A Flux-Corrected Transport Based Hydrodynamic Model for the Plasmasphere Refilling Problem following Geomagnetic Storms

NASA Astrophysics Data System (ADS)

Chatterjee, K.; Schunk, R. W.

2017-12-01

The refilling of the plasmasphere following a geomagnetic storm remains one of the longstanding problems in the area of ionosphere-magnetosphere coupling. Both diffusion and hydrodynamic approximations have been adopted for the modeling and solution of this problem. The diffusion approximation neglects the nonlinear inertial term in the momentum equation and so this approximation is not rigorously valid immediately after the storm. Over the last few years, we have developed a hydrodynamic refilling model using the flux-corrected transport method, a numerical method that is extremely well suited to handling nonlinear problems with shocks and discontinuities. The plasma transport equations are solved along 1D closed magnetic field lines that connect conjugate ionospheres and the model currently includes three ion (H+, O+, He+) and two neutral (O, H) species. In this work, each ion species under consideration has been modeled as two separate streams emanating from the conjugate hemispheres and the model correctly predicts supersonic ion speeds and the presence of high levels of Helium during the early hours of refilling. The ultimate objective of this research is the development of a 3D model for the plasmasphere refilling problem and with additional development, the same methodology can potentially be applied to the study of other complex space plasma coupling problems in closed flux tube geometries. Index Terms: 2447 Modeling and forecasting [IONOSPHERE] 2753 Numerical modeling [MAGNETOSPHERIC PHYSICS] 7959 Models [SPACE WEATHER

Analysis of the geometrical-probabilistic models of electrocrystallization

NASA Astrophysics Data System (ADS)

Isaev, V. A.; Grishenkova, O. V.; Zaykov, Yu. P.

2016-08-01

The formation of a three-dimensional electrode deposit under potentiostatic conditions, including the stages of nucleation, growth, and overlap of growing new-phase clusters and their diffusion zones, is considered. The models of electrochemical phase formation for kinetics- and diffusion-controlled growth are analyzed, and the correctness of the approximations used in these models is estimated. The possibility of application of these models to an analysis of the electrodeposition of silicon from molten salts is discussed.

Comptonization of X-rays by low-temperature electrons. [photon wavelength redistribution in cosmic sources

NASA Technical Reports Server (NTRS)

Illarionov, A.; Kallman, T.; Mccray, R.; Ross, R.

1979-01-01

A method is described for calculating the spectrum that results from the Compton scattering of a monochromatic source of X-rays by low-temperature electrons, both for initial-value relaxation problems and for steady-state spatial diffusion problems. The method gives an exact solution of the inital-value problem for evolution of the spectrum in an infinite homogeneous medium if Klein-Nishina corrections to the Thomson cross section are neglected. This, together with approximate solutions for problems in which Klein-Nishina corrections are significant and/or spatial diffusion occurs, shows spectral structure near the original photon wavelength that may be used to infer physical conditions in cosmic X-ray sources. Explicit results, shown for examples of time relaxation in an infinite medium and spatial diffusion through a uniform sphere, are compared with results obtained by Monte Carlo calculations and by solving the appropriate Fokker-Planck equation.

Wealth and price distribution by diffusive approximation in a repeated prediction market

NASA Astrophysics Data System (ADS)

Bottazzi, Giulio; Giachini, Daniele

2017-04-01

The approximate agents' wealth and price invariant densities of a repeated prediction market model is derived using the Fokker-Planck equation of the associated continuous-time jump process. We show that the approximation obtained from the evolution of log-wealth difference can be reliably exploited to compute all the quantities of interest in all the acceptable parameter space. When the risk aversion of the trader is high enough, we are able to derive an explicit closed-form solution for the price distribution which is asymptotically correct.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging

NASA Astrophysics Data System (ADS)

Custo, Anna; Wells, William M., III; Barnett, Alex H.; Hillman, Elizabeth M. C.; Boas, David A.

2006-07-01

An efficient computation of the time-dependent forward solution for photon transport in a head model is a key capability for performing accurate inversion for functional diffuse optical imaging of the brain. The diffusion approximation to photon transport is much faster to simulate than the physically correct radiative transport equation (RTE); however, it is commonly assumed that scattering lengths must be much smaller than all system dimensions and all absorption lengths for the approximation to be accurate. Neither of these conditions is satisfied in the cerebrospinal fluid (CSF). Since line-of-sight distances in the CSF are small, of the order of a few millimeters, we explore the idea that the CSF scattering coefficient may be modeled by any value from zero up to the order of the typical inverse line-of-sight distance, or approximately 0.3 mm-1, without significantly altering the calculated detector signals or the partial path lengths relevant for functional measurements. We demonstrate this in detail by using a Monte Carlo simulation of the RTE in a three-dimensional head model based on clinical magnetic resonance imaging data, with realistic optode geometries. Our findings lead us to expect that the diffusion approximation will be valid even in the presence of the CSF, with consequences for faster solution of the inverse problem.

Deterministic diffusion in flower-shaped billiards.

PubMed

Harayama, Takahisa; Klages, Rainer; Gaspard, Pierre

2002-08-01

We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent.

The Stokes-Einstein relation at moderate Schmidt number.

PubMed

Balboa Usabiaga, Florencio; Xie, Xiaoyi; Delgado-Buscalioni, Rafael; Donev, Aleksandar

2013-12-07

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

Relativistic theory of particles in a scattering flow III: photon transport.

NASA Astrophysics Data System (ADS)

Achterberg, A.; Norman, C. A.

2018-06-01

We use the theory developed in Achterberg & Norman (2018a) and Achterberg & Norman (2018b) to calculate the stress due to photons that are scattered elastically by a relativistic flow. We show that the energy-momentum tensor of the radiation takes the form proposed by Eckart (1940). In particular we show that no terms associated with a bulk viscosity appear if one makes the diffusion approximation for radiation transport and treats the radiation as a separate fluid. We find only shear (dynamic) viscosity terms and heat flow terms in our expression for the energy-momentum tensor. This conclusion holds quite generally for different forms of scattering: Krook-type integral scattering, diffusive (Fokker-Planck) scattering and Thomson scattering. We also derive the transport equation in the diffusion approximation that shows the effects of the flow on the photon gas in the form of a combination of adiabatic heating and an irreversible heating term. We find no diffusive changes to the comoving number density and energy density of the scattered photons, in contrast with some published results in Radiation Hydrodynamics. It is demonstrated that these diffusive corrections to the number- and energy density of the photons are in fact higher-order terms that can (and should) be neglected in the diffusion approximation. Our approach eliminates these terms at the root of the expansion that yields the anisotropic terms in the phase-space density of particles and photons, the terms responsible for the photon viscosity.

Stability of Gradient Field Corrections for Quantitative Diffusion MRI.

PubMed

Rogers, Baxter P; Blaber, Justin; Welch, E Brian; Ding, Zhaohua; Anderson, Adam W; Landman, Bennett A

2017-02-11

In magnetic resonance diffusion imaging, gradient nonlinearity causes significant bias in the estimation of quantitative diffusion parameters such as diffusivity, anisotropy, and diffusion direction in areas away from the magnet isocenter. This bias can be substantially reduced if the scanner- and coil-specific gradient field nonlinearities are known. Using a set of field map calibration scans on a large (29 cm diameter) phantom combined with a solid harmonic approximation of the gradient fields, we predicted the obtained b-values and applied gradient directions throughout a typical field of view for brain imaging for a typical 32-direction diffusion imaging sequence. We measured the stability of these predictions over time. At 80 mm from scanner isocenter, predicted b-value was 1-6% different than intended due to gradient nonlinearity, and predicted gradient directions were in error by up to 1 degree. Over the course of one month the change in these quantities due to calibration-related factors such as scanner drift and variation in phantom placement was <0.5% for b-values, and <0.5 degrees for angular deviation. The proposed calibration procedure allows the estimation of gradient nonlinearity to correct b-values and gradient directions ahead of advanced diffusion image processing for high angular resolution data, and requires only a five-minute phantom scan that can be included in a weekly or monthly quality assurance protocol.

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.

Approximation of epidemic models by diffusion processes and their statistical inference.

PubMed

Guy, Romain; Larédo, Catherine; Vergu, Elisabeta

2015-02-01

Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.

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

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2008-02-01

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

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

NASA Astrophysics Data System (ADS)

Konkoli, Zoran

2004-01-01

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

Diffusive Cosmic-Ray Acceleration at Shock Waves of Arbitrary Speed with Magnetostatic Turbulence. I. General Theory and Correct Nonrelativistic Speed Limit

NASA Astrophysics Data System (ADS)

Schlickeiser, R.; Oppotsch, J.

2017-12-01

The analytical theory of diffusive acceleration of cosmic rays at parallel stationary shock waves of arbitrary speed with magnetostatic turbulence is developed from first principles. The theory is based on the diffusion approximation to the gyrotropic cosmic-ray particle phase-space distribution functions in the respective rest frames of the up- and downstream medium. We derive the correct cosmic-ray jump conditions for the cosmic-ray current and density, and match the up- and downstream distribution functions at the position of the shock. It is essential to account for the different particle momentum coordinates in the up- and downstream media. Analytical expressions for the momentum spectra of shock-accelerated cosmic rays are calculated. These are valid for arbitrary shock speeds including relativistic shocks. The correctly taken limit for nonrelativistic shock speeds leads to a universal broken power-law momentum spectrum of accelerated particles with velocities well above the injection velocity threshold, where the universal power-law spectral index q≃ 2-{γ }1-4 is independent of the flow compression ratio r. For nonrelativistic shock speeds, we calculate for the first time the injection velocity threshold, settling the long-standing injection problem for nonrelativistic shock acceleration.

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

NASA Astrophysics Data System (ADS)

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

2007-10-01

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

Erratum: A Comparison of Closures for Stochastic Advection-Diffusion Equations

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

Jarman, Kenneth D.; Tartakovsky, Alexandre M.

2015-01-01

This note corrects an error in the authors' article [SIAM/ASA J. Uncertain. Quantif., 1 (2013), pp. 319 347] in which the cited work [Neuman, Water Resour. Res., 29(3) (1993), pp. 633 645] was incorrectly represented and attributed. Concentration covariance equations presented in our article as new were in fact previously derived in the latter work. In the original abstract, the phrase " . . .we propose a closed-form approximation to two-point covariance as a measure of uncertainty. . ." should be replaced by the phrase " . . .we study a closed-form approximation to two-point covariance, previously derived in [Neumanmore » 1993], as a measure of uncertainty." The primary results in our article--the analytical and numerical comparison of existing closure methods for specific example problems are not changed by this correction.« less

A DYNAMIC DENSITY FUNCTIONAL THEORY APPROACH TO DIFFUSION IN WHITE DWARFS AND NEUTRON STAR ENVELOPES

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

Diaw, A.; Murillo, M. S.

2016-09-20

We develop a multicomponent hydrodynamic model based on moments of the Born–Bogolyubov–Green–Kirkwood–Yvon hierarchy equations for physical conditions relevant to astrophysical plasmas. These equations incorporate strong correlations through a density functional theory closure, while transport enters through a relaxation approximation. This approach enables the introduction of Coulomb coupling correction terms into the standard Burgers equations. The diffusive currents for these strongly coupled plasmas is self-consistently derived. The settling of impurities and its impact on cooling can be greatly affected by strong Coulomb coupling, which we show can be quantified using the direct correlation function.

Intensity-Value Corrections for Integrating Sphere Measurements of Solid Samples Measured Behind Glass

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

Johnson, Timothy J.; Bernacki, Bruce E.; Redding, Rebecca L.

2014-11-01

Accurate and calibrated directional-hemispherical reflectance spectra of solids are important for both in situ and remote sensing. Many solids are in the form of powders or granules and to measure their diffuse reflectance spectra in the laboratory, it is often necessary to place the samples behind a transparent medium such as glass for the ultraviolet (UV), visible, or near-infrared spectral regions. Using both experimental methods and a simple optical model, we demonstrate that glass (fused quartz in our case) leads to artifacts in the reflectance values. We report our observations that the measured reflectance values, for both hemispherical and diffusemore » reflectance, are distorted by the additional reflections arising at the air–quartz and sample–quartz interfaces. The values are dependent on the sample reflectance and are offset in intensity in the hemispherical case, leading to measured values up to ~6% too high for a 2% reflectance surface, ~3.8% too high for 10% reflecting surfaces, approximately correct for 40–60% diffuse-reflecting surfaces, and ~1.5% too low for 99% reflecting Spectralon® surfaces. For the case of diffuse-only reflectance, the measured values are uniformly too low due to the polished glass, with differences of nearly 6% for a 99% reflecting matte surface. The deviations arise from the added reflections from the quartz surfaces, as verified by both theory and experiment, and depend on sphere design. Finally, empirical correction factors were implemented into post-processing software to redress the artifact for hemispherical and diffuse reflectance data across the 300–2300 nm range.« less

Scalar dissipation rates in non-conservative transport systems

PubMed Central

Engdahl, Nicholas B.; Ginn, Timothy R.; Fogg, Graham E.

2014-01-01

This work considers how the inferred mixing state of diffusive and advective-diffusive systems will vary over time when the solute masses are not constant over time. We develop a number of tools that allow the scalar dissipation rate to be used as a mixing measure in these systems without calculating local concentration gradients. The behavior of dissipation rates are investigated for single and multi-component kinetic reactions and a commonly studied equilibrium reaction. The scalar dissipation rate of a tracer experiencing first order decay can be determined exactly from the decay constant and the dissipation rate of a passive tracer, and the mixing rate of a conservative component is not the superposition of the solute specific mixing rates. We then show how the behavior of the scalar dissipation rate can be determined from a limited subset of an infinite domain. Corrections are derived for constant and time dependent limits of integration the latter is used to approximate dissipation rates in advective-diffusive systems. Several of the corrections exhibit similarities to the previous work on mixing, including non-Fickian mixing. This illustrates the importance of accounting for the effects that reaction systems or limited monitoring areas may have on the inferred mixing state. PMID:23584457

A first-principles study of elastic and diffusion properties of magnesium based alloys

NASA Astrophysics Data System (ADS)

Ganeshan, Swetha

2011-12-01

In this thesis, the influence of alloying elements on the elastic and diffusion properties of Magnesium (Mg) has been studied based on first-principles density functional theory. The stress-strain method has been used to predict the elastic constants of the Mg based alloys studied herein. This method involves calculating the resultant change in stress due to application of strain. The validity of this method has been successfully tested for both 0K as well as at finite temperatures. The elastic constants predicted in this work have been correlated to ductility, fracture toughness, stiffness, elastic anisotropy and bond directionality, thus providing a better understanding of the influence of alloying elements on the mechanical and physical properties of Mg. Elastic constants, as a function of temperature have been predicted using first-principles quasi-static approximation. In this approach elastic stiffness coefficients calculated with respect to volume (cij( V)) have been correlated to the equilibrium volume as a function of temperature V(T) from phonon calculations to obtain temperature dependence of elastic stiffness coefficients cij(T). To compare our calculated temperature dependent elastic constants with that of experiments an isentropic correction term has been introduced. It is seen that the influence of this isentropic correction term on the elastic constants becomes significant at high temperatures. The quasi-static approximation has been primarily applied to calculate temperature dependent elastic constants of Mg2Ge, Mg2Si, Mg 2Sn and Mg2Pb. In the case of dilute Mg alloys, a 36 atom supercell with 35 atoms of Mg and one atom of the alloying impurity has been used for calculating the corresponding elastic constants. It is seen that there is a direct correspondence between the trends in the elastic constants and the lattice parameters of all the Mg based alloys studied herein. Elements that cause a decrease (increase) in the lattice constants result in an increase (decrease) in the bulk modulus. Self-diffusion calculations of Mg have been performed within both LDA and GGA. It is seen that, in the absence of surface corrections, while results of the two approximations (i.e. LDA and GGA) bound experimental data, better agreement is seen with respect to results from LDA, in comparison with experimental measurements. The effect of thermal expansion on the diffusivity of Mg has been studied using both HA and QHA. It is seen that the influence of anharmonicity on the diffusivity of Mg is negligible. Self-diffusion of Mg is faster in the basal plane than between adjacent basal planes. Partial correlation factors corresponding to the diffusion of a Mg atom from one basal plane to the adjacent basal plane, i.e. fBx and fBz, decrease with temperature whereas the partial correlation factor corresponding to the diffusion of Mg atom within the basal plane, i.e. fAx , increases with temperature. The ratio of jump frequencies w⊥/w∥ for self-diffusion of Mg increase with increase in temperature. The method used to calculate self-diffusion coefficients has been extended to compute impurity diffusion coefficients of Al, Ca, Sn and Zn in Mg. For these calculations, a 36 atom supercell with 1 vacant site and 1 impurity has been used. The 8-frequencey model has been implemented to obtain the different atom jump frequencies in order to calculate impurity diffusion coefficients in Mg. The trend in the impurity diffusion coefficients, with the exception of DZn-Mg is as follows: D Mg-Ca>DMg>DMg-Sn> DMg-Al. For impurity diffusion of Zn in Mg, at high temperatures DMg-Zn overlaps with that of DMg-Al , while at low temperatures it overlaps with that of D Mg-Sn. The different atom jump frequencies computed during the diffusion calculations are seen to be temperature dependent, increasing with increase in temperature. The correlation factors for all the alloy systems considered herein, is close to 1. This is expected to be due to the close packing of Mg lattice. (Abstract shortened by UMI.)

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Correction of spin diffusion during iterative automated NOE assignment

NASA Astrophysics Data System (ADS)

Linge, Jens P.; Habeck, Michael; Rieping, Wolfgang; Nilges, Michael

2004-04-01

Indirect magnetization transfer increases the observed nuclear Overhauser enhancement (NOE) between two protons in many cases, leading to an underestimation of target distances. Wider distance bounds are necessary to account for this error. However, this leads to a loss of information and may reduce the quality of the structures generated from the inter-proton distances. Although several methods for spin diffusion correction have been published, they are often not employed to derive distance restraints. This prompted us to write a user-friendly and CPU-efficient method to correct for spin diffusion that is fully integrated in our program ambiguous restraints for iterative assignment (ARIA). ARIA thus allows automated iterative NOE assignment and structure calculation with spin diffusion corrected distances. The method relies on numerical integration of the coupled differential equations which govern relaxation by matrix squaring and sparse matrix techniques. We derive a correction factor for the distance restraints from calculated NOE volumes and inter-proton distances. To evaluate the impact of our spin diffusion correction, we tested the new calibration process extensively with data from the Pleckstrin homology (PH) domain of Mus musculus β-spectrin. By comparing structures refined with and without spin diffusion correction, we show that spin diffusion corrected distance restraints give rise to structures of higher quality (notably fewer NOE violations and a more regular Ramachandran map). Furthermore, spin diffusion correction permits the use of tighter error bounds which improves the distinction between signal and noise in an automated NOE assignment scheme.

Efficacy of distortion correction on diffusion imaging: comparison of FSL eddy and eddy_correct using 30 and 60 directions diffusion encoding.

PubMed

Yamada, Haruyasu; Abe, Osamu; Shizukuishi, Takashi; Kikuta, Junko; Shinozaki, Takahiro; Dezawa, Ko; Nagano, Akira; Matsuda, Masayuki; Haradome, Hiroki; Imamura, Yoshiki

2014-01-01

Diffusion imaging is a unique noninvasive tool to detect brain white matter trajectory and integrity in vivo. However, this technique suffers from spatial distortion and signal pileup or dropout originating from local susceptibility gradients and eddy currents. Although there are several methods to mitigate these problems, most techniques can be applicable either to susceptibility or eddy-current induced distortion alone with a few exceptions. The present study compared the correction efficiency of FSL tools, "eddy_correct" and the combination of "eddy" and "topup" in terms of diffusion-derived fractional anisotropy (FA). The brain diffusion images were acquired from 10 healthy subjects using 30 and 60 directions encoding schemes based on the electrostatic repulsive forces. For the 30 directions encoding, 2 sets of diffusion images were acquired with the same parameters, except for the phase-encode blips which had opposing polarities along the anteroposterior direction. For the 60 directions encoding, non-diffusion-weighted and diffusion-weighted images were obtained with forward phase-encoding blips and non-diffusion-weighted images with the same parameter, except for the phase-encode blips, which had opposing polarities. FA images without and with distortion correction were compared in a voxel-wise manner with tract-based spatial statistics. We showed that images corrected with eddy and topup possessed higher FA values than images uncorrected and corrected with eddy_correct with trilinear (FSL default setting) or spline interpolation in most white matter skeletons, using both encoding schemes. Furthermore, the 60 directions encoding scheme was superior as measured by increased FA values to the 30 directions encoding scheme, despite comparable acquisition time. This study supports the combination of eddy and topup as a superior correction tool in diffusion imaging rather than the eddy_correct tool, especially with trilinear interpolation, using 60 directions encoding scheme.

Linear single-step image reconstruction in the presence of nonscattering regions.

PubMed

Dehghani, H; Delpy, D T

2002-06-01

There is growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in using this technique for obtaining tomographic images of the neonatal head, with the view of determining the level of oxygenated and deoxygenated blood within the brain. Because of computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases where a nonscattering region exists. We present reconstructed images, using linear algorithms, of models that contain a nonscattering region within a diffusing material. The forward data are calculated by using the radiosity-diffusion model, and the inverse problem is solved by using either the radiosity-diffusion model or the diffusion-only model. When using data from a model containing a clear layer and reconstructing with the correct model, one can reconstruct the anomaly, but the qualitative accuracy and the position of the reconstructed anomaly depend on the size and the position of the clear regions. If the inverse model has no information about the clear regions (i.e., it is a purely diffusing model), an anomaly can be reconstructed, but the resulting image has very poor qualitative accuracy and poor localization of the anomaly. The errors in quantitative and localization accuracies depend on the size and location of the clear regions.

Linear single-step image reconstruction in the presence of nonscattering regions

NASA Astrophysics Data System (ADS)

Dehghani, H.; Delpy, D. T.

2002-06-01

There is growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in using this technique for obtaining tomographic images of the neonatal head, with the view of determining the level of oxygenated and deoxygenated blood within the brain. Because of computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases where a nonscattering region exists. We present reconstructed images, using linear algorithms, of models that contain a nonscattering region within a diffusing material. The forward data are calculated by using the radiosity-diffusion model, and the inverse problem is solved by using either the radiosity-diffusion model or the diffusion-only model. When using data from a model containing a clear layer and reconstructing with the correct model, one can reconstruct the anomaly, but the qualitative accuracy and the position of the reconstructed anomaly depend on the size and the position of the clear regions. If the inverse model has no information about the clear regions (i.e., it is a purely diffusing model), an anomaly can be reconstructed, but the resulting image has very poor qualitative accuracy and poor localization of the anomaly. The errors in quantitative and localization accuracies depend on the size and location of the clear regions.

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

NASA Astrophysics Data System (ADS)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Modeling and calculation of turbulent lifted diffusion flames

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

Sanders, J.P.H.; Lamers, A.P.G.G.

1994-01-01

Liftoff heights of turbulent diffusion flames have been modeled using the laminar diffusion flamelet concept of Peters and Williams. The strain rate of the smallest eddies is used as the stretch describing parameter, instead of the more common scalar dissipation rate. The h(U) curve, which is the mean liftoff height as a function of fuel exit velocity can be accurately predicted, while this was impossible with the scalar dissipation rate. Liftoff calculations performed in the flames as well as in the equivalent isothermal jets, using a standard k-[epsilon] turbulence model yield approximately the same correct slope for the h(U) curvemore » while the offset has to be reproduced by choosing an appropriate coefficient in the strain rate model. For the flame calculations a model for the pdf of the fluctuating flame base is proposed. The results are insensitive to its width. The temperature field is qualitatively different from the field calculated by Bradley et al. who used a premixed flamelet model for diffusion flames.« less

Motion Artifact Reduction in Pediatric Diffusion Tensor Imaging Using Fast Prospective Correction

PubMed Central

Alhamud, A.; Taylor, Paul A.; Laughton, Barbara; van der Kouwe, André J.W.; Meintjes, Ernesta M.

2014-01-01

Purpose To evaluate the patterns of head motion in scans of young children and to examine the influence of corrective techniques, both qualitatively and quantitatively. We investigate changes that both retrospective (with and without diffusion table reorientation) and prospective (implemented with a short navigator sequence) motion correction induce in the resulting diffusion tensor measures. Materials and Methods Eighteen pediatric subjects (aged 5–6 years) were scanned using 1) a twice-refocused, 2D diffusion pulse sequence, 2) a prospectively motion-corrected, navigated diffusion sequence with reacquisition of a maximum of five corrupted diffusion volumes, and 3) a T1-weighted structural image. Mean fractional anisotropy (FA) values in white and gray matter regions, as well as tractography in the brainstem and projection fibers, were evaluated to assess differences arising from retrospective (via FLIRT in FSL) and prospective motion correction. In addition to human scans, a stationary phantom was also used for further evaluation. Results In several white and gray matter regions retrospective correction led to significantly (P < 0.05) reduced FA means and altered distributions compared to the navigated sequence. Spurious tractographic changes in the retrospectively corrected data were also observed in subject data, as well as in phantom and simulated data. Conclusion Due to the heterogeneity of brain structures and the comparatively low resolution (~2 mm) of diffusion data using 2D single shot sequencing, retrospective motion correction is susceptible to distortion from partial voluming. These changes often negatively bias diffusion tensor imaging parameters. Prospective motion correction was shown to produce smaller changes. PMID:24935904

Motion artifact reduction in pediatric diffusion tensor imaging using fast prospective correction.

