using Monte-Carlo simulations and in-vivo dMRI data. The results show that the estimated disturbance coefficients can distinguish different types of microstructural organization of axons. PMID:27751940

Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusion.

PubMed

Ning, Lipeng; Özarslan, Evren; Westin, Carl-Fredrik; Rathi, Yogesh

2017-02-01

Inferring the microstructure of complex media from the diffusive motion of molecules is a challenging problem in diffusion physics. In this paper, we introduce a novel representation of diffusion MRI (dMRI) signal from tissue with spatially-varying diffusivity using a diffusion disturbance function. This disturbance function contains information about the (intra-voxel) spatial fluctuations in diffusivity due to restrictions, hindrances and tissue heterogeneity of the underlying tissue substrate. We derive the short- and long-range disturbance coefficients from this disturbance function to characterize the tissue structure and organization. Moreover, we provide an exact relation between the disturbance coefficients and the time-varying moments of the diffusion propagator, as well as their relation to specific tissue microstructural information such as the intra-axonal volume fraction and the apparent axon radius. The proposed approach is quite general and can model dMRI signal for any type of gradient sequence (rectangular, oscillating, etc.) without using the Gaussian phase approximation. The relevance of the proposed PICASO model is explored using Monte-Carlo simulations and in-vivo dMRI data. The results show that the estimated disturbance coefficients can distinguish different types of microstructural organization of axons. Copyright © 2016 Elsevier Inc. All rights reserved.

Simulations on the Influence of Myelin Water in Diffusion-Weighted Imaging

PubMed Central

Harkins, Kevin D.; Does, Mark D.

2016-01-01

While myelinated axons present an important barrier to water diffusion, many models used to interpret DWI signal neglect other potential influences of myelin. In this work, Monte Carlo simulations were used to test the sensitivity of DWI results to the diffusive properties of water within myelin. Within these simulations, the apparent diffusion coefficient (Dapp) varied slowly over several orders of magnitude of the coefficient of myelin water diffusion (Dm), but exhibited important differences compared to Dapp values simulated that neglect Dm (=0). Compared to Dapp, the apparent diffusion kurtosis (Kapp) was generally more sensitive to Dm. Simulations also tested the sensitivity of Dapp and Kapp to the amount of myelin present. Unique variations in Dapp and Kapp caused by differences in the myelin volume fraction were diminished when myelin water diffusion was included. Also, expected trends in Dapp and Kapp with experimental echo time were reduced or inverted when accounting for myelin water diffusion, and these reduced/inverted trends were seen experimentally in ex vivo rat brain DWI experiments. In general, myelin water has the potential to subtly influence DWI results and bias models of DWI that neglect these components of white matter. PMID:27271991

Characteristics of lesional and extra-lesional cortical grey matter in relapsing-remitting and secondary progressive multiple sclerosis: A magnetisation transfer and diffusion tensor imaging study.

PubMed

Yaldizli, Özgür; Pardini, Matteo; Sethi, Varun; Muhlert, Nils; Liu, Zheng; Tozer, Daniel J; Samson, Rebecca S; Wheeler-Kingshott, Claudia Am; Yousry, Tarek A; Miller, David H; Chard, Declan T

2016-02-01

In multiple sclerosis (MS), diffusion tensor and magnetisation transfer imaging are both abnormal in lesional and extra-lesional cortical grey matter, but differences between clinical subtypes and associations with clinical outcomes have only been partly assessed. To compare mean diffusivity, fractional anisotropy and magnetisation transfer ratio (MTR) in cortical grey matter lesions (detected using phase-sensitive inversion recovery (PSIR) imaging) and extra-lesional cortical grey matter, and assess associations with disability in relapse-onset MS. Seventy-two people with MS (46 relapsing-remitting (RR), 26 secondary progressive (SP)) and 36 healthy controls were included in this study. MTR, mean diffusivity and fractional anisotropy were measured in lesional and extra-lesional cortical grey matter. Mean fractional anisotropy was higher and MTR lower in lesional compared with extra-lesional cortical grey matter. In extra-lesional cortical grey matter mean fractional anisotropy and MTR were lower, and mean diffusivity was higher in the MS group compared with controls. Mean MTR was lower and mean diffusivity was higher in lesional and extra-lesional cortical grey matter in SPMS when compared with RRMS. These differences were independent of disease duration. In multivariate analyses, MTR in extra-lesional more so than lesional cortical grey matter was associated with disability. Magnetic resonance abnormalities in lesional and extra-lesional cortical grey matter are greater in SPMS than RRMS. Changes in extra-lesional compared with lesional cortical grey matter are more consistently associated with disability. © The Author(s), 2015.

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.

Implementation and assessment of diffusion-weighted partial Fourier readout-segmented echo-planar imaging.

PubMed

Frost, Robert; Porter, David A; Miller, Karla L; Jezzard, Peter

2012-08-01

Single-shot echo-planar imaging has been used widely in diffusion magnetic resonance imaging due to the difficulties in correcting motion-induced phase corruption in multishot data. Readout-segmented EPI has addressed the multishot problem by introducing a two-dimensional nonlinear navigator correction with online reacquisition of uncorrectable data to enable acquisition of high-resolution diffusion data with reduced susceptibility artifact and T*(2) blurring. The primary shortcoming of readout-segmented EPI in its current form is its long acquisition time (longer than similar resolution single-shot echo-planar imaging protocols by approximately the number of readout segments), which limits the number of diffusion directions. By omitting readout segments at one side of k-space and using partial Fourier reconstruction, readout-segmented EPI imaging times could be reduced. In this study, the effects of homodyne and projection onto convex sets reconstructions on estimates of the fractional anisotropy, mean diffusivity, and diffusion orientation in fiber tracts and raw T(2)- and trace-weighted signal are compared, along with signal-to-noise ratio results. It is found that projections onto convex sets reconstruction with 3/5 segments in a 2 mm isotropic diffusion tensor image acquisition and 9/13 segments in a 0.9 × 0.9 × 4.0 mm(3) diffusion-weighted image acquisition provide good fidelity relative to the full k-space parameters. This allows application of readout-segmented EPI to tractography studies, and clinical stroke and oncology protocols. Copyright © 2011 Wiley-Liss, Inc.

Dynamic arsenic aging processes and their mechanisms in nine types of Chinese soils.

PubMed

Wang, Yanan; Zeng, Xibai; Lu, Yahai; Bai, Lingyu; Su, Shiming; Wu, Cuixia

2017-11-01

Although specific soil properties controlling the arsenic (As) aging process have been studied extensively, few investigations have attempted to determine how soil types influence As bioavailability and fractionations in soils. Nine types of soil were selected from typical grain producing areas in China, and the bioavailability and fractionations of As during aging were measured. Results showed that available As in all soils rapidly decreased in the first 30 days and slowly declined thereafter. In spiked soils, As easily became less available and less toxic in low pH soils compared to high pH soils, demonstrating the importance of soil pH on As availability. Results from fitting kinetic equations revealed that the pseudo-second-order model described the As aging processes well in all soils (R 2  = 0.945-0.999, P < 0.01, SE = 0.09-4.25), implying that the mechanism for As aging combined adsorption, external diffusion, and internal diffusion. Fe oxides were more important than Al oxides for determining the As aging rate (|k|). Based on these results, we are the first to propose the approximate aging equilibrium time (T) for As, which was mainly influenced by soil clay content. The shortest time for approximate stabilization of As aging was 28 d in latosol soils (LS), while the longest approximate equilibrium time was 169 d in cinnamon soils (CS). Individual soil properties controlling the variation in different As fractionations further confirmed that the influences of soil types on As aging were the result of the combined effects of soil properties and a time-consuming redistribution process. Copyright © 2017 Elsevier Ltd. All rights reserved.

Kappa Distribution in a Homogeneous Medium: Adiabatic Limit of a Super-diffusive Process?

NASA Astrophysics Data System (ADS)

Roth, I.

2015-12-01

The classical statistical theory predicts that an ergodic, weakly interacting system like charged particles in the presence of electromagnetic fields, performing Brownian motions (characterized by small range deviations in phase space and short-term microscopic memory), converges into the Gibbs-Boltzmann statistics. Observation of distributions with a kappa-power-law tails in homogeneous systems contradicts this prediction and necessitates a renewed analysis of the basic axioms of the diffusion process: characteristics of the transition probability density function (pdf) for a single interaction, with a possibility of non-Markovian process and non-local interaction. The non-local, Levy walk deviation is related to the non-extensive statistical framework. Particles bouncing along (solar) magnetic field with evolving pitch angles, phases and velocities, as they interact resonantly with waves, undergo energy changes at undetermined time intervals, satisfying these postulates. The dynamic evolution of a general continuous time random walk is determined by pdf of jumps and waiting times resulting in a fractional Fokker-Planck equation with non-integer derivatives whose solution is given by a Fox H-function. The resulting procedure involves the known, although not frequently used in physics fractional calculus, while the local, Markovian process recasts the evolution into the standard Fokker-Planck equation. Solution of the fractional Fokker-Planck equation with the help of Mellin transform and evaluation of its residues at the poles of its Gamma functions results in a slowly converging sum with power laws. It is suggested that these tails form the Kappa function. Gradual vs impulsive solar electron distributions serve as prototypes of this description.

Reduced fractional anisotropy on diffusion tensor magnetic resonance imaging after hypoxic-ischemic encephalopathy.

PubMed

Ward, Phil; Counsell, Serena; Allsop, Joanna; Cowan, Frances; Shen, Yuji; Edwards, David; Rutherford, Mary

2006-04-01

Apparent diffusion coefficients (ADC) that are measured by diffusion-weighted imaging are reduced in severe white matter (WM) and in some severe basal ganglia and thalamic (BGT) injury in infants who present with hypoxic-ischemic encephalopathy (HIE). However, ADC values may pseudonormalize or even be high during this time in some less severe but clinically significant injuries. We hypothesized that fractional anisotropy (FA), a measure of the directional diffusivity of water made using diffusion tensor imaging, may be abnormal in these less severe injuries; therefore, the objective of this study was to use diffusion tensor imaging to measure ADC and FA in infants with moderate and severe hypoxic-ischemic brain injury. Twenty infants with HIE and 7 normal control infants were studied. All infants were born at >36 weeks' gestational age, and MRI scans were obtained within 3 weeks of delivery. Data were examined for normality, and comparisons were made using analysis of variance or Kruskal-Wallis as appropriate. During the first week, FA values were decreased with both severe and moderate WM and BGT injury as assessed by conventional imaging, whereas ADC values were reduced only in severe WM injury and some severe BGT injury. Abnormal ADC values pseudonormalized during the second week, whereas FA values continued to decrease. FA is reduced in moderate brain injury after HIE. A low FA may reflect a breakdown in WM organization. Moderate BGT injury may result in atrophy but not overt infarction; it is possible that delayed apoptosis is more marked than immediate necrosis, and this may account for normal early ADC values. The accompanying low FA within some severe and all moderate gray matter lesions, which is associated with significant later impairment, may help to confirm clinically significant abnormality in infants with normal ADC values.

Fractional domain varying-order differential denoising method

NASA Astrophysics Data System (ADS)

Zhang, Yan-Shan; Zhang, Feng; Li, Bing-Zhao; Tao, Ran

2014-10-01

Removal of noise is an important step in the image restoration process, and it remains a challenging problem in image processing. Denoising is a process used to remove the noise from the corrupted image, while retaining the edges and other detailed features as much as possible. Recently, denoising in the fractional domain is a hot research topic. The fractional-order anisotropic diffusion method can bring a less blocky effect and preserve edges in image denoising, a method that has received much interest in the literature. Based on this method, we propose a new method for image denoising, in which fractional-varying-order differential, rather than constant-order differential, is used. The theoretical analysis and experimental results show that compared with the state-of-the-art fractional-order anisotropic diffusion method, the proposed fractional-varying-order differential denoising model can preserve structure and texture well, while quickly removing noise, and yields good visual effects and better peak signal-to-noise ratio.

Short-scan-time multi-slice diffusion MRI of the mouse cervical spinal cord using echo planar imaging.

PubMed

Callot, Virginie; Duhamel, Guillaume; Cozzone, Patrick J; Kober, Frank

2008-10-01

Mouse spinal cord (SC) diffusion-weighted imaging (DWI) provides important information on tissue morphology and structural changes that may occur during pathologies such as multiple sclerosis or SC injury. The acquisition scheme of the commonly used DWI techniques is based on conventional spin-echo encoding, which is time-consuming. The purpose of this work was to investigate whether the use of echo planar imaging (EPI) would provide good-quality diffusion MR images of mouse SC, as well as accurate measurements of diffusion-derived metrics, and thus enable diffusion tensor imaging (DTI) and highly resolved DWI within reasonable scan times. A four-shot diffusion-weighted spin-echo EPI (SE-EPI) sequence was evaluated at 11.75 T on a group of healthy mice (n = 10). SE-EPI-derived apparent diffusion coefficients of gray and white matter were compared with those obtained using a conventional spin-echo sequence (c-SE) to validate the accuracy of the method. To take advantage of the reduction in acquisition time offered by the EPI sequence, multi-slice DTI acquisitions were performed covering the cervical segments (six slices, six diffusion-encoding directions, three b values) within 30 min (vs 2 h for c-SE). From these measurements, fractional anisotropy and mean diffusivities were calculated, and fiber tracking along the C1 to C6 cervical segments was performed. In addition, high-resolution images (74 x 94 microm(2)) were acquired within 5 min per direction. Clear delineation of gray and white matter and identical apparent diffusion coefficient values were obtained, with a threefold reduction in acquisition time compared with c-SE. While overcoming the difficulties associated with high spatially and temporally resolved DTI measurements, the present SE-EPI approach permitted identification of reliable quantitative parameters with a reproducibility compatible with the detection of pathologies. The SE-EPI method may be particularly valuable when multiple sets of images from the SC are needed, in cases of rapidly evolving conditions, to decrease the duration of anesthesia or to improve MR exploration by including additional MR measurements. Copyright (c) 2008 John Wiley & Sons, Ltd.