PubMed

Alhamud, A; Taylor, Paul A; Laughton, Barbara; van der Kouwe, André J W; Meintjes, Ernesta M

2015-05-01

To evaluate the patterns of head motion in scans of young children and to examine the influence of corrective techniques, both qualitatively and quantitatively. We investigate changes that both retrospective (with and without diffusion table reorientation) and prospective (implemented with a short navigator sequence) motion correction induce in the resulting diffusion tensor measures. Eighteen pediatric subjects (aged 5-6 years) were scanned using 1) a twice-refocused, 2D diffusion pulse sequence, 2) a prospectively motion-corrected, navigated diffusion sequence with reacquisition of a maximum of five corrupted diffusion volumes, and 3) a T1 -weighted structural image. Mean fractional anisotropy (FA) values in white and gray matter regions, as well as tractography in the brainstem and projection fibers, were evaluated to assess differences arising from retrospective (via FLIRT in FSL) and prospective motion correction. In addition to human scans, a stationary phantom was also used for further evaluation. In several white and gray matter regions retrospective correction led to significantly (P < 0.05) reduced FA means and altered distributions compared to the navigated sequence. Spurious tractographic changes in the retrospectively corrected data were also observed in subject data, as well as in phantom and simulated data. Due to the heterogeneity of brain structures and the comparatively low resolution (∼2 mm) of diffusion data using 2D single shot sequencing, retrospective motion correction is susceptible to distortion from partial voluming. These changes often negatively bias diffusion tensor imaging parameters. Prospective motion correction was shown to produce smaller changes. © 2014 Wiley Periodicals, Inc.

Efficacy of Distortion Correction on Diffusion Imaging: Comparison of FSL Eddy and Eddy_Correct Using 30 and 60 Directions Diffusion Encoding

PubMed Central

Yamada, Haruyasu; Abe, Osamu; Shizukuishi, Takashi; Kikuta, Junko; Shinozaki, Takahiro; Dezawa, Ko; Nagano, Akira; Matsuda, Masayuki; Haradome, Hiroki; Imamura, Yoshiki

2014-01-01

Diffusion imaging is a unique noninvasive tool to detect brain white matter trajectory and integrity in vivo. However, this technique suffers from spatial distortion and signal pileup or dropout originating from local susceptibility gradients and eddy currents. Although there are several methods to mitigate these problems, most techniques can be applicable either to susceptibility or eddy-current induced distortion alone with a few exceptions. The present study compared the correction efficiency of FSL tools, “eddy_correct” and the combination of “eddy” and “topup” in terms of diffusion-derived fractional anisotropy (FA). The brain diffusion images were acquired from 10 healthy subjects using 30 and 60 directions encoding schemes based on the electrostatic repulsive forces. For the 30 directions encoding, 2 sets of diffusion images were acquired with the same parameters, except for the phase-encode blips which had opposing polarities along the anteroposterior direction. For the 60 directions encoding, non–diffusion-weighted and diffusion-weighted images were obtained with forward phase-encoding blips and non–diffusion-weighted images with the same parameter, except for the phase-encode blips, which had opposing polarities. FA images without and with distortion correction were compared in a voxel-wise manner with tract-based spatial statistics. We showed that images corrected with eddy and topup possessed higher FA values than images uncorrected and corrected with eddy_correct with trilinear (FSL default setting) or spline interpolation in most white matter skeletons, using both encoding schemes. Furthermore, the 60 directions encoding scheme was superior as measured by increased FA values to the 30 directions encoding scheme, despite comparable acquisition time. This study supports the combination of eddy and topup as a superior correction tool in diffusion imaging rather than the eddy_correct tool, especially with trilinear interpolation, using 60 directions encoding scheme. PMID:25405472

Correction of eddy current distortions in high angular resolution diffusion imaging.

PubMed

Zhuang, Jiancheng; Lu, Zhong-Lin; Vidal, Christine Bouteiller; Damasio, Hanna

2013-06-01

To correct distortions caused by eddy currents induced by large diffusion gradients during high angular resolution diffusion imaging without any auxiliary reference scans. Image distortion parameters were obtained by image coregistration, performed only between diffusion-weighted images with close diffusion gradient orientations. A linear model that describes distortion parameters (translation, scale, and shear) as a function of diffusion gradient directions was numerically computed to allow individualized distortion correction for every diffusion-weighted image. The assumptions of the algorithm were successfully verified in a series of experiments on phantom and human scans. Application of the proposed algorithm in high angular resolution diffusion images markedly reduced eddy current distortions when compared to results obtained with previously published methods. The method can correct eddy current artifacts in the high angular resolution diffusion images, and it avoids the problematic procedure of cross-correlating images with significantly different contrasts resulting from very different gradient orientations or strengths. Copyright © 2012 Wiley Periodicals, Inc.

Transport Coefficients in weakly compressible turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Erlebacher, Gordon

1996-01-01

A theory of transport coefficients in weakly compressible turbulence is derived by applying Yoshizawa's two-scale direct interaction approximation to the compressible equations of motion linearized about a state of incompressible turbulence. The result is a generalization of the eddy viscosity representation of incompressible turbulence. In addition to the usual incompressible eddy viscosity, the calculation generates eddy diffusivities for entropy and pressure, and an effective bulk viscosity acting on the mean flow. The compressible fluctuations also generate an effective turbulent mean pressure and corrections to the speed of sound. Finally, a prediction unique to Yoshizawa's two-scale approximation is that terms containing gradients of incompressible turbulence quantities also appear in the mean flow equations. The form these terms take is described.

Comparison and analysis of theoretical models for diffusion-controlled dissolution.

PubMed

Wang, Yanxing; Abrahamsson, Bertil; Lindfors, Lennart; Brasseur, James G

2012-05-07

Dissolution models require, at their core, an accurate diffusion model. The accuracy of the model for diffusion-dominated dissolution is particularly important with the trend toward micro- and nanoscale drug particles. Often such models are based on the concept of a "diffusion layer." Here a framework is developed for diffusion-dominated dissolution models, and we discuss the inadequacy of classical models that are based on an unphysical constant diffusion layer thickness assumption, or do not correctly modify dissolution rate due to "confinement effects": (1) the increase in bulk concentration from confinement of the dissolution process, (2) the modification of the flux model (the Sherwood number) by confinement. We derive the exact mathematical solution for a spherical particle in a confined fluid with impermeable boundaries. Using this solution, we analyze the accuracy of a time-dependent "infinite domain model" (IDM) and "quasi steady-state model" (QSM), both formally derived for infinite domains but which can be applied in approximate fashion to confined dissolution with proper adjustment of a concentration parameter. We show that dissolution rate is sensitive to the degree of confinement or, equivalently, to the total concentration C(tot). The most practical model, the QSM, is shown to be very accurate for most applications and, consequently, can be used with confidence in design-level dissolution models so long as confinement is accurately treated. The QSM predicts the ratio of diffusion layer thickness to particle radius (the Sherwood number) as a constant plus a correction that depends on the degree of confinement. The QSM also predicts that the time required for complete saturation or dissolution in diffusion-controlled dissolution experiments is singular (i.e., infinite) when total concentration equals the solubility. Using the QSM, we show that measured differences in dissolution rate in a diffusion-controlled dissolution experiment are a result of differences in the degree of confinement on the increase in bulk concentration independent of container geometry and polydisperse vs single particle dissolution. We conclude that the constant diffusion-layer thickness assumption is incorrect in principle and should be replaced by the QSM with accurate treatment of confinement in models of diffusion-controlled dissolution.

Experimental Assessment and Enhancement of Planar Laser-Induced Fluorescence Measurements of Nitric Oxide in an Inverse Diffusion Flame

NASA Technical Reports Server (NTRS)

Partridge, William P.; Laurendeau, Normand M.

1997-01-01

We have experimentally assessed the quantitative nature of planar laser-induced fluorescence (PLIF) measurements of NO concentration in a unique atmospheric pressure, laminar, axial inverse diffusion flame (IDF). The PLIF measurements were assessed relative to a two-dimensional array of separate laser saturated fluorescence (LSF) measurements. We demonstrated and evaluated several experimentally-based procedures for enhancing the quantitative nature of PLIF concentration images. Because these experimentally-based PLIF correction schemes require only the ability to make PLIF and LSF measurements, they produce a more broadly applicable PLIF diagnostic compared to numerically-based correction schemes. We experimentally assessed the influence of interferences on both narrow-band and broad-band fluorescence measurements at atmospheric and high pressures. Optimum excitation and detection schemes were determined for the LSF and PLIF measurements. Single-input and multiple-input, experimentally-based PLIF enhancement procedures were developed for application in test environments with both negligible and significant quench-dependent error gradients. Each experimentally-based procedure provides an enhancement of approximately 50% in the quantitative nature of the PLIF measurements, and results in concentration images nominally as quantitative as LSF point measurements. These correction procedures can be applied to other species, including radicals, for which no experimental data are available from which to implement numerically-based PLIF enhancement procedures.

Transport of water and ions in partially water-saturated porous media. Part 2. Filtration effects

NASA Astrophysics Data System (ADS)

Revil, A.

2017-05-01

A new set of constitutive equations describing the transport of the ions and water through charged porous media and considering the effect of ion filtration is applied to the problem of reverse osmosis and diffusion of a salt. Starting with the constitutive equations derived in Paper 1, I first determine specific formula for the osmotic coefficient and effective diffusion coefficient of a binary symmetric 1:1 salt (such as KCl or NaCl) as a function of a dimensionless number Θ corresponding to the ratio between the cation exchange capacity (CEC) and the salinity. The modeling is first carried with the Donnan model used to describe the concentrations of the charge carriers in the pore water phase. Then a new model is developed in the thin double layer approximation to determine these concentrations. These models provide explicit relationships between the concentration of the ionic species in the pore space and those in a neutral reservoir in local equilibrium with the pore space and the CEC. The case of reverse osmosis and diffusion coefficient are analyzed in details for the case of saturated and partially saturated porous materials. Comparisons are done with experimental data from the literature obtained on bentonite. The model predicts correctly the influence of salinity (including membrane behavior at high salinities), porosity, cation type (K+ versus Na+), and water saturation on the osmotic coefficient. It also correctly predicts the dependence of the diffusion coefficient of the salt with the salinity.

Quantum Landau damping in dipolar Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Mendonça, J. T.; Terças, H.; Gammal, A.

2018-06-01

We consider Landau damping of elementary excitations in Bose-Einstein condensates (BECs) with dipolar interactions. We discuss quantum and quasiclassical regimes of Landau damping. We use a generalized wave-kinetic description of BECs which, apart from the long-range dipolar interactions, also takes into account the quantum fluctuations and the finite-energy corrections to short-range interactions. Such a description is therefore more general than the usual mean-field approximation. The present wave-kinetic approach is well suited for the study of kinetic effects in BECs, such as those associated with Landau damping, atom trapping, and turbulent diffusion. The inclusion of quantum fluctuations and energy corrections changes the dispersion relation and the damping rates, leading to possible experimental signatures of these effects. Quantum Landau damping is described with generality, and particular examples of dipolar condensates in two and three dimensions are studied. The occurrence of roton-maxon excitations, and their relevance to Landau damping, are also considered in detail. The present approach is mainly based on a linear perturbative procedure, but the nonlinear regime of Landau damping, which includes atom trapping and atom diffusion, is also briefly discussed.

Reduction of skylight reflection effects in the above-water measurement of diffuse marine reflectance.

PubMed

Fougnie, B; Frouin, R; Lecomte, P; Deschamps, P Y

1999-06-20

Reflected skylight in above-water measurements of diffuse marine reflectance can be reduced substantially by viewing the surface through an analyzer transmitting the vertically polarized component of incident radiance. For maximum reduction of effects, radiometric measurements should be made at a viewing zenith angle of approximately 45 degrees (near the Brewster angle) and a relative azimuth angle between solar and viewing directions greater than 90 degrees (backscattering), preferably 135 degrees. In this case the residual reflected skylight in the polarized signal exhibits minimum sensitivity to the sea state and can be corrected to within a few 10(-4) in reflectance units. For most oceanic waters the resulting relative error on the diffuse marine reflectance in the blue and green is less than 1%. Since the water body polarizes incident skylight, the measured polarized reflectance differs from the total reflectance. The difference, however, is small for the considered geometry. Measurements made at the Scripps Institution of Oceanography pier in La Jolla, Calif., with a specifically designed scanning polarization radiometer, confirm the theoretical findings and demonstrate the usefulness of polarization radiometry for measuring diffuse marine reflectance.

Asymptotic expansions for 2D symmetrical laminar wakes

NASA Astrophysics Data System (ADS)

Belan, Marco; Tordella, Daniela

1999-11-01

An extension of the well known asymptotic representation of the 2D laminar incompressible wake past a symmetrical body is presented. Using the thin free shear layer approximation we determined solutions in terms of infinite asymptotic expansions. These are power series of the streamwise space variable with fractional negative coefficients. The general n-th order term has been analytically established. Through analysis of the behaviour of the same expansions inserted into the Navier-Stokes equations, we verified the self-consistency of the approximation showing that at the third order the correction due to pressure variations identically vanishes while the contribution of the longitudinal diffusion is still two-three order of magnitude smaller than that of the transversal diffusion, depending on Re. When the procedure is applied to the Navier-Stokes equations, we showed that further mathematical difficulties do not arise. Where opportune one may thus easily shift to the complete model. Through a spatial multiscaling approach, a brief account on the stability properties of these expansions as representing the non parallel basic flow of 2D wakes will be given.

An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods.

PubMed

Frank, Florian; Liu, Chen; Scanziani, Alessio; Alpak, Faruk O; Riviere, Beatrice

2018-08-01

We consider an energy-based boundary condition to impose an equilibrium wetting angle for the Cahn-Hilliard-Navier-Stokes phase-field model on voxel-set-type computational domains. These domains typically stem from μCT (micro computed tomography) imaging of porous rock and approximate a (on μm scale) smooth domain with a certain resolution. Planar surfaces that are perpendicular to the main axes are naturally approximated by a layer of voxels. However, planar surfaces in any other directions and curved surfaces yield a jagged/topologically rough surface approximation by voxels. For the standard Cahn-Hilliard formulation, where the contact angle between the diffuse interface and the domain boundary (fluid-solid interface/wall) is 90°, jagged surfaces have no impact on the contact angle. However, a prescribed contact angle smaller or larger than 90° on jagged voxel surfaces is amplified. As a remedy, we propose the introduction of surface energy correction factors for each fluid-solid voxel face that counterbalance the difference of the voxel-set surface area with the underlying smooth one. The discretization of the model equations is performed with the discontinuous Galerkin method. However, the presented semi-analytical approach of correcting the surface energy is equally applicable to other direct numerical methods such as finite elements, finite volumes, or finite differences, since the correction factors appear in the strong formulation of the model. Copyright © 2018 Elsevier Inc. All rights reserved.

Effects of stomata clustering on leaf gas exchange.

PubMed

Lehmann, Peter; Or, Dani

2015-09-01

A general theoretical framework for quantifying the stomatal clustering effects on leaf gaseous diffusive conductance was developed and tested. The theory accounts for stomatal spacing and interactions among 'gaseous concentration shells'. The theory was tested using the unique measurements of Dow et al. (2014) that have shown lower leaf diffusive conductance for a genotype of Arabidopsis thaliana with clustered stomata relative to uniformly distributed stomata of similar size and density. The model accounts for gaseous diffusion: through stomatal pores; via concentration shells forming at pore apertures that vary with stomata spacing and are thus altered by clustering; and across the adjacent air boundary layer. Analytical approximations were derived and validated using a numerical model for 3D diffusion equation. Stomata clustering increases the interactions among concentration shells resulting in larger diffusive resistance that may reduce fluxes by 5-15%. A similar reduction in conductance was found for clusters formed by networks of veins. The study resolves ambiguities found in the literature concerning stomata end-corrections and stomatal shape, and provides a new stomata density threshold for diffusive interactions of overlapping vapor shells. The predicted reduction in gaseous exchange due to clustering, suggests that guard cell function is impaired, limiting stomatal aperture opening. © 2015 The Authors. New Phytologist © 2015 New Phytologist Trust.

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility. Part 1; Steady Predictions

NASA Technical Reports Server (NTRS)

Allgood, Daniel C.; Graham, Jason S.; Ahuja, Vineet; Hosangadi, Ashvin

2010-01-01

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively.

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers. 2; Numerical Results

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

We present numerical results of the diffusion coefficients (DCs) in the coupled diffusion model derived in the preceding paper for a semiconductor quantum well. These include self and mutual DCs in the general two-component case, as well as density- and temperature-related DCs under the single-component approximation. The results are analyzed from the viewpoint of free Fermi gas theory with many-body effects incorporated. We discuss in detail the dependence of these DCs on densities and temperatures in order to identify different roles played by the free carrier contributions including carrier statistics and carrier-LO phonon scattering, and many-body corrections including bandgap renormalization and electron-hole (e-h) scattering. In the general two-component case, it is found that the self- and mutual- diffusion coefficients are determined mainly by the free carrier contributions, but with significant many-body corrections near the critical density. Carrier-LO phonon scattering is dominant at low density, but e-h scattering becomes important in determining their density dependence above the critical electron density. In the single-component case, it is found that many-body effects suppress the density coefficients but enhance the temperature coefficients. The modification is of the order of 10% and reaches a maximum of over 20% for the density coefficients. Overall, temperature elevation enhances the diffusive capability or DCs of carriers linearly, and such an enhancement grows with density. Finally, the complete dataset of various DCs as functions of carrier densities and temperatures provides necessary ingredients for future applications of the model to various spatially inhomogeneous optoelectronic devices.

Analytic expressions for ULF wave radiation belt radial diffusion coefficients

PubMed Central

Ozeke, Louis G; Mann, Ian R; Murphy, Kyle R; Jonathan Rae, I; Milling, David K

2014-01-01

We present analytic expressions for ULF wave-derived radiation belt radial diffusion coefficients, as a function of L and Kp, which can easily be incorporated into global radiation belt transport models. The diffusion coefficients are derived from statistical representations of ULF wave power, electric field power mapped from ground magnetometer data, and compressional magnetic field power from in situ measurements. We show that the overall electric and magnetic diffusion coefficients are to a good approximation both independent of energy. We present example 1-D radial diffusion results from simulations driven by CRRES-observed time-dependent energy spectra at the outer boundary, under the action of radial diffusion driven by the new ULF wave radial diffusion coefficients and with empirical chorus wave loss terms (as a function of energy, Kp and L). There is excellent agreement between the differential flux produced by the 1-D, Kp-driven, radial diffusion model and CRRES observations of differential electron flux at 0.976 MeV—even though the model does not include the effects of local internal acceleration sources. Our results highlight not only the importance of correct specification of radial diffusion coefficients for developing accurate models but also show significant promise for belt specification based on relatively simple models driven by solar wind parameters such as solar wind speed or geomagnetic indices such as Kp. Key Points Analytic expressions for the radial diffusion coefficients are presented The coefficients do not dependent on energy or wave m value The electric field diffusion coefficient dominates over the magnetic PMID:26167440

Multiple Echo Diffusion Tensor Acquisition Technique (MEDITATE) on a 3T clinical scanner

PubMed Central

Baete, Steven H.; Cho, Gene; Sigmund, Eric E.

2013-01-01

This paper describes the concepts and implementation of an MRI method, Multiple Echo Diffusion Tensor Acquisition Technique (MEDITATE), which is capable of acquiring apparent diffusion tensor maps in two scans on a 3T clinical scanner. In each MEDITATE scan, a set of RF-pulses generates multiple echoes whose amplitudes are diffusion-weighted in both magnitude and direction by a pattern of diffusion gradients. As a result, two scans acquired with different diffusion weighting strengths suffice for accurate estimation of diffusion tensor imaging (DTI)-parameters. The MEDITATE variation presented here expands previous MEDITATE approaches to adapt to the clinical scanner platform, such as exploiting longitudinal magnetization storage to reduce T2-weighting. Fully segmented multi-shot Cartesian encoding is used for image encoding. MEDITATE was tested on isotropic (agar gel), anisotropic diffusion phantoms (asparagus), and in vivo skeletal muscle in healthy volunteers with cardiac-gating. Comparisons of accuracy were performed with standard twice-refocused spin echo (TRSE) DTI in each case and good quantitative agreement was found between diffusion eigenvalues, mean diffusivity, and fractional anisotropy derived from TRSE-DTI and from the MEDITATE sequence. Orientation patterns were correctly reproduced in both isotropic and anisotropic phantoms, and approximately so for in vivo imaging. This illustrates that the MEDITATE method of compressed diffusion encoding is feasible on the clinical scanner platform. With future development and employment of appropriate view-sharing image encoding this technique may be used in clinical applications requiring time-sensitive acquisition of DTI parameters such as dynamical DTI in muscle. PMID:23828606

Topological quantum error correction in the Kitaev honeycomb model

NASA Astrophysics Data System (ADS)

Lee, Yi-Chan; Brell, Courtney G.; Flammia, Steven T.

2017-08-01

The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of topological quantum codes that are typically studied, but its exact solubility makes it more amenable to analysis of effects arising in this noncommutative setting than a generic topologically ordered Hamiltonian. Here we study quantum error correction in the honeycomb model using both analytic and numerical techniques. We first prove explicit exponential bounds on the approximate degeneracy, local indistinguishability, and correctability of the code space. These bounds are tighter than can be achieved using known general properties of topological phases. Our proofs are specialized to the honeycomb model, but some of the methods may nonetheless be of broader interest. Following this, we numerically study noise caused by thermalization processes in the perturbative regime close to the toric code renormalization group fixed point. The appearance of non-topological excitations in this setting has no significant effect on the error correction properties of the honeycomb model in the regimes we study. Although the behavior of this model is found to be qualitatively similar to that of the standard toric code in most regimes, we find numerical evidence of an interesting effect in the low-temperature, finite-size regime where a preferred lattice direction emerges and anyon diffusion is geometrically constrained. We expect this effect to yield an improvement in the scaling of the lifetime with system size as compared to the standard toric code.

Approximate Bayesian Computation in the estimation of the parameters of the Forbush decrease model

NASA Astrophysics Data System (ADS)

Wawrzynczak, A.; Kopka, P.

2017-12-01

Realistic modeling of the complicated phenomena as Forbush decrease of the galactic cosmic ray intensity is a quite challenging task. One aspect is a numerical solution of the Fokker-Planck equation in five-dimensional space (three spatial variables, the time and particles energy). The second difficulty arises from a lack of detailed knowledge about the spatial and time profiles of the parameters responsible for the creation of the Forbush decrease. Among these parameters, the central role plays a diffusion coefficient. Assessment of the correctness of the proposed model can be done only by comparison of the model output with the experimental observations of the galactic cosmic ray intensity. We apply the Approximate Bayesian Computation (ABC) methodology to match the Forbush decrease model to experimental data. The ABC method is becoming increasing exploited for dynamic complex problems in which the likelihood function is costly to compute. The main idea of all ABC methods is to accept samples as an approximate posterior draw if its associated modeled data are close enough to the observed one. In this paper, we present application of the Sequential Monte Carlo Approximate Bayesian Computation algorithm scanning the space of the diffusion coefficient parameters. The proposed algorithm is adopted to create the model of the Forbush decrease observed by the neutron monitors at the Earth in March 2002. The model of the Forbush decrease is based on the stochastic approach to the solution of the Fokker-Planck equation.

Correlation of transarterial transport of various dextrans with their physicochemical properties.

PubMed

Elmalak, O; Lovich, M A; Edelman, E

2000-11-01

Local vascular drug delivery provides elevated concentrations of drug in the target tissue while minimizing systemic side effects. To better characterize local pharmacokinetics we examined the arterial transport of locally applied dextran and dextran derivatives in vivo. Using a two-compartment pharmacokinetic model to correct the measured transmural flux of these compounds for systemic redistribution and elimination as delivered from a photopolymerizable hydrogel surrounding rat carotid arteries, we found that the diffusivities and the transendothelial permeabilities were strongly dependent on molecular weight and charge. For neutral dextrans, the effective diffusive resistance in the media increased with molecular weight approximately 4.1-fold between the molecular weights of 10 and 282 kDa. Similarly, endothelial resistance increased 28-fold over the same molecular weight range. The effective medial diffusive resistance was unaffected by cationic charge as such molecules moved identically to neutral compounds, but increased approximately 40% when dextrans were negatively charged. Transendothelial resistance was 20-fold lower for the cationic dextrans, and 11-fold higher for the anionic dextrans, when both were compared to neutral counterparts. These results suggest that, while low molecular weight drugs will rapidly traverse the arterial wall with the endothelium posing a minimal barrier, the reverse is true for high molecular weight agents. With these data, the deposition and distribution of locally released vasotherapeutic compounds might be predicted based upon chemical properties, such as molecular weight and charge.

Effects of high-frequency damping on iterative convergence of implicit viscous solver

NASA Astrophysics Data System (ADS)

Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko

2017-11-01

This paper discusses effects of high-frequency damping on iterative convergence of an implicit defect-correction solver for viscous problems. The study targets a finite-volume discretization with a one parameter family of damped viscous schemes. The parameter α controls high-frequency damping: zero damping with α = 0, and larger damping for larger α (> 0). Convergence rates are predicted for a model diffusion equation by a Fourier analysis over a practical range of α. It is shown that the convergence rate attains its minimum at α = 1 on regular quadrilateral grids, and deteriorates for larger values of α. A similar behavior is observed for regular triangular grids. In both quadrilateral and triangular grids, the solver is predicted to diverge for α smaller than approximately 0.5. Numerical results are shown for the diffusion equation and the Navier-Stokes equations on regular and irregular grids. The study suggests that α = 1 and 4/3 are suitable values for robust and efficient computations, and α = 4 / 3 is recommended for the diffusion equation, which achieves higher-order accuracy on regular quadrilateral grids. Finally, a Jacobian-Free Newton-Krylov solver with the implicit solver (a low-order Jacobian approximately inverted by a multi-color Gauss-Seidel relaxation scheme) used as a variable preconditioner is recommended for practical computations, which provides robust and efficient convergence for a wide range of α.

Transport tensors in perfectly aligned low-density fluids: Self-diffusion and thermal conductivity

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

Singh, G. S.; Kumar, B.

2001-06-01

The modified Taxman equation for the kinetic theory of low-density fluids composed of rigid aspherical molecules possessing internal degrees of freedom is generalized to obtain the transport tensors in a fluid of aligned molecules. The theory takes care of the shape of the particles exactly but the solution has been obtained only for the case of perfectly aligned hard spheroids within the framework of the first Sonine polynomial approximation. The expressions for the thermal-conductivity components have been obtained for the first time whereas the self-diffusion components obtained here turn out to be exactly the same as those derived by Kumarmore » and Masters [Mol. Phys. >81, 491 (1994)] through the solution of the Lorentz-Boltzmann equation. All our expressions yield correct results in the hard-sphere limit.« less

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

PubMed

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

2016-09-01

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

Finite-Size Effects of Binary Mutual Diffusion Coefficients from Molecular Dynamics

PubMed Central

2018-01-01

Molecular dynamics simulations were performed for the prediction of the finite-size effects of Maxwell-Stefan diffusion coefficients of molecular mixtures and a wide variety of binary Lennard–Jones systems. A strong dependency of computed diffusivities on the system size was observed. Computed diffusivities were found to increase with the number of molecules. We propose a correction for the extrapolation of Maxwell–Stefan diffusion coefficients to the thermodynamic limit, based on the study by Yeh and Hummer (J. Phys. Chem. B, 2004, 108, 15873−15879). The proposed correction is a function of the viscosity of the system, the size of the simulation box, and the thermodynamic factor, which is a measure for the nonideality of the mixture. Verification is carried out for more than 200 distinct binary Lennard–Jones systems, as well as 9 binary systems of methanol, water, ethanol, acetone, methylamine, and carbon tetrachloride. Significant deviations between finite-size Maxwell–Stefan diffusivities and the corresponding diffusivities at the thermodynamic limit were found for mixtures close to demixing. In these cases, the finite-size correction can be even larger than the simulated (finite-size) Maxwell–Stefan diffusivity. Our results show that considering these finite-size effects is crucial and that the suggested correction allows for reliable computations. PMID:29664633

Extracting dielectric fixed charge density on highly doped crystalline-silicon surfaces using photoconductance measurements

NASA Astrophysics Data System (ADS)

To, A.; Hoex, B.

2017-11-01

A novel method for the extraction of fixed interface charge, Qf, and the surface recombination parameters, Sn0 and Sp0, from the injection-level dependent effective minority carrier lifetime measurements is presented. Unlike conventional capacitance-voltage measurements, this technique can be applied to highly doped surfaces provided the surface carrier concentration transitions into strong depletion or inversion with increased carrier injection. By simulating the injection level dependent Auger-corrected inverse lifetime curve of symmetrically passivated and diffused samples after sequential annealing and corona charging, it was revealed that Qf, Sn0, and Sp0 have unique signatures. Therefore, these important electronic parameters, in some instances, can independently be resolved. Furthermore, it was shown that this non-linear lifetime behaviour is exhibited on both p-type and n-type diffused inverted surfaces, by demonstrating the approach with phosphorous diffused n+pn+ structures and boron diffused p+np+ structures passivated with aluminium oxide (AlOx) and silicon nitride, respectively (SiNx). The results show that the approximation of a mid-gap Shockley-Read-Hall defect level with equal capture cross sections is able to, in the samples studied in this work, reproduce the observed injection level dependent lifetime behaviour.

An extended source for CN jets in Comet P/Halley

NASA Technical Reports Server (NTRS)

Klavetter, James Jay; A'Hearn, Michael F.

1994-01-01

We examined radial intensity profiles of CN jets in comparison with the diffuse, isotropic component of the CN coma of Comet P/Halley. All images were bias-subtracted, flat-fielded, and continuum-subtracted. We calculated the diffuse profiles by finding the azimuthal mean of the coma least contaminated by jets yielding profiles similar to those of vectorial and Haser models of simple photodissociation. We found the jet profiles by calculating a mean around a Gaussian-fitted center in r-theta space. There is an unmistakable difference between the profiles of the CN jets and the profiles of the diffuse CN. Spatial derivatives of these profiles, corrected for geometrical expansion, show that the diffuse component is consistent with a simple photodissociation process, but the jet component is not. The peak production of the jet profile occurs 6000 km from the nucleus at a heliocentric distance of 1.4 AU. Modeling of both components of the coma indicate results that are consistent with the diffuse CN photochemically produced, but the CN jets need an additional extended source. We found that about one-half of the CN in the coma of Comet P/Halley originated from the jets, the rest from the diffuse component. These features, along with the width of the jet being approximately constant, are consistent with a CHON grain origin for the jets.

Mass transport in polyelectrolyte solutions

NASA Astrophysics Data System (ADS)

Schipper, F. J. M.; Leyte, J. C.

1999-02-01

The self-diffusion coefficients of the three components of a salt-free heavy-water solution of polymethacrylic acid, completely neutralized with tetra-methylammonium hydroxide, were measured over a broad concentration range. Three concentration regions were observed for the self-diffusion of both the polyions and the counterions. At polyion concentrations below 0.01 mol monomer kg-1, the dilute concentration regime for the polymer, the polyion self-diffusion coefficient approaches the self-diffusion coefficient of a freely diffusing rod upon dilution. At polyelectrolyte concentrations above 0.1 mol monomer kg-1, the self-diffusion coefficients of the solvent, the counterions and the polymer decreased with concentration, suggesting that this decrease is due to a topological constraint on the motions of the components. In the intermediate-concentration region, the self-diffusion coefficients of the polyions and the counterions are independent of the concentration. The polyion dynamic behaviour is, in the intermediate- and high-concentration regions, reasonably well described by that of a hard sphere, with a radius of 3.7 nm. A correct prediction for the solvent dynamics is given by the obstruction effect of this hard sphere on the solvent. The relative counterion self-diffusion coefficient is predicted almost quantitatively over the entire concentration range with the Poisson-Boltzmann-Smoluchowski model for the spherical cell, provided that the sphere radius and the number of charges are chosen appropriately (approximately the number of charges in a persistence length). Using this model, the dependence of the counterion self-diffusion coefficient on the ionic strength, polyion concentration and counterion radius is calculated quantitatively over a large concentration range.

Geometric distortion correction in prostate diffusion-weighted MRI and its effect on quantitative apparent diffusion coefficient analysis.

PubMed

Nketiah, Gabriel; Selnaes, Kirsten M; Sandsmark, Elise; Teruel, Jose R; Krüger-Stokke, Brage; Bertilsson, Helena; Bathen, Tone F; Elschot, Mattijs

2018-05-01

To evaluate the effect of correction for B 0 inhomogeneity-induced geometric distortion in echo-planar diffusion-weighted imaging on quantitative apparent diffusion coefficient (ADC) analysis in multiparametric prostate MRI. Geometric distortion correction was performed in echo-planar diffusion-weighted images (b = 0, 50, 400, 800 s/mm 2 ) of 28 patients, using two b 0 scans with opposing phase-encoding polarities. Histology-matched tumor and healthy tissue volumes of interest delineated on T 2 -weighted images were mapped to the nondistortion-corrected and distortion-corrected data sets by resampling with and without spatial coregistration. The ADC values were calculated on the volume and voxel level. The effect of distortion correction on ADC quantification and tissue classification was evaluated using linear-mixed models and logistic regression, respectively. Without coregistration, the absolute differences in tumor ADC (range: 0.0002-0.189 mm 2 /s×10 -3 (volume level); 0.014-0.493 mm 2 /s×10 -3 (voxel level)) between the nondistortion-corrected and distortion-corrected were significantly associated (P < 0.05) with distortion distance (mean: 1.4 ± 1.3 mm; range: 0.3-5.3 mm). No significant associations were found upon coregistration; however, in patients with high rectal gas residue, distortion correction resulted in improved spatial representation and significantly better classification of healthy versus tumor voxels (P < 0.05). Geometric distortion correction in DWI could improve quantitative ADC analysis in multiparametric prostate MRI. Magn Reson Med 79:2524-2532, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Analysis of nonlocal phonon thermal conductivity simulations showing the ballistic to diffusive crossover

NASA Astrophysics Data System (ADS)

Allen, Philip B.

2018-04-01

Simulations [e.g., X. W. Zhou et al., Phys. Rev. B 79, 115201 (2009), 10.1103/PhysRevB.79.115201] show nonlocal effects of the ballistic/diffusive crossover. The local temperature has nonlinear spatial variation not contained in the local Fourier law j ⃗(r ⃗) =-κ ∇ ⃗T (r ⃗) . The heat current j ⃗(r ⃗) depends not just on the local temperature gradient ∇ ⃗T (r ⃗) but also on temperatures at points r⃗' within phonon mean free paths, which can be micrometers long. This paper uses the Peierls-Boltzmann transport theory in nonlocal form to analyze the spatial variation Δ T (r ⃗) . The relaxation-time approximation (RTA) is used because the full solution is very challenging. Improved methods of extrapolation to obtain the bulk thermal conductivity κ are proposed. Callaway invented an approximate method of correcting RTA for the q ⃗ (phonon wave vector or crystal momentum) conservation of N (Normal as opposed to Umklapp) anharmonic collisions. This method is generalized to the nonlocal case where κ (k ⃗) depends on the wave vector of the current j ⃗(k ⃗) and temperature gradient i k ⃗Δ T (k ⃗) .

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

Spin-diffusions and diffusive molecular dynamics

NASA Astrophysics Data System (ADS)

Farmer, Brittan; Luskin, Mitchell; Plecháč, Petr; Simpson, Gideon

2017-12-01

Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

3-D residual eddy current field characterisation: applied to diffusion weighted magnetic resonance imaging.

PubMed

O'Brien, Kieran; Daducci, Alessandro; Kickler, Nils; Lazeyras, Francois; Gruetter, Rolf; Feiweier, Thorsten; Krueger, Gunnar

2013-08-01

Clinical use of the Stejskal-Tanner diffusion weighted images is hampered by the geometric distortions that result from the large residual 3-D eddy current field induced. In this work, we aimed to predict, using linear response theory, the residual 3-D eddy current field required for geometric distortion correction based on phantom eddy current field measurements. The predicted 3-D eddy current field induced by the diffusion-weighting gradients was able to reduce the root mean square error of the residual eddy current field to ~1 Hz. The model's performance was tested on diffusion weighted images of four normal volunteers, following distortion correction, the quality of the Stejskal-Tanner diffusion-weighted images was found to have comparable quality to image registration based corrections (FSL) at low b-values. Unlike registration techniques the correction was not hindered by low SNR at high b-values, and results in improved image quality relative to FSL. Characterization of the 3-D eddy current field with linear response theory enables the prediction of the 3-D eddy current field required to correct eddy current induced geometric distortions for a wide range of clinical and high b-value protocols.

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

PubMed Central

Zheng, Likun; Nie, Qing

2016-01-01

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

Analytical model of diffuse reflectance spectrum of skin tissue

NASA Astrophysics Data System (ADS)

Lisenko, S. A.; Kugeiko, M. M.; Firago, V. A.; Sobchuk, A. N.

2014-01-01

We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions.

Relativistic theory of particles in a scattering flow I: basic equations, diffusion and drift.

NASA Astrophysics Data System (ADS)

Achterberg, A.; Norman, C. A.

2018-06-01

We reconsider the theory of particle transport in a scattering medium, allowing for relativistic flow velocities. The theory uses a mixed set of variables, with position and time measured in the Laboratory Frame, and particle energy and momentum measured in the Fluid Rest Frame, the reference frame where scattering is assumed to be elastic. We give a new derivation for the fictitious force terms in the equation of motion that are present if the Fluid Rest Frame is not an inertial frame. By using a 3+1 notation we discuss the physical interpretation of the different terms in the fictitious force. It is shown that different approaches to the problem of particle propagation in a magnetized medium due to Skilling (1975) and Kulsrud (1983) are largely equivalent. We extend known results for non-relativistic flows to include the effects of cross-field diffusion for cosmic rays in a magnetized plasma. We also carefully consider the correct form of the diffusion approximation for scattering, and show that the resulting equations can be cast in conservation form.

PSF mapping-based correction of eddy-current-induced distortions in diffusion-weighted echo-planar imaging.

PubMed

In, Myung-Ho; Posnansky, Oleg; Speck, Oliver

2016-05-01

To accurately correct diffusion-encoding direction-dependent eddy-current-induced geometric distortions in diffusion-weighted echo-planar imaging (DW-EPI) and to minimize the calibration time at 7 Tesla (T). A point spread function (PSF) mapping based eddy-current calibration method is newly presented to determine eddy-current-induced geometric distortions even including nonlinear eddy-current effects within the readout acquisition window. To evaluate the temporal stability of eddy-current maps, calibration was performed four times within 3 months. Furthermore, spatial variations of measured eddy-current maps versus their linear superposition were investigated to enable correction in DW-EPIs with arbitrary diffusion directions without direct calibration. For comparison, an image-based eddy-current correction method was additionally applied. Finally, this method was combined with a PSF-based susceptibility-induced distortion correction approach proposed previously to correct both susceptibility and eddy-current-induced distortions in DW-EPIs. Very fast eddy-current calibration in a three-dimensional volume is possible with the proposed method. The measured eddy-current maps are very stable over time and very similar maps can be obtained by linear superposition of principal-axes eddy-current maps. High resolution in vivo brain results demonstrate that the proposed method allows more efficient eddy-current correction than the image-based method. The combination of both PSF-based approaches allows distortion-free images, which permit reliable analysis in diffusion tensor imaging applications at 7T. © 2015 Wiley Periodicals, Inc.

Slip and barodiffusion phenomena in slow flows of a gas mixture

NASA Astrophysics Data System (ADS)

Zhdanov, V. M.

2017-03-01

The slip and barodiffusion problems for the slow flows of a gas mixture are investigated on the basis of the linearized moment equations following from the Boltzmann equation. We restrict ourselves to the set of the third-order moment equations and state two general relations (resembling conservation equations) for the moments of the distribution function similar to the conditions used by Loyalka [S. K. Loyalka, Phys. Fluids 14, 2291 (1971), 10.1063/1.1693331] in his approximation method (the modified Maxwell method). The expressions for the macroscopic velocities of the gas mixture species, the partial viscous stress tensors, and the reduced heat fluxes for the stationary slow flow of a gas mixture in the semi-infinite space over a plane wall are obtained as a result of the exact solution of the linearized moment equations in the 10- and 13-moment approximations. The general expression for the slip velocity and the simple and accurate expressions for the viscous, thermal, diffusion slip, and baroslip coefficients, which are given in terms of the basic transport coefficients, are derived by using the modified Maxwell method. The solutions of moment equations are also used for investigation of the flow and diffusion of a gas mixture in a channel formed by two infinite parallel plates. A fundamental result is that the barodiffusion factor in the cross-section-averaged expression for the diffusion flux contains contributions associated with the viscous transfer of momentum in the gas mixture and the effect of the Knudsen layer. Our study revealed that the barodiffusion factor is equal to the diffusion slip coefficient (correct to the opposite sign). This result is consistent with the Onsager's reciprocity relations for kinetic coefficients following from nonequilibrium thermodynamics of the discontinuous systems.

Analysis of diffuse radiation data for Beer Sheva: Measured (shadow ring) versus calculated (global-horizontal beam) values

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

Kudish, A.I.; Ianetz, A.

1993-12-01

The authors have utilized concurrently measured global, normal incidence beam, and diffuse radiation data, the latter measured by means of a shadow ring pyranometer to study the relative magnitude of the anisotropic contribution (circumsolar region and nonuniform sky conditions) to the diffuse radiation. In the case of Beer Sheva, the monthly average hourly anisotropic correction factor varies from 2.9 to 20.9%, whereas the [open quotes]standard[close quotes] geometric correction factor varies from 5.6 to 14.0%. The monthly average hourly overall correction factor (combined anisotropic and geometric factors) varies from 8.9 to 37.7%. The data have also been analyzed using a simplemore » model of sky radiance developed by Steven in 1984. His anisotropic correction factor is a function of the relative strength and angular width of the circumsolar radiation region. The results of this analysis are in agreement with those previously reported for Quidron on the Dead Sea, viz. the anisotropy and relative strength of the circumsolar radiation are significantly greater than at any of the sites analyzed by Steven. In addition, the data have been utilized to validate a model developed by LeBaron et al. in 1990 for correcting shadow ring diffuse radiation data. The monthly average deviation between the corrected and true diffuse radiation values varies from 4.55 to 7.92%.« less

Characterization and correction of eddy-current artifacts in unipolar and bipolar diffusion sequences using magnetic field monitoring.

PubMed

Chan, Rachel W; von Deuster, Constantin; Giese, Daniel; Stoeck, Christian T; Harmer, Jack; Aitken, Andrew P; Atkinson, David; Kozerke, Sebastian

2014-07-01

Diffusion tensor imaging (DTI) of moving organs is gaining increasing attention but robust performance requires sequence modifications and dedicated correction methods to account for system imperfections. In this study, eddy currents in the "unipolar" Stejskal-Tanner and the velocity-compensated "bipolar" spin-echo diffusion sequences were investigated and corrected for using a magnetic field monitoring approach in combination with higher-order image reconstruction. From the field-camera measurements, increased levels of second-order eddy currents were quantified in the unipolar sequence relative to the bipolar diffusion sequence while zeroth and linear orders were found to be similar between both sequences. Second-order image reconstruction based on field-monitoring data resulted in reduced spatial misalignment artifacts and residual displacements of less than 0.43 mm and 0.29 mm (in the unipolar and bipolar sequences, respectively) after second-order eddy-current correction. Results demonstrate the need for second-order correction in unipolar encoding schemes but also show that bipolar sequences benefit from second-order reconstruction to correct for incomplete intrinsic cancellation of eddy-currents. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

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

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

PubMed

Horowitz, Jordan M

2015-07-28

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

Ocean Observations with EOS/MODIS: Algorithm Development and Post Launch Studies

NASA Technical Reports Server (NTRS)

Gordon, Howard R.

1997-01-01

Significant accomplishments made during the present reporting period are as follows: (1) We developed a new method for identifying the presence of absorbing aerosols and, simultaneously, performing atmospheric correction. The algorithm consists of optimizing the match between the top-of-atmosphere radiance spectrum and the result of models of both the ocean and aerosol optical properties; (2) We developed an algorithm for providing an accurate computation of the diffuse transmittance of the atmosphere given an aerosol model. A module for inclusion into the MODIS atmospheric-correction algorithm was completed; (3) We acquired reflectance data for oceanic whitecaps during a cruise on the RV Ka'imimoana in the Tropical Pacific (Manzanillo, Mexico to Honolulu, Hawaii). The reflectance spectrum of whitecaps was found to be similar to that for breaking waves in the surf zone measured by Frouin, Schwindling and Deschamps, however, the drop in augmented reflectance from 670 to 860 nm was not as great, and the magnitude of the augmented reflectance was significantly less than expected; and (4) We developed a method for the approximate correction for the effects of the MODIS polarization sensitivity. The correction, however, requires adequate characterization of the polarization sensitivity of MODIS prior to launch.

Mathematical modeling of synthesis gas fueled electrochemistry and transport including H2/CO co-oxidation and surface diffusion in solid oxide fuel cell

NASA Astrophysics Data System (ADS)

Bao, Cheng; Jiang, Zeyi; Zhang, Xinxin

2015-10-01

Fuel flexibility is a significant advantage of solid oxide fuel cell (SOFC). A comprehensive macroscopic framework is proposed for synthesis gas (syngas) fueled electrochemistry and transport in SOFC anode with two main novelties, i.e. analytical H2/CO electrochemical co-oxidation, and correction of gas species concentration at triple phase boundary considering competitive absorption and surface diffusion. Staring from analytical approximation of the decoupled charge and mass transfer, we present analytical solutions of two defined variables, i.e. hydrogen current fraction and enhancement factor. Giving explicit answer (rather than case-by-case numerical calculation) on how many percent of the current output contributed by H2 or CO and on how great the water gas shift reaction plays role on, this approach establishes at the first time an adaptive superposition mechanism of H2-fuel and CO-fuel electrochemistry for syngas fuel. Based on the diffusion equivalent circuit model, assuming series-connected resistances of surface diffusion and bulk diffusion, the model predicts well at high fuel utilization by keeping fixed porosity/tortuosity ratio. The model has been validated by experimental polarization behaviors in a wide range of operation on a button cell for H2-H2O-CO-CO2-N2 fuel systems. The framework could be helpful to narrow the gap between macro-scale and meso-scale SOFC modeling.

Dynamic and Inherent B0 Correction for DTI Using Stimulated Echo Spiral Imaging

PubMed Central

Avram, Alexandru V.; Guidon, Arnaud; Truong, Trong-Kha; Liu, Chunlei; Song, Allen W.

2013-01-01

Purpose To present a novel technique for high-resolution stimulated echo (STE) diffusion tensor imaging (DTI) with self-navigated interleaved spirals (SNAILS) readout trajectories that can inherently and dynamically correct for image artifacts due to spatial and temporal variations in the static magnetic field (B0) resulting from eddy currents, tissue susceptibilities, subject/physiological motion, and hardware instabilities. Methods The Hahn spin echo formed by the first two 90° radio-frequency pulses is balanced to consecutively acquire two additional images with different echo times (TE) and generate an inherent field map, while the diffusion-prepared STE signal remains unaffected. For every diffusion-encoding direction, an intrinsically registered field map is estimated dynamically and used to effectively and inherently correct for off-resonance artifacts in the reconstruction of the corresponding diffusion-weighted image (DWI). Results After correction with the dynamically acquired field maps, local blurring artifacts are specifically removed from individual STE DWIs and the estimated diffusion tensors have significantly improved spatial accuracy and larger fractional anisotropy. Conclusion Combined with the SNAILS acquisition scheme, our new method provides an integrated high-resolution short-TE DTI solution with inherent and dynamic correction for both motion-induced phase errors and off-resonance effects. PMID:23630029

Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

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

Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.

2015-11-01

A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less

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

PubMed

Vellela, Melissa; Qian, Hong

2009-10-06

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

Caliber Corrected Markov Modeling (C2M2): Correcting Equilibrium Markov Models.

PubMed

Dixit, Purushottam D; Dill, Ken A

2018-02-13

Rate processes are often modeled using Markov State Models (MSMs). Suppose you know a prior MSM and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them while also giving the wrong overall folding rate when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (C 2 M 2 ), an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory-based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.

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

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

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

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

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

Anomalous transport from holography. Part I

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2016-11-01

We revisit the transport properties induced by the chiral anomaly in a charged plasma holographically dual to anomalous U(1) V ×U(1) A Maxwell theory in Schwarzschild-AdS5. Off-shell constitutive relations for vector and axial currents are derived using various approximations generalising most of known in the literature anomaly-induced phenomena and revealing some new ones. In a weak external field approximation, the constitutive relations have all-order derivatives resummed into six momenta-dependent transport co-efficient functions: the diffusion, the electric/magnetic conductivity, and three anomaly induced functions. The latter generalise the chiral magnetic and chiral separation effects. Nonlinear transport is studied assuming presence of constant background external fields. The chiral magnetic effect, including all order nonlinearity in magnetic field, is proven to be exact when the magnetic field is the only external field that is turned on. Non-linear corrections to the constitutive relations due to electric and axial external fields are computed.

Diffusion of Small Solute Particles in Viscous Liquids: Cage Diffusion, a Result of Decoupling of Solute-Solvent Dynamics, Leads to Amplification of Solute Diffusion.

PubMed

Acharya, Sayantan; Nandi, Manoj K; Mandal, Arkajit; Sarkar, Sucharita; Bhattacharyya, Sarika Maitra

2015-08-27

We study the diffusion of small solute particles through solvent by keeping the solute-solvent interaction repulsive and varying the solvent properties. The study involves computer simulations, development of a new model to describe diffusion of small solutes in a solvent, and also mode coupling theory (MCT) calculations. In a viscous solvent, a small solute diffuses via coupling to the solvent hydrodynamic modes and also through the transient cages formed by the solvent. The model developed can estimate the independent contributions from these two different channels of diffusion. Although the solute diffusion in all the systems shows an amplification, the degree of it increases with solvent viscosity. The model correctly predicts that when the solvent viscosity is high, the solute primarily diffuses by exploiting the solvent cages. In such a scenario the MCT diffusion performed for a static solvent provides a correct estimation of the cage diffusion.

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility. Part 1; Steady Predictions

NASA Technical Reports Server (NTRS)

Allgood, Daniel C.; Graham, Jason S.; Ahuja, Vineet; Hosangadi, Ashvin

2008-01-01

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively. The Mach Number distribution shows small yet distinct differences between the two cases such as locations of shocks/shock reflections and a slightly different impingement point on the wall of the diffuser from the expansion at the exit of the nozzle. Similarly the temperature distribution indicates different flow recirculation patterns in the test cell. Both cases capture all the essential flow phenomena such as the shock-boundary layer interaction, plume expansion, expansion of the first stage ejectors, mixing between the engine plume and the first stage ejector flow and pressurization due to the first stage ejectors. The final paper will discuss thermal loads on the walls of the diffuser and cooling mechanisms investigated.

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.

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

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Weighted Mean of Signal Intensity for Unbiased Fiber Tracking of Skeletal Muscles: Development of a New Method and Comparison With Other Correction Techniques.