WE-G-BRD-01: Diffusion Weighted MRI for Response Assessment of Inoperable Lung Tumors for Patients Undergoing SBRT Treatment

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

Tyagi, N; Wengler, K; Yorke, E

2014-06-15

Purpose: To investigate early changes in tumor Apparent Diffusion Coefficients derived from diffusion weighted (DW)-MRI of lung cancer patients undergoing SBRT, as a possible early predictor of treatment response. Methods: DW-MRI scans were performed in this prospective phase I IRB-approved study of inoperable lung tumors at various time-points during the course of SBRT treatments. Axial DW scan using multi b-values ranging from 0–1000 s/mm{sup 2} were acquired in treatment position on a 3T Philips MR scanner during simulation, one hour after the first fraction (8 Gy), after a total of 5 fractions (40 Gy) and 4 weeks after SBRT delivery.more » A monoexponential model based on a least square fit from all b values was performed on a pixel-by-pixel basis and ADC was calculated. GTVs drawn on 4DCT for planning were mapped on the T2w MRI (acquired at exhale) after deformable registration. These volumes were then mapped on DWI scan for ADC calculation after rigid registration between the anatomical scan and diffusion scan. T2w scan on followup time points were deformably registered to the pretreatment T2 scan. Results: The first two patients in this study were analyzed. Median ADC values were 1.48, 1.48, 1.62 and 1.83 (10{sup −3}×) mm{sup 2}/s at pretreatment, after 8 Gy, after 40 Gy and 4 weeks posttreatment for the first patient and 1.57, 1.53, 1.66 and 1.72 (10{sup −3}×) mm{sup 2}/s for the second patient. ADC increased more significantly after 4 weeks of treatment rather than immediately post treatment, implying that late ADC value may be a better predictor of tumor response for SBRT treatment. The fraction of tumor pixels at high ADC values increased at 4 weeks post treatment. Conclusion: The observed increase in ADC values before the end of radiotherapy may be a surrogate for tumor response, but further patient accrual will be necessary to determine its value.« less

Diffusion related isotopic fractionation effects with one-dimensional advective-dispersive transport.

PubMed

Xu, Bruce S; Lollar, Barbara Sherwood; Passeport, Elodie; Sleep, Brent E

2016-04-15

Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining "observable" DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C0), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (Dmech/Deff). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective-dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C0/MDL ratios of 50 or higher. Much larger C0/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1m) for a relatively young diffusive plume (<100years), and DRIF will not easily be detected by using the conventional sampling approach with "typical" well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where Dmech/Deff is larger than 10, DRIF effects will likely not be observable for common groundwater contaminants. Importantly, under most field conditions, Dmech/Deff≥10 is usually satisfied in the longitudinal direction, suggesting that DRIF is not likely to be observable in most groundwater systems in which contaminant transport is predominantly one-dimensional. Given the importance in the MDL it is recommended that MDL should always be explicitly reported in both modeling and field studies. Copyright © 2016. Published by Elsevier B.V.

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

PubMed

Fan, Yang; Gao, Jia-Hong

2015-07-01

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

Fractional motion model for characterization of anomalous diffusion from NMR signals

NASA Astrophysics Data System (ADS)

Fan, Yang; Gao, Jia-Hong

2015-07-01

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

Multi-site Study of Diffusion Metric Variability: Characterizing the Effects of Site, Vendor, Field Strength, and Echo Time using the Histogram Distance

PubMed Central

Helmer, K. G.; Chou, M-C.; Preciado, R. I.; Gimi, B.; Rollins, N. K.; Song, A.; Turner, J.; Mori, S.

2016-01-01

MRI-based multi-site trials now routinely include some form of diffusion-weighted imaging (DWI) in their protocol. These studies can include data originating from scanners built by different vendors, each with their own set of unique protocol restrictions, including restrictions on the number of available gradient directions, whether an externally-generated list of gradient directions can be used, and restrictions on the echo time (TE). One challenge of multi-site studies is to create a common imaging protocol that will result in a reliable and accurate set of diffusion metrics. The present study describes the effect of site, scanner vendor, field strength, and TE on two common metrics: the first moment of the diffusion tensor field (mean diffusivity, MD), and the fractional anisotropy (FA). We have shown in earlier work that ROI metrics and the mean of MD and FA histograms are not sufficiently sensitive for use in site characterization. Here we use the distance between whole brain histograms of FA and MD to investigate within- and between-site effects. We concluded that the variability of DTI metrics due to site, vendor, field strength, and echo time could influence the results in multi-center trials and that histogram distance is sensitive metrics for each of these variables. PMID:27350723

Mannitol Improves Brain Tissue Oxygenation in a Model of Diffuse Traumatic Brain Injury.

PubMed

Schilte, Clotilde; Bouzat, Pierre; Millet, Anne; Boucheix, Perrine; Pernet-Gallay, Karin; Lemasson, Benjamin; Barbier, Emmanuel L; Payen, Jean-François

2015-10-01

Based on evidence supporting a potential relation between posttraumatic brain hypoxia and microcirculatory derangements with cell edema, we investigated the effects of the antiedematous agent mannitol on brain tissue oxygenation in a model of diffuse traumatic brain injury. Experimental study. Neurosciences and physiology laboratories. Adult male Wistar rats. Thirty minutes after diffuse traumatic brain injury (impact-acceleration model), rats were IV administered with either a saline solution (traumatic brain injury-saline group) or 20% mannitol (1 g/kg) (traumatic brain injury-mannitol group). Sham-saline and sham-mannitol groups received no insult. Two series of experiments were conducted 2 hours after traumatic brain injury (or equivalent) to investigate 1) the effect of mannitol on brain edema and oxygenation, using a multiparametric magnetic resonance-based approach (n = 10 rats per group) to measure the apparent diffusion coefficient, tissue oxygen saturation, mean transit time, and blood volume fraction in the cortex and caudoputamen; 2) the effect of mannitol on brain tissue PO2 and on venous oxygen saturation of the superior sagittal sinus (n = 5 rats per group); and 3) the cortical ultrastructural changes after treatment (n = 1 per group, taken from the first experiment). Compared with the sham-saline group, the traumatic brain injury-saline group had significantly lower tissue oxygen saturation, brain tissue PO2, and venous oxygen saturation of the superior sagittal sinus values concomitant with diffuse brain edema. These effects were associated with microcirculatory collapse due to astrocyte swelling. Treatment with mannitol after traumatic brain injury reversed all these effects. In the absence of traumatic brain injury, mannitol had no effect on brain oxygenation. Mean transit time and blood volume fraction were comparable between the four groups of rats. The development of posttraumatic brain edema can limit the oxygen utilization by brain tissue without evidence of brain ischemia. Our findings indicate that an antiedematous agent such as mannitol can improve brain tissue oxygenation, possibly by limiting astrocyte swelling and restoring capillary perfusion.

Nanoporous Au: An experimental study on the porosity of dealloyed AuAg leafs

NASA Astrophysics Data System (ADS)

Grillo, R.; Torrisi, V.; Ruffino, F.

2016-12-01

We present a study on the fraction of porosity for dealloyed nanoporous Au leafs. Nanoporous Au is attracting great scientific interest due to its peculiar plasmonic properties and the high exposed surface (∼10 m2/g). As examples, it was used in prototypes of chemical and biological devices. However, the maximization of the devices sensitivity is subjected to the maximization of the exposed surface by the nanoporous Au, i. e. maximization of the porosity fraction. So, we report on the analyses of the porosity fraction in nanoporous Au leafs as a function of the fabrication process parameters. We dealloyed 60 μm-thick Au23Ag77 at.% leafs and we show that: a) for dealloying time till to 6 h, only a 450 nm-thick surface layer of the leafs assumes a nanoporous structure with a porosity fraction of 32%. For a dealloying time of 20 h the leafs result fragmented in small black pieces with a porosity fraction increased to 60%. b) After 600 °C-30 minutes annealing of the previous samples, the nanopores disappear due to the Au/residual Ag inter-diffusion. c) After a second dealloying process on the previously annealed samples, the surface nanoporous structure is, again, obtained with the porosity fraction increased to 50%.

Determination of relative amounts of ribosome and subunits in Escherichia coli using asymmetrical flow field-flow fractionation.

PubMed

Nilsson, M; Birnbaum, S; Wahlund, K G

1996-10-15

The 30S and 50S subunits and the 70S ribosome of Escherichia coli were separated in 6 minutes by using asymmetrical flow field-flow fractionation (FFF). The total analysis time for determination of the relative amounts of ribosomes and free subunits in a preparation from a cell suspension was 8 min. The method can detect a change in the mass fraction of ribosomes if it exceeds approx, 10%. The separation is based on differences in diffusion coefficients, i.e., hydrodynamic diameters, and these can be determined from observed retention times. The hydrodynamic diameters were in good agreement with literature values obtained from electron microscopy. The mass fraction of ribosomes changed as a function of the magnesium ion concentration which confirms previous knowledge and shows the accuracy of the method. The method appears as an alternative to ultracentrifugation analysis and avoids some of its drawbacks and artefacts. An obvious application can be the optimisation of cell design in metabolic engineering in order to maximise translation and protein production.

White matter microstructure in athletes with a history of concussion: Comparing diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI).

PubMed

Churchill, Nathan W; Caverzasi, Eduardo; Graham, Simon J; Hutchison, Michael G; Schweizer, Tom A

2017-08-01

Sport concussion is associated with disturbances in brain function in the absence of gross anatomical lesions, and may have long-term health consequences. Diffusion-weighted magnetic resonance imaging (MRI) methods provide a powerful tool for investigating alterations in white matter microstructure reflecting the long-term effects of concussion. In a previous study, diffusion tensor imaging (DTI) showed that athletes with a history of concussion had elevated fractional anisotropy (FA) and reduced mean diffusivity (MD) parameters. To better understand these effects, this study compared DTI results to neurite orientation dispersion and density imaging (NODDI), which was used to estimate the intracellular volume fraction (V IC ) and orientation dispersion index (ODI). Sixty-eight (68) varsity athletes were recruited, including 37 without a history of concussion and 31 with concussion >6 months prior to imaging. Univariate analyses showed elevated FA and decreased MD for concussed athletes, along with increased V IC and reduced ODI, indicating greater neurite density and coherence of neurite orientation within white matter. Multivariate analyses also showed that for athletes with a history of concussion, white matter regions with increased FA had increased V IC and decreased ODI, with greater effects among athletes who were imaged a longer time since their last concussion. These findings enhance our understanding of the relationship between the biophysics of water diffusion and concussion neurobiology for young, healthy adults. Hum Brain Mapp 38:4201-4211, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Recovering an unknown source in a fractional diffusion problem

NASA Astrophysics Data System (ADS)

Rundell, William; Zhang, Zhidong

2018-09-01

A standard inverse problem is to determine a source which is supported in an unknown domain D from external boundary measurements. Here we consider the case of a time-independent situation where the source is equal to unity in an unknown subdomain D of a larger given domain Ω and the boundary of D has the star-like shape, i.e.

NMR signals within the generalized Langevin model for fractional Brownian motion

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-03-01

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

Communication: Unusual structure and transport in ionic liquid-hexane mixtures

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

Liang, Min; Khatun, Sufia; Castner, Edward W., E-mail: ecastner@rci.rutgers.edu

2015-03-28

Ionic liquids having a sufficiently amphiphilic cation can dissolve large volume fractions of alkanes, leading to mixtures with intriguing properties on molecular length scales. The trihexyl(tetradecyl)phosphonium cation paired with the bis(trifluoromethylsulfonyl)amide anion provides an ionic liquid that can dissolve large mole fractions of hexane. We present experimental results on mixtures of n-C{sub 6}D{sub 14} with this ionic liquid. High-energy X-ray scattering studies reveal a persistence of the characteristic features of ionic liquid structure even for 80% dilution with n-C{sub 6}D{sub 14}. Nuclear magnetic resonance self-diffusion results reveal decidedly non-hydrodynamic behavior where the self-diffusion of the neutral, non-polar n-C{sub 6}D{sub 14}more » is on average a factor of 21 times faster than for the cation. Exploitation of the unique structural and transport properties of these mixtures may lead to new opportunities for designer solvents for enhanced chemical reactivity and interface science.« less

Transport properties of elastically coupled fractional Brownian motors

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

Communication: Unusual structure and transport in ionic liquid-hexane mixtures

DOE PAGES

Liang, Min; Khatun, Sufia; Castner, Edward W.

2015-03-28

Ionic liquids having a sufficiently amphiphilic cation can dissolve large volume fractions of alkanes, leading to mixtures with intriguing properties on molecular length scales. The trihexyl(tetradecyl)phosphonium cation paired with the bis(trifluoromethylsulfonyl)amide anion provides an ionic liquid that can dissolve large mole fractions of hexane. We present experimental results on mixtures of n-C 6D 14 with this ionic liquid. High- energy X-ray scattering studies reveal a persistence of the characteristic features of ionic liquid structure even for 80% dilution with n-C 6D 14. NMR self-diffusion results reveal decidedly non-hydrodynamic behavior where the self-diffusion of the neutral, non-polar n-C 6D 14 ismore » on average a factor of 21 times faster than for the cation. Exploitation of the unique structural and transport properties of these mixtures may lead to new opportunities for designer solvents for enhanced chemical reactivity and interface science.« less

Magnetic resonance imaging evidence for presymptomatic change in thalamus and caudate in familial Alzheimer's disease.