PubMed

Giraudo, Chiara; Motyka, Stanislav; Weber, Michael; Resinger, Christoph; Thorsten, Feiweier; Traxler, Hannes; Trattnig, Siegfried; Bogner, Wolfgang

2017-08-01

The aim of this study was to investigate the origin of random image artifacts in stimulated echo acquisition mode diffusion tensor imaging (STEAM-DTI), assess the role of averaging, develop an automated artifact postprocessing correction method using weighted mean of signal intensities (WMSIs), and compare it with other correction techniques. Institutional review board approval and written informed consent were obtained. The right calf and thigh of 10 volunteers were scanned on a 3 T magnetic resonance imaging scanner using a STEAM-DTI sequence.Artifacts (ie, signal loss) in STEAM-based DTI, presumably caused by involuntary muscle contractions, were investigated in volunteers and ex vivo (ie, human cadaver calf and turkey leg using the same DTI parameters as for the volunteers). An automated postprocessing artifact correction method based on the WMSI was developed and compared with previous approaches (ie, iteratively reweighted linear least squares and informed robust estimation of tensors by outlier rejection [iRESTORE]). Diffusion tensor imaging and fiber tracking metrics, using different averages and artifact corrections, were compared for region of interest- and mask-based analyses. One-way repeated measures analysis of variance with Greenhouse-Geisser correction and Bonferroni post hoc tests were used to evaluate differences among all tested conditions. Qualitative assessment (ie, images quality) for native and corrected images was performed using the paired t test. Randomly localized and shaped artifacts affected all volunteer data sets. Artifact burden during voluntary muscle contractions increased on average from 23.1% to 77.5% but were absent ex vivo. Diffusion tensor imaging metrics (mean diffusivity, fractional anisotropy, radial diffusivity, and axial diffusivity) had a heterogeneous behavior, but in the range reported by literature. Fiber track metrics (number, length, and volume) significantly improved in both calves and thighs after artifact correction in region of interest- and mask-based analyses (P < 0.05 each). Iteratively reweighted linear least squares and iRESTORE showed equivalent results, but WMSI was faster than iRESTORE. Muscle delineation and artifact load significantly improved after correction (P < 0.05 each). Weighted mean of signal intensity correction significantly improved STEAM-based quantitative DTI analyses and fiber tracking of lower-limb muscles, providing a robust tool for musculoskeletal applications.

Numerical method for angle-of-incidence correction factors for diffuse radiation incident photovoltaic modules

DOE PAGES

Marion, Bill

2017-03-27

Here, a numerical method is provided for solving the integral equation for the angle-of-incidence (AOI) correction factor for diffuse radiation incident photovoltaic (PV) modules. The types of diffuse radiation considered include sky, circumsolar, horizon, and ground-reflected. The method permits PV module AOI characteristics to be addressed when calculating AOI losses associated with diffuse radiation. Pseudo code is provided to aid users in the implementation, and results are shown for PV modules with tilt angles from 0° to 90°. Diffuse AOI losses are greatest for small PV module tilt angles. Including AOI losses associated with the diffuse irradiance will improve predictionsmore » of PV system performance.« less

Analysis of corrections to the eikonal approximation

NASA Astrophysics Data System (ADS)

Hebborn, C.; Capel, P.

2017-11-01

Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.

Effects of motion and b-matrix correction for high resolution DTI with short-axis PROPELLER-EPI

PubMed Central

Aksoy, Murat; Skare, Stefan; Holdsworth, Samantha; Bammer, Roland

2010-01-01

Short-axis PROPELLER-EPI (SAP-EPI) has been proven to be very effective in providing high-resolution diffusion-weighted and diffusion tensor data. The self-navigation capabilities of SAP-EPI allow one to correct for motion, phase errors, and geometric distortion. However, in the presence of patient motion, the change in the effective diffusion-encoding direction (i.e. the b-matrix) between successive PROPELLER ‘blades’ can decrease the accuracy of the estimated diffusion tensors, which might result in erroneous reconstruction of white matter tracts in the brain. In this study, we investigate the effects of alterations in the b-matrix as a result of patient motion on the example of SAP-EPI DTI and eliminate these effects by incorporating our novel single-step non-linear diffusion tensor estimation scheme into the SAP-EPI post-processing procedure. Our simulations and in-vivo studies showed that, in the presence of patient motion, correcting the b-matrix is necessary in order to get more accurate diffusion tensor and white matter pathway reconstructions. PMID:20222149

Transport Corrections in Nodal Diffusion Codes for HTR Modeling

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

Abderrafi M. Ougouag; Frederick N. Gleicher

2010-08-01

The cores and reflectors of High Temperature Reactors (HTRs) of the Next Generation Nuclear Plant (NGNP) type are dominantly diffusive media from the point of view of behavior of the neutrons and their migration between the various structures of the reactor. This means that neutron diffusion theory is sufficient for modeling most features of such reactors and transport theory may not be needed for most applications. Of course, the above statement assumes the availability of homogenized diffusion theory data. The statement is true for most situations but not all. Two features of NGNP-type HTRs require that the diffusion theory-based solutionmore » be corrected for local transport effects. These two cases are the treatment of burnable poisons (BP) in the case of the prismatic block reactors and, for both pebble bed reactor (PBR) and prismatic block reactor (PMR) designs, that of control rods (CR) embedded in non-multiplying regions near the interface between fueled zones and said non-multiplying zones. The need for transport correction arises because diffusion theory-based solutions appear not to provide sufficient fidelity in these situations.« less

Revisiting the time until fixation of a neutral mutant in a finite population - A coalescent theory approach.

PubMed

Greenbaum, Gili

2015-09-07

Evaluation of the time scale of the fixation of neutral mutations is crucial to the theoretical understanding of the role of neutral mutations in evolution. Diffusion approximations of the Wright-Fisher model are most often used to derive analytic formulations of genetic drift, as well as for the time scales of the fixation of neutral mutations. These approximations require a set of assumptions, most notably that genetic drift is a stochastic process in a continuous allele-frequency space, an assumption appropriate for large populations. Here equivalent approximations are derived using a coalescent theory approach which relies on a different set of assumptions than the diffusion approach, and adopts a discrete allele-frequency space. Solutions for the mean and variance of the time to fixation of a neutral mutation derived from the two approaches converge for large populations but slightly differ for small populations. A Markov chain analysis of the Wright-Fisher model for small populations is used to evaluate the solutions obtained, showing that both the mean and the variance are better approximated by the coalescent approach. The coalescence approximation represents a tighter upper-bound for the mean time to fixation than the diffusion approximation, while the diffusion approximation and coalescence approximation form an upper and lower bound, respectively, for the variance. The converging solutions and the small deviations of the two approaches strongly validate the use of diffusion approximations, but suggest that coalescent theory can provide more accurate approximations for small populations. Copyright © 2015 Elsevier Ltd. All rights reserved.

The Ponseti method in Latin America: initial impact and barriers to its diffusion and implementation.

PubMed

Boardman, Allison; Jayawardena, Asitha; Oprescu, Florin; Cook, Thomas; Morcuende, Jose A

2011-01-01

The Ponseti method for correcting clubfoot is a safe, effective, and minimally invasive treatment that has recently been implemented in Latin America. This study evaluates the initial impact and unique barriers to the diffusion of the Ponseti method throughout this region. Structured interviews were conducted with 30 physicians practicing the Ponseti method in three socioeconomically diverse countries: Chile, Peru and Guatemala. Since learning the Ponseti method, these physicians have treated approximately 1,740 clubfoot patients, with an estimated 1,705 (98%) patients treated using the Ponseti method, and 35 (2%) patients treated using surgical techniques. The barriers were classified into the following themes: physician education, health care system of the country, culture and beliefs of patients, physical distance and transport, financial barriers for patients, and parental compliance with the method. The results yielded several common barriers throughout Latin America including lack of physician education, physical distance to the treatment centers, and financial barriers for patients. Information from this study can be used to inform, and to implement and evaluate specific strategies to improve the diffusion of the Ponseti method for treating clubfoot throughout Latin America.

Correcting for diffusion in carbon-14 dating of ground water

USGS Publications Warehouse

Sanford, W.E.

1997-01-01

It has generally been recognized that molecular diffusion can be a significant process affecting the transport of carbon-14 in the subsurface when occurring either from a permeable aquifer into a confining layer or from a fracture into a rock matrix. An analytical solution that is valid for steady-state radionuclide transport through fractured rock is shown to be applicable to many multilayered aquifer systems. By plotting the ratio of the rate of diffusion to the rate of decay of carbon-14 over the length scales representative of several common hydrogeologic settings, it is demonstrated that diffusion of carbon-14 should often be not only a significant process, but a dominant one relative to decay. An age-correction formula is developed and applied to the Bangkok Basin of Thailand, where a mean carbon-14-based age of 21,000 years was adjusted to 11,000 years to account for diffusion. This formula and its graphical representation should prove useful for many studies, for they can be used first to estimate the potential role of diffusion and then to make a simple first-order age correction if necessary.It has generally been recognized that molecular diffusion can be a significant process affecting the transport of carbon-14 in the subsurface when occurring either from a permeable aquifer into a confining layer or from a fracture into a rock matrix. An analytical solution that is valid for steady-state radionuclide transport through fractured rock is shown to be applicable to many multilayered aquifer systems. By plotting the ratio of the rate of diffusion to the rate of decay of carbon-14 over the length scales representative of several common hydrogeologic settings, it is demonstrated that diffusion of carbon-14 should often be not only a significant process, but a dominant one relative to decay. An age-correction formula is developed and applied to the Bangkok Basin of Thailand, where a mean carbon-14-based age of 21,000 years was adjusted to 11,000 years to account for diffusion. This formula and its graphical representation should prove useful for many studies, for they can be used first to estimate the potential role of diffusion and then to make a simple first-order age correction if necessary.

Tensor Based Representation and Analysis of Diffusion-Weighted Magnetic Resonance Images

ERIC Educational Resources Information Center

Barmpoutis, Angelos

2009-01-01

Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue.…

Exact diffusion constant in a lattice-gas wind-tree model on a Bethe lattice

NASA Astrophysics Data System (ADS)

Zhang, Guihua; Percus, J. K.

1992-02-01

Kong and Cohen [Phys. Rev. B 40, 4838 (1989)] obtained the diffusion constant of a lattice-gas wind-tree model in the Boltzmann approximation. The result is consistent with computer simulations for low tree concentration. In this Brief Report we find the exact diffusion constant of the model on a Bethe lattice, which turns out to be identical with the Kong-Cohen and Gunn-Ortuño results. Our interpretation is that the Boltzmann approximation is exact for this type of diffusion on a Bethe lattice in the same sense that the Bethe-Peierls approximation is exact for the Ising model on a Bethe lattice.

High angular resolution diffusion imaging with stimulated echoes: compensation and correction in experiment design and analysis.

PubMed

Lundell, Henrik; Alexander, Daniel C; Dyrby, Tim B

2014-08-01

Stimulated echo acquisition mode (STEAM) diffusion MRI can be advantageous over pulsed-gradient spin-echo (PGSE) for diffusion times that are long compared with T2 . It therefore has potential for biomedical diffusion imaging applications at 7T and above where T2 is short. However, gradient pulses other than the diffusion gradients in the STEAM sequence contribute much greater diffusion weighting than in PGSE and lead to a disrupted experimental design. Here, we introduce a simple compensation to the STEAM acquisition that avoids the orientational bias and disrupted experiment design that these gradient pulses can otherwise produce. The compensation is simple to implement by adjusting the gradient vectors in the diffusion pulses of the STEAM sequence, so that the net effective gradient vector including contributions from diffusion and other gradient pulses is as the experiment intends. High angular resolution diffusion imaging (HARDI) data were acquired with and without the proposed compensation. The data were processed to derive standard diffusion tensor imaging (DTI) maps, which highlight the need for the compensation. Ignoring the other gradient pulses, a bias in DTI parameters from STEAM acquisition is found, due both to confounds in the analysis and the experiment design. Retrospectively correcting the analysis with a calculation of the full B matrix can partly correct for these confounds, but an acquisition that is compensated as proposed is needed to remove the effect entirely. © 2014 The Authors. NMR in Biomedicine published by John Wiley & Sons, Ltd.

Comparison of the Radiative Two-Flux and Diffusion Approximations

NASA Technical Reports Server (NTRS)

Spuckler, Charles M.

2006-01-01

Approximate solutions are sometimes used to determine the heat transfer and temperatures in a semitransparent material in which conduction and thermal radiation are acting. A comparison of the Milne-Eddington two-flux approximation and the diffusion approximation for combined conduction and radiation heat transfer in a ceramic material was preformed to determine the accuracy of the diffusion solution. A plane gray semitransparent layer without a substrate and a non-gray semitransparent plane layer on an opaque substrate were considered. For the plane gray layer the material is semitransparent for all wavelengths and the scattering and absorption coefficients do not vary with wavelength. For the non-gray plane layer the material is semitransparent with constant absorption and scattering coefficients up to a specified wavelength. At higher wavelengths the non-gray plane layer is assumed to be opaque. The layers are heated on one side and cooled on the other by diffuse radiation and convection. The scattering and absorption coefficients were varied. The error in the diffusion approximation compared to the Milne-Eddington two flux approximation was obtained as a function of scattering coefficient and absorption coefficient. The percent difference in interface temperatures and heat flux through the layer obtained using the Milne-Eddington two-flux and diffusion approximations are presented as a function of scattering coefficient and absorption coefficient. The largest errors occur for high scattering and low absorption except for the back surface temperature of the plane gray layer where the error is also larger at low scattering and low absorption. It is shown that the accuracy of the diffusion approximation can be improved for some scattering and absorption conditions if a reflectance obtained from a Kubelka-Munk type two flux theory is used instead of a reflection obtained from the Fresnel equation. The Kubelka-Munk reflectance accounts for surface reflection and radiation scattered back by internal scattering sites while the Fresnel reflection only accounts for surface reflections.

Experimental measurements of the SP response to concentration and temperature gradients in sandstones with application to subsurface geophysical monitoring

NASA Astrophysics Data System (ADS)

Leinov, E.; Jackson, M. D.

2014-09-01

Exclusion-diffusion potentials arising from temperature gradients are widely neglected in self-potential (SP) surveys, despite the ubiquitous presence of temperature gradients in subsurface settings such as volcanoes and hot springs, geothermal fields, and oil reservoirs during production via water or steam injection. Likewise, with the exception of borehole SP logging, exclusion-diffusion potentials arising from concentration gradients are also neglected or, at best, it is assumed that the diffusion potential dominates. To better interpret these SP sources requires well-constrained measurements of the various coupling terms. We report measurements of thermoelectric and electrochemical exclusion-diffusion potentials across sandstones saturated with NaCl brine and find that electrode effects can dominate the measured voltage. After correcting for these, we find that Hittorf transport numbers are the same within experimental error regardless of whether ion transport occurs in response to temperature or concentration gradients over the range of NaCl concentration investigated that is typical of natural systems. Diffusion potentials dominate only if the pore throat radius is more than approximately 4000 times larger than the diffuse layer thickness. In fine-grained sandstones with small pore throat diameter, this condition is likely to be met only if the saturating brine is of relatively high salinity; thus, in many cases of interest to earth scientists, exclusion-diffusion potentials will comprise significant contributions from both ionic diffusion through, and ionic exclusion from, the pore space of the rock. However, in coarse-grained sandstones, or sandstones saturated with high-salinity brine, exclusion-diffusion potentials can be described using end-member models in which ionic exclusion is neglected. Exclusion-diffusion potentials in sandstones depend upon pore size and salinity in a complex way: they may be positive, negative, or zero depending upon sandstone rock texture (expressed here by the pore radius r) and salinity.

Remediating High School Students' Misconceptions Concerning Diffusion and Osmosis through Concept Mapping and Conceptual Change Text.

ERIC Educational Resources Information Center

Tekkaya, Ceren

2003-01-01

Investigates the effectiveness of combining conceptual change text and concept mapping strategies on students' understanding of diffusion and osmosis. Results indicate that while the average percentage of students in the experimental group holding a scientifically correct view rose, the percentage of correct responses in the control group…

Multi-Objective Memetic Search for Robust Motion and Distortion Correction in Diffusion MRI.

PubMed

Hering, Jan; Wolf, Ivo; Maier-Hein, Klaus H

2016-10-01

Effective image-based artifact correction is an essential step in the analysis of diffusion MR images. Many current approaches are based on retrospective registration, which becomes challenging in the realm of high b -values and low signal-to-noise ratio, rendering the corresponding correction schemes more and more ineffective. We propose a novel registration scheme based on memetic search optimization that allows for simultaneous exploitation of different signal intensity relationships between the images, leading to more robust registration results. We demonstrate the increased robustness and efficacy of our method on simulated as well as in vivo datasets. In contrast to the state-of-art methods, the median target registration error (TRE) stayed below the voxel size even for high b -values (3000 s ·mm -2 and higher) and low SNR conditions. We also demonstrate the increased precision in diffusion-derived quantities by evaluating Neurite Orientation Dispersion and Density Imaging (NODDI) derived measures on a in vivo dataset with severe motion artifacts. These promising results will potentially inspire further studies on metaheuristic optimization in diffusion MRI artifact correction and image registration in general.

Correction of Gradient Nonlinearity Bias in Quantitative Diffusion Parameters of Renal Tissue with Intra Voxel Incoherent Motion.

PubMed

Malyarenko, Dariya I; Pang, Yuxi; Senegas, Julien; Ivancevic, Marko K; Ross, Brian D; Chenevert, Thomas L

2015-12-01

Spatially non-uniform diffusion weighting bias due to gradient nonlinearity (GNL) causes substantial errors in apparent diffusion coefficient (ADC) maps for anatomical regions imaged distant from magnet isocenter. Our previously-described approach allowed effective removal of spatial ADC bias from three orthogonal DWI measurements for mono-exponential media of arbitrary anisotropy. The present work evaluates correction feasibility and performance for quantitative diffusion parameters of the two-component IVIM model for well-perfused and nearly isotropic renal tissue. Sagittal kidney DWI scans of a volunteer were performed on a clinical 3T MRI scanner near isocenter and offset superiorly. Spatially non-uniform diffusion weighting due to GNL resulted both in shift and broadening of perfusion-suppressed ADC histograms for off-center DWI relative to unbiased measurements close to isocenter. Direction-average DW-bias correctors were computed based on the known gradient design provided by vendor. The computed bias maps were empirically confirmed by coronal DWI measurements for an isotropic gel-flood phantom. Both phantom and renal tissue ADC bias for off-center measurements was effectively removed by applying pre-computed 3D correction maps. Comparable ADC accuracy was achieved for corrections of both b -maps and DWI intensities in presence of IVIM perfusion. No significant bias impact was observed for IVIM perfusion fraction.

Correction of Gradient Nonlinearity Bias in Quantitative Diffusion Parameters of Renal Tissue with Intra Voxel Incoherent Motion

PubMed Central

Malyarenko, Dariya I.; Pang, Yuxi; Senegas, Julien; Ivancevic, Marko K.; Ross, Brian D.; Chenevert, Thomas L.

2015-01-01

Spatially non-uniform diffusion weighting bias due to gradient nonlinearity (GNL) causes substantial errors in apparent diffusion coefficient (ADC) maps for anatomical regions imaged distant from magnet isocenter. Our previously-described approach allowed effective removal of spatial ADC bias from three orthogonal DWI measurements for mono-exponential media of arbitrary anisotropy. The present work evaluates correction feasibility and performance for quantitative diffusion parameters of the two-component IVIM model for well-perfused and nearly isotropic renal tissue. Sagittal kidney DWI scans of a volunteer were performed on a clinical 3T MRI scanner near isocenter and offset superiorly. Spatially non-uniform diffusion weighting due to GNL resulted both in shift and broadening of perfusion-suppressed ADC histograms for off-center DWI relative to unbiased measurements close to isocenter. Direction-average DW-bias correctors were computed based on the known gradient design provided by vendor. The computed bias maps were empirically confirmed by coronal DWI measurements for an isotropic gel-flood phantom. Both phantom and renal tissue ADC bias for off-center measurements was effectively removed by applying pre-computed 3D correction maps. Comparable ADC accuracy was achieved for corrections of both b-maps and DWI intensities in presence of IVIM perfusion. No significant bias impact was observed for IVIM perfusion fraction. PMID:26811845

Numerical Evaluation of Lateral Diffusion Inside Diffusive Gradients in Thin Films Samplers

PubMed Central

2015-01-01

Using numerical simulation of diffusion inside diffusive gradients in thin films (DGT) samplers, we show that the effect of lateral diffusion inside the sampler on the solute flux into the sampler is a nonlinear function of the diffusion layer thickness and the physical sampling window size. In contrast, earlier work concluded that this effect was constant irrespective of parameters of the sampler geometry. The flux increase caused by lateral diffusion inside the sampler was determined to be ∼8.8% for standard samplers, which is considerably lower than the previous estimate of ∼20%. Lateral diffusion is also propagated to the diffusive boundary layer (DBL), where it leads to a slightly stronger decrease in the mass uptake than suggested by the common 1D diffusion model that is applied for evaluating DGT results. We introduce a simple correction procedure for lateral diffusion and demonstrate how the effect of lateral diffusion on diffusion in the DBL can be accounted for. These corrections often result in better estimates of the DBL thickness (δ) and the DGT-measured concentration than earlier approaches and will contribute to more accurate concentration measurements in solute monitoring in waters. PMID:25877251

Motion-induced phase error estimation and correction in 3D diffusion tensor imaging.

PubMed

Van, Anh T; Hernando, Diego; Sutton, Bradley P

2011-11-01

A multishot data acquisition strategy is one way to mitigate B0 distortion and T2∗ blurring for high-resolution diffusion-weighted magnetic resonance imaging experiments. However, different object motions that take place during different shots cause phase inconsistencies in the data, leading to significant image artifacts. This work proposes a maximum likelihood estimation and k-space correction of motion-induced phase errors in 3D multishot diffusion tensor imaging. The proposed error estimation is robust, unbiased, and approaches the Cramer-Rao lower bound. For rigid body motion, the proposed correction effectively removes motion-induced phase errors regardless of the k-space trajectory used and gives comparable performance to the more computationally expensive 3D iterative nonlinear phase error correction method. The method has been extended to handle multichannel data collected using phased-array coils. Simulation and in vivo data are shown to demonstrate the performance of the method.

Density, structure, and dynamics of water: The effect of van der Waals interactions

NASA Astrophysics Data System (ADS)

Wang, Jue; Román-Pérez, G.; Soler, Jose M.; Artacho, Emilio; Fernández-Serra, M.-V.

2011-01-01

It is known that ab initio molecular dynamics (AIMD) simulations of liquid water at ambient conditions, based on the generalized gradient approximation (GGA) to density functional theory (DFT), with commonly used functionals fail to produce structural and diffusive properties in reasonable agreement with experiment. This is true for canonical, constant temperature simulations where the density of the liquid is fixed to the experimental density. The equilibrium density, at ambient conditions, of DFT water has recently been shown by Schmidt et al. [J. Phys. Chem. B, 113, 11959 (2009)] to be underestimated by different GGA functionals for exchange and correlation, and corrected by the addition of interatomic pair potentials to describe van der Waals (vdW) interactions. In this contribution we present a DFT-AIMD study of liquid water using several GGA functionals as well as the van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. As expected, we find that the density of water is grossly underestimated by GGA functionals. When a vdW-DF is used, the density improves drastically and the experimental diffusivity is reproduced without the need of thermal corrections. We analyze the origin of the density differences between all the functionals. We show that the vdW-DF increases the population of non-H-bonded interstitial sites, at distances between the first and second coordination shells. However, it excessively weakens the H-bond network, collapsing the second coordination shell. This structural problem is partially associated to the choice of GGA exchange in the vdW-DF. We show that a different choice for the exchange functional is enough to achieve an overall improvement both in structure and diffusivity.

Isotropic resolution diffusion tensor imaging of lumbosacral and sciatic nerves using a phase‐corrected diffusion‐prepared 3D turbo spin echo

PubMed Central

Van, Anh T.; Weidlich, Dominik; Kooijman, Hendrick; Hock, Andreas; Rummeny, Ernst J.; Gersing, Alexandra; Kirschke, Jan S.; Karampinos, Dimitrios C.

2018-01-01

Purpose To perform in vivo isotropic‐resolution diffusion tensor imaging (DTI) of lumbosacral and sciatic nerves with a phase‐navigated diffusion‐prepared (DP) 3D turbo spin echo (TSE) acquisition and modified reconstruction incorporating intershot phase‐error correction and to investigate the improvement on image quality and diffusion quantification with the proposed phase correction. Methods Phase‐navigated DP 3D TSE included magnitude stabilizers to minimize motion and eddy‐current effects on the signal magnitude. Phase navigation of motion‐induced phase errors was introduced before readout in 3D TSE. DTI of lower back nerves was performed in vivo using 3D TSE and single‐shot echo planar imaging (ss‐EPI) in 13 subjects. Diffusion data were phase‐corrected per k z plane with respect to T2‐weighted data. The effects of motion‐induced phase errors on DTI quantification was assessed for 3D TSE and compared with ss‐EPI. Results Non–phase‐corrected 3D TSE resulted in artifacts in diffusion‐weighted images and overestimated DTI parameters in the sciatic nerve (mean diffusivity [MD] = 2.06 ± 0.45). Phase correction of 3D TSE DTI data resulted in reductions in all DTI parameters (MD = 1.73 ± 0.26) of statistical significance (P ≤ 0.001) and in closer agreement with ss‐EPI DTI parameters (MD = 1.62 ± 0.21). Conclusion DP 3D TSE with phase correction allows distortion‐free isotropic diffusion imaging of lower back nerves with robustness to motion‐induced artifacts and DTI quantification errors. Magn Reson Med 80:609–618, 2018. © 2018 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes. PMID:29380414

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

Zardecki, A.

The effect of multiple scattering on the validity of the Beer-Lambert law is discussed for a wide range of particle-size parameters and optical depths. To predict the amount of received radiant power, appropriate correction terms are introduced. For particles larger than or comparable to the wavelength of radiation, the small-angle approximation is adequate; whereas for small densely packed particles, the diffusion theory is advantageously employed. These two approaches are used in the context of the problem of laser-beam propagation in a dense aerosol medium. In addition, preliminary results obtained by using a two-dimensional finite-element discrete-ordinates transport code are described. Multiple-scatteringmore » effects for laser propagation in fog, cloud, rain, and aerosol cloud are modeled.« less

Distortion correction of echo-planar diffusion-weighted images of uterine cervix.