PubMed

Ryan, Natalie S; Keihaninejad, Shiva; Shakespeare, Timothy J; Lehmann, Manja; Crutch, Sebastian J; Malone, Ian B; Thornton, John S; Mancini, Laura; Hyare, Harpreet; Yousry, Tarek; Ridgway, Gerard R; Zhang, Hui; Modat, Marc; Alexander, Daniel C; Rossor, Martin N; Ourselin, Sebastien; Fox, Nick C

2013-05-01

Amyloid imaging studies of presymptomatic familial Alzheimer's disease have revealed the striatum and thalamus to be the earliest sites of amyloid deposition. This study aimed to investigate whether there are associated volume and diffusivity changes in these subcortical structures during the presymptomatic and symptomatic stages of familial Alzheimer's disease. As the thalamus and striatum are involved in neural networks subserving complex cognitive and behavioural functions, we also examined the diffusion characteristics in connecting white matter tracts. A cohort of 20 presenilin 1 mutation carriers underwent volumetric and diffusion tensor magnetic resonance imaging, neuropsychological and clinical assessments; 10 were symptomatic, 10 were presymptomatic and on average 5.6 years younger than their expected age at onset; 20 healthy control subjects were also studied. We conducted region of interest analyses of volume and diffusivity changes in the thalamus, caudate, putamen and hippocampus and examined diffusion behaviour in the white matter tracts of interest (fornix, cingulum and corpus callosum). Voxel-based morphometry and tract-based spatial statistics were also used to provide unbiased whole-brain analyses of group differences in volume and diffusion indices, respectively. We found that reduced volumes of the left thalamus and bilateral caudate were evident at a presymptomatic stage, together with increased fractional anisotropy of bilateral thalamus and left caudate. Although no significant hippocampal volume loss was evident presymptomatically, reduced mean diffusivity was observed in the right hippocampus and reduced mean and axial diffusivity in the right cingulum. In contrast, symptomatic mutation carriers showed increased mean, axial and in particular radial diffusivity, with reduced fractional anisotropy, in all of the white matter tracts of interest. The symptomatic group also showed atrophy and increased mean diffusivity in all of the subcortical grey matter regions of interest, with increased fractional anisotropy in bilateral putamen. We propose that axonal injury may be an early event in presymptomatic Alzheimer's disease, causing an initial fall in axial and mean diffusivity, which then increases with loss of axonal density. The selective degeneration of long-coursing white matter tracts, with relative preservation of short interneurons, may account for the increase in fractional anisotropy that is seen in the thalamus and caudate presymptomatically. It may be owing to their dense connectivity that imaging changes are seen first in the thalamus and striatum, which then progress to involve other regions in a vulnerable neuronal network.

Lattice Boltzmann Simulation of Kinetic Isotope Effect During Snow Crystal Formation

NASA Astrophysics Data System (ADS)

Lu, G.; Depaolo, D. J.; Kang, Q.; Zhang, D.

2007-12-01

The isotopic composition of precipitation, especially that of snow, plays a special role in the global hydrological cycle and in reconstruction of past climates using polar ice cores. The fractionation of the major water isotope species (HHO, HDO, HHO-18) during ice crystal formation is critical to understanding the global distribution of isotopes in precipitation. Ice crystal growth in clouds is traditionally treated with a spherically-symmetric steady state diffusion model, with semi-empirical modifications added to account for ventilation and for complex crystal morphology. Although it is known that crystal growth rate, which depends largely on the degree of vapor over- saturation, determines crystal morphology, there are no quantitative models that relate morphology to the vapor saturation factor. Since kinetic (vapor phase diffusion-controlled) isotopic fractionation also depends on growth rate, there should be direct relationships between vapor saturation, crystal morphology, and crystal isotopic composition. We use a 2D lattice Boltzmann model to simulate diffusion-controlled ice crystal growth from vapor- oversaturated air. In the model, crystals grow solely according to the diffusive fluxes just above the crystal surfaces, and hence crystal morphology arises from the initial and boundary conditions in the model and does not need to be specified a priori. Crystal growth patterns can be varied between random growth and deterministic growth (along the maximum concentration gradient for example). The input parameters needed are the isotope- dependent vapor deposition rate constant (k) and the water vapor diffusivity in air (D). The values of both k and D can be computed from kinetic theory, and there are also experimentally determined values of D. The deduced values of k are uncertain to the extent that the condensation coefficient for ice is uncertain. The ratio D/k is a length (order 1 micron) that determines the minimum scale of dendritic growth features and allows us to scale the numerical calculations to atmospheric conditions. Our calculations confirm that the crystal/vapor isotopic fractionation approaches the equilibrium value, and the crystals are compact (circular in 2D) as the saturation factor approaches unity (S= 1.0). However, few natural crystals form under such conditions. At higher oversaturation (e.g. S = 1.2), dendritic crystals of millimeter size develop on timescales appropriate to cloud processes, and kinetic effects control isotopic fractionation. Fractionation factors for dendritic crystals are similar to those predicted by the spherical diffusion model, but the model also gives estimates of crystal heterogeneity. Dendritic crystals are constrained to be relatively large, with dimension much greater than about 20D/k. The most difficult aspect of the modeling is to account for the large density difference between air and ice, which requires us to use a fictitious higher density for the vapor-oversaturated air and scale the crystal growth time accordingly. An approach using a larger scale simulation and the domain decomposition method can provide a vapor flux for a nested smaller scale calculation. The results clarify the controls on crystal growth, and the relationships between saturation state, growth rate, crystal morphology and isotopic fractionation.

Lattice Boltzmann Simulation of Water Isotope Fractionation During Growth of Ice Crystals in Clouds

NASA Astrophysics Data System (ADS)

Lu, G.; Depaolo, D.; Kang, Q.; Zhang, D.

2006-12-01

The isotopic composition of precipitation, especially that of snow, plays a special role in the global hydrological cycle and in reconstruction of past climates using polar ice cores. The fractionation of the major water isotope species (HHO, HDO, HHO-18) during ice crystal formation is critical to understanding the global distribution of isotopes in precipitation. Ice crystal growth in clouds is traditionally treated with a spherically- symmetric steady state diffusion model, with semi-empirical modifications added to account for ventilation and for complex crystal morphology. Although it is known that crystal growth rate, which depends largely on the degree of vapor over-saturation, determines crystal morphology, there are no existing quantitative models that directly relate morphology to the vapor saturation factor. Since kinetic (vapor phase diffusion-controlled) isotopic fractionation also depends on growth rate, there should be a direct relationship between vapor saturation, crystal morphology, and crystal isotopic composition. We use a 2D Lattice-Boltzmann model to simulate diffusion-controlled ice crystal growth from vapor- oversaturated air. In the model, crystals grow solely according to the diffusive fluxes just above the crystal surfaces, and hence crystal morphology arises from the initial and boundary conditions in the model and does not need to be specified a priori. The input parameters needed are the isotope-dependent vapor deposition rate constant (k) and the water vapor diffusivity in air (D). The values of both k and D can be computed from kinetic theory, and there are also experimentally determined values of D. The deduced values of k are uncertain to the extent that the sticking coefficient (or accommodation coefficient) for ice is uncertain. The ratio D/k is a length that determines the minimum scale of dendritic growth features and allows us to scale the numerical calculations to atmospheric conditions using a dimensionless Damkohler number: Da = kh/D, where h is the width of the 2D calculation domain. Varying the nondimensional Da in the model is equivalent to varying the scale (h) in the model. Our calculations confirm that the crystal/vapor isotopic fractionation approaches the equilibrium value, and the crystals are compact (circular in 2D) as the saturation factor approaches unity (S= 1.0). At higher oversaturation (e.g. S = 1.2), dendritic crystals of millimeter size develop on timescales appropriate to cloud processes, the isotopic fractionations are dominated by kinetic effects, and similar to those predicted by the spherical diffusion model. Dendritic crystals are constrained to be relatively large, with dimension much greater than D/k. The most difficult aspect of the modeling is to account for the large density difference between air and ice, which requires us to use a fictitious higher density for the vapor-oversaturated air and scale the crystal growth time accordingly. A different approach, using a larger scale simulation to derive boundary conditions for a nested smaller scale calculation is in progress. The results to date clarify the controls on dendritic crystal growth, the relationships between saturation state, growth rate, crystal morphology and isotopic fractionation, and provide limits on the value of the accommodation coefficient.

Large-amplitude jumps and non-Gaussian dynamics in highly concentrated hard sphere fluids.

PubMed

Saltzman, Erica J; Schweizer, Kenneth S

2008-05-01

Our microscopic stochastic nonlinear Langevin equation theory of activated dynamics has been employed to study the real-space van Hove function of dense hard sphere fluids and suspensions. At very short times, the van Hove function is a narrow Gaussian. At sufficiently high volume fractions, such that the entropic barrier to relaxation is greater than the thermal energy, its functional form evolves with time to include a rapidly decaying component at small displacements and a long-range exponential tail. The "jump" or decay length scale associated with the tail increases with time (or particle root-mean-square displacement) at fixed volume fraction, and with volume fraction at the mean alpha relaxation time. The jump length at the alpha relaxation time is predicted to be proportional to a measure of the decoupling of self-diffusion and structural relaxation. At long times corresponding to mean displacements of order a particle diameter, the volume fraction dependence of the decay length disappears. A good superposition of the exponential tail feature based on the jump length as a scaling variable is predicted at high volume fractions. Overall, the theoretical results are in good accord with recent simulations and experiments. The basic aspects of the theory are also compared with a classic jump model and a dynamically facilitated continuous time random-walk model. Decoupling of the time scales of different parts of the relaxation process predicted by the theory is qualitatively similar to facilitated dynamics models based on the concept of persistence and exchange times if the elementary event is assumed to be associated with transport on a length scale significantly smaller than the particle size.

Military blast exposure, ageing and white matter integrity

PubMed Central

Trotter, Benjamin B.; Robinson, Meghan E.; Milberg, William P.; McGlinchey, Regina E.

2015-01-01

Mild traumatic brain injury, or concussion, is associated with a range of neural changes including altered white matter structure. There is emerging evidence that blast exposure—one of the most pervasive causes of casualties in the recent overseas conflicts in Iraq and Afghanistan—is accompanied by a range of neurobiological events that may result in pathological changes to brain structure and function that occur independently of overt concussion symptoms. The potential effects of brain injury due to blast exposure are of great concern as a history of mild traumatic brain injury has been identified as a risk factor for age-associated neurodegenerative disease. The present study used diffusion tensor imaging to investigate whether military-associated blast exposure influences the association between age and white matter tissue structure integrity in a large sample of veterans of the recent conflicts (n = 190 blast-exposed; 59 without exposure) between the ages of 19 and 62 years. Tract-based spatial statistics revealed a significant blast exposure × age interaction on diffusion parameters with blast-exposed individuals exhibiting a more rapid cross-sectional age trajectory towards reduced tissue integrity. Both distinct and overlapping voxel clusters demonstrating the interaction were observed among the examined diffusion contrast measures (e.g. fractional anisotropy and radial diffusivity). The regions showing the effect on fractional anisotropy included voxels both within and beyond the boundaries of the regions exhibiting a significant negative association between fractional anisotropy and age in the entire cohort. The regional effect was sensitive to the degree of blast exposure, suggesting a ‘dose-response’ relationship between the number of blast exposures and white matter integrity. Additionally, there was an age-independent negative association between fractional anisotropy and years since most severe blast exposure in a subset of the blast-exposed group, suggesting a specific influence of time since exposure on tissue structure, and this effect was also independent of post-traumatic stress symptoms. Overall, these data suggest that blast exposure may negatively affect brain-ageing trajectories at the microstructural tissue level. Additional work examining longitudinal changes in brain tissue integrity in individuals exposed to military blast forces will be an important future direction to the initial findings presented here. PMID:26033970

The solar ultraviolet B radiation protection provided by shading devices with regard to its diffuse component.

PubMed

Kudish, Avraham I; Harari, Marco; Evseev, Efim G

2011-10-01

The composition of the incident solar global ultraviolet B (UVB) radiation with regard to its beam and diffuse radiation fractions is highly relevant with regard to outdoor sun protection. This is especially true with respect to sun protection during leisure-time outdoor sun exposure at the shore and pools, where people tend to escape the sun under shade trees or different types of shading devices, e.g., umbrellas, overhangs, etc., believing they offer protection from the erythemal solar radiation. The degree of sun protection offered by such devices is directly related to the composition of the solar global UVB radiation, i.e., its beam and diffuse fractions. The composition of the incident solar global UVB radiation can be determined by measuring the global UVB (using Solar Light Co. Inc., Model 501A UV-Biometer) and either of its components. The beam component of the UVB radiation was determined by measuring the normal incidence beam radiation using a prototype, tracking instrument consisting of a Solar Light Co. Inc. Model 501A UV-Biometer mounted on an Eppley Solar Tracker Model St-1. The horizontal beam component of the global UVB radiation was calculated from the measured normal incidence using a simple geometric correlation and the diffuse component is determined as the difference between global and horizontal beam radiations. Horizontal and vertical surfaces positioned under a horizontal overhang/sunshade or an umbrella are not fully protected from exposure to solar global UVB radiation. They can receive a significant fraction of the UVB radiation, depending on their location beneath the shading device, the umbrella radius and the albedo (reflectance) of the surrounding ground surface in the case of a vertical surface. Shading devices such as an umbrella or horizontal overhang/shade provide relief from the solar global radiation and do block the solar global UVB radiation to some extent; nevertheless, a significant fraction of the solar global UVB radiation does penetrate this supposedly 'protective or comfort zone'. As a result, it is imperative to either apply sunscreen or cover up the exposed body surfaces even when under such shading devices. © 2011 John Wiley & Sons A/S.

Diffusion tensor imaging of the brainstem in children with achondroplasia

PubMed Central

BOSEMANI, THANGAMADHAN; ORMAN, GUNES; CARSON, KATHRYN A; MEODED, AVNER; HUISMAN, THIERRY A G M; PORETTI, ANDREA

2014-01-01

Aim The aims of this study were to compare, using diffusion tensor imaging (DTI) of the brainstem, microstructural integrity of the white matter in children with achondroplasia and age-matched participants and to correlate the severity of craniocervical junction (CCJ) narrowing and neurological findings with DTI scalars in children with achondroplasia. This study also aimed to assess the potential role of fibroblast growth factor receptor type 3 on white matter microstructure. Method Diffusion tensor imaging was performed using a 1.5T magnetic resonance scanner and balanced pairs of diffusion gradients along 20 non-collinear directions. Measurements were obtained from regions of interest, sampled in each pontine corticospinal tract (CST), medial lemniscus, and middle cerebellar peduncle, as well as in the lower brainstem and centrum semiovale, for fractional anisotropy and for mean, axial and radial diffusivity. In addition, a severity score for achondroplasia was assessed by measuring CCJ narrowing. Result Eight patients with achondroplasia (seven males, one female; mean age 5y 6mo, range 1y 1mo–15y 1mo) and eight age- and sex-matched comparison participants (mean age 5y 2mo, range 1y 1mo–14y 11mo) were included in this study. Fractional anisotropy was lower and mean diffusivity and radial diffusivity were higher in the lower brainstem of patients with achondroplasia than in age-matched comparison participants. The CST and middle cerebellar peduncle of the participants showed increases in mean, axial, and radial diffusivity. Fractional anisotropy in the lower brainstem was negatively correlated with the degree of CCJ narrowing. No differences in the DTI metrics of the centrum semiovale were observed between the two groups. Interpretation The reduction in fractional anisotropy and increase in diffusivities in the lower brainstem of participants with achondroplasia may reflect secondary encephalomalacic degeneration and cavitation of the affected white matter tracts as shown by histology. In children with achondroplasia, DTI may serve as a potential biomarker for brainstem white matter injury and aid in the care and management of these patients. PMID:24825324

Diffusion tensor imaging of the brainstem in children with achondroplasia.

PubMed

Bosemani, Thangamadhan; Orman, Gunes; Carson, Kathryn A; Meoded, Avner; Huisman, Thierry A G M; Poretti, Andrea

2014-11-01

The aims of this study were to compare, using diffusion tensor imaging (DTI) of the brainstem, microstructural integrity of the white matter in children with achondroplasia and age-matched participants and to correlate the severity of craniocervical junction (CCJ) narrowing and neurological findings with DTI scalars in children with achondroplasia. This study also aimed to assess the potential role of fibroblast growth factor receptor type 3 on white matter microstructure. Diffusion tensor imaging was performed using a 1.5T magnetic resonance scanner and balanced pairs of diffusion gradients along 20 non-collinear directions. Measurements were obtained from regions of interest, sampled in each pontine corticospinal tract (CST), medial lemniscus, and middle cerebellar peduncle, as well as in the lower brainstem and centrum semiovale, for fractional anisotropy and for mean, axial, and radial diffusivity. In addition, a severity score for achondroplasia was assessed by measuring CCJ narrowing. Eight patients with achondroplasia (seven males, one female; mean age 5y 6mo, range 1y 1mo-15y 1mo) and eight age- and sex-matched comparison participants (mean age 5y 2mo, range 1y 1mo-14y 11mo) were included in this study. Fractional anisotropy was lower and mean diffusivity and radial diffusivity were higher in the lower brainstem of patients with achondroplasia than in age-matched comparison participants. The CST and middle cerebellar peduncle of the participants showed increases in mean, axial, and radial diffusivity. Fractional anisotropy in the lower brainstem was negatively correlated with the degree of CCJ narrowing. No differences in the DTI metrics of the centrum semiovale were observed between the two groups. The reduction in fractional anisotropy and increase in diffusivities in the lower brainstem of participants with achondroplasia may reflect secondary encephalomalacic degeneration and cavitation of the affected white matter tracts as shown by histology. In children with achondroplasia, DTI may serve as a potential biomarker for brainstem white matter injury and aid in the care and management of these patients. © 2014 Mac Keith Press.

Experimental studies and model analysis of noble gas fractionation in low-permeability porous media

NASA Astrophysics Data System (ADS)

Ding, Xin; Mack Kennedy, B.; Molins, Sergi; Kneafsey, Timothy; Evans, William C.

2017-05-01

Gas flow through the vadose zone from sources at depth involves fractionation effects that can obscure the nature of transport and even the identity of the source. Transport processes are particularly complex in low permeability media but as shown in this study, can be elucidated by measuring the atmospheric noble gases. A series of laboratory column experiments was conducted to evaluate the movement of noble gas from the atmosphere into soil in the presence of a net efflux of CO2, a process that leads to fractionation of the noble gases from their atmospheric abundance ratios. The column packings were designed to simulate natural sedimentary deposition by interlayering low permeability ceramic plates and high permeability beach sand. Gas samples were collected at different depths at CO2 fluxes high enough to cause extreme fractionation of the noble gases (4He/36Ar > 20 times the air ratio). The experimental noble gas fractionation-depth profiles were in good agreement with those predicted by the dusty gas (DG) model, demonstrating the applicability of the DG model across a broad spectrum of environmental conditions. A governing equation based on the dusty gas model was developed to specifically describe noble gas fractionation at each depth that is controlled by the binary diffusion coefficient, Knudsen diffusion coefficient and the ratio of total advection flux to total flux. Finally, the governing equation was used to derive the noble gas fractionation pattern and illustrate how it is influenced by soil CO2 flux, sedimentary sequence, thickness of each sedimentary layer and each layer's physical parameters. Three potential applications of noble gas fractionation are provided: evaluating soil attributes in the path of gas flow from a source at depth to the atmosphere, testing leakage through low permeability barriers used to isolate buried waste, and tracking biological methanogenesis and methane oxidation associated with hydrocarbon degradation.

A space-fractional Monodomain model for cardiac electrophysiology combining anisotropy and heterogeneity on realistic geometries

NASA Astrophysics Data System (ADS)

Cusimano, N.; Gerardo-Giorda, L.

2018-06-01

Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatio-temporal description of excitation waves propagation. We consider a modification of the Monodomain model obtained by replacing the diffusive term of the classical formulation with a fractional power of the operator, defined in the spectral sense. The resulting nonlocal model describes different levels of tissue heterogeneity as the fractional exponent is varied. The numerical method for the solution of the fractional Monodomain relies on an integral representation of the nonlocal operator combined with a finite element discretisation in space, allowing to handle in a natural way bounded domains in more than one spatial dimension. Numerical tests in two spatial dimensions illustrate the features of the model. Activation times, action potential duration and its dispersion throughout the domain are studied as a function of the fractional parameter: the expected peculiar behaviour driven by tissue heterogeneities is recovered.

Whole-brain diffusion tensor imaging in correlation to visual-evoked potentials in multiple sclerosis: a tract-based spatial statistics analysis.

PubMed

Lobsien, D; Ettrich, B; Sotiriou, K; Classen, J; Then Bergh, F; Hoffmann, K-T

2014-01-01

Functional correlates of microstructural damage of the brain affected by MS are incompletely understood. The purpose of this study was to evaluate correlations of visual-evoked potentials with microstructural brain changes as determined by DTI in patients with demyelinating central nervous disease. Sixty-one patients with clinically isolated syndrome or MS were prospectively recruited. The mean P100 visual-evoked potential latencies of the right and left eyes of each patient were calculated and used for the analysis. For DTI acquisition, a single-shot echo-planar imaging pulse sequence with 80 diffusion directions was performed at 3T. Fractional anisotropy, radial diffusivity, and axial diffusivity were calculated and correlated with mean P100 visual-evoked potentials by tract-based spatial statistics. Significant negative correlations between mean P100 visual-evoked potentials and fractional anisotropy and significant positive correlations between mean P100 visual-evoked potentials and radial diffusivity were found widespread over the whole brain. The highest significance was found in the optic radiation, frontoparietal white matter, and corpus callosum. Significant positive correlations between mean P100 visual-evoked potentials and axial diffusivity were less widespread, notably sparing the optic radiation. Microstructural changes of the whole brain correlated significantly with mean P100 visual-evoked potentials. The distribution of the correlations showed clear differences among axial diffusivity, fractional anisotropy, and radial diffusivity, notably in the optic radiation. This finding suggests a stronger correlation of mean P100 visual-evoked potentials to demyelination than to axonal damage. © 2014 by American Journal of Neuroradiology.

Long-term white matter tract reorganization following prolonged febrile seizures.

PubMed

Pujar, Suresh S; Seunarine, Kiran K; Martinos, Marina M; Neville, Brian G R; Scott, Rod C; Chin, Richard F M; Clark, Chris A

2017-05-01

Diffusion magnetic resonance imaging (MRI) studies have demonstrated acute white matter changes following prolonged febrile seizures (PFS), but their longer-term evolution is unknown. We investigated a population-based cohort to determine white matter diffusion properties 8 years after PFS. We used diffusion tensor imaging (DTI) and applied Tract-Based Spatial Statistics for voxel-wise comparison of white matter microstructure between 26 children with PFS and 27 age-matched healthy controls. Age, gender, handedness, and hippocampal volumes were entered as covariates for voxel-wise analysis. Mean duration between the episode of PFS and follow-up was 8.2 years (range 6.7-9.6). All children were neurologically normal, and had normal conventional neuroimaging. On voxel-wise analysis, compared to controls, the PFS group had (1) increased fractional anisotropy in early maturing central white matter tracts, (2) increased mean and axial diffusivity in several peripheral white matter tracts and late-maturing central white matter tracts, and (3) increased radial diffusivity in peripheral white matter tracts. None of the tracts had reduced fractional anisotropy or diffusivity indices in the PFS group. In this homogeneous, population-based sample, we found increased fractional anisotropy in early maturing central white matter tracts and increased mean and axial diffusivity with/without increased radial diffusivity in several late-maturing peripheral white matter tracts 8 years post-PFS. We propose disruption in white matter maturation secondary to seizure-induced axonal injury, with subsequent neuroplasticity and microstructural reorganization as a plausible explanation. © 2017 The Authors. Epilepsia published by Wiley Periodicals, Inc. on behalf of International League Against Epilepsy.

Ex Vivo Diffusion Tensor Imaging of Spinal Cord Injury in Rats of Varying Degrees of Severity

PubMed Central

Jirjis, Michael B.; Kurpad, Shekar N.

2013-01-01

Abstract The aim of this study was to characterize magnetic resonance diffusion tensor imaging (DTI) in proximal regions of the spinal cord following a thoracic spinal cord injury (SCI). Sprague–Dawley rats (n=40) were administered a control, mild, moderate, or severe contusion injury at the T8 vertebral level. Six direction diffusion weighted images (DWIs) were collected ex vivo along the length of the spinal cord, with an echo/repetition time of 31.6 ms/14 sec and b=500 sec/mm2. Diffusion metrics were correlated to hindlimb motor function. Significant differences were found for whole cord region of interest (ROI) drawings for fractional anisotropy (FA), mean diffusivity (MD), longitudinal diffusion coefficient (LD), and radial diffusion coefficient (RD) at each of the cervical levels (p<0.01). Motor function correlated with MD in the cervical segments of the spinal cord (r2=0.80). The diffusivity of water significantly decreased throughout “uninjured” portions of the spinal cord following a contusion injury (p<0.05). Diffusivity metrics were found to be altered following SCI in both white and gray matter regions. Injury severity was associated with diffusion changes over the entire length of the cord. This study demonstrates that DTI is sensitive to SCI in regions remote from injury, suggesting that the diffusion metrics may be used as a biomarker for severity of injury. PMID:23782233

Gestational Age at Birth and Brain White Matter Development in Term-Born Infants and Children.

PubMed

Ou, X; Glasier, C M; Ramakrishnaiah, R H; Kanfi, A; Rowell, A C; Pivik, R T; Andres, A; Cleves, M A; Badger, T M

2017-12-01

Studies on infants and children born preterm have shown that adequate gestational length is critical for brain white matter development. Less is known regarding how variations in gestational age at birth in term infants and children affect white matter development, which was evaluated in this study. Using DTI tract-based spatial statistics methods, we evaluated white matter microstructures in 2 groups of term-born (≥37 weeks of gestation) healthy subjects: 2-week-old infants ( n = 44) and 8-year-old children ( n = 63). DTI parameters including fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity were calculated by voxelwise and ROI methods and were correlated with gestational age at birth, with potential confounding factors such as postnatal age and sex controlled. Fractional anisotropy values, which are markers for white matter microstructural integrity, positively correlated ( P < .05, corrected) with gestational age at birth in most major white matter tracts/regions for the term infants. Mean diffusivity values, which are measures of water diffusivities in the brain, and axial and radial diffusivity values, which are markers for axonal growth and myelination, respectively, negatively correlated ( P < .05, corrected) with gestational age at birth in all major white matter tracts/regions excluding the body and splenium of the corpus callosum for the term infants. No significant correlations with gestational age were observed for any tracts/regions for the term-born 8-year-old children. Our results indicate that longer gestation during the normal term period is associated with significantly greater infant white matter development (as reflected by higher fractional anisotropy and lower mean diffusivity, axial diffusivity, and radial diffusivity values); however, similar associations were not observable in later childhood. © 2017 by American Journal of Neuroradiology.

White matter alterations in the brains of patients with active, remitted, and cured cushing syndrome: a DTI study.

PubMed

Pires, P; Santos, A; Vives-Gilabert, Y; Webb, S M; Sainz-Ruiz, A; Resmini, E; Crespo, I; de Juan-Delago, M; Gómez-Anson, B

2015-06-01

Cushing syndrome appears after chronic exposure to elevated glucocorticoid levels. Cortisol excess may alter white matter microstructure. Our purpose was to study WM changes in patients with Cushing syndrome compared with controls by using DTI and the influence of hypercortisolism. Thirty-five patients with Cushing syndrome and 35 healthy controls, matched for age, education, and sex, were analyzed through DTI (tract-based spatial statistics) for fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity (general linear model, family-wise error, and threshold-free cluster enhancement corrections, P < .05). Furthermore, the influence of hypercortisolism on WM DTI changes was studied by comparing 4 subgroups: 8 patients with Cushing syndrome with active hypercortisolism, 7 with Cushing syndrome with medication-remitted cortisol, 20 surgically cured, and 35 controls. Cardiovascular risk factors were used as covariates. In addition, correlations were analyzed among DTI values, concomitant 24-hour urinary free cortisol levels, and disease duration. There were widespread alterations (reduced fractional anisotropy, and increased mean diffusivity, axial diffusivity, and radial diffusivity values; P < .05) in patients with Cushing syndrome compared with controls, independent of the cardiovascular risk factors present. Both active and cured Cushing syndrome subgroups showed similar changes compared with controls. Patients with medically remitted Cushing syndrome also had reduced fractional anisotropy and increased mean diffusivity and radial diffusivity values, compared with controls. No correlations were found between DTI maps and 24-hour urinary free cortisol levels or with disease duration. Diffuse WM alterations in patients with Cushing syndrome suggest underlying loss of WM integrity and demyelination. Once present, they seem to be independent of concomitant hypercortisolism, persisting after remission/cure. © 2015 by American Journal of Neuroradiology.