PubMed

deSouza, Nandita M; Orton, Matthew; Downey, Kate; Morgan, Veronica A; Collins, David J; Giles, Sharon L; Payne, Geoffrey S

2016-05-01

To investigate the clinical utility of the reverse gradient algorithm in correcting distortions in diffusion-weighted images of the cervix and for increasing diagnostic performance. Forty-one patients ages 25-72 years (mean 40 ± 11 years) with suspected or early stage cervical cancer were imaged at 3T using an endovaginal coil. T2 -weighted (W) and diffusion-weighted images with right and left phase-encode gradient directions were obtained coronal to the cervix (b = 0, 100, 300, 500, 800 s mm(-2) ). Differences in angle of the endocervical canal to the x-axis between T2 W and right-gradient, left-gradient, and corrected images were measured. Uncorrected and corrected images were assessed for diagnostic performance when viewed together with T2 W images by two independent observers against subsequent histology. The angles of the endocervical canal relative to the x-axis were significantly different between the T2 W images and the right-gradient images (P = 0.007), approached significance for left-gradient images (P = 0.055), and were not significantly different after correction (P = 0.95). Corrected images enabled a definitive diagnosis in 34% (n = 14) of patients classified as equivocal on uncorrected images. Tumor volume in this subset was 0.18 ± 0.44 cm(3) (mean ± SD; sensitivity of detection 100% [8/8], specificity 50% [3/6] for an experienced observer). Correction did not improve diagnostic performance for the less-experienced observer. Distortion-corrected diffusion-weighted images improved correspondence with T2 W images and diagnostic performance in a third of cases. © 2015 The Authors Journal of Magnetic Resonance Imaging published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

An efficient approach for treating composition-dependent diffusion within organic particles

DOE PAGES

O'Meara, Simon; Topping, David O.; Zaveri, Rahul A.; ...

2017-09-07

Mounting evidence demonstrates that under certain conditions the rate of component partitioning between the gas and particle phase in atmospheric organic aerosol is limited by particle-phase diffusion. To date, however, particle-phase diffusion has not been incorporated into regional atmospheric models. An analytical rather than numerical solution to diffusion through organic particulate matter is desirable because of its comparatively small computational expense in regional models. Current analytical models assume diffusion to be independent of composition and therefore use a constant diffusion coefficient. To realistically model diffusion, however, it should be composition-dependent (e.g. due to the partitioning of components that plasticise, vitrifymore » or solidify). This study assesses the modelling capability of an analytical solution to diffusion corrected to account for composition dependence against a numerical solution. Results show reasonable agreement when the gas-phase saturation ratio of a partitioning component is constant and particle-phase diffusion limits partitioning rate (<10% discrepancy in estimated radius change). However, when the saturation ratio of the partitioning component varies, a generally applicable correction cannot be found, indicating that existing methodologies are incapable of deriving a general solution. Until such time as a general solution is found, caution should be given to sensitivity studies that assume constant diffusivity. Furthermore, the correction was implemented in the polydisperse, multi-process Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) and is used to illustrate how the evolution of number size distribution may be accelerated by condensation of a plasticising component onto viscous organic particles.« less

An efficient approach for treating composition-dependent diffusion within organic particles

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

O'Meara, Simon; Topping, David O.; Zaveri, Rahul A.

Mounting evidence demonstrates that under certain conditions the rate of component partitioning between the gas and particle phase in atmospheric organic aerosol is limited by particle-phase diffusion. To date, however, particle-phase diffusion has not been incorporated into regional atmospheric models. An analytical rather than numerical solution to diffusion through organic particulate matter is desirable because of its comparatively small computational expense in regional models. Current analytical models assume diffusion to be independent of composition and therefore use a constant diffusion coefficient. To realistically model diffusion, however, it should be composition-dependent (e.g. due to the partitioning of components that plasticise, vitrifymore » or solidify). This study assesses the modelling capability of an analytical solution to diffusion corrected to account for composition dependence against a numerical solution. Results show reasonable agreement when the gas-phase saturation ratio of a partitioning component is constant and particle-phase diffusion limits partitioning rate (<10% discrepancy in estimated radius change). However, when the saturation ratio of the partitioning component varies, a generally applicable correction cannot be found, indicating that existing methodologies are incapable of deriving a general solution. Until such time as a general solution is found, caution should be given to sensitivity studies that assume constant diffusivity. Furthermore, the correction was implemented in the polydisperse, multi-process Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) and is used to illustrate how the evolution of number size distribution may be accelerated by condensation of a plasticising component onto viscous organic particles.« less

Short-Path Statistics and the Diffusion Approximation

NASA Astrophysics Data System (ADS)

Blanco, Stéphane; Fournier, Richard

2006-12-01

In the field of first return time statistics in bounded domains, short paths may be defined as those paths for which the diffusion approximation is inappropriate. This is at the origin of numerous open questions concerning the characterization of residence time distributions. We show here how general integral constraints can be derived that make it possible to address short-path statistics indirectly by application of the diffusion approximation to long paths. Application to the moments of the distribution at the low-Knudsen limit leads to simple practical results and novel physical pictures.

Glycosylases utilize ``stop and go'' motion to locate DNA damage

NASA Astrophysics Data System (ADS)

Nelson, Shane

2015-03-01

Oxidative damage to DNA results in alterations that are mutagenic or even cytotoxic. Base excision repair is a mechanism that functions to identify and correct these lesions, and is present in organisms ranging from bacteria to humans. DNA glycosylases are the first enzymes in this pathway and function to locate and remove oxidatively damaged bases, and do so utilizing only thermal energy. However, the question remains of how these enzymes locate and recognize a damaged base among millions of undamaged bases. Utilizing fluorescence video microscopy with high spatial and temporal resolution, we have observed a number of different fluorescently labeled glycosylases (including bacterial FPG, NEI, and NTH as well as mammalian MutyH and OGG). These enzymes diffuse along DNA tightropes at approximately 0.01 +/- 0.005 μm2/s with binding lifetimes ranging from one second to several minutes. Chemically induced damage to the DNA substrate causes a ~ 50% reduction in diffusion coefficients and a ~ 400% increase in binding lifetimes, while mutation of the key ``wedge residue'' - which has been shown to be responsible for damage detection - results in a 200% increase in the diffusion coefficient. Utilizing a sliding window approach to measure diffusion coefficients within individual trajectories, we observe that distributions of diffusion coefficients are bimodal, consistent with periods of diffusive motion interspersed with immobile periods. Utilizing a unique chemo-mechanical simulation approach, we demonstrate that the motion of these glycosylases can be explained as free diffusion along the helical pitch of the DNA, punctuated with two different types of pauses: 1) rapid, short-lived pauses as the enzyme rapidly probes DNA bases to interrogate for damage and, 2) less frequent, longer lived pauses that reflect the enzyme bound to and catalytically removing a damaged base. These simulations also indicate that the wedge residue is critical for interrogation and recognition of damage, and thus enzymes missing this residue diffuse faster. Similarly, chemically induced damage increases the frequency with which the enzymes encounter damaged bases, resulting in slower diffusion.

Resolving Fast, Confined Diffusion in Bacteria with Image Correlation Spectroscopy.

PubMed

Rowland, David J; Tuson, Hannah H; Biteen, Julie S

2016-05-24

By following single fluorescent molecules in a microscope, single-particle tracking (SPT) can measure diffusion and binding on the nanometer and millisecond scales. Still, although SPT can at its limits characterize the fastest biomolecules as they interact with subcellular environments, this measurement may require advanced illumination techniques such as stroboscopic illumination. Here, we address the challenge of measuring fast subcellular motion by instead analyzing single-molecule data with spatiotemporal image correlation spectroscopy (STICS) with a focus on measurements of confined motion. Our SPT and STICS analysis of simulations of the fast diffusion of confined molecules shows that image blur affects both STICS and SPT, and we find biased diffusion rate measurements for STICS analysis in the limits of fast diffusion and tight confinement due to fitting STICS correlation functions to a Gaussian approximation. However, we determine that with STICS, it is possible to correctly interpret the motion that blurs single-molecule images without advanced illumination techniques or fast cameras. In particular, we present a method to overcome the bias due to image blur by properly estimating the width of the correlation function by directly calculating the correlation function variance instead of using the typical Gaussian fitting procedure. Our simulation results are validated by applying the STICS method to experimental measurements of fast, confined motion: we measure the diffusion of cytosolic mMaple3 in living Escherichia coli cells at 25 frames/s under continuous illumination to illustrate the utility of STICS in an experimental parameter regime for which in-frame motion prevents SPT and tight confinement of fast diffusion precludes stroboscopic illumination. Overall, our application of STICS to freely diffusing cytosolic protein in small cells extends the utility of single-molecule experiments to the regime of fast confined diffusion without requiring advanced microscopy techniques. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Baseline Correction of Diffuse Reflection Near-Infrared Spectra Using Searching Region Standard Normal Variate (SRSNV).

PubMed

Genkawa, Takuma; Shinzawa, Hideyuki; Kato, Hideaki; Ishikawa, Daitaro; Murayama, Kodai; Komiyama, Makoto; Ozaki, Yukihiro

2015-12-01

An alternative baseline correction method for diffuse reflection near-infrared (NIR) spectra, searching region standard normal variate (SRSNV), was proposed. Standard normal variate (SNV) is an effective pretreatment method for baseline correction of diffuse reflection NIR spectra of powder and granular samples; however, its baseline correction performance depends on the NIR region used for SNV calculation. To search for an optimal NIR region for baseline correction using SNV, SRSNV employs moving window partial least squares regression (MWPLSR), and an optimal NIR region is identified based on the root mean square error (RMSE) of cross-validation of the partial least squares regression (PLSR) models with the first latent variable (LV). The performance of SRSNV was evaluated using diffuse reflection NIR spectra of mixture samples consisting of wheat flour and granular glucose (0-100% glucose at 5% intervals). From the obtained NIR spectra of the mixture in the 10 000-4000 cm(-1) region at 4 cm intervals (1501 spectral channels), a series of spectral windows consisting of 80 spectral channels was constructed, and then SNV spectra were calculated for each spectral window. Using these SNV spectra, a series of PLSR models with the first LV for glucose concentration was built. A plot of RMSE versus the spectral window position obtained using the PLSR models revealed that the 8680–8364 cm(-1) region was optimal for baseline correction using SNV. In the SNV spectra calculated using the 8680–8364 cm(-1) region (SRSNV spectra), a remarkable relative intensity change between a band due to wheat flour at 8500 cm(-1) and that due to glucose at 8364 cm(-1) was observed owing to successful baseline correction using SNV. A PLSR model with the first LV based on the SRSNV spectra yielded a determination coefficient (R2) of 0.999 and an RMSE of 0.70%, while a PLSR model with three LVs based on SNV spectra calculated in the full spectral region gave an R2 of 0.995 and an RMSE of 2.29%. Additional evaluation of SRSNV was carried out using diffuse reflection NIR spectra of marzipan and corn samples, and PLSR models based on SRSNV spectra showed good prediction results. These evaluation results indicate that SRSNV is effective in baseline correction of diffuse reflection NIR spectra and provides regression models with good prediction accuracy.

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

DOE PAGES

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory; ...

2015-02-25

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Influence of Sub-grid-Scale Isentropic Transports on McRAS Evaluations using ARM-CART SCM Datasets

NASA Technical Reports Server (NTRS)

Sud, Y. C.; Walker, G. K.; Tao, W. K.

2004-01-01

In GCM-physics evaluations with the currently available ARM-CART SCM datasets, McRAS produced very similar character of near surface errors of simulated temperature and humidity containing typically warm and moist biases near the surface and cold and dry biases aloft. We argued it must have a common cause presumably rooted in the model physics. Lack of vertical adjustment of horizontal transport was thought to be a plausible source. Clearly, debarring such a freedom would force the incoming air to diffuse into the grid-cell which would naturally bias the surface air to become warm and moist while the upper air becomes cold and dry, a characteristic feature of McRAS biases. Since, the errors were significantly larger in the two winter cases that contain potentially more intense episodes of cold and warm advective transports, it further reaffirmed our argument and provided additional motivation to introduce the corrections. When the horizontal advective transports were suitably modified to allow rising and/or sinking following isentropic pathways of subgrid scale motions, the outcome was to cool and dry (or warm and moisten) the lower (or upper) levels. Ever, crude approximations invoking such a correction reduced the temperature and humidity biases considerably. The tests were performed on all the available ARM-CART SCM cases with consistent outcome. With the isentropic corrections implemented through two different numerical approximations, virtually similar benefits were derived further confirming the robustness of our inferences. These results suggest the need for insentropic advective transport adjustment in a GCM due to subgrid scale motions.

Retina imaging system with adaptive optics for the eye with or without myopia

NASA Astrophysics Data System (ADS)

Li, Chao; Xia, Mingliang; Jiang, Baoguang; Mu, Quanquan; Chen, Shaoyuan; Xuan, Li

2009-04-01

An adaptive optics system for the retina imaging is introduced in the paper. It can be applied to the eye with myopia from 0 to 6 diopters without any adjustment of the system. A high-resolution liquid crystal on silicon (LCOS) device is used as the wave-front corrector. The aberration is detected by a Shack-Harmann wave-front sensor (HASO) that has a Root Mean Square (RMS) measurement accuracy of λ/100 ( λ = 0.633 μm). And an equivalent scale model eye is constructed with a short focal length lens (˜18 mm) and a diffuse reflection object (paper screen) as the retina. By changing the distance between the paper screen and the lens, we simulate the eye with larger diopters than 5 and the depth of field. The RMS value both before and after correction is obtained by the wave-front sensor. After correction, the system reaches the diffraction-limited resolution approximately 230 cycles/mm at the object space. It is proved that if the myopia is smaller than 6 diopters and the depth of field is between -40 and +50 mm, the system can correct the aberration very well.

Anomalous transport from holography: part II

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2017-03-01

This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous U(1)_V× U(1)_A Maxwell theory in Schwarzschild-AdS_5 spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the presence of a static spatially inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative B^2-correction to the diffusion constant. We also find modifications to the chiral magnetic wave nonlinear in B. In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second.

A diffusion-matched principal component analysis (DM-PCA) based two-channel denoising procedure for high-resolution diffusion-weighted MRI

PubMed Central

Chang, Hing-Chiu; Bilgin, Ali; Bernstein, Adam; Trouard, Theodore P.

2018-01-01

Over the past several years, significant efforts have been made to improve the spatial resolution of diffusion-weighted imaging (DWI), aiming at better detecting subtle lesions and more reliably resolving white-matter fiber tracts. A major concern with high-resolution DWI is the limited signal-to-noise ratio (SNR), which may significantly offset the advantages of high spatial resolution. Although the SNR of DWI data can be improved by denoising in post-processing, existing denoising procedures may potentially reduce the anatomic resolvability of high-resolution imaging data. Additionally, non-Gaussian noise induced signal bias in low-SNR DWI data may not always be corrected with existing denoising approaches. Here we report an improved denoising procedure, termed diffusion-matched principal component analysis (DM-PCA), which comprises 1) identifying a group of (not necessarily neighboring) voxels that demonstrate very similar magnitude signal variation patterns along the diffusion dimension, 2) correcting low-frequency phase variations in complex-valued DWI data, 3) performing PCA along the diffusion dimension for real- and imaginary-components (in two separate channels) of phase-corrected DWI voxels with matched diffusion properties, 4) suppressing the noisy PCA components in real- and imaginary-components, separately, of phase-corrected DWI data, and 5) combining real- and imaginary-components of denoised DWI data. Our data show that the new two-channel (i.e., for real- and imaginary-components) DM-PCA denoising procedure performs reliably without noticeably compromising anatomic resolvability. Non-Gaussian noise induced signal bias could also be reduced with the new denoising method. The DM-PCA based denoising procedure should prove highly valuable for high-resolution DWI studies in research and clinical uses. PMID:29694400

Diffuse reflectance relations based on diffusion dipole theory for large absorption and reduced scattering

NASA Astrophysics Data System (ADS)

Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.

2013-08-01

Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 m at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys. 19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime scenes.

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

PubMed

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

2016-02-01

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

A consistent transported PDF model for treating differential molecular diffusion

NASA Astrophysics Data System (ADS)

Wang, Haifeng; Zhang, Pei

2016-11-01

Differential molecular diffusion is a fundamentally significant phenomenon in all multi-component turbulent reacting or non-reacting flows caused by the different rates of molecular diffusion of energy and species concentrations. In the transported probability density function (PDF) method, the differential molecular diffusion can be treated by using a mean drift model developed by McDermott and Pope. This model correctly accounts for the differential molecular diffusion in the scalar mean transport and yields a correct DNS limit of the scalar variance production. The model, however, misses the molecular diffusion term in the scalar variance transport equation, which yields an inconsistent prediction of the scalar variance in the transported PDF method. In this work, a new model is introduced to remedy this problem that can yield a consistent scalar variance prediction. The model formulation along with its numerical implementation is discussed, and the model validation is conducted in a turbulent mixing layer problem.

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, Larry R.; Gorney, David J.

1992-01-01

Two refinements to the quasi-linear theory of ion radial diffusion are proposed and examined analytically with simulations of particle trajectories. The resonance-broadening correction by Dungey (1965) is applied to the quasi-linear diffusion theory by Faelthammar (1965) for an individual model storm. Quasi-linear theory is then applied to the mean diffusion coefficients resulting from simulations of particle trajectories in 20 model storms. The correction for drift-resonance broadening results in quasi-linear diffusion coefficients with discrepancies from the corresponding simulated values that are reduced by a factor of about 3. Further reductions in the discrepancies are noted following the averaging of the quasi-linear diffusion coefficients, the simulated coefficients, and the resonance-broadened coefficients for the 20 storms. Quasi-linear theory provides good descriptions of particle transport for a single storm but performs even better in conjunction with the present ensemble-averaging.

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics

PubMed Central

Jakse, Noel; Pasturel, Alain

2013-01-01

We present a study of dynamic properties of liquid aluminum using density-functional theory within the local-density (LDA) and generalized gradient (GGA) approximations. We determine the temperature dependence of the self-diffusion coefficient as well the viscosity using direct methods. Comparisons with experimental data favor the LDA approximation to compute dynamic properties of liquid aluminum. We show that the GGA approximation induce more important backscattering effects due to an enhancement of the icosahedral short range order (ISRO) that impact directly dynamic properties like the self-diffusion coefficient. All these results are then used to test the Stokes-Einstein relation and the universal scaling law relating the diffusion coefficient and the excess entropy of a liquid. PMID:24190311

Apparent resistivity for transient electromagnetic induction logging and its correction in radial layer identification

NASA Astrophysics Data System (ADS)

Meng, Qingxin; Hu, Xiangyun; Pan, Heping; Xi, Yufei

2018-04-01

We propose an algorithm for calculating all-time apparent resistivity from transient electromagnetic induction logging. The algorithm is based on the whole-space transient electric field expression of the uniform model and Halley's optimisation. In trial calculations for uniform models, the all-time algorithm is shown to have high accuracy. We use the finite-difference time-domain method to simulate the transient electromagnetic field in radial two-layer models without wall rock and convert the simulation results to apparent resistivity using the all-time algorithm. The time-varying apparent resistivity reflects the radially layered geoelectrical structure of the models and the apparent resistivity of the earliest time channel follows the true resistivity of the inner layer; however, the apparent resistivity at larger times reflects the comprehensive electrical characteristics of the inner and outer layers. To accurately identify the outer layer resistivity based on the series relationship model of the layered resistance, the apparent resistivity and diffusion depth of the different time channels are approximately replaced by related model parameters; that is, we propose an apparent resistivity correction algorithm. By correcting the time-varying apparent resistivity of radial two-layer models, we show that the correction results reflect the radially layered electrical structure and the corrected resistivities of the larger time channels follow the outer layer resistivity. The transient electromagnetic fields of radially layered models with wall rock are simulated to obtain the 2D time-varying profiles of the apparent resistivity and corrections. The results suggest that the time-varying apparent resistivity and correction results reflect the vertical and radial geoelectrical structures. For models with small wall-rock effect, the correction removes the effect of the low-resistance inner layer on the apparent resistivity of the larger time channels.

Effect of respiratory and cardiac gating on the major diffusion-imaging metrics

PubMed Central

Hamaguchi, Hiroyuki; Sugimori, Hiroyuki; Nakanishi, Mitsuhiro; Nakagawa, Shin; Fujiwara, Taro; Yoshida, Hirokazu; Takamori, Sayaka; Shirato, Hiroki

2016-01-01

The effect of respiratory gating on the major diffusion-imaging metrics and that of cardiac gating on mean kurtosis (MK) are not known. For evaluation of whether the major diffusion-imaging metrics—MK, fractional anisotropy (FA), and mean diffusivity (MD) of the brain—varied between gated and non-gated acquisitions, respiratory-gated, cardiac-gated, and non-gated diffusion-imaging of the brain were performed in 10 healthy volunteers. MK, FA, and MD maps were constructed for all acquisitions, and the histograms were constructed. The normalized peak height and location of the histograms were compared among the acquisitions by use of Friedman and post hoc Wilcoxon tests. The effect of the repetition time (TR) on the diffusion-imaging metrics was also tested, and we corrected for its variation among acquisitions, if necessary. The results showed a shift in the peak location of the MK and MD histograms to the right with an increase in TR (p ≤ 0.01). The corrected peak location of the MK histograms, the normalized peak height of the FA histograms, the normalized peak height and the corrected peak location of the MD histograms varied significantly between the gated and non-gated acquisitions (p < 0.05). These results imply an influence of respiration and cardiac pulsation on the major diffusion-imaging metrics. The gating conditions must be kept identical if reproducible results are to be achieved. PMID:27073115

A class of renormalised meshless Laplacians for boundary value problems

NASA Astrophysics Data System (ADS)

Basic, Josip; Degiuli, Nastia; Ban, Dario

2018-02-01

A meshless approach to approximating spatial derivatives on scattered point arrangements is presented in this paper. Three various derivations of approximate discrete Laplace operator formulations are produced using the Taylor series expansion and renormalised least-squares correction of the first spatial derivatives. Numerical analyses are performed for the introduced Laplacian formulations, and their convergence rate and computational efficiency are examined. The tests are conducted on regular and highly irregular scattered point arrangements. The results are compared to those obtained by the smoothed particle hydrodynamics method and the finite differences method on a regular grid. Finally, the strong form of various Poisson and diffusion equations with Dirichlet or Robin boundary conditions are solved in two and three dimensions by making use of the introduced operators in order to examine their stability and accuracy for boundary value problems. The introduced Laplacian operators perform well for highly irregular point distribution and offer adequate accuracy for mesh and mesh-free numerical methods that require frequent movement of the grid or point cloud.

Evolution of CMB spectral distortion anisotropies and tests of primordial non-Gaussianity

NASA Astrophysics Data System (ADS)

Chluba, Jens; Dimastrogiovanni, Emanuela; Amin, Mustafa A.; Kamionkowski, Marc

2017-04-01

Anisotropies in distortions to the frequency spectrum of the cosmic microwave background (CMB) can be created through spatially varying heating processes in the early Universe. For instance, the dissipation of small-scale acoustic modes does create distortion anisotropies, in particular for non-Gaussian primordial perturbations. In this work, we derive approximations that allow describing the associated distortion field. We provide a systematic formulation of the problem using Fourier-space window functions, clarifying and generalizing previous approximations. Our expressions highlight the fact that the amplitudes of the spectral-distortion fluctuations induced by non-Gaussianity depend also on the homogeneous value of those distortions. Absolute measurements are thus required to obtain model-independent distortion constraints on primordial non-Gaussianity. We also include a simple description for the evolution of distortions through photon diffusion, showing that these corrections can usually be neglected. Our formulation provides a systematic framework for computing higher order correlation functions of distortions with CMB temperature anisotropies and can be extended to describe correlations with polarization anisotropies.

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

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

PubMed

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

2002-06-01

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

Improved Correction of IR Loss in Diffuse Shortwave Measurements: An ARM Value-Added Product

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

Younkin, K; Long, CN

Simple single black detector pyranometers, such as the Eppley Precision Spectral Pyranometer (PSP) used by the Atmospheric Radiation Measurement (ARM) Program, are known to lose energy via infrared (IR) emission to the sky. This is especially a problem when making clear-sky diffuse shortwave (SW) measurements, which are inherently of low magnitude and suffer the greatest IR loss. Dutton et al. (2001) proposed a technique using information from collocated pyrgeometers to help compensate for this IR loss. The technique uses an empirically derived relationship between the pyrgeometer detector data (and alternatively the detector data plus the difference between the pyrgeometer casemore » and dome temperatures) and the nighttime pyranometer IR loss data. This relationship is then used to apply a correction to the diffuse SW data during daylight hours. We developed an ARM value-added product (VAP) called the SW DIFF CORR 1DUTT VAP to apply the Dutton et al. correction technique to ARM PSP diffuse SW measurements.« less

On the Equivalence of FCS and FRAP: Simultaneous Lipid Membrane Measurements.

PubMed

Macháň, Radek; Foo, Yong Hwee; Wohland, Thorsten

2016-07-12

Fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP) are widely used methods to determine diffusion coefficients. However, they often do not yield the same results. With the advent of camera-based imaging FCS, which measures the diffusion coefficient in each pixel of an image, and proper bleaching corrections, it is now possible to measure the diffusion coefficient by FRAP and FCS in the exact same images. We thus performed simultaneous FCS and FRAP measurements on supported lipid bilayers and live cell membranes to test how far the two methods differ in their results and whether the methodological differences, in particular the high bleach intensity in FRAP, the bleach corrections, and the fitting procedures in the two methods explain observed differences. Overall, we find that the FRAP bleach intensity does not measurably influence the diffusion in the samples, but that bleach correction and fitting introduce large uncertainties in FRAP. We confirm our results by simulations. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins.

PubMed

Ghose, R; Fushman, D; Cowburn, D

2001-04-01

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand. Copyright 2001 Academic Press.