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

NASA Astrophysics Data System (ADS)

Hughes, Barry D.; Fellner, Klemens

2013-10-01

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

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

PubMed

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

2014-01-01

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

Cross-sectional investigation of correlation between hepatic steatosis and IVIM perfusion on MR imaging.

PubMed

Lee, James T; Liau, Joy; Murphy, Paul; Schroeder, Michael E; Sirlin, Claude B; Bydder, Mark

2012-05-01

The purpose of this study was to investigate the relationship between liver fat fraction (FF) and diffusion parameters derived from the intravoxel incoherent motion (IVIM) model. Thirty-six subjects with suspected nonalcoholic fatty liver disease underwent diffusion-weighted magnetic resonance imaging with 10 b-values and spoiled gradient recalled echo imaging with six echoes for fat quantification. Correlations were measured between FF, transverse relaxivity (R2), diffusivity (D) and perfusion fraction (f). The primary finding was that no significant correlation was obtained for D vs. FF or f vs. FF. Significant correlations were obtained for D vs. R2 (r=-0.490, P=.002) and f vs. D (r=-0.458, P=.005). The conclusion is that hepatic steatosis does not affect measurement of perfusion or diffusion and therefore is unlikely to confound the use of apparent diffusivity to evaluate hepatic fibrosis. Copyright © 2012 Elsevier Inc. All rights reserved.

Determination of molecular diffusion coefficient in n-alkane binary mixtures: empirical correlations.

PubMed

De Mezquia, D Alonso; Bou-Ali, M Mounir; Larrañaga, M; Madariaga, J A; Santamaría, C

2012-03-08

In this work we have measured the molecular diffusion coefficient of the n-alkane binary series nC(i)-nC(6), nC(i)-nC(10), and nC(i)-nC(12) at 298 K and 1 atm and a mass fraction of 0.5 by using the so-called sliding symmetric tubes technique. The results show that the diffusion coefficient at this concentration is proportional to the inverse viscosity of the mixture. In addition, we have also measured the diffusion coefficient of the systems nC(12)-nC(6), nC(12)-nC(7), and nC(12)-nC(8) as a function of concentration. From the data obtained, it is shown that the diffusion coefficient of the n-alkane binary mixtures at any concentration can be calculated from the molecular weight of the components and the dynamic viscosity of the corresponding mixture at 50% mass fraction.

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

The faint galaxy contribution to the diffuse extragalactic background light

NASA Technical Reports Server (NTRS)

Cole, Shaun; Treyer, Marie-Agnes; Silk, Joseph

1992-01-01

Models of the faint galaxy contribution to the diffuse extragalactic background light are presented, which are consistent with current data on faint galaxy number counts and redshifts. The autocorrelation function of surface brightness fluctuations in the extragalactic diffuse light is predicted, and the way in which these predictions depend on the cosmological model and assumptions of biasing is determined. It is confirmed that the recent deep infrared number counts are most compatible with a high density universe (Omega-0 is approximately equal to 1) and that the steep blue counts then require an extra population of rapidly evolving blue galaxies. The faintest presently detectable galaxies produce an interesting contribution to the extragalactic diffuse light, and still fainter galaxies may also produce a significant contribution. These faint galaxies still only produce a small fraction of the total optical diffuse background light, but on scales of a few arcminutes to a few degrees, they produce a substantial fraction of the fluctuations in the diffuse light.

Isotope effect of mercury diffusion in air

PubMed Central

Koster van Groos, Paul G.; Esser, Bradley K.; Williams, Ross W.; Hunt, James R.

2014-01-01

Identifying and reducing impacts from mercury sources in the environment remains a considerable challenge and requires process based models to quantify mercury stocks and flows. The stable isotope composition of mercury in environmental samples can help address this challenge by serving as a tracer of specific sources and processes. Mercury isotope variations are small and result only from isotope fractionation during transport, equilibrium, and transformation processes. Because these processes occur in both industrial and environmental settings, knowledge of their associated isotope effects is required to interpret mercury isotope data. To improve the mechanistic modeling of mercury isotope effects during gas phase diffusion, an experimental program tested the applicability of kinetic gas theory. Gas-phase elemental mercury diffusion through small bore needles from finite sources demonstrated mass dependent diffusivities leading to isotope fractionation described by a Rayleigh distillation model. The measured relative atomic diffusivities among mercury isotopes in air are large and in agreement with kinetic gas theory. Mercury diffusion in air offers a reasonable explanation of recent field results reported in the literature. PMID:24364380

Isotope effect of mercury diffusion in air.

PubMed

Koster van Groos, Paul G; Esser, Bradley K; Williams, Ross W; Hunt, James R

2014-01-01

Identifying and reducing impacts from mercury sources in the environment remains a considerable challenge and requires process based models to quantify mercury stocks and flows. The stable isotope composition of mercury in environmental samples can help address this challenge by serving as a tracer of specific sources and processes. Mercury isotope variations are small and result only from isotope fractionation during transport, equilibrium, and transformation processes. Because these processes occur in both industrial and environmental settings, knowledge of their associated isotope effects is required to interpret mercury isotope data. To improve the mechanistic modeling of mercury isotope effects during gas phase diffusion, an experimental program tested the applicability of kinetic gas theory. Gas-phase elemental mercury diffusion through small bore needles from finite sources demonstrated mass dependent diffusivities leading to isotope fractionation described by a Rayleigh distillation model. The measured relative atomic diffusivities among mercury isotopes in air are large and in agreement with kinetic gas theory. Mercury diffusion in air offers a reasonable explanation of recent field results reported in the literature.

Microstructural changes in memory and reticular formation neural pathway after simple concussion☆

PubMed Central

Ouyang, Lin; Shi, Rongyue; Xiao, Yuhui; Meng, Jiarong; Guo, Yihe; Lu, Guangming

2012-01-01

Patients with concussion often present with temporary disturbance of consciousness. The microstructural and functional changes in the brain associated with concussion, as well as the relationship with transient cognitive disorders, are currently unclear. In the present study, a rabbit model of simple concussion was established. Magnetic resonance-diffusion tensor imaging results revealed that the corona radiata and midbrain exhibited significantly decreased fractional anisotropy values in the neural pathways associated with memory and the reticular formation. In addition, the apparent diffusion coefficient values were significantly increased following injury compared with those before injury. Following a 1-hour period of quiet rest, the fractional anisotropy values significantly increased, and apparent diffusion coefficient values significantly decreased, returning to normal pre-injury levels. In contrast, the fractional anisotropy values and apparent diffusion coefficient values in the corpus callosum, thalamus and hippocampus showed no statistical significant alterations following injury. These findings indicate that the neural pathways associated with memory and the reticular formation pathway exhibit reversible microstructural white matter changes when concussion occurs, and these changes are exhibited to a different extent in different regions. PMID:25538741

An evolutionary game for the diffusion of rumor in complex networks

NASA Astrophysics Data System (ADS)

Li, Dandan; Ma, Jing; Tian, Zihao; Zhu, Hengmin

2015-09-01

In this paper, we investigate the rumor diffusion process according to the evolutionary game framework. By using three real social network datasets, we find that increasing the judgment ability of individuals could curb the diffusion of rumor effectively. Under the same level of punishment cost, there are more spreaders in the network that has larger average degree. Moreover, the punishment fraction has more significant impact than the risk coefficient on the controlling of rumor diffusion. There exist some optimal risk coefficients and punishment fractions that could help more people refusing to spread rumor. In addition, the effect of the tie strength on the final fraction of spreaders is investigated. The results indicate that the rumor can be suppressed soon if the individuals preferentially select the neighbor either weaker or stronger ties persistently to update their strategy. However, choosing neighbor blindly may promote the spread of rumor. Finally, by comparing three kinds of punishment mechanisms, we show that taking the lead in punishing the higher degree nodes is the most effective measure to reduce the coverage of rumor.

Microstructural changes in memory and reticular formation neural pathway after simple concussion.

PubMed

Ouyang, Lin; Shi, Rongyue; Xiao, Yuhui; Meng, Jiarong; Guo, Yihe; Lu, Guangming

2012-10-05

Patients with concussion often present with temporary disturbance of consciousness. The microstructural and functional changes in the brain associated with concussion, as well as the relationship with transient cognitive disorders, are currently unclear. In the present study, a rabbit model of simple concussion was established. Magnetic resonance-diffusion tensor imaging results revealed that the corona radiata and midbrain exhibited significantly decreased fractional anisotropy values in the neural pathways associated with memory and the reticular formation. In addition, the apparent diffusion coefficient values were significantly increased following injury compared with those before injury. Following a 1-hour period of quiet rest, the fractional anisotropy values significantly increased, and apparent diffusion coefficient values significantly decreased, returning to normal pre-injury levels. In contrast, the fractional anisotropy values and apparent diffusion coefficient values in the corpus callosum, thalamus and hippocampus showed no statistical significant alterations following injury. These findings indicate that the neural pathways associated with memory and the reticular formation pathway exhibit reversible microstructural white matter changes when concussion occurs, and these changes are exhibited to a different extent in different regions.

Long-term aging behaviors in a model soft colloidal system.

PubMed

Li, Qi; Peng, Xiaoguang; McKenna, Gregory B

2017-02-15

Colloidal and molecular systems share similar behaviors near to the glass transition volume fraction or temperature. Here, aging behaviors after volume fraction up-jump (induced by performing temperature down-jumps) conditions for a PS-PNIPAM/AA soft colloidal system were investigated using light scattering (diffusing wave spectroscopy, DWS). Both aging responses and equilibrium dynamics were investigated. For the aging responses, long-term experiments (100 000 s) were performed, and both equilibrium and non-equilibrium behaviors of the system were obtained. In the equilibrium state, as effective volume fraction increases (or temperature decreases), the colloidal dispersion displays a transition from the liquid to a glassy state. The equilibrium α-relaxation dynamics strongly depend on both the effective volume fraction and the initial mass concentration for the studied colloidal systems. Compared with prior results from our lab [X. Di, X. Peng and G. B. McKenna, J. Chem. Phys., 2014, 140, 054903], the effective volume fractions investigated spanned a wider range, to deeper into the glassy domain. The results show that the α-relaxation time τ α of the samples aged into equilibrium deviate from the classical Vogel-Fulcher-Tammann (VFT)-type expectations and the super-Arrhenius signature disappears above the glass transition volume fraction. The non-equilibrium aging response shows that the time for the structural evolution into equilibrium and the α-relaxation time are decoupled. The DWS investigation of the aging behavior after different volume fraction jumps reveals a different non-equilibrium or aging behavior for the considered colloidal systems compared with either molecular glasses or the macroscopic rheology of a similar colloidal dispersions.

The contribution of water soluble and water insoluble organic fractions to oxygen uptake rate during high rate composting.

PubMed

Giuliana, D'Imporzano; Fabrizio, Adani

2007-02-01

This study aims to establish the contribution of the water soluble and water insoluble organic fractions to total oxygen uptake rate during high rate composting process of a mixture of organic fraction of municipal solid waste and lignocellulosic material. This mixture was composted using a 20 l self-heating pilot scale composter for 250 h. The composter was fully equipped to record both the biomass-temperature and oxygen uptake rate. Representative compost samples were taken at 0, 70, 100, 110, 160, and 250 h from starting time. Compost samples were fractionated in water soluble and water insoluble fractions. The water soluble fraction was then fractionated in hydrophilic, hydrophobic, and neutral hydrophobic fractions. Each fraction was then studied using quantitative (total organic carbon) and qualitative analysis (diffuse reflectance infrared spectroscopy and biodegradability test). Oxygen uptake rates were high during the initial stages of the process due to rapid degradation of the soluble degradable organic fraction (hydrophilic plus hydrophobic fractions). Once this fraction was depleted, polymer hydrolysis accounted for most of the oxygen uptake rate. Finally, oxygen uptake rate could be modeled using a two term kinetic. The first term provides the oxygen uptake rate resulting from the microbial growth kinetic type on easily available, no-limiting substrate (soluble fraction), while the second term considers the oxygen uptake rate caused by the degradation of substrate produced by polymer hydrolysis.

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

PubMed Central

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Characterization of the Lung Parenchyma Using Ultrasound Multiple Scattering.

PubMed

Mohanty, Kaustav; Blackwell, John; Egan, Thomas; Muller, Marie

2017-05-01

The purpose of the study described here was to showcase the application of ultrasound to quantitative characterization of the micro-architecture of the lung parenchyma to predict the extent of pulmonary edema. The lung parenchyma is a highly complex and diffusive medium for which ultrasound techniques have remained qualitative. The approach presented here is based on ultrasound multiple scattering and exploits the complexity of ultrasound propagation in the lung structure. The experimental setup consisted of a linear transducer array with an 8-MHz central frequency placed in contact with the lung surface. The diffusion constant D and transport mean free path L* of the lung parenchyma were estimated by separating the incoherent and coherent intensities in the near field and measuring the growth of the incoherent diffusive halo over time. Significant differences were observed between the L* values obtained in healthy and edematous rat lungs in vivo. In the control rat lung, L* was found to be 332 μm (±48.8 μm), whereas in the edematous lung, it was 1040 μm (±90 μm). The reproducibility of the measurements of L* and D was tested in vivo and in phantoms made of melamine sponge with varying air volume fractions. Two-dimensional finite difference time domain numerical simulations were carried out on rabbit lung histology images with varying degrees of lung collapse. Significant correlations were observed between air volume fraction and L* in simulation (r = -0.9542, p < 0.0117) and sponge phantom (r = -0.9932, p < 0.0068) experiments. Ex vivo measurements of a rat lung in which edema was simulated by adding phosphate-buffered saline revealed a linear relationship between the fluid volume fraction and L*. These results illustrate the potential of methods based on ultrasound multiple scattering for the quantitative characterization of the lung parenchyma. Copyright © 2017 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Solute redistribution in dendritic solidification with diffusion in the solid

NASA Technical Reports Server (NTRS)

Ganesan, S.; Poirier, D. R.

1989-01-01

An investigation of solute redistribution during dendritic solidification with diffusion in the solid has been performed using numerical techniques. The extent of diffusion is characterized by the instantaneous and average diffusion parameters. These parameters are functions of the diffusion Fourier number, the partition ratio and the fraction solid. Numerical results are presented as an approximate model, which is used to predict the average diffusion parameter and calculate the composition of the interdendritic liquid during solidification.

Efficient estimation of diffusion during dendritic solidification

NASA Technical Reports Server (NTRS)

Yeum, K. S.; Poirier, D. R.; Laxmanan, V.

1989-01-01

A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing the computed results with the results of an analytical solution derived by Kobayashi (1988) for the assumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a parabolic rate of the advancement of the solid/liquid interface. The flexibility of the method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy.

Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-alginate gel beads.

PubMed

Ha, Jiyeon; Engler, Cady R; Lee, Seung Jae

2008-07-01

Diffusion characteristics of chlorferon and diethylthiophosphate (DETP) in Ca-alginate gel beads were studied to assist in designing and operating bioreactor systems. Diffusion coefficients for chlorferon and DETP in Ca-alginate gel beads determined at conditions suitable for biodegradation studies were 2.70 x 10(-11) m(2)/s and 4.28 x 10(-11) m(2)/s, respectively. Diffusivities of chlorferon and DETP were influenced by several factors, including viscosity of the bulk solution, agitation speed, and the concentrations of diffusing substrate and immobilized cells. Diffusion coefficients increased with increasing agitation speed, probably due to poor mixing at low speed and some attrition of beads at high speeds. Diffusion coefficients also increased with decreasing substrate concentration. Increased cell concentration in the gel beads caused lower diffusivity. Theoretical models to predict diffusivities as a function of cell weight fraction overestimated the effective diffusivities for both chlorferon and DETP, but linear relations between effective diffusivity and cell weight fraction were derived from experimental data. Calcium-alginate gel beads with radii of 1.65-1.70 mm used in this study were not subject to diffusional limitations: external mass transfer resistances were negligible based on Biot number calculations and effectiveness factors indicated that internal mass transfer resistance was negligible. Therefore, the degradation rates of chlorferon and DETP inside Ca-alginate gel beads were reaction-limited. (c) 2007 Wiley Periodicals, Inc.

Simulations on the influence of myelin water in diffusion-weighted imaging

NASA Astrophysics Data System (ADS)

Harkins, K. D.; Does, M. D.

2016-07-01

While myelinated axons present an important barrier to water diffusion, many models used to interpret DWI signal neglect other potential influences of myelin. In this work, Monte Carlo simulations were used to test the sensitivity of DWI results to the diffusive properties of water within myelin. Within these simulations, the apparent diffusion coefficient (D app) varied slowly over several orders of magnitude of the coefficient of myelin water diffusion (D m), but exhibited important differences compared to D app values simulated that neglect D m (=0). Compared to D app, the apparent diffusion kurtosis (K app) was generally more sensitive to D m. Simulations also tested the sensitivity of D app and K app to the amount of myelin present. Unique variations in D app and K app caused by differences in the myelin volume fraction were diminished when myelin water diffusion was included. Also, expected trends in D app and K app with experimental echo time were reduced or inverted when accounting for myelin water diffusion, and these reduced/inverted trends were seen experimentally in ex vivo rat brain DWI experiments. In general, myelin water has the potential to subtly influence DWI results and bias models of DWI that neglect these components of white matter.

Simulations on the influence of myelin water in diffusion-weighted imaging.

PubMed

Harkins, K D; Does, M D

2016-07-07

While myelinated axons present an important barrier to water diffusion, many models used to interpret DWI signal neglect other potential influences of myelin. In this work, Monte Carlo simulations were used to test the sensitivity of DWI results to the diffusive properties of water within myelin. Within these simulations, the apparent diffusion coefficient (D app) varied slowly over several orders of magnitude of the coefficient of myelin water diffusion (D m), but exhibited important differences compared to D app values simulated that neglect D m (=0). Compared to D app, the apparent diffusion kurtosis (K app) was generally more sensitive to D m. Simulations also tested the sensitivity of D app and K app to the amount of myelin present. Unique variations in D app and K app caused by differences in the myelin volume fraction were diminished when myelin water diffusion was included. Also, expected trends in D app and K app with experimental echo time were reduced or inverted when accounting for myelin water diffusion, and these reduced/inverted trends were seen experimentally in ex vivo rat brain DWI experiments. In general, myelin water has the potential to subtly influence DWI results and bias models of DWI that neglect these components of white matter.

Quantitative diffusion and swelling kinetic measurements using large-angle interferometric refractometry.

PubMed

Saunders, John E; Chen, Hao; Brauer, Chris; Clayton, McGregor; Chen, Weijian; Barnes, Jack A; Loock, Hans-Peter

2015-12-07

The uptake and release of sorbates into films and coatings is typically accompanied by changes of the films' refractive index and thickness. We provide a comprehensive model to calculate the concentration of the sorbate from the average refractive index and the film thickness, and validate the model experimentally. The mass fraction of the analyte partitioned into a film is described quantitatively by the Lorentz-Lorenz equation and the Clausius-Mosotti equation. To validate the model, the uptake kinetics of water and other solvents into SU-8 films (d = 40-45 μm) were explored. Large-angle interferometric refractometry measurements can be used to characterize films that are between 15 μm to 150 μm thick and, Fourier analysis, is used to determine independently the thickness, the average refractive index and the refractive index at the film-substrate interface at one-second time intervals. From these values the mass fraction of water in SU-8 was calculated. The kinetics were best described by two independent uptake processes having different rates. Each process followed one-dimensional Fickian diffusion kinetics with diffusion coefficients for water into SU-8 photoresist film of 5.67 × 10(-9) cm(2) s(-1) and 61.2 × 10(-9) cm(2) s(-1).

Dynamics of proteins: Light scattering study of dilute and dense colloidal suspensions of eye lens homogenates

NASA Astrophysics Data System (ADS)

Giannopoulou, A.; Aletras, A. J.; Pharmakakis, N.; Papatheodorou, G. N.; Yannopoulos, S. N.

2007-11-01

We report a dynamic light scattering study on protein suspensions of bovine lens homogenates at conditions (pH and ionic strength) similar to the physiological ones. Light scattering data were collected at two temperatures, 20 and 37°C, over a wide range of concentrations from the very dilute limit up to the dense regime approaching the physiological lens concentration. A comparison with experimental data from intact bovine lenses was advanced, revealing differences between dispersions and lenses at similar concentrations. In the dilute regime, two scattering entities were detected and identified with the long-time self-diffusion modes of α-crystallins and their aggregates, which naturally exist in lens nucleus. Upon increasing protein concentration, significant changes in time correlation function were observed starting at ˜75mgml-1, where a new mode originating from collective diffusive motions becomes visible. Self-diffusion coefficients are temperature insensitive, whereas the collective diffusion coefficient depends strongly on temperature revealing a reduction of the net repulsive interparticle forces with decreasing temperature. While there are no rigorous theoretical approaches on particle diffusion properties for multicomponent, nonideal hard sphere polydispersed systems, as the suspensions studied here, a discussion of the volume fraction dependence of the long-time self-diffusion coefficient in the context of existing theoretical approaches was undertaken. This study is purported to provide some insight into the complex light scattering pattern of intact lenses and the interactions between the constituent proteins that are responsible for lens transparency. This would lead to understand basic mechanisms of specific protein interactions that lead to lens opacification (cataract) under pathological conditions.

Effects of Fuel Preheat on Soot Formation in Microgravity Laminar Diffusion Flames

NASA Technical Reports Server (NTRS)

Konsur, Bogdan; Megaridis, Constantine M.; Griffin, DeVon W.

1997-01-01

Nonbuoyant flames offer themselves as an attractive and promising platform to gain a better understanding of soot mechanisms. The effects of buoyancy can be eliminated temporarily in drop towers which sustain brief intervals of reduced gravity-typically lower than 10(exp -3)g- extending up to several seconds at a time. Microgravity facilities have been employed to show that nonbuoyant flames are longer, wider and sootier than their normal-gravity counterparts. Sunderland et al. recently verified the existence of smoke point in laminar nonbuoyant flames. As reported, microgravity flames operating above their smoke point displayed a blunt tip and much broader soot-containing regimes in comparison to their buoyant counterparts. Mortazavi et al. established that residence times in microgravity laminar jet diffusion flames with Re=0(100) tend to be proportional to burner diameter and inversely proportional to burner exit velocity. This offers the capability to alter residence times in nonbuoyant laminar jet diffusion flames when varying the burner exit diameters and velocities. Megaridis et al. presented a quantitative definition of the soot-field structure within laminar microgravity jet diffusion flames which operated well above their smoke point. The experimental methodology involved a full-field laser-light extinction technique and jet diffusion flames of nitrogen-diluted (50% vol.) acetylene fuel burning in quiescent air at atmospheric pressure. The work was conducted at the 2.2s drop tower of the NASA Lewis Research Center (NASA-LeRC). Parallel work on 1-g flames was also presented in (6) to facilitate comparisons on the effect of gravity on the soot fields. As reported, the soot spatial distributions in 0-g flames did not change in a detectable manner after 1s within a typical 2.2s experiment. During that period, the soot field was shown to sustain a pronounced annular structure throughout the luminous nonbuoyant-flame zone. The maximum soot volume fraction measured at 0-g was nearly a factor of two higher than that at 1-g, thus confirming the enhanced sooting tendency of nonbuoyant flames. Greenberg and Ku presented a similar study and reported trends that matched those of for the 50% (vol.) nitrogen-diluted acetylene fuel. Furthermore, they examined pure acetylene flames and reported similar trends with respect to the influence of gravity on maximum soot volume fractions and flame cross-section-averaged soot loadings. Both studies clearly demonstrated the improved spatial resolution of microgravity flames compared to their normal-gravity counterparts. The current study evaluates the influence of moderate fuel preheat on soot formation within 0-g laminar gas jet diffusion flames. While fuel temperature variations have little influence on residence times in 1-g, they have a much more significant effect in 0-g. The primary objective of this program is to quantify this effect and its consequences on sooting by comparing soot volume fraction distributions under preheated and unpreheated-fuel conditions. Furthermore, the current work aims at expanding the limited soot database available for nonbuoyant flames. Soot fields in such flames can be used to perform additional tests of recently developed soot sub-models which have the potential to become powerful predicting tools in combustion design.

Enriched reproducing kernel particle method for fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

2018-06-01

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

Neonatal brain structure on MRI and diffusion tensor imaging, sex, and neurodevelopment in very-low-birthweight preterm children.

PubMed

Rose, Jessica; Butler, Erin E; Lamont, Lauren E; Barnes, Patrick D; Atlas, Scott W; Stevenson, David K

2009-07-01

The neurological basis of an increased incidence of cerebral palsy (CP) in preterm males is unknown. This study examined neonatal brain structure on magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI) at term-equivalent age, sex, and neurodevelopment at 1 year 6 months on the basis of the Amiel-Tison neurological examination, Gross Motor Function Classification System, and Bayley Scales of Infant Development in 78 very-low-birthweight preterm children (41 males, 37 females; mean gestational age 27.6 wks, SD 2.5; mean birthweight 1021 g, SD 339). Brain abnormalities on MRI and DTI were not different between males and females except in the splenium of the corpus callosum, where males had lower DTI fractional anisotropy (p=0.025) and a higher apparent diffusion coefficient (p=0.013), indicating delayed splenium development. In the 26 infants who were at higher risk on the basis of DTI, males had more abnormalities on MRI (p=0.034) and had lower fractional anisotropy and a higher apparent diffusion coefficient in the splenium (p=0.049; p=0.025) and right posterior limb of the internal capsule (PLIC; p=0.003; p=0.033). Abnormal neurodevelopment was more common in males (n=9) than in females (n=2; p=0.036). Children with abnormal neurodevelopment had more abnormalities on MRI (p=0.014) and reduced splenium and right PLIC fractional anisotropy (p=0.001; p=0.035). In children with abnormal neurodevelopment, right PLIC fractional anisotropy was lower than left (p=0.035), whereas in those with normal neurodevelopment right PLIC fractional anisotropy was higher than left (p=0.001). Right PLIC fractional anisotropy correlated to neurodevelopment (rho=0.371, p=0.002). Logistic regression predicted neurodevelopment with 94% accuracy; only right PLIC fractional anisotropy was a significant logistic coefficient. Results indicate that the higher incidence of abnormal neurodevelopment in preterm males relates to greater incidence and severity of brain abnormalities, including reduced PLIC and splenium development.

Thermal diffusion behavior of hard-sphere suspensions.

PubMed

Ning, Hui; Buitenhuis, Johan; Dhont, Jan K G; Wiegand, Simone

2006-11-28

We studied the thermal diffusion behavior of octadecyl coated silica particles (R(h)=27 nm) in toluene between 15.0 and 50.0 degrees C in a volume fraction range of 1%-30% by means of thermal diffusion forced Rayleigh scattering. The colloidal particles behave like hard spheres at high temperatures and as sticky spheres at low temperatures. With increasing temperature, the obtained Soret coefficient S(T) of the silica particles changed sign from negative to positive, which implies that the colloidal particles move to the warm side at low temperatures, whereas they move to the cold side at high temperatures. Additionally, we observed also a sign change of the Soret coefficient from positive to negative with increasing volume fraction. This is the first colloidal system for which a sign change with temperature and volume fraction has been observed. The concentration dependence of the thermal diffusion coefficient of the colloidal spheres is related to the colloid-colloid interactions, and will be compared with an existing theoretical description for interacting spherical particles. To characterize the particle-particle interaction parameters, we performed static and dynamic light scattering experiments. The temperature dependence of the thermal diffusion coefficient is predominantly determined by single colloidal particle properties, which are related to colloid-solvent molecule interactions.