Determination of the Rotational Diffusion Tensor of Macromolecules in Solution from NMR Relaxation Data with a Combination of Exact and Approximate Methods—Application to the Determination of Interdomain Orientation in Multidomain Proteins

NASA Astrophysics Data System (ADS)

Ghose, Ranajeet; Fushman, David; Cowburn, David

2001-04-01

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.

Retrospective Correction of Physiological Noise in DTI Using an Extended Tensor Model and Peripheral Measurements

PubMed Central

Mohammadi, Siawoosh; Hutton, Chloe; Nagy, Zoltan; Josephs, Oliver; Weiskopf, Nikolaus

2013-01-01

Diffusion tensor imaging is widely used in research and clinical applications, but this modality is highly sensitive to artefacts. We developed an easy-to-implement extension of the original diffusion tensor model to account for physiological noise in diffusion tensor imaging using measures of peripheral physiology (pulse and respiration), the so-called extended tensor model. Within the framework of the extended tensor model two types of regressors, which respectively modeled small (linear) and strong (nonlinear) variations in the diffusion signal, were derived from peripheral measures. We tested the performance of four extended tensor models with different physiological noise regressors on nongated and gated diffusion tensor imaging data, and compared it to an established data-driven robust fitting method. In the brainstem and cerebellum the extended tensor models reduced the noise in the tensor-fit by up to 23% in accordance with previous studies on physiological noise. The extended tensor model addresses both large-amplitude outliers and small-amplitude signal-changes. The framework of the extended tensor model also facilitates further investigation into physiological noise in diffusion tensor imaging. The proposed extended tensor model can be readily combined with other artefact correction methods such as robust fitting and eddy current correction. PMID:22936599

Pitch angle scattering of relativistic electrons from stationary magnetic waves: Continuous Markov process and quasilinear theory

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

Lemons, Don S.

2012-01-15

We develop a Markov process theory of charged particle scattering from stationary, transverse, magnetic waves. We examine approximations that lead to quasilinear theory, in particular the resonant diffusion approximation. We find that, when appropriate, the resonant diffusion approximation simplifies the result of the weak turbulence approximation without significant further restricting the regime of applicability. We also explore a theory generated by expanding drift and diffusion rates in terms of a presumed small correlation time. This small correlation time expansion leads to results valid for relatively small pitch angle and large wave energy density - a regime that may govern pitchmore » angle scattering of high-energy electrons into the geomagnetic loss cone.« less

Symmetric Positive 4th Order Tensors & Their Estimation from Diffusion Weighted MRI⋆

PubMed Central

Barmpoutis, Angelos; Jian, Bing; Vemuri, Baba C.; Shepherd, Timothy M.

2009-01-01

In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. It is now well known that this 2nd-order approximation fails to approximate complex local tissue structures, such as fibers crossings. In this paper we employ a 4th order symmetric positive semi-definite (PSD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the PSD property. There have been several published articles in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positive semi-definite constraint, which is a fundamental constraint since negative values of the diffusivity coefficients are not meaningful. In our methods, we parameterize the 4th order tensors as a sum of squares of quadratic forms by using the so called Gram matrix method from linear algebra and its relation to the Hilbert’s theorem on ternary quartics. This parametric representation is then used in a nonlinear-least squares formulation to estimate the PSD tensors of order 4 from the data. We define a metric for the higher-order tensors and employ it for regularization across the lattice. Finally, performance of this model is depicted on synthetic data as well as real DW-MRI from an isolated rat hippocampus. PMID:17633709

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

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium.

PubMed

Hibi, Yoshihiko; Kashihara, Ayumi

2018-03-01

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10 -13 to 10 -11  m 2 . The results showed that the Knudsen diffusion coefficient of N 2 (D N2 ) (cm 2 /s) was related to the effective permeability coefficient k e (m 2 ) as D N2  = 7.39 × 10 7 k e 0.767 . Thus, the Knudsen diffusion coefficients of N 2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium. Copyright © 2018 Elsevier B.V. All rights reserved.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium

NASA Astrophysics Data System (ADS)

Hibi, Yoshihiko; Kashihara, Ayumi

2018-03-01

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10-13 to 10-11 m2. The results showed that the Knudsen diffusion coefficient of N2 (DN2) (cm2/s) was related to the effective permeability coefficient ke (m2) as DN2 = 7.39 × 107ke0.767. Thus, the Knudsen diffusion coefficients of N2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium.

Parsing the roles of neck-linker docking and tethered head diffusion in the stepping dynamics of kinesin.

PubMed

Zhang, Zhechun; Goldtzvik, Yonathan; Thirumalai, D

2017-11-14

Kinesin walks processively on microtubules (MTs) in an asymmetric hand-over-hand manner consuming one ATP molecule per 16-nm step. The individual contributions due to docking of the approximately 13-residue neck linker to the leading head (deemed to be the power stroke) and diffusion of the trailing head (TH) that contributes in propelling the motor by 16 nm have not been quantified. We use molecular simulations by creating a coarse-grained model of the MT-kinesin complex, which reproduces the measured stall force as well as the force required to dislodge the motor head from the MT, to show that nearly three-quarters of the step occurs by bidirectional stochastic motion of the TH. However, docking of the neck linker to the leading head constrains the extent of diffusion and minimizes the probability that kinesin takes side steps, implying that both the events are necessary in the motility of kinesin and for the maintenance of processivity. Surprisingly, we find that during a single step, the TH stochastically hops multiple times between the geometrically accessible neighboring sites on the MT before forming a stable interaction with the target binding site with correct orientation between the motor head and the [Formula: see text] tubulin dimer.

Renormalization group analysis of anisotropic diffusion in turbulent shear flows

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Barton, J. Michael

1991-01-01

The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity-scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.

Diffusing light probing of aged wet foams

NASA Astrophysics Data System (ADS)

Slavnetskov, I. O.; Kalacheva, A. V.; Yuvchenko, S. A.; Markova, N. S.; Zimnyakov, D. A.

2018-04-01

Features of diffusing light probes of aged liquid foams are discussed. These probes were carried out using broadband and laser radiation with the wavelength of 532 nm. Experimental data were obtained for aged samples of Gillette shaving cream as a model foamed substance. The coefficients of diffusion and collimated transmittance were applied for characterization of the structural changes in the aged wet foams. Also, the changes in the liquid fraction due to gravitational drainage were monitored using volumometric measurements in the course of the foam aging. Obtained empirical data on the diffuse and collimated transmittance were used as the reference values for correction of the spectral measurements in the visible range with a broadband source of probe light. The problem of correction of the collimated transmittance partially corrupted by the diffusing component of multiply scattered light is discussed.

A numerical study of the steady scalar convective diffusion equation for small viscosity

NASA Technical Reports Server (NTRS)

Giles, M. B.; Rose, M. E.

1983-01-01

A time-independent convection diffusion equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

A variational image-based approach to the correction of susceptibility artifacts in the alignment of diffusion weighted and structural MRI.

PubMed

Tao, Ran; Fletcher, P Thomas; Gerber, Samuel; Whitaker, Ross T

2009-01-01

This paper presents a method for correcting the geometric and greyscale distortions in diffusion-weighted MRI that result from inhomogeneities in the static magnetic field. These inhomogeneities may due to imperfections in the magnet or to spatial variations in the magnetic susceptibility of the object being imaged--so called susceptibility artifacts. Echo-planar imaging (EPI), used in virtually all diffusion weighted acquisition protocols, assumes a homogeneous static field, which generally does not hold for head MRI. The resulting distortions are significant, sometimes more than ten millimeters. These artifacts impede accurate alignment of diffusion images with structural MRI, and are generally considered an obstacle to the joint analysis of connectivity and structure in head MRI. In principle, susceptibility artifacts can be corrected by acquiring (and applying) a field map. However, as shown in the literature and demonstrated in this paper, field map corrections of susceptibility artifacts are not entirely accurate and reliable, and thus field maps do not produce reliable alignment of EPIs with corresponding structural images. This paper presents a new, image-based method for correcting susceptibility artifacts. The method relies on a variational formulation of the match between an EPI baseline image and a corresponding T2-weighted structural image but also specifically accounts for the physics of susceptibility artifacts. We derive a set of partial differential equations associated with the optimization, describe the numerical methods for solving these equations, and present results that demonstrate the effectiveness of the proposed method compared with field-map correction.

On the use of water phantom images to calibrate and correct eddy current induced artefacts in MR diffusion tensor imaging.

PubMed

Bastin, M E; Armitage, P A

2000-07-01

The accurate determination of absolute measures of diffusion anisotropy in vivo using single-shot, echo-planar imaging techniques requires the acquisition of a set of high signal-to-noise ratio, diffusion-weighted images that are free from eddy current induced image distortions. Such geometric distortions can be characterized and corrected in brain imaging data using magnification (M), translation (T), and shear (S) distortion parameters derived from separate water phantom calibration experiments. Here we examine the practicalities of using separate phantom calibration data to correct high b-value diffusion tensor imaging data by investigating the stability of these distortion parameters, and hence the eddy currents, with time. It is found that M, T, and S vary only slowly with time (i.e., on the order of weeks), so that calibration scans need not be performed after every patient examination. This not only minimises the scan time required to collect the calibration data, but also the computational time needed to characterize these eddy current induced distortions. Examples of how measurements of diffusion anisotropy are improved using this post-processing scheme are also presented.

Quantitative Characterization of the Microstructure and Transport Properties of Biopolymer Networks

PubMed Central

Jiao, Yang; Torquato, Salvatore

2012-01-01

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient De and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient De for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation, and the Torquato approximation. The Hashin-Strikman upper bound on the effective diffusion coefficient De and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient De as well as the mean survival time τ, which is related to nuclear magnetic resonance (NMR) relaxation times. Our numerical results for De are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of De for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Yeong and Torquato [J. Chem. Phys. 106, 8814 (1997)]. We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed. PMID:22683739

Phase-field modeling of two-dimensional crystal growth with anisotropic diffusion.

PubMed

Meca, Esteban; Shenoy, Vivek B; Lowengrub, John

2013-11-01

In the present article, we introduce a phase-field model for thin-film growth with anisotropic step energy, attachment kinetics, and diffusion, with second-order (thin-interface) corrections. We are mainly interested in the limit in which kinetic anisotropy dominates, and hence we study how the expected shape of a crystallite, which in the long-time limit is the kinetic Wulff shape, is modified by anisotropic diffusion. We present results that prove that anisotropic diffusion plays an important, counterintuitive role in the evolving crystal shape, and we add second-order corrections to the model that provide a significant increase in accuracy for small supersaturations. We also study the effect of different crystal symmetries and discuss the influence of the deposition rate.

Quantum theory of terahertz conductivity of semiconductor nanostructures

NASA Astrophysics Data System (ADS)

Ostatnický, T.; Pushkarev, V.; Němec, H.; Kužel, P.

2018-02-01

Efficient and controlled charge carrier transport through nanoelements is currently a primordial question in the research of nanoelectronic materials and structures. We develop a quantum-mechanical theory of the conductivity spectra of confined charge carriers responding to an electric field from dc regime up to optical frequencies. The broken translation symmetry induces a broadband drift-diffusion current, which is not taken into account in the analysis based on Kubo formula and relaxation time approximation. We show that this current is required to ensure that the dc conductivity of isolated nanostructures correctly attains zero. It causes a significant reshaping of the conductivity spectra up to terahertz or multiterahertz spectral ranges, where the electron scattering rate is typically comparable to or larger than the probing frequency.

A Simple Noise Correction Scheme for Diffusional Kurtosis Imaging

PubMed Central

Glenn, G. Russell; Tabesh, Ali; Jensen, Jens H.

2014-01-01

Purpose Diffusional kurtosis imaging (DKI) is sensitive to the effects of signal noise due to strong diffusion weightings and higher order modeling of the diffusion weighted signal. A simple noise correction scheme is proposed to remove the majority of the noise bias in the estimated diffusional kurtosis. Methods Weighted linear least squares (WLLS) fitting together with a voxel-wise, subtraction-based noise correction from multiple, independent acquisitions are employed to reduce noise bias in DKI data. The method is validated in phantom experiments and demonstrated for in vivo human brain for DKI-derived parameter estimates. Results As long as the signal-to-noise ratio (SNR) for the most heavily diffusion weighted images is greater than 2.1, errors in phantom diffusional kurtosis estimates are found to be less than 5 percent with noise correction, but as high as 44 percent for uncorrected estimates. In human brain, noise correction is also shown to improve diffusional kurtosis estimates derived from measurements made with low SNR. Conclusion The proposed correction technique removes the majority of noise bias from diffusional kurtosis estimates in noisy phantom data and is applicable to DKI of human brain. Features of the method include computational simplicity and ease of integration into standard WLLS DKI post-processing algorithms. PMID:25172990

Free-Propagator Reweighting Integrator for Single-Particle Dynamics in Reaction-Diffusion Models of Heterogeneous Protein-Protein Interaction Systems

PubMed Central

Hummer, Gerhard

2015-01-01

We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green's function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR) method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions. PMID:26005592

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

Region of Interest Correction Factors Improve Reliability of Diffusion Imaging Measures Within and Across Scanners and Field Strengths

PubMed Central

Venkatraman, Vijay K; Gonzalez, Christopher E.; Landman, Bennett; Goh, Joshua; Reiter, David A.; An, Yang; Resnick, Susan M.

2017-01-01

Diffusion tensor imaging (DTI) measures are commonly used as imaging markers to investigate individual differences in relation to behavioral and health-related characteristics. However, the ability to detect reliable associations in cross-sectional or longitudinal studies is limited by the reliability of the diffusion measures. Several studies have examined reliability of diffusion measures within (i.e. intra-site) and across (i.e. inter-site) scanners with mixed results. Our study compares the test-retest reliability of diffusion measures within and across scanners and field strengths in cognitively normal older adults with a follow-up interval less than 2.25 years. Intra-class correlation (ICC) and coefficient of variation (CoV) of fractional anisotropy (FA) and mean diffusivity (MD) were evaluated in sixteen white matter and twenty-six gray matter bilateral regions. The ICC for intra-site reliability (0.32 to 0.96 for FA and 0.18 to 0.95 for MD in white matter regions; 0.27 to 0.89 for MD and 0.03 to 0.79 for FA in gray matter regions) and inter-site reliability (0.28 to 0.95 for FA in white matter regions, 0.02 to 0.86 for MD in gray matter regions) with longer follow-up intervals were similar to earlier studies using shorter follow-up intervals. The reliability of across field strengths comparisons was lower than intra- and inter-site reliability. Within and across scanner comparisons showed that diffusion measures were more stable in larger white matter regions (> 1500 mm3). For gray matter regions, the MD measure showed stability in specific regions and was not dependent on region size. Linear correction factor estimated from cross-sectional or longitudinal data improved the reliability across field strengths. Our findings indicate that investigations relating diffusion measures to external variables must consider variable reliability across the distinct regions of interest and that correction factors can be used to improve consistency of measurement across field strengths. An important result of this work is that inter-scanner and field strength effects can be partially mitigated with linear correction factors specific to regions of interest. These data-driven linear correction techniques can be applied in cross-sectional or longitudinal studies. PMID:26146196

Effect of respiratory and cardiac gating on the major diffusion-imaging metrics.

PubMed

Hamaguchi, Hiroyuki; Tha, Khin Khin; Sugimori, Hiroyuki; Nakanishi, Mitsuhiro; Nakagawa, Shin; Fujiwara, Taro; Yoshida, Hirokazu; Takamori, Sayaka; Shirato, Hiroki

2016-08-01

The effect of respiratory gating on the major diffusion-imaging metrics and that of cardiac gating on mean kurtosis (MK) are not known. For evaluation of whether the major diffusion-imaging metrics-MK, fractional anisotropy (FA), and mean diffusivity (MD) of the brain-varied between gated and non-gated acquisitions, respiratory-gated, cardiac-gated, and non-gated diffusion-imaging of the brain were performed in 10 healthy volunteers. MK, FA, and MD maps were constructed for all acquisitions, and the histograms were constructed. The normalized peak height and location of the histograms were compared among the acquisitions by use of Friedman and post hoc Wilcoxon tests. The effect of the repetition time (TR) on the diffusion-imaging metrics was also tested, and we corrected for its variation among acquisitions, if necessary. The results showed a shift in the peak location of the MK and MD histograms to the right with an increase in TR (p ≤ 0.01). The corrected peak location of the MK histograms, the normalized peak height of the FA histograms, the normalized peak height and the corrected peak location of the MD histograms varied significantly between the gated and non-gated acquisitions (p < 0.05). These results imply an influence of respiration and cardiac pulsation on the major diffusion-imaging metrics. The gating conditions must be kept identical if reproducible results are to be achieved. © The Author(s) 2016.

Numerical models for the diffuse ionized gas in galaxies. I. Synthetic spectra of thermally excited gas with turbulent magnetic reconnection as energy source

NASA Astrophysics Data System (ADS)

Hoffmann, T. L.; Lieb, S.; Pauldrach, A. W. A.; Lesch, H.; Hultzsch, P. J. N.; Birk, G. T.

2012-08-01

Aims: The aim of this work is to verify whether turbulent magnetic reconnection can provide the additional energy input required to explain the up to now only poorly understood ionization mechanism of the diffuse ionized gas (DIG) in galaxies and its observed emission line spectra. Methods: We use a detailed non-LTE radiative transfer code that does not make use of the usual restrictive gaseous nebula approximations to compute synthetic spectra for gas at low densities. Excitation of the gas is via an additional heating term in the energy balance as well as by photoionization. Numerical values for this heating term are derived from three-dimensional resistive magnetohydrodynamic two-fluid plasma-neutral-gas simulations to compute energy dissipation rates for the DIG under typical conditions. Results: Our simulations show that magnetic reconnection can liberate enough energy to by itself fully or partially ionize the gas. However, synthetic spectra from purely thermally excited gas are incompatible with the observed spectra; a photoionization source must additionally be present to establish the correct (observed) ionization balance in the gas.

Phase stability of TiO 2 polymorphs from diffusion Quantum Monte Carlo

DOE PAGES

Luo, Ye; Benali, Anouar; Shulenburger, Luke; ...

2016-11-24

Titanium dioxide, TiO 2, has multiple applications in catalysis, energy conversion and memristive devices because of its electronic structure. Most of applications utilize the naturally existing phases: rutile, anatase and brookite. In spite of the simple form of TiO 2 and its wide uses, there is long- standing disagreement between theory and experiment on the energetic ordering of these phases that has never been resolved. We present the first analysis of phase stability at zero temperature using the highly accurate many-body fixed node diffusion Quantum Monte Carlo (QMC) method. We include temperature effects by calculating the Helmholtz free energy includingmore » both internal energy corrected by QMC and vibrational contributions from phonon calculations within the quasi harmonic approximation via density functional perturbation theory. Our QMC calculations find that anatase is the most stable phase at zero temperature, consistent with many previous mean- field calculations. Furthermore, at elevated temperatures, rutile becomes the most stable phase. For all finite temperatures, brookite is always the least stable phase.« less

Correction of Altitude-Induced Changes in Performance of the Volumetric Diffusive Respirator

DTIC Science & Technology

2017-04-05

to a plateau pressure. The positive pressure delivery of each percussive pulse is followed by a passive fall in pressure as the spring moves the ...AFRL-SA-WP-SR-2017-0007 Correction of Altitude- Induced Changes in Performance of the Volumetric Diffusive Respirator Thomas...Blakeman, MSc RRT April 2017 Air Force Research Laboratory 711th Human Performance Wing U.S. Air Force School of Aerospace

High-Resolution Multi-Shot Spiral Diffusion Tensor Imaging with Inherent Correction of Motion-Induced Phase Errors

PubMed Central

Truong, Trong-Kha; Guidon, Arnaud

2014-01-01

Purpose To develop and compare three novel reconstruction methods designed to inherently correct for motion-induced phase errors in multi-shot spiral diffusion tensor imaging (DTI) without requiring a variable-density spiral trajectory or a navigator echo. Theory and Methods The first method simply averages magnitude images reconstructed with sensitivity encoding (SENSE) from each shot, whereas the second and third methods rely on SENSE to estimate the motion-induced phase error for each shot, and subsequently use either a direct phase subtraction or an iterative conjugate gradient (CG) algorithm, respectively, to correct for the resulting artifacts. Numerical simulations and in vivo experiments on healthy volunteers were performed to assess the performance of these methods. Results The first two methods suffer from a low signal-to-noise ratio (SNR) or from residual artifacts in the reconstructed diffusion-weighted images and fractional anisotropy maps. In contrast, the third method provides high-quality, high-resolution DTI results, revealing fine anatomical details such as a radial diffusion anisotropy in cortical gray matter. Conclusion The proposed SENSE+CG method can inherently and effectively correct for phase errors, signal loss, and aliasing artifacts caused by both rigid and nonrigid motion in multi-shot spiral DTI, without increasing the scan time or reducing the SNR. PMID:23450457

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: Permeability and diffusivity

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

Chen, Li; Zhang, Lei; Kang, Qinjun

Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsicmore » permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.« less

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: Permeability and diffusivity

DOE PAGES

Chen, Li; Zhang, Lei; Kang, Qinjun; ...

2015-01-28

Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsicmore » permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.« less

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity

PubMed Central

Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan

2015-01-01

Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed. PMID:25627247

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.

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

NASA Astrophysics Data System (ADS)

Kilcrease, D. P.; Brookes, S.

2013-12-01

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. A simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert-Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. We also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.

High accuracy diffuse horizontal irradiance measurements without a shadowband

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

Schlemmer, J.A; Michalsky, J.J.

1995-12-31

The standard method for measuring diffuse horizontal irradiance uses a fixed shadowband to block direct solar radiation. This method requires a correction for the excess skylight blocked by the band, and this correction varies with sky conditions. Alternately, diffuse horizontal irradiance may be calculated from total horizontal and direct normal irradiance. This method is in error because of angular (cosine) response of the total horizontal pyranometer to direct beam irradiance. This paper describes an improved calculation of diffuse horizontal irradiance from total horizontal and direct normal irradiance using a predetermination of the angular response of the total horizontal pyranometer. Wemore » compare these diffuse horizontal irradiance calculations with measurements made with a shading-disk pyranometer that shields direct irradiance using a tracking disk. Results indicate significant improvement in most cases. Remaining disagreement most likely arises from undetected tracking errors and instrument leveling.« less

High accuracy diffuse horizontal irradiance measurements without a shadowband

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

Schlemmer, J.A.; Michalsky, J.J.

1995-10-01

The standard method for measuring diffuse horizontal irradiance uses a fixed shadowband to block direct solar radiation. This method requires a correction for the excess skylight blocked by the band, and this correction varies with sky conditions. Alternately, diffuse horizontal irradiance may be calculated from the total horizontal and direct normal irradiance. This method is in error because of the angular (often referred to as cosine) response of the total horizontal pyranometer to direct beam irradiance. This paper describes an improved calculation of diffuse horizontal irradiance from total horizontal and direct normal irradiance using a predetermination of the angular responsemore » of the total horizontal pyranometer. The authors compare these diffuse horizontal irradiance calculations with measurements made with a shading-disk pyranometer that shields direct irradiance using a tracking disk. The results indicate significant improvement in most cases. The remaining disagreement most likely arises from undetected tracking errors and instrument leveling.« less

Fast Approximations of the Rotational Diffusion Tensor and their Application to Structural Assembly of Molecular Complexes

PubMed Central

Berlin, Konstantin; O’Leary, Dianne P.; Fushman, David

2011-01-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. PMID:21604302

Theoretical studies of floating-reference method for NIR blood glucose sensing

NASA Astrophysics Data System (ADS)

Shi, Zhenzhi; Yang, Yue; Zhao, Huijuan; Chen, Wenliang; Liu, Rong; Xu, Kexin

2011-03-01

Non-invasive blood glucose monitoring using NIR light has been suffered from the variety of optical background that is mainly caused by the change of human body, such as the change of temperature, water concentration, and so on. In order to eliminate these internal influence and external interference a so called floating-reference method has been proposed to provide an internal reference. From the analysis of the diffuse reflectance spectrum, a position has been found where diffuse reflection of light is not sensitive to the glucose concentrations. Our previous work has proved the existence of reference position using diffusion equation. However, since glucose monitoring generally use the NIR light in region of 1000-2000nm, diffusion equation is not valid because of the high absorption coefficient and small source-detector separations. In this paper, steady-state high-order approximate model is used to further investigate the existence of the floating reference position in semi-infinite medium. Based on the analysis of different optical parameters on the impact of spatially resolved reflectance of light, we find that the existence of the floating-reference position is the result of the interaction of optical parameters. Comparing to the results of Monte Carlo simulation, the applicable region of diffusion approximation and higher-order approximation for the calculation of floating-reference position is discussed at the wavelength of 1000nm-1800nm, using the intralipid solution of different concentrations. The results indicate that when the reduced albedo is greater than 0.93, diffusion approximation results are more close to simulation results, otherwise the high order approximation is more applicable.

Fast approximations of the rotational diffusion tensor and their application to structural assembly of molecular complexes.

PubMed

Berlin, Konstantin; O'Leary, Dianne P; Fushman, David

2011-07-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. Copyright © 2011 Wiley-Liss, Inc.

Quantitative model of diffuse speckle contrast analysis for flow measurement.

PubMed

Liu, Jialin; Zhang, Hongchao; Lu, Jian; Ni, Xiaowu; Shen, Zhonghua

2017-07-01

Diffuse speckle contrast analysis (DSCA) is a noninvasive optical technique capable of monitoring deep tissue blood flow. However, a detailed study of the speckle contrast model for DSCA has yet to be presented. We deduced the theoretical relationship between speckle contrast and exposure time and further simplified it to a linear approximation model. The feasibility of this linear model was validated by the liquid phantoms which demonstrated that the slope of this linear approximation was able to rapidly determine the Brownian diffusion coefficient of the turbid media at multiple distances using multiexposure speckle imaging. Furthermore, we have theoretically quantified the influence of optical property on the measurements of the Brownian diffusion coefficient which was a consequence of the fact that the slope of this linear approximation was demonstrated to be equal to the inverse of correlation time of the speckle.