Isolation, identification, and antibacterial activity of chemical compounds from ethanolic extract of suji leaf (Pleomele angusifolia NE Brown)

NASA Astrophysics Data System (ADS)

Faridah; Natalia; Lina, Maria; W, Hendig

2014-03-01

Suji (Pleomele angustifolia NE Brown) is one of the medicinal plants of the tribe of Liliaceae, empirically useful to treat coughs and respiratory diseases such as tuberculosis (TB) and pneumonia. In this study, ethanolic extract of suji leaves was tested its activity against bacteria that attacks the respiratory organs, namely Mycobacterium tuberculosis and Streptococcus pneumoniae, using a paper disc diffusion and dilution agar method. These extracts have activity in inhibiting the growth of M. tuberculosis at a concentration of 8 mg and against S. pneumoniae at a concentration of 4 mg. The fractions were tested their antibacterial activity against Streptococcus pneumoniae using paper disc diffusion method. The most active fraction was chosen based on the inhibition diameter. The fractions contained flavonoids, steroids, and essential oils. The precipitate isolated from the extraction process shows needle-shaped, white, cold and tasteless crystals. Moreover, the HPLC analysis of isolate revealed a single peak with a retention time of 7.183 minutes. The exact compounds in the isolate could not be determined but it was known the compounds contained the functional groups of alkene, alkane, C=O, -OH. Test results obtained from UV-Vis spectrophotometer provides maximum absorption at a wavelength of 203.0 nm.

Empirical single sample quantification of bias and variance in Q-ball imaging.

PubMed

Hainline, Allison E; Nath, Vishwesh; Parvathaneni, Prasanna; Blaber, Justin A; Schilling, Kurt G; Anderson, Adam W; Kang, Hakmook; Landman, Bennett A

2018-02-06

The bias and variance of high angular resolution diffusion imaging methods have not been thoroughly explored in the literature and may benefit from the simulation extrapolation (SIMEX) and bootstrap techniques to estimate bias and variance of high angular resolution diffusion imaging metrics. The SIMEX approach is well established in the statistics literature and uses simulation of increasingly noisy data to extrapolate back to a hypothetical case with no noise. The bias of calculated metrics can then be computed by subtracting the SIMEX estimate from the original pointwise measurement. The SIMEX technique has been studied in the context of diffusion imaging to accurately capture the bias in fractional anisotropy measurements in DTI. Herein, we extend the application of SIMEX and bootstrap approaches to characterize bias and variance in metrics obtained from a Q-ball imaging reconstruction of high angular resolution diffusion imaging data. The results demonstrate that SIMEX and bootstrap approaches provide consistent estimates of the bias and variance of generalized fractional anisotropy, respectively. The RMSE for the generalized fractional anisotropy estimates shows a 7% decrease in white matter and an 8% decrease in gray matter when compared with the observed generalized fractional anisotropy estimates. On average, the bootstrap technique results in SD estimates that are approximately 97% of the true variation in white matter, and 86% in gray matter. Both SIMEX and bootstrap methods are flexible, estimate population characteristics based on single scans, and may be extended for bias and variance estimation on a variety of high angular resolution diffusion imaging metrics. © 2018 International Society for Magnetic Resonance in Medicine.

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.

Short Diffusion Time Diffusion-Weighted Imaging With Oscillating Gradient Preparation as an Early Magnetic Resonance Imaging Biomarker for Radiation Therapy Response Monitoring in Glioblastoma: A Preclinical Feasibility Study.

PubMed

Bongers, Andre; Hau, Eric; Shen, Han

2018-01-04

To investigate a novel alternative diffusion-weighted imaging (DWI) approach using oscillating gradients preparation (OGSE) to obtain much shorter effective diffusion times (Δ eff ) for tumor response monitoring by apparent diffusion coefficient (ADC) mapping in a glioblastoma mouse model. Twenty-four BALB/c nude mice inoculated with U87 glioblastoma cells were randomized into a control group and an irradiation group, which underwent a 15-day fractioned radiation therapy (RT) course with 2 Gy/d. Therapy response was assessed by mapping of ADCs at 6 time points using an in-house implementation of a cos-OGSE DWI sequence with Δ eff  = 1.25 ms and compared with a standard pulsed gradient DWI protocol (PGSE) with typical clinical diffusion time Δ eff  = 18 ms. Longitudinal ADC changes in tumor and contralateral white matter (WM) were statistically assessed using repeated-measures analysis of variance and post hoc (Sidak) testing. On short Δ eff OGSE maps tumor ADC was generally 30%-50% higher than in surrounding WM. Areas correlated well with histology. Tumor identification was generally more difficult on PGSE maps owing to nonsignificant WM/tumor contrast. During RT, OGSE maps also showed significant tumor ADC increase (approximately 15%) in response to radiation, consistently seen after 14-Gy RT dose. The clinical reference (PGSE) showed lower sensitivity to radiation changes, and no significant response across the radiation group and time course could be detected. Our short Δ eff DWI method using OGSE better reflected histologically defined tumor areas and enabled more consistent and earlier detection of microstructural radiation changes than conventional methods. Oscillating gradients preparation offers significant potential as a robust microstructural RT response biomarker, potentially helping to shift important therapy decisions to earlier stages in the RT time course. Copyright © 2018 Elsevier Inc. All rights reserved.

White matter microstructure on diffusion tensor imaging is associated with conventional magnetic resonance imaging findings and cognitive function in adolescents born preterm

PubMed Central

FELDMAN, HEIDI M; LEE, ELIANA S; LOE, IRENE M; YEOM, KRISTEN W; GRILL-SPECTOR, KALANIT; LUNA, BEATRIZ

2013-01-01

AIM Diffusion tensor imaging (DTI) was used to evaluate white matter architecture after preterm birth. The goals were (1) to compare white matter microstructure in two cohorts of preterm- and term-born children; and (2) within preterm groups, to determine if sex, gestational age, birthweight, white matter injury score from conventional magnetic resonance imaging (MRI), or IQ was associated with DTI measures. METHOD Participants (n=121; 66 females, 55 males) were aged 9 to 16 years. They comprised 58 preterm children (site 1, n=25; and site 2, n=33) born at less than 36 weeks’ gestation (mean 29.4wks; birthweight 1289g) and 63 term children (site 1, n=40; site 2, n=23) born at more than 37 weeks’ gestation. DTI was analyzed using tract-based spatial statistics. Diffusion measures were fractional anisotropy, axial, radial, and mean diffusivity. RESULTS In no region of the white matter skeleton was fractional anisotropy lower in the preterm group at either site. Within the preterm groups, fractional anisotropy was significantly associated with white matter injury score, but not sex, gestational age, or birthweight. At site 1, fractional anisotropy was associated with IQ. INTERPRETATION DTI contributes to understanding individual differences after preterm birth but may not differentiate a relatively high-functioning group of preterm children from a matched group of term-born children. PMID:22803787

Monitoring of caffeine consumption effect on skin blood properties by diffuse reflectance spectroscopy

NASA Astrophysics Data System (ADS)

Milanic, Matija; Marin, Ana; Stergar, Jost; Verdel, Nina; Majaron, Boris

2017-07-01

Caffeine is the most widely consumed psychoactive substance in the world. It affects many tissues and organs, in particular central nervous system, heart, and blood vessels. The effect of caffeine on vascular smooth muscle cells is an initial transient contraction followed by significant vasodilatation. In this study we investigate the use of diffuse reflectance spectroscopy (DRS) for monitoring of vascular changes in human skin induced by caffeine consumption. DRS spectra were recorded on volar sides of the forearms of ten healthy volunteers at time delays of 0, 30, 60, 120, and 180 minutes after consumption of caffeine, while one subject served as a negative control. Analytical diffusion approximation solutions for diffuse reflectance from three-layer structures were used to assess skin composition (e.g., dermal blood volume fraction and oxygen saturation) by fitting to experimental data. The results demonstrate that cutaneous vasodynamics induced by caffeine consumption can be monitored by DRS, while changes in the control subject not consuming caffeine were insignificant.

Persistence of abnormalities in white matter in children with type 1 diabetes.

PubMed

Fox, Larry A; Hershey, Tamara; Mauras, Nelly; Arbeláez, Ana Maria; Tamborlane, William V; Buckingham, Bruce; Tsalikian, Eva; Englert, Kim; Raman, Mira; Jo, Booil; Shen, Hanyang; Reiss, Allan; Mazaika, Paul

2018-07-01

Prior studies suggest white matter growth is reduced and white matter microstructure is altered in the brains of young children with type 1 diabetes when compared with brains of non-diabetic children, due in part to adverse effects of hyperglycaemia. This longitudinal observational study examines whether dysglycaemia alters the developmental trajectory of white matter microstructure over time in young children with type 1 diabetes. One hundred and eighteen children, aged 4 to <10 years old with type 1 diabetes and 58 age-matched, non-diabetic children were studied at baseline and 18 months, at five Diabetes Research in Children Network clinical centres. We analysed longitudinal trajectories of white matter using diffusion tensor imaging. Continuous glucose monitoring profiles and HbA 1c levels were obtained every 3 months. Axial diffusivity was lower in children with diabetes at baseline (p = 0.022) and at 18 months (p = 0.015), indicating that differences in white matter microstructure persist over time in children with diabetes. Within the diabetes group, lower exposure to hyperglycaemia, averaged over the time since diagnosis, was associated with higher fractional anisotropy (p = 0.037). Fractional anisotropy was positively correlated with performance (p < 0.002) and full-scale IQ (p < 0.02). These results suggest that hyperglycaemia is associated with altered white matter development, which may contribute to the mild cognitive deficits in this population.

Detecting and Correcting Melt Inclusion Modification

NASA Astrophysics Data System (ADS)

Cottrell, E.; Kelley, K. A.

2008-12-01

Post entrapment diffusive modification of melt inclusions may mute or erase primary signatures. Corrections for post-entrapment crystallization (PEC) and Fe-loss are routinely applied and, because recent experimental studies suggest rapid diffusion of trace components into and out of olivine-hosted inclusions, the ability to discriminate between primary and secondary signatures is now even more critical. Two tools may assist in this endeavor. XANES measurements of Fe3+/ΣFe ratios in undegassed ol-hosted basaltic melt inclusions from global arcs are 16-36% (n=16), significantly higher than the 7-10% commonly assumed, and higher than in MORB or BABB lavas (Kelley and Cottrell, this mtg). The Fe3+/ΣFe ratios indicate melt-host equilibrium, with significantly less PEC or Fe-loss than would have been otherwise assumed. We conclude that Fe2+ diffusion has been minimal; therefore the residence time of these primitive inclusions in an evolved magma must have been short. Fe3+/ΣFe correlates positively with water concentration, but not with CO2 and S concentrations or Mg#. The oxidized nature of arc lavas and melt inclusions may therefore indicate an oxidized source rather than late-stage degassing or fractionation. Trace element concentrations evolve with time if an inclusion is out of equilibrium with its host. The numerical model of Cottrell et al., 2002, makes specific predictions about how suites of melt inclusions evolve, creating a tool to detect post-entrapment modification. Recent laboratory measurements of REE diffusion in olivine greatly diverge (at 1300°C, 1015 vs 1019m2/s). If REE diffusivity is extremely fast, melt inclusion HREE diversity shouldn't survive more than a few years in a magma chamber; but if slow, HREE variance could be preserved for >104 yrs. Model analysis of published suites of ol-hosted inclusions indicates that either REE diffusion is quite slow, or the residence time of melt inclusions at high temperature is very short. Loss of variance in suites of pl-hosted inclusions is consistent with long (>103 yrs) residence times. Suites of ol- and pl-hosted inclusions from the same magmatic system can therefore bracket residence times if diffusivities are known, or put reasonable bounds on diffusion rates.

Diffusion and related transport mechanisms in brain tissue

NASA Astrophysics Data System (ADS)

Nicholson, Charles

2001-07-01

Diffusion plays a crucial role in brain function. The spaces between cells can be likened to the water phase of a foam and many substances move within this complicated region. Diffusion in this interstitial space can be accurately modelled with appropriate modifications of classical equations and quantified from measurements based on novel micro-techniques. Besides delivering glucose and oxygen from the vascular system to brain cells, diffusion also moves informational substances between cells, a process known as volume transmission. Deviations from expected results reveal how local uptake, degradation or bulk flow may modify the transport of molecules. Diffusion is also essential to many therapies that deliver drugs to the brain. The diffusion-generated concentration distributions of well-chosen molecules also reveal the structure of brain tissue. This structure is represented by the volume fraction (void space) and the tortuosity (hindrance to diffusion imposed by local boundaries or local viscosity). Analysis of these parameters also reveals how the local geometry of the brain changes with time or under pathological conditions. Theoretical and experimental approaches borrow from classical diffusion theory and from porous media concepts. Earlier studies were based on radiotracers but the recent methods use a point-source paradigm coupled with micro-sensors or optical imaging of macromolecules labelled with fluorescent tags. These concepts and methods are likely to be applicable elsewhere to measure diffusion properties in very small volumes of highly structured but delicate material.

Magnetic resonance imaging evidence for presymptomatic change in thalamus and caudate in familial Alzheimer’s disease

PubMed Central

Keihaninejad, Shiva; Shakespeare, Timothy J.; Lehmann, Manja; Crutch, Sebastian J.; Malone, Ian B.; Thornton, John S.; Mancini, Laura; Hyare, Harpreet; Yousry, Tarek; Ridgway, Gerard R.; Zhang, Hui; Modat, Marc; Alexander, Daniel C.; Rossor, Martin N.; Ourselin, Sebastien; Fox, Nick C.