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

NASA Astrophysics Data System (ADS)

Zhao, Xin; Shen, Hayley

2016-11-01

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

Molecular dynamics simulation of real-fluid mutual diffusion coefficients with the Lennard-Jones potential model

NASA Astrophysics Data System (ADS)

Stoker, J. M.; Rowley, R. L.

1989-09-01

Mutual diffusion coefficients for selected alkanes in carbon tetrachloride were calculated using molecular dynamics and Lennard-Jones (LJ) potentials. Use of effective spherical LJ parameters is desirable when possible for two reasons: (i) computer time is saved due to the simplicity of the model and (ii) the number of parameters in the model is kept to a minimum. Results of this study indicate that mutual diffusivity is particularly sensitive to the molecular size cross parameter, σ12, and that the commonly used Lorentz-Berthelot rules are inadequate for mixtures in which the component structures differ significantly. Good agreement between simulated and experimental mutual diffusivities is obtained with a combining rule for σ12 which better represents these asymmetric mixtures using pure component LJ parameters obtained from self-diffusion coefficient data. The effect of alkane chain length on the mutual diffusion coefficient is correctly predicted. While the effects of alkane branching upon the diffusion coefficient are comparable in size to the uncertainty of these calculations, the qualitative trend due to branching is also correctly predicted by the MD results.

Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2017-04-01

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

Reconciling phase diffusion and Hartree-Fock approximation in condensate systems

NASA Astrophysics Data System (ADS)

Giorgi, Gian Luca; de Pasquale, Ferdinando

2012-01-01

Despite the weakly interacting regime, the physics of Bose-Einstein condensates is widely affected by particle-particle interactions. They determine quantum phase diffusion, which is known to be the main cause of loss of coherence. Studying a simple model of two interacting Bose systems, we show how to predict the appearance of phase diffusion beyond the Bogoliubov approximation, providing a self-consistent treatment in the framework of a generalized Hartree-Fock-Bogoliubov perturbation theory.

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

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

Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M.; Dekeyser, W.

2016-01-15

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assumingmore » equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.« less

Higher order corrections to mixed QCD-EW contributions to Higgs boson production in gluon fusion

NASA Astrophysics Data System (ADS)

Bonetti, Marco; Melnikov, Kirill; Tancredi, Lorenzo

2018-03-01

We present an estimate of the next-to-leading-order (NLO) QCD corrections to mixed QCD-electroweak contributions to the Higgs boson production cross section in gluon fusion, combining the recently computed three-loop virtual corrections and the approximate treatment of real emission in the soft approximation. We find that the NLO QCD corrections to the mixed QCD-electroweak contributions are nearly identical to NLO QCD corrections to QCD Higgs production. Our result confirms an earlier estimate of these O (α αs2) effects by Anastasiou et al. [J. High Energy Phys. 04 (2009) 003, 10.1088/1126-6708/2009/04/003] and provides further support for the factorization approximation of QCD and electroweak corrections.

New Method for the Approximation of Corrected Calcium Concentrations in Chronic Kidney Disease Patients.

PubMed

Kaku, Yoshio; Ookawara, Susumu; Miyazawa, Haruhisa; Ito, Kiyonori; Ueda, Yuichirou; Hirai, Keiji; Hoshino, Taro; Mori, Honami; Yoshida, Izumi; Morishita, Yoshiyuki; Tabei, Kaoru

2016-02-01

The following conventional calcium correction formula (Payne) is broadly applied for serum calcium estimation: corrected total calcium (TCa) (mg/dL) = TCa (mg/dL) + (4 - albumin (g/dL)); however, it is inapplicable to chronic kidney disease (CKD) patients. A total of 2503 venous samples were collected from 942 all-stage CKD patients, and levels of TCa (mg/dL), ionized calcium ([iCa(2+) ] mmol/L), phosphate (mg/dL), albumin (g/dL), and pH, and other clinical parameters were measured. We assumed corrected TCa (the gold standard) to be equal to eight times the iCa(2+) value (measured corrected TCa). Then, we performed stepwise multiple linear regression analysis by using the clinical parameters and derived a simple formula for corrected TCa approximation. The following formula was devised from multiple linear regression analysis: Approximated  corrected TCa (mg/dL) = TCa + 0.25 × (4 - albumin) + 4 × (7.4 - p H) + 0.1 × (6 - phosphate) + 0.3. Receiver operating characteristic curves analysis illustrated that area under the curve of approximated corrected TCa for detection of measured corrected TCa ≥ 8.4 mg/dL and ≤ 10.4 mg/dL were 0.994 and 0.919, respectively. The intraclass correlation coefficient demonstrated superior agreement using this new formula compared to other formulas (new formula: 0.826, Payne: 0.537, Jain: 0.312, Portale: 0.582, Ferrari: 0.362). In CKD patients, TCa correction should include not only albumin but also pH and phosphate. The approximated corrected TCa from this formula demonstrates superior agreement with the measured corrected TCa in comparison to other formulas. © 2016 International Society for Apheresis, Japanese Society for Apheresis, and Japanese Society for Dialysis Therapy.

Conditions for extreme sensitivity of protein diffusion in membranes to cell environments

PubMed Central

Tserkovnyak, Yaroslav; Nelson, David R.

2006-01-01

We study protein diffusion in multicomponent lipid membranes close to a rigid substrate separated by a layer of viscous fluid. The large-distance, long-time asymptotics for Brownian motion are calculated by using a nonlinear stochastic Navier–Stokes equation including the effect of friction with the substrate. The advective nonlinearity, neglected in previous treatments, gives only a small correction to the renormalized viscosity and diffusion coefficient at room temperature. We find, however, that in realistic multicomponent lipid mixtures, close to a critical point for phase separation, protein diffusion acquires a strong power-law dependence on temperature and the distance to the substrate H, making it much more sensitive to cell environment, unlike the logarithmic dependence on H and very small thermal correction away from the critical point. PMID:17008402

Rotational Diffusion Depends on Box Size in Molecular Dynamics Simulations.

PubMed

Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

2018-06-07

We show that the rotational dynamics of proteins and nucleic acids determined from molecular dynamics simulations under periodic boundary conditions suffer from significant finite-size effects. We remove the box-size dependence of the rotational diffusion coefficients by adding a hydrodynamic correction k B T/6 ηV with k B Boltzmann's constant, T the absolute temperature, η the solvent shear viscosity, and V the box volume. We show that this correction accounts for the finite-size dependence of the rotational diffusion coefficients of horse-heart myoglobin and a B-DNA dodecamer in aqueous solution. The resulting hydrodynamic radii are in excellent agreement with experiment.

Many-Body Theory of Proton-Generated Point Defects for Losses of Electron Energy and Photons in Quantum Wells

NASA Astrophysics Data System (ADS)

Huang, Danhong; Iurov, Andrii; Gao, Fei; Gumbs, Godfrey; Cardimona, D. A.

2018-02-01

The effects of point defects on the loss of either energies of ballistic electron beams or incident photons are studied by using a many-body theory in a multi-quantum-well system. This theory includes the defect-induced vertex correction to a bare polarization function of electrons within the ladder approximation, and the intralayer and interlayer screening of defect-electron interactions is also taken into account in the random-phase approximation. The numerical results of defect effects on both energy-loss and optical-absorption spectra are presented and analyzed for various defect densities, numbers of quantum wells, and wave vectors. The diffusion-reaction equation is employed for calculating distributions of point defects in a layered structure. For completeness, the production rate for Frenkel-pair defects and their initial concentration are obtained based on atomic-level molecular-dynamics simulations. By combining the defect-effect, diffusion-reaction, and molecular-dynamics models with an available space-weather-forecast model, it will be possible in the future to enable specific designing for electronic and optoelectronic quantum devices that will be operated in space with radiation-hardening protection and, therefore, effectively extend the lifetime of these satellite onboard electronic and optoelectronic devices. Specifically, this theory can lead to a better characterization of quantum-well photodetectors not only for high quantum efficiency and low dark current density but also for radiation tolerance or mitigating the effects of the radiation.

Structural Stability and Defect Energetics of ZnO from Diffusion Quantum Monte Carlo

DOE PAGES

Santana Palacio, Juan A.; Krogel, Jaron T.; Kim, Jeongnim; ...

2015-04-28

We have applied the many-body ab-initio diffusion quantum Monte Carlo (DMC) method to study Zn and ZnO crystals under pressure, and the energetics of the oxygen vacancy, zinc interstitial and hydrogen impurities in ZnO. We show that DMC is an accurate and practical method that can be used to characterize multiple properties of materials that are challenging for density functional theory approximations. DMC agrees with experimental measurements to within 0.3 eV, including the band-gap of ZnO, the ionization potential of O and Zn, and the atomization energy of O2, ZnO dimer, and wurtzite ZnO. DMC predicts the oxygen vacancy asmore » a deep donor with a formation energy of 5.0(2) eV under O-rich conditions and thermodynamic transition levels located between 1.8 and 2.5 eV from the valence band maximum. Our DMC results indicate that the concentration of zinc interstitial and hydrogen impurities in ZnO should be low under n-type, and Zn- and H-rich conditions because these defects have formation energies above 1.4 eV under these conditions. Comparison of DMC and hybrid functionals shows that these DFT approximations can be parameterized to yield a general correct qualitative description of ZnO. However, the formation energy of defects in ZnO evaluated with DMC and hybrid functionals can differ by more than 0.5 eV.« less

Weyl corrections to diffusion and chaos in holography

NASA Astrophysics Data System (ADS)

Li, Wei-Jia; Liu, Peng; Wu, Jian-Pin

2018-04-01

Using holographic methods in the Einstein-Maxwell-dilaton-axion (EMDA) theory, it was conjectured that the thermal diffusion in a strongly coupled metal without quasi-particles saturates an universal lower bound that is associated with the chaotic property of the system at infrared (IR) fixed points [1]. In this paper, we investigate the thermal transport and quantum chaos in the EMDA theory with a small Weyl coupling term. It is found that the Weyl coupling correct the thermal diffusion constant D Q and butterfly velocity v B in different ways, hence resulting in a modified relation between the two at IR fixed points. Unlike that in the EMDA case, our results show that the ratio D Q /( v B 2 τ L ) always contains a non-universal Weyl correction which depends also on the bulk fields as long as the U(1) current is marginally relevant in the IR.

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

PubMed

Strehl, Robert; Ilie, Silvana

2015-12-21

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

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.

Prospective and retrospective high order eddy current mitigation for diffusion weighted echo planar imaging.

PubMed

Xu, Dan; Maier, Joseph K; King, Kevin F; Collick, Bruce D; Wu, Gaohong; Peters, Robert D; Hinks, R Scott

2013-11-01

The proposed method is aimed at reducing eddy current (EC) induced distortion in diffusion weighted echo planar imaging, without the need to perform further image coregistration between diffusion weighted and T2 images. These ECs typically have significant high order spatial components that cannot be compensated by preemphasis. High order ECs are first calibrated at the system level in a protocol independent fashion. The resulting amplitudes and time constants of high order ECs can then be used to calculate imaging protocol specific corrections. A combined prospective and retrospective approach is proposed to apply correction during data acquisition and image reconstruction. Various phantom, brain, body, and whole body diffusion weighted images with and without the proposed method are acquired. Significantly reduced image distortion and misregistration are consistently seen in images with the proposed method compared with images without. The proposed method is a powerful (e.g., effective at 48 cm field of view and 30 cm slice coverage) and flexible (e.g., compatible with other image enhancements and arbitrary scan plane) technique to correct high order ECs induced distortion and misregistration for various diffusion weighted echo planar imaging applications, without the need for further image post processing, protocol dependent prescan, or sacrifice in signal-to-noise ratio. Copyright © 2013 Wiley Periodicals, Inc.

QIN DAWG Validation of Gradient Nonlinearity Bias Correction Workflow for Quantitative Diffusion-Weighted Imaging in Multicenter Trials.

PubMed

Malyarenko, Dariya I; Wilmes, Lisa J; Arlinghaus, Lori R; Jacobs, Michael A; Huang, Wei; Helmer, Karl G; Taouli, Bachir; Yankeelov, Thomas E; Newitt, David; Chenevert, Thomas L

2016-12-01

Previous research has shown that system-dependent gradient nonlinearity (GNL) introduces a significant spatial bias (nonuniformity) in apparent diffusion coefficient (ADC) maps. Here, the feasibility of centralized retrospective system-specific correction of GNL bias for quantitative diffusion-weighted imaging (DWI) in multisite clinical trials is demonstrated across diverse scanners independent of the scanned object. Using corrector maps generated from system characterization by ice-water phantom measurement completed in the previous project phase, GNL bias correction was performed for test ADC measurements from an independent DWI phantom (room temperature agar) at two offset locations in the bore. The precomputed three-dimensional GNL correctors were retrospectively applied to test DWI scans by the central analysis site. The correction was blinded to reference DWI of the agar phantom at magnet isocenter where the GNL bias is negligible. The performance was evaluated from changes in ADC region of interest histogram statistics before and after correction with respect to the unbiased reference ADC values provided by sites. Both absolute error and nonuniformity of the ADC map induced by GNL (median, 12%; range, -35% to +10%) were substantially reduced by correction (7-fold in median and 3-fold in range). The residual ADC nonuniformity errors were attributed to measurement noise and other non-GNL sources. Correction of systematic GNL bias resulted in a 2-fold decrease in technical variability across scanners (down to site temperature range). The described validation of GNL bias correction marks progress toward implementation of this technology in multicenter trials that utilize quantitative DWI.

QIN DAWG Validation of Gradient Nonlinearity Bias Correction Workflow for Quantitative Diffusion-Weighted Imaging in Multicenter Trials

PubMed Central

Malyarenko, Dariya I.; Wilmes, Lisa J.; Arlinghaus, Lori R.; Jacobs, Michael A.; Huang, Wei; Helmer, Karl G.; Taouli, Bachir; Yankeelov, Thomas E.; Newitt, David; Chenevert, Thomas L.

2017-01-01

Previous research has shown that system-dependent gradient nonlinearity (GNL) introduces a significant spatial bias (nonuniformity) in apparent diffusion coefficient (ADC) maps. Here, the feasibility of centralized retrospective system-specific correction of GNL bias for quantitative diffusion-weighted imaging (DWI) in multisite clinical trials is demonstrated across diverse scanners independent of the scanned object. Using corrector maps generated from system characterization by ice-water phantom measurement completed in the previous project phase, GNL bias correction was performed for test ADC measurements from an independent DWI phantom (room temperature agar) at two offset locations in the bore. The precomputed three-dimensional GNL correctors were retrospectively applied to test DWI scans by the central analysis site. The correction was blinded to reference DWI of the agar phantom at magnet isocenter where the GNL bias is negligible. The performance was evaluated from changes in ADC region of interest histogram statistics before and after correction with respect to the unbiased reference ADC values provided by sites. Both absolute error and nonuniformity of the ADC map induced by GNL (median, 12%; range, −35% to +10%) were substantially reduced by correction (7-fold in median and 3-fold in range). The residual ADC nonuniformity errors were attributed to measurement noise and other non-GNL sources. Correction of systematic GNL bias resulted in a 2-fold decrease in technical variability across scanners (down to site temperature range). The described validation of GNL bias correction marks progress toward implementation of this technology in multicenter trials that utilize quantitative DWI. PMID:28105469

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation.

PubMed

Safdari, Hadiseh; Cherstvy, Andrey G; Chechkin, Aleksei V; Bodrova, Anna; Metzler, Ralf

2017-01-01

We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation

NASA Astrophysics Data System (ADS)

Safdari, Hadiseh; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Bodrova, Anna; Metzler, Ralf

2017-01-01

We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

Correlating hydrodynamic radii with that of two-dimensional nanoparticles

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

Yue, Yuan; Kan, Yuwei; Clearfield, Abraham

2015-12-21

Dynamic light scattering (DLS) is one of the most adapted methods to measure the size of nanoparticles, as referred to the hydrodynamic radii (R{sub h}). However, the R{sub h} represents only that of three-dimensional spherical nanoparticles. In the present research, the size of two-dimensional (2D) nanoparticles of yttrium oxide (Y{sub 2}O{sub 3}) and zirconium phosphate (ZrP) was evaluated through comparing their hydrodynamic diameters via DLS with lateral sizes obtained using scanning and transmission electron microscopy. We demonstrate that the hydrodynamic radii are correlated with the lateral sizes of both square and circle shaped 2D nanoparticles. Two proportional coefficients, i.e., correctingmore » factors, are proposed for the Brownian motion status of 2D nanoparticles. The correction is possible by simplifying the calculation of integrals in the case of small thickness approximation. The correcting factor has great significance for investigating the translational diffusion behavior of 2D nanoparticles in a liquid and in effective and low-cost measurement in terms of size and morphology of shape-specific nanoparticles.« less

Reduced xenon diffusion for quantitative lung study--the role of SF(6)

NASA Technical Reports Server (NTRS)

Mair, R. W.; Hoffmann, D.; Sheth, S. A.; Wong, G. P.; Butler, J. P.; Patz, S.; Topulos, G. P.; Walsworth, R. L.

2000-01-01

The large diffusion coefficients of gases result in significant spin motion during the application of gradient pulses that typically last a few milliseconds in most NMR experiments. In restricted environments, such as the lung, this rapid gas diffusion can lead to violations of the narrow pulse approximation, a basic assumption of the standard Stejskal-Tanner NMR method of diffusion measurement. We therefore investigated the effect of a common, biologically inert buffer gas, sulfur hexafluoride (SF(6)), on (129)Xe NMR and diffusion. We found that the contribution of SF(6) to (129)Xe T(1) relaxation in a 1:1 xenon/oxygen mixture is negligible up to 2 bar of SF(6) at standard temperature. We also measured the contribution of SF(6) gas to (129)Xe T(2) relaxation, and found it to scale inversely with pressure, with this contribution approximately equal to 1 s for 1 bar SF(6) pressure and standard temperature. Finally, we found the coefficient of (129)Xe diffusion through SF(6) to be approximately 4.6 x 10(-6) m(2)s(-1) for 1 bar pressure of SF(6) and standard temperature, which is only 1.2 times smaller than the (129)Xe self diffusion coefficient for 1 bar (129)Xe pressure and standard temperature. From these measurements we conclude that SF(6) will not sufficiently reduce (129)Xe diffusion to allow accurate surface-area/volume ratio measurements in human alveoli using time-dependent gas diffusion NMR.

Retrospective correction of bias in diffusion tensor imaging arising from coil combination mode.

PubMed

Sakaie, Ken; Lowe, Mark

2017-04-01

To quantify and retrospectively correct for systematic differences in diffusion tensor imaging (DTI) measurements due to differences in coil combination mode. Multi-channel coils are now standard among MRI systems. There are several options for combining signal from multiple coils during image reconstruction, including sum-of-squares (SOS) and adaptive combine (AC). This contribution examines the bias between SOS- and AC-derived measures of tissue microstructure and a strategy for limiting that bias. Five healthy subjects were scanned under an institutional review board-approved protocol. Each set of raw image data was reconstructed twice-once with SOS and once with AC. The diffusion tensor was calculated from SOS- and AC-derived data by two algorithms-standard log-linear least squares and an approach that accounts for the impact of coil combination on signal statistics. Systematic differences between SOS and AC in terms of tissue microstructure (axial diffusivity, radial diffusivity, mean diffusivity and fractional anisotropy) were evaluated on a voxel-by-voxel basis. SOS-based tissue microstructure values are systematically lower than AC-based measures throughout the brain in each subject when using the standard tensor calculation method. The difference between SOS and AC can be virtually eliminated by taking into account the signal statistics associated with coil combination. The impact of coil combination mode on diffusion tensor-based measures of tissue microstructure is statistically significant but can be corrected retrospectively. The ability to do so is expected to facilitate pooling of data among imaging protocols. Copyright © 2016 Elsevier Inc. All rights reserved.

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

DOE PAGES

Kilcrease, D. P.; Brookes, S.

2013-08-19

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. Additionally, a simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure formore » the Born cross-sections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. Furthermore, we also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.« less

Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model

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

Knessl, C.; Tier, C.

1999-10-01

In Part 1 the authors formulated and solved a diffusion model for two tandem queues with exponential servers and general renewal arrivals. They thus obtained the easy traffic diffusion approximation to the steady state joint queue length distribution for this network. Here they study asymptotic and numerical properties of the diffusion approximation. In particular, analytical expressions are obtained for the tail probabilities. Both the joint distribution of the two queues and the marginal distribution of the second queue are considered. They also give numerical illustrations of how this marginal is affected by changes in the arrival and service processes.

Ion-Scale Structure in Mercury's Magnetopause Reconnection Diffusion Region

NASA Technical Reports Server (NTRS)

Gershman, Daniel J.; Dorelli, John C.; DiBraccio, Gina A.; Raines, Jim M.; Slavin, James A.; Poh, Gangkai; Zurbuchen, Thomas H.

2016-01-01

The strength and time dependence of the electric field in a magnetopause diffusion region relate to the rate of magnetic reconnection between the solar wind and a planetary magnetic field. Here we use approximately 150 milliseconds measurements of energetic electrons from the Mercury Surface, Space Environment, GEochemistry, and Ranging (MESSENGER) spacecraft observed over Mercury's dayside polar cap boundary (PCB) to infer such small-scale changes in magnetic topology and reconnection rates. We provide the first direct measurement of open magnetic topology in flux transfer events at Mercury, structures thought to account for a significant portion of the open magnetic flux transport throughout the magnetosphere. In addition, variations in PCB latitude likely correspond to intermittent bursts of approximately 0.3 to 3 millivolts per meter reconnection electric fields separated by approximately 5 to10 seconds, resulting in average and peak normalized dayside reconnection rates of approximately 0.02 and approximately 0.2, respectively. These data demonstrate that structure in the magnetopause diffusion region at Mercury occurs at the smallest ion scales relevant to reconnection physics.

[Joint correction for motion artifacts and off-resonance artifacts in multi-shot diffusion magnetic resonance imaging].

PubMed

Wu, Wenchuan; Fang, Sheng; Guo, Hua

2014-06-01

Aiming at motion artifacts and off-resonance artifacts in multi-shot diffusion magnetic resonance imaging (MRI), we proposed a joint correction method in this paper to correct the two kinds of artifacts simultaneously without additional acquisition of navigation data and field map. We utilized the proposed method using multi-shot variable density spiral sequence to acquire MRI data and used auto-focusing technique for image deblurring. We also used direct method or iterative method to correct motion induced phase errors in the process of deblurring. In vivo MRI experiments demonstrated that the proposed method could effectively suppress motion artifacts and off-resonance artifacts and achieve images with fine structures. In addition, the scan time was not increased in applying the proposed method.

The role of hypothetico-deductive reasoning and physical analogues of molecular interactions in conceptual change

NASA Astrophysics Data System (ADS)

Lawson, Anton E.; Baker, William P.; Didonato, Lisa; Verdi, Michael P.; Johnson, Margaret A.

Two hypotheses about theoretical concept acquisition, application, and change were tested. College biology students classified as intuitive, transitional, or reflective (hypothetico-deductive) reasoners were first taught two theoretical concepts (molecular polarity and bonding) to explain the mixing of dye with water, but not with oil, when all three were shaken in a container. The students were then tested in a context in which they misapplied the concepts in an attempt to explain the gradual spread of blue dye in standing water. Next students were taught another theoretical concept (diffusion), with and without the use of physical analogues. They were retested to see which students acquired the concept of diffusion and which students changed from use of the incorrect polarity and bonding concepts (i.e., the misconceptions) to use of the diffusion concept to correctly explain the dye's gradual spread. As predicted, the experimental/analogy group scored significantly higher than the control group on a posttest question that required the definition of diffusion. Also as predicted, hypothetico-deductive reasoning skill was significantly related to correct application of the diffusion concept and to a change from the misapplication of the polarity and bonding concepts to the correct application of the diffusion concept to explain the gradual spread of the blue dye. Thus, the results support the hypotheses that physical analogues are helpful in theoretical concept acquisition and that hypothetico-deductive reasoning is needed for successful concept application and change. Educational implications are drawn.

Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation

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

Traytak, Sergey D., E-mail: sergtray@mail.ru; Le STUDIUM; Semenov Institute of Chemical Physics RAS, 4 Kosygina St., 117977 Moscow

The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problemmore » and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.« less

Thermal transport at the nanoscale: A Fourier's law vs. phonon Boltzmann equation study

NASA Astrophysics Data System (ADS)

Kaiser, J.; Feng, T.; Maassen, J.; Wang, X.; Ruan, X.; Lundstrom, M.

2017-01-01

Steady-state thermal transport in nanostructures with dimensions comparable to the phonon mean-free-path is examined. Both the case of contacts at different temperatures with no internal heat generation and contacts at the same temperature with internal heat generation are considered. Fourier's law results are compared to finite volume method solutions of the phonon Boltzmann equation in the gray approximation. When the boundary conditions are properly specified, results obtained using Fourier's law without modifying the bulk thermal conductivity are in essentially exact quantitative agreement with the phonon Boltzmann equation in the ballistic and diffusive limits. The errors between these two limits are examined in this paper. For the four cases examined, the error in the apparent thermal conductivity as deduced from a correct application of Fourier's law is less than 6%. We also find that the Fourier's law results presented here are nearly identical to those obtained from a widely used ballistic-diffusive approach but analytically much simpler. Although limited to steady-state conditions with spatial variations in one dimension and to a gray model of phonon transport, the results show that Fourier's law can be used for linear transport from the diffusive to the ballistic limit. The results also contribute to an understanding of how heat transport at the nanoscale can be understood in terms of the conceptual framework that has been established for electron transport at the nanoscale.

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

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

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

2015-12-21

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

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

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

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM, Trilateral Euregio Cluster, P.O. Box 1207, 3430 BE Nieuwegein

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possiblemore » to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part II, cylindrical approximations are treated for heat waves traveling towards the plasma edge assuming a semi-infinite domain.« less

Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory.