2013-01-01

Amyloid imaging studies of presymptomatic familial Alzheimer’s disease have revealed the striatum and thalamus to be the earliest sites of amyloid deposition. This study aimed to investigate whether there are associated volume and diffusivity changes in these subcortical structures during the presymptomatic and symptomatic stages of familial Alzheimer’s disease. As the thalamus and striatum are involved in neural networks subserving complex cognitive and behavioural functions, we also examined the diffusion characteristics in connecting white matter tracts. A cohort of 20 presenilin 1 mutation carriers underwent volumetric and diffusion tensor magnetic resonance imaging, neuropsychological and clinical assessments; 10 were symptomatic, 10 were presymptomatic and on average 5.6 years younger than their expected age at onset; 20 healthy control subjects were also studied. We conducted region of interest analyses of volume and diffusivity changes in the thalamus, caudate, putamen and hippocampus and examined diffusion behaviour in the white matter tracts of interest (fornix, cingulum and corpus callosum). Voxel-based morphometry and tract-based spatial statistics were also used to provide unbiased whole-brain analyses of group differences in volume and diffusion indices, respectively. We found that reduced volumes of the left thalamus and bilateral caudate were evident at a presymptomatic stage, together with increased fractional anisotropy of bilateral thalamus and left caudate. Although no significant hippocampal volume loss was evident presymptomatically, reduced mean diffusivity was observed in the right hippocampus and reduced mean and axial diffusivity in the right cingulum. In contrast, symptomatic mutation carriers showed increased mean, axial and in particular radial diffusivity, with reduced fractional anisotropy, in all of the white matter tracts of interest. The symptomatic group also showed atrophy and increased mean diffusivity in all of the subcortical grey matter regions of interest, with increased fractional anisotropy in bilateral putamen. We propose that axonal injury may be an early event in presymptomatic Alzheimer’s disease, causing an initial fall in axial and mean diffusivity, which then increases with loss of axonal density. The selective degeneration of long-coursing white matter tracts, with relative preservation of short interneurons, may account for the increase in fractional anisotropy that is seen in the thalamus and caudate presymptomatically. It may be owing to their dense connectivity that imaging changes are seen first in the thalamus and striatum, which then progress to involve other regions in a vulnerable neuronal network. PMID:23539189

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

PubMed

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

2009-04-01

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

Two-time scale subordination in physical processes with long-term memory

NASA Astrophysics Data System (ADS)

Stanislavsky, Aleksander; Weron, Karina

2008-03-01

We describe dynamical processes in continuous media with a long-term memory. Our consideration is based on a stochastic subordination idea and concerns two physical examples in detail. First we study a temporal evolution of the species concentration in a trapping reaction in which a diffusing reactant is surrounded by a sea of randomly moving traps. The analysis uses the random-variable formalism of anomalous diffusive processes. We find that the empirical trapping-reaction law, according to which the reactant concentration decreases in time as a product of an exponential and a stretched exponential function, can be explained by a two-time scale subordination of random processes. Another example is connected with a state equation for continuous media with memory. If the pressure and the density of a medium are subordinated in two different random processes, then the ordinary state equation becomes fractional with two-time scales. This allows one to arrive at the Bagley-Torvik type of state equation.

Fractional Ablative Laser Followed by Transdermal Acoustic Pressure Wave Device to Enhance the Drug Delivery of Aminolevulinic Acid: In Vivo Fluorescence Microscopy Study.

PubMed

Waibel, Jill S; Rudnick, Ashley; Nousari, Carlos; Bhanusali, Dhaval G

2016-01-01

Topical drug delivery is the foundation of all dermatological therapy. Laser-assisted drug delivery (LAD) using fractional ablative laser is an evolving modality that may allow for a greater precise depth of penetration by existing topical medications, as well as more efficient transcutaneous delivery of large drug molecules. Additional studies need to be performed using energy-driven methods that may enhance drug delivery in a synergistic manner. Processes such as iontophoresis, electroporation, sonophoresis, and the use of photomechanical waves aid in penetration. This study evaluated in vivo if there is increased efficacy of fractional CO2 ablative laser with immediate acoustic pressure wave device. Five patients were treated and biopsied at 4 treatment sites: 1) topically applied aminolevulinic acid (ALA) alone; 2) fractional ablative CO2 laser and topical ALA alone; 3) fractional ablative CO2 laser and transdermal acoustic pressure wave device delivery system; and 4) topical ALA with transdermal delivery system. The comparison of the difference in the magnitude of diffusion with both lateral spread of ALA and depth diffusion of ALA was measured by fluorescence microscopy. For fractional ablative CO2 laser, ALA, and transdermal acoustic pressure wave device, the protoporphyrin IX lateral fluorescence was 0.024 mm on average vs 0.0084 mm for fractional ablative CO2 laser and ALA alone. The diffusion for the acoustic pressure wave device was an order of magnitude greater. We found that our combined approach of fractional ablative CO2 laser paired with the transdermal acoustic pressure wave device increased the depth of penetration of ALA.

Hydrodynamic theory of diffusion in two-temperature multicomponent plasmas

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

Ramshaw, J.D.; Chang, C.H.

Detailed numerical simulations of multicomponent plasmas require tractable expressions for species diffusion fluxes, which must be consistent with the given plasma current density J{sub q} to preserve local charge neutrality. The common situation in which J{sub q} = 0 is referred to as ambipolar diffusion. The use of formal kinetic theory in this context leads to results of formidable complexity. We derive simple tractable approximations for the diffusion fluxes in two-temperature multicomponent plasmas by means of a generalization of the hydrodynamical approach used by Maxwell, Stefan, Furry, and Williams. The resulting diffusion fluxes obey generalized Stefan-Maxwell equations that contain drivingmore » forces corresponding to ordinary, forced, pressure, and thermal diffusion. The ordinary diffusion fluxes are driven by gradients in pressure fractions rather than mole fractions. Simplifications due to the small electron mass are systematically exploited and lead to a general expression for the ambipolar electric field in the limit of infinite electrical conductivity. We present a self-consistent effective binary diffusion approximation for the diffusion fluxes. This approximation is well suited to numerical implementation and is currently in use in our LAVA computer code for simulating multicomponent thermal plasmas. Applications to date include a successful simulation of demixing effects in an argon-helium plasma jet, for which selected computational results are presented. Generalizations of the diffusion theory to finite electrical conductivity and nonzero magnetic field are currently in progress.« less

Transverse Diffusivity of Cerebral Parenchyma Predicts Visual Tracking Performance in Relapsing-Remitting Multiple Sclerosis

ERIC Educational Resources Information Center

Warlop, Nele P.; Achten, Eric; Fieremans, Els; Debruyne, Jan; Vingerhoets, Guy

2009-01-01

This study investigated the relation between cerebral damage related to multiple sclerosis (MS) and cognitive decline as determined by two classical mental tracking tests. Cerebral damage in 15 relapsing-remitting MS patients was measured by diffusion tensor imaging (DTI). Fractional anisotropy, longitudinal and transverse diffusivity were defined…

Measurement and modeling of solar irradiance components on horizontal and tilted planes

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

Padovan, Andrea; Col, Davide del

2010-12-15

In this work new measurements of global and diffuse solar irradiance on the horizontal plane and global irradiance on planes tilted at 20 and 30 oriented due South and at 45 and 65 oriented due East are used to discuss the modeling of solar radiation. Irradiance data are collected in Padova (45.4 N, 11.9 E, 12 m above sea level), Italy. Some diffuse fraction correlations have been selected to model the hourly diffuse radiation on the horizontal plane. The comparison with the present experimental data shows that their prediction accuracy strongly depends on the sky characteristics. The hourly irradiance measurementsmore » taken on the tilted planes are compared with the estimations given by one isotropic and three anisotropic transposition models. The use of an anisotropic model, based on a physical description of the diffuse radiation, provides a much better accuracy, especially when measurements of the diffuse irradiance on the horizontal plane are not available and thus transposition models have to be applied in combination with a diffuse fraction correlation. This is particularly significant for the planes oriented away from South. (author)« less

Lack of thermal energy in superbubbles: hint of cosmic rays?

NASA Astrophysics Data System (ADS)

Gupta, Siddhartha; Nath, Biman B.; Sharma, Prateek; Eichler, David

2018-01-01

Using analytic methods and 1D two-fluid simulations, we study the effect of cosmic rays (CRs) on the dynamics of interstellar superbubbles (ISBs) driven by multiple supernovae (SNe)/stellar winds in OB associations. In addition to CR advection and diffusion, our models include thermal conduction and radiative cooling. We find that CR injection at the reverse shock or within a central wind-driving region can affect the thermal profiles of ISBs and hence their X-ray properties. Even if a small fraction (10-20 per cent) of the total mechanical power is injected into CRs, a significant fraction of the ram pressure at the reverse shock can be transferred to CRs. The energy transfer becomes efficient if (1) the reverse shock gas Mach number exceeds a critical value (Mth ≳ 12) and (2) the CR acceleration time-scale τacc ∼ κcr/v2 is shorter than the dynamical time, where κcr is a CR diffusion coefficient and v is the upstream velocity. We show that CR affected bubbles can exhibit a volume-averaged hot gas temperature 1-5 × 106 K, lower by a factor of 2 - 10 than without CRs. Thus, CRs can potentially solve the long-standing problem of the observed low ISB temperatures.

Structure of turbulent non-premixed flames modeled with two-step chemistry

NASA Technical Reports Server (NTRS)

Chen, J. H.; Mahalingam, S.; Puri, I. K.; Vervisch, L.

1992-01-01

Direct numerical simulations of turbulent diffusion flames modeled with finite-rate, two-step chemistry, A + B yields I, A + I yields P, were carried out. A detailed analysis of the turbulent flame structure reveals the complex nature of the penetration of various reactive species across two reaction zones in mixture fraction space. Due to this two zone structure, these flames were found to be robust, resisting extinction over the parameter ranges investigated. As in single-step computations, mixture fraction dissipation rate and the mixture fraction were found to be statistically correlated. Simulations involving unequal molecular diffusivities suggest that the small scale mixing process and, hence, the turbulent flame structure is sensitive to the Schmidt number.

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.

An in-depth assessment into simultaneous monitoring of dissolved reactive phosphorus (DRP) and low-molecular-weight organic phosphorus (LMWOP) in aquatic environments using diffusive gradients in thin films (DGT).

PubMed

Mohr, Christian Wilhelm; Vogt, Rolf David; Røyset, Oddvar; Andersen, Tom; Parekh, Neha Amit

2015-04-01

Long-term laborious and thus costly monitoring of phosphorus (P) fractions is required in order to provide reasonable estimates of the levels of bioavailable phosphorus for eutrophication studies. A practical solution to this problem is the application of passive samplers, known as Diffusive Gradient in Thin films (DGTs), providing time-average concentrations. DGT, with the phosphate adsorbent Fe-oxide based binding gel, is capable of collecting both orthophosphate and low molecular weight organic phosphorus (LMWOP) compounds, such as adenosine monophosphate (AMP) and myo-inositol hexakisphosphate (IP6). The diffusion coefficient (D) is a key parameter relating the amount of analyte determined from the DGT to a time averaged ambient concentration. D at 20 °C for AMP and IP6 were experimentally determined to be 2.9 × 10(-6) cm(2) s(-1) and 1.0 × 10(-6) cm(2) s(-1), respectively. Estimations by conceptual models of LMWOP uptake by DGTs indicated that this fraction constituted more than 75% of the dissolved organic phosphorus (DOP) accumulated. Since there is no one D for LMWOP, a D range was estimated through assessment of D models. The models tested for estimating D for a variety of common LMWOP molecules proved to be still too uncertain for practical use. The experimentally determined D for AMP and IP6 were therefore used as upper and lower D, respectively, in order to estimate minimum and maximum ambient concentrations of LMWOP. Validation of the DGT data was performed by comparing concentrations of P fractions determined in natural water samples with concentration of P fractions determined using DGT. Stream water draining three catchments with different land-use (forest, mixed and agriculture) showed clear differences in relative and absolute concentrations of dissolved reactive phosphorus (DRP) and dissolved organic P (DOP). There was no significant difference between water sample and DGT DRP (p > 0.05). Moreover, the upper and lower limit D for LMWOP proved reasonable as water sample determined DOP was found to lie in-between the limits of DGT LMWOP concentrations, indicating that on average DOP consists mainly of LMWOP. "Best fit" D was determined for each stream in order to practically use the DGTs for estimating time average DOP. Applying DGT in a eutrophic lake provided insight into P cycling in the water column.

Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport

NASA Astrophysics Data System (ADS)

Gherardi, Marco; Calabrese, Ludovico; Tamm, Mikhail; Cosentino Lagomarsino, Marco

2017-10-01

The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.

A Novel Diffuse Fraction-Based Two-Leaf Light Use Efficiency Model: An Application Quantifying Photosynthetic Seasonality across 20 AmeriFlux Flux Tower Sites

NASA Astrophysics Data System (ADS)

Yan, Hao; Wang, Shao-Qiang; Yu, Kai-Liang; Wang, Bin; Yu, Qin; Bohrer, Gil; Billesbach, Dave; Bracho, Rosvel; Rahman, Faiz; Shugart, Herman H.

2017-10-01

Diffuse radiation can increase canopy light use efficiency (LUE). This creates the need to differentiate the effects of direct and diffuse radiation when simulating terrestrial gross primary production (GPP). Here, we present a novel GPP model, the diffuse-fraction-based two-leaf model (DTEC), which includes the leaf response to direct and diffuse radiation, and treats maximum LUE for shaded leaves (ɛmsh defined as a power function of the diffuse fraction (Df)) and sunlit leaves (ɛmsu defined as a constant) separately. An Amazonian rainforest site (KM67) was used to calibrate the model by simulating the linear relationship between monthly canopy LUE and Df. This showed a positive response of forest GPP to atmospheric diffuse radiation, and suggested that diffuse radiation was more limiting than global radiation and water availability for Amazon rainforest GPP on a monthly scale. Further evaluation at 20 independent AmeriFlux sites showed that the DTEC model, when driven by monthly meteorological data and MODIS leaf area index (LAI) products, explained 70% of the variability observed in monthly flux tower GPP. This exceeded the 51% accounted for by the MODIS 17A2 big-leaf GPP product. The DTEC model's explicit accounting for the impacts of diffuse radiation and soil water stress along with its parameterization for C4 and C3 plants was responsible for this difference. The evaluation of DTEC at Amazon rainforest sites demonstrated its potential to capture the unique seasonality of higher GPP during the diffuse radiation-dominated wet season. Our results highlight the importance of diffuse radiation in seasonal GPP simulation.