PubMed

Contini, D; Martelli, F; Zaccanti, G

1997-07-01

The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.

Computation of Steady and Unsteady Laminar Flames: Theory

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Radhakrishnan, Krishnan; Zhou, Ruhai

1999-01-01

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

Structural, electronic, and dynamical properties of liquid water by ab initio molecular dynamics based on SCAN functional within the canonical ensemble

NASA Astrophysics Data System (ADS)

Zheng, Lixin; Chen, Mohan; Sun, Zhaoru; Ko, Hsin-Yu; Santra, Biswajit; Dhuvad, Pratikkumar; Wu, Xifan

2018-04-01

We perform ab initio molecular dynamics (AIMD) simulation of liquid water in the canonical ensemble at ambient conditions using the strongly constrained and appropriately normed (SCAN) meta-generalized-gradient approximation (GGA) functional approximation and carry out systematic comparisons with the results obtained from the GGA-level Perdew-Burke-Ernzerhof (PBE) functional and Tkatchenko-Scheffler van der Waals (vdW) dispersion correction inclusive PBE functional. We analyze various properties of liquid water including radial distribution functions, oxygen-oxygen-oxygen triplet angular distribution, tetrahedrality, hydrogen bonds, diffusion coefficients, ring statistics, density of states, band gaps, and dipole moments. We find that the SCAN functional is generally more accurate than the other two functionals for liquid water by not only capturing the intermediate-range vdW interactions but also mitigating the overly strong hydrogen bonds prescribed in PBE simulations. We also compare the results of SCAN-based AIMD simulations in the canonical and isothermal-isobaric ensembles. Our results suggest that SCAN provides a reliable description for most structural, electronic, and dynamical properties in liquid water.

Fokker-Planck description of electron and photon transport in homogeneous media

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

Akcasu, A.Z.; Holloway, J.P.

1997-06-01

Starting from a Fokker-Planck description of particle transport, which is valid when the scattering is forwardly peaked and the energy change in scattering is small, we systematically obtain an approximate diffusionlike equation for the particle density by eliminating the direction variable {bold {cflx {Omega}}} with an elimination scheme based on Zwanzig{close_quote}s projection operator formalism in the interaction representation. The elimination procedure closely follows one described by Grigolini and Marchesoni [in {ital Memory Function Approaches to Stochastic Problems in Condensed Matter}, edited by Myron W. Evans, Paolo Grigolini, and Guiseppe P. Parravicini, Advances in Physical Chemistry, Vol. 62 (Wiley-Interscience, New York,more » 1985), Chap. II, p. 29], but with a different projection operator. The resulting diffusion equation is correct up to the second order in the coupling operator between the particle direction and position variable. The diffusion coefficients and mobility in the resulting diffusion equation depend on the initial distribution of the particles in direction and on the path length traveled by the particles. The full solution is obtained for a monoenergetic and monodirectional pulsed point source of particles in an infinite homogeneous medium. This solution is used to study the penetration and the transverse and longitudinal spread of the particles as they are transported through the medium. Application to diffusive wave spectroscopy in calculating the path-length distribution of photons, as well as application to dose calculations in tissue due to an electron beam are mentioned. {copyright} {ital 1997} {ital The American Physical Society}« less

Kinetic Monte Carlo simulations of electrodeposition: Crossover from continuous to instantaneous homogeneous nucleation within Avrami’s law

NASA Astrophysics Data System (ADS)

Frank, Stefan; Rikvold, Per Arne

2006-06-01

The influence of lateral adsorbate diffusion on the dynamics of the first-order phase transition in a two-dimensional Ising lattice gas with attractive nearest-neighbor interactions is investigated by means of kinetic Monte Carlo simulations. For example, electrochemical underpotential deposition proceeds by this mechanism. One major difference from adsorption in vacuum surface science is that under control of the electrode potential and in the absence of mass-transport limitations, local adsorption equilibrium is approximately established. We analyze our results using the theory of Kolmogorov, Johnson and Mehl, and Avrami (KJMA), which we extend to an exponentially decaying nucleation rate. Such a decay may occur due to a suppression of nucleation around existing clusters in the presence of lateral adsorbate diffusion. Correlation functions prove the existence of such exclusion zones. By comparison with microscopic results for the nucleation rate I and the interface velocity of the growing clusters v, we can show that the KJMA theory yields the correct order of magnitude for Iv2. This is true even though the spatial correlations mediated by diffusion are neglected. The decaying nucleation rate causes a gradual crossover from continuous to instantaneous nucleation, which is complete when the decay of the nucleation rate is very fast on the time scale of the phase transformation. Hence, instantaneous nucleation can be homogeneous, producing negative minima in the two-point correlation functions. We also present in this paper an n-fold way Monte Carlo algorithm for a square lattice gas with adsorption/desorption and lateral diffusion.

Airborne detection of diffuse carbon dioxide emissions at Mammoth Mountain, California

USGS Publications Warehouse

Gerlach, T.M.; Doukas, M.P.; McGee, K.A.; Kessler, R.

1999-01-01

We report the first airborne detection of CO2 degassing from diffuse volcanic sources. Airborne measurement of diffuse CO2 degassing offers a rapid alternative for monitoring CO2 emission rates at Mammoth Mountain. CO2 concentrations, temperatures, and barometric pressures were measured at ~2,500 GPS-referenced locations during a one-hour, eleven-orbit survey of air around Mammoth Mountain at ~3 km from the summit and altitudes of 2,895-3,657 m. A volcanic CO2 anomaly 4-5 km across with CO2 levels ~1 ppm above background was revealed downwind of tree-kill areas. It contained a 1-km core with concentrations exceeding background by >3 ppm. Emission rates of ~250 t d-1 are indicated. Orographic winds may play a key role in transporting the diffusely degassed CO2 upslope to elevations where it is lofted into the regional wind system.We report the first airborne detection of CO2 degassing from diffuse volcanic sources. Airborne measurement of diffuse CO2 degassing offers a rapid alternative for monitoring CO2 emission rates at Mammoth Mountain. CO2 concentrations, temperatures, and barometric pressures were measured at approximately 2,500 GPS-referenced locations during a one-hour, eleven-orbit survey of air around Mammoth Mountain at approximately 3 km from the summit and altitudes of 2,895-3,657 m. A volcanic CO2 anomaly 4-5 km across with CO2 levels approximately 1 ppm above background was revealed downwind of tree-kill areas. It contained a 1-km core with concentrations exceeding background by >3 ppm. Emission rates of approximately 250 t d-1 are indicated. Orographic winds may play a key role in transporting the diffusely degassed CO2 upslope to elevations where it is lofted into the regional wind system.

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Indispensable finite time corrections for Fokker-Planck equations from time series data.

PubMed

Ragwitz, M; Kantz, H

2001-12-17

The reconstruction of Fokker-Planck equations from observed time series data suffers strongly from finite sampling rates. We show that previously published results are degraded considerably by such effects. We present correction terms which yield a robust estimation of the diffusion terms, together with a novel method for one-dimensional problems. We apply these methods to time series data of local surface wind velocities, where the dependence of the diffusion constant on the state variable shows a different behavior than previously suggested.

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.

Development and pilot line production of lithium doped silicon solar cells

NASA Technical Reports Server (NTRS)

Payne, P. A.

1972-01-01

Scaling up the BCl3 without O2 diffusion beyond 30 to 40 cells was investigated by using a 100 cell capacity diffusion boat which held the cells vertically. Sheet resistances and I-V curves were uniform with 10 to 20 cells spaced along the entire boat, so the quantity was increased to 40 and then 60 cells per diffusion. There was no change in cell output and uniformity going from 20 to 40 cells per diffusion; however only half the lithium cells fabricated from slices diffused in the 60 cell diffusion had efficiencies of 11% or better. Although uniform sheet resistances and I-V characteristic curves were obtained with up to 60 cells in the BCl3 with O2 diffusion, the short circuit currents were approximately 15% lower than the anticipated 135 to 140 mA. Consequently, work on this diffusion process has been aimed solely at increasing the short circuit current. The diffusion temperature was lowered from 1055 to 1000 and 950 C, and at each of these temperatures variations in diffusion time were investigated. At 1000 C short circuit currents were approximately 10 mA higher, 130 rather than 120 mA average.

Modelling the effect of diffuse light on canopy photosynthesis in controlled environments

NASA Technical Reports Server (NTRS)

Cavazzoni, James; Volk, Tyler; Tubiello, Francesco; Monje, Oscar; Janes, H. W. (Principal Investigator)

2002-01-01

A layered canopy model was used to analyze the effects of diffuse light on canopy gross photosynthesis in controlled environment plant growth chambers, where, in contrast to the field, highly diffuse light can occur at high irradiance. The model suggests that high diffuse light fractions (approximately 0.7) and irradiance (1400 micromoles m-2 s-1) may enhance crop life-cycle canopy gross photosynthesis for hydroponic wheat by about 20% compared to direct light at the same irradiance. Our simulations suggest that high accuracy is not needed in specifying diffuse light fractions in chambers between approximately 0.7 and 1, because simulated photosynthesis for closed canopies plateau in this range. We also examined the effect of leaf angle distribution on canopy photosynthesis under growth chamber conditions, as these distributions determine canopy extinction coefficients for direct and diffuse light. We show that the spherical leaf angle distribution is not suitable for modeling photosynthesis of planophile canopies (e.g., soybean and peanut) in growth chambers. Also, the absorption of the light reflected from the surface below the canopy should generally be included in model simulations, as the corresponding albedo values in the photosynthetically active range may be quite high in growth chambers (e.g., approximately 0.5). In addition to the modeling implications, our results suggest that diffuse light conditions should be considered when drawing conclusions from experiments in controlled environments.

High-throughput ab-initio dilute solute diffusion database.

PubMed

Wu, Henry; Mayeshiba, Tam; Morgan, Dane

2016-07-19

We demonstrate automated generation of diffusion databases from high-throughput density functional theory (DFT) calculations. A total of more than 230 dilute solute diffusion systems in Mg, Al, Cu, Ni, Pd, and Pt host lattices have been determined using multi-frequency diffusion models. We apply a correction method for solute diffusion in alloys using experimental and simulated values of host self-diffusivity. We find good agreement with experimental solute diffusion data, obtaining a weighted activation barrier RMS error of 0.176 eV when excluding magnetic solutes in non-magnetic alloys. The compiled database is the largest collection of consistently calculated ab-initio solute diffusion data in the world.

A simple but fully nonlocal correction to the random phase approximation

NASA Astrophysics Data System (ADS)

Ruzsinszky, Adrienn; Perdew, John P.; Csonka, Gábor I.

2011-03-01

The random phase approximation (RPA) stands on the top rung of the ladder of ground-state density functional approximations. The simple or direct RPA has been found to predict accurately many isoelectronic energy differences. A nonempirical local or semilocal correction to this direct RPA leaves isoelectronic energy differences almost unchanged, while improving total energies, ionization energies, etc., but fails to correct the RPA underestimation of molecular atomization energies. Direct RPA and its semilocal correction may miss part of the middle-range multicenter nonlocality of the correlation energy in a molecule. Here we propose a fully nonlocal, hybrid-functional-like addition to the semilocal correction. The added full nonlocality is important in molecules, but not in atoms. Under uniform-density scaling, this fully nonlocal correction scales like the second-order-exchange contribution to the correlation energy, an important part of the correction to direct RPA, and like the semilocal correction itself. For the atomization energies of ten molecules, and with the help of one fit parameter, it performs much better than the elaborate second-order screened exchange correction.

Lateral diffusion of rhodopsin in photoreceptor membrane: a reappraisal.

PubMed

Govardovskii, Victor I; Korenyak, Darya A; Shukolyukov, Sergei A; Zueva, Lidia V

2009-08-28

In a series of works between 1972 and 1984, it was established that rhodopsin undergoes rotational and lateral Brownian motion in the plane of photoreceptor membrane. The concept of free movement of proteins of phototransduction cascade is an essential principle of the present scheme of vertebrate phototransduction. This has recently been challenged by findings that show that in certain conditions rhodopsin in the membrane may be dimeric and form extended areas of paracrystalline organization. Such organization seems incompatible with earlier data on free rhodopsin diffusion. Thus we decided to reinvestigate lateral diffusion of rhodopsin and products of its photolysis in photoreceptor membrane specifically looking for indications of possible oligomeric organization. Diffusion exchange by rhodopsin and its photoproducts between bleached and unbleached halves of rod outer segment was traced using high-speed dichroic microspectrophotometer. Measurements were conducted on amphibian (frog, toad, and salamander) and gecko rods. We found that the curves that are supposed to reflect the process of diffusion equilibration of rhodopsin in nonuniformly bleached outer segment largely show production of long-lived bleaching intermediate, metarhodopsin III (Meta III). After experimental elimination of Meta III contribution, we observed rhodopsin equilibration time constant was threefold to tenfold longer than estimated previously. However, after proper correction for the geometry of rod discs, it translates into generally accepted value of diffusion constant of approximately 5 x 10(-9) cm(2) s(-1). Yet, we found that there exists an immobile rhodopsin fraction whose size can vary from virtually zero to 100%, depending on poorly defined factors. Controls suggest that the formation of the immobile fraction is not due to fragmentation of rod outer segment discs but supposedly reflects oligomerization of rhodopsin. Implications of the new findings for the present model of phototransduction are discussed. We hypothesize that formation of paracrystalline areas, if controlled physiologically, could be an extra mechanism of cascade regulation.

The rationale for microcirculatory guided fluid therapy.

PubMed

Ince, Can

2014-06-01

The ultimate purpose of fluid administration in states of hypovolemia is to correct cardiac output to improve microcirculatory perfusion and tissue oxygenation. Observation of the microcirculation using handheld microscopes gives insight into the nature of convective and diffusive defect in hypovolemia. The purpose of this article is to introduce a new platform for hemodynamic-targeted fluid therapy based on the correction of tissue and microcirculatory perfusion assumed to be at risk during hypovolemia. Targeting systemic hemodynamic targets and/or clinical surrogates of hypovolemia gives inadequate guarantee for the correction of tissue perfusion by fluid therapy especially in conditions of distributive shock as occur in inflammation and sepsis. Findings are presented, which support the idea that only clinical signs of hypovolemia associated with low microcirculatory flow can be expected to benefit from fluid therapy and that fluid overload causes a defect in the diffusion of oxygen transport. We hypothesized that the optimal amount of fluid needed for correction of hypovolemia is defined by a physiologically based functional microcirculatory hemodynamic platform where convection and diffusion need to be optimized. Future clinical trials using handheld microscopes able to automatically evaluate the microcirculation at the bedside will show whether such a platform will indeed optimize fluid therapy.

Parameter Variability and Distributional Assumptions in the Diffusion Model

ERIC Educational Resources Information Center

Ratcliff, Roger

2013-01-01

If the diffusion model (Ratcliff & McKoon, 2008) is to account for the relative speeds of correct responses and errors, it is necessary that the components of processing identified by the model vary across the trials of a task. In standard applications, the rate at which information is accumulated by the diffusion process is assumed to be normally…

Interpreting the Weibull fitting parameters for diffusion-controlled release data

NASA Astrophysics Data System (ADS)

Ignacio, Maxime; Chubynsky, Mykyta V.; Slater, Gary W.

2017-11-01

We examine the diffusion-controlled release of molecules from passive delivery systems using both analytical solutions of the diffusion equation and numerically exact Lattice Monte Carlo data. For very short times, the release process follows a √{ t } power law, typical of diffusion processes, while the long-time asymptotic behavior is exponential. The crossover time between these two regimes is determined by the boundary conditions and initial loading of the system. We show that while the widely used Weibull function provides a reasonable fit (in terms of statistical error), it has two major drawbacks: (i) it does not capture the correct limits and (ii) there is no direct connection between the fitting parameters and the properties of the system. Using a physically motivated interpolating fitting function that correctly includes both time regimes, we are able to predict the values of the Weibull parameters which allows us to propose a physical interpretation.

A Monte Carlo Study on the Performance of a Corrected Formula for Epsilon Approximate Suggested by Lecoutre.

ERIC Educational Resources Information Center

Chen, Ru San; Dunlap, William P.

1994-01-01

The present simulation study confirms that the corrected epsilon approximate test of B. Lecoutre yields a less biased estimation of population epsilon and reduces Type I error rates when compared to the epsilon approximate test of H. Huynh and L. S. Feldt. (SLD)

Diffusion length measurements of thin GaAs solar cells by means of energetic electrons

NASA Technical Reports Server (NTRS)

Vonross, O.

1980-01-01

A calculation of the short circuit current density (j sub sc) of a thin GaAs solar cell induced by fast electrons is presented. It is shown that in spite of the disparity in thickness between the N-type portion of the junction and the P-type portion of the junction, the measurement of the bulk diffusion length L sub p of the N-type part of the junction is seriously hampered due to the presence of a sizable contribution to the j sub sc from the P-type region of the junction. Corrections of up to 50% had to be made in order to interpret the data correctly. Since these corrections were not amenable to direct measurements it is concluded that the electron beam method for the determination of the bulk minority carrier diffusion length, which works so well for Si solar cells, is a poor method when applied to thin GaAs cells.

Minimisation of Signal Intensity Differences in Distortion Correction Approaches of Brain Magnetic Resonance Diffusion Tensor Imaging.

PubMed

Lee, Dong-Hoon; Lee, Do-Wan; Henry, David; Park, Hae-Jin; Han, Bong-Soo; Woo, Dong-Cheol

2018-04-12

To evaluate the effects of signal intensity differences between the b0 image and diffusion tensor imaging (DTI) in the image registration process. To correct signal intensity differences between the b0 image and DTI data, a simple image intensity compensation (SIMIC) method, which is a b0 image re-calculation process from DTI data, was applied before the image registration. The re-calculated b0 image (b0 ext ) from each diffusion direction was registered to the b0 image acquired through the MR scanning (b0 nd ) with two types of cost functions and their transformation matrices were acquired. These transformation matrices were then used to register the DTI data. For quantifications, the dice similarity coefficient (DSC) values, diffusion scalar matrix, and quantified fibre numbers and lengths were calculated. The combined SIMIC method with two cost functions showed the highest DSC value (0.802 ± 0.007). Regarding diffusion scalar values and numbers and lengths of fibres from the corpus callosum, superior longitudinal fasciculus, and cortico-spinal tract, only using normalised cross correlation (NCC) showed a specific tendency toward lower values in the brain regions. Image-based distortion correction with SIMIC for DTI data would help in image analysis by accounting for signal intensity differences as one additional option for DTI analysis. • We evaluated the effects of signal intensity differences at DTI registration. • The non-diffusion-weighted image re-calculation process from DTI data was applied. • SIMIC can minimise the signal intensity differences at DTI registration.

Automated correction of improperly rotated diffusion gradient orientations in diffusion weighted MRI.

PubMed

Jeurissen, Ben; Leemans, Alexander; Sijbers, Jan

2014-10-01

Ensuring one is using the correct gradient orientations in a diffusion MRI study can be a challenging task. As different scanners, file formats and processing tools use different coordinate frame conventions, in practice, users can end up with improperly oriented gradient orientations. Using such wrongly oriented gradient orientations for subsequent diffusion parameter estimation will invalidate all rotationally variant parameters and fiber tractography results. While large misalignments can be detected by visual inspection, small rotations of the gradient table (e.g. due to angulation of the acquisition plane), are much more difficult to detect. In this work, we propose an automated method to align the coordinate frame of the gradient orientations with that of the corresponding diffusion weighted images, using a metric based on whole brain fiber tractography. By transforming the gradient table and measuring the average fiber trajectory length, we search for the transformation that results in the best global 'connectivity'. To ensure a fast calculation of the metric we included a range of algorithmic optimizations in our tractography routine. To make the optimization routine robust to spurious local maxima, we use a stochastic optimization routine that selects a random set of seed points on each evaluation. Using simulations, we show that our method can recover the correct gradient orientations with high accuracy and precision. In addition, we demonstrate that our technique can successfully recover rotated gradient tables on a wide range of clinically realistic data sets. As such, our method provides a practical and robust solution to an often overlooked pitfall in the processing of diffusion MRI. Copyright © 2014 Elsevier B.V. All rights reserved.

Fiberfox: facilitating the creation of realistic white matter software phantoms.

PubMed

Neher, Peter F; Laun, Frederik B; Stieltjes, Bram; Maier-Hein, Klaus H

2014-11-01

Phantom-based validation of diffusion-weighted image processing techniques is an important key to innovation in the field and is widely used. Openly available and user friendly tools for the flexible generation of tailor-made datasets for the specific tasks at hand can greatly facilitate the work of researchers around the world. We present an open-source framework, Fiberfox, that enables (1) the intuitive definition of arbitrary artificial white matter fiber tracts, (2) signal generation from those fibers by means of the most recent multi-compartment modeling techniques, and (3) simulation of the actual MR acquisition that allows for the introduction of realistic MRI-related effects into the final image. We show that real acquisitions can be closely approximated by simulating the acquisition of the well-known FiberCup phantom. We further demonstrate the advantages of our framework by evaluating the effects of imaging artifacts and acquisition settings on the outcome of 12 tractography algorithms. Our findings suggest that experiments on a realistic software phantom might change the conclusions drawn from earlier hardware phantom experiments. Fiberfox may find application in validating and further developing methods such as tractography, super-resolution, diffusion modeling or artifact correction. Copyright © 2013 Wiley Periodicals, Inc.

Variable diffusion in stock market fluctuations

NASA Astrophysics Data System (ADS)

Hua, Jia-Chen; Chen, Lijian; Falcon, Liberty; McCauley, Joseph L.; Gunaratne, Gemunu H.

2015-02-01

We analyze intraday fluctuations in several stock indices to investigate the underlying stochastic processes using techniques appropriate for processes with nonstationary increments. The five most actively traded stocks each contains two time intervals during the day where the variance of increments can be fit by power law scaling in time. The fluctuations in return within these intervals follow asymptotic bi-exponential distributions. The autocorrelation function for increments vanishes rapidly, but decays slowly for absolute and squared increments. Based on these results, we propose an intraday stochastic model with linear variable diffusion coefficient as a lowest order approximation to the real dynamics of financial markets, and to test the effects of time averaging techniques typically used for financial time series analysis. We find that our model replicates major stylized facts associated with empirical financial time series. We also find that ensemble averaging techniques can be used to identify the underlying dynamics correctly, whereas time averages fail in this task. Our work indicates that ensemble average approaches will yield new insight into the study of financial markets' dynamics. Our proposed model also provides new insight into the modeling of financial markets dynamics in microscopic time scales.

Distortion correction for diffusion-weighted MRI tractography and fMRI in the temporal lobes.

PubMed

Embleton, Karl V; Haroon, Hamied A; Morris, David M; Ralph, Matthew A Lambon; Parker, Geoff J M

2010-10-01

Single shot echo-planar imaging (EPI) sequences are currently the most commonly used sequences for diffusion-weighted imaging (DWI) and functional magnetic resonance imaging (fMRI) as they allow relatively high signal to noise with rapid acquisition time. A major drawback of EPI is the substantial geometric distortion and signal loss that can occur due to magnetic field inhomogeneities close to air-tissue boundaries. If DWI-based tractography and fMRI are to be applied to these regions, then the distortions must be accurately corrected to achieve meaningful results. We describe robust acquisition and processing methods for correcting such distortions in spin echo (SE) EPI using a variant of the reversed direction k space traversal method with a number of novel additions. We demonstrate that dual direction k space traversal with maintained diffusion-encoding gradient strength and direction results in correction of the great majority of eddy current-associated distortions in DWI, in addition to those created by variations in magnetic susceptibility. We also provide examples to demonstrate that the presence of severe distortions cannot be ignored if meaningful tractography results are desired. The distortion correction routine was applied to SE-EPI fMRI acquisitions and allowed detection of activation in the temporal lobe that had been previously found using PET but not conventional fMRI. © 2010 Wiley-Liss, Inc.

Eliminating the blood-flow confounding effect in intravoxel incoherent motion (IVIM) using the non-negative least square analysis in liver.

PubMed

Gambarota, Giulio; Hitti, Eric; Leporq, Benjamin; Saint-Jalmes, Hervé; Beuf, Olivier

2017-01-01

Tissue perfusion measurements using intravoxel incoherent motion (IVIM) diffusion-MRI are of interest for investigations of liver pathologies. A confounding factor in the perfusion quantification is the partial volume between liver tissue and large blood vessels. The aim of this study was to assess and correct for this partial volume effect in the estimation of the perfusion fraction. MRI experiments were performed at 3 Tesla with a diffusion-MRI sequence at 12 b-values. Diffusion signal decays in liver were analyzed using the non-negative least square (NNLS) method and the biexponential fitting approach. In some voxels, the NNLS analysis yielded a very fast-decaying component that was assigned to partial volume with the blood flowing in large vessels. Partial volume correction was performed by biexponential curve fitting, where the first data point (b = 0 s/mm 2 ) was eliminated in voxels with a very fast-decaying component. Biexponential fitting with partial volume correction yielded parametric maps with perfusion fraction values smaller than biexponential fitting without partial volume correction. The results of the current study indicate that the NNLS analysis in combination with biexponential curve fitting allows to correct for partial volume effects originating from blood flow in IVIM perfusion fraction measurements. Magn Reson Med 77:310-317, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

General relativistic screening in cosmological simulations

NASA Astrophysics Data System (ADS)

Hahn, Oliver; Paranjape, Aseem

2016-10-01

We revisit the issue of interpreting the results of large volume cosmological simulations in the context of large-scale general relativistic effects. We look for simple modifications to the nonlinear evolution of the gravitational potential ψ that lead on large scales to the correct, fully relativistic description of density perturbations in the Newtonian gauge. We note that the relativistic constraint equation for ψ can be cast as a diffusion equation, with a diffusion length scale determined by the expansion of the Universe. Exploiting the weak time evolution of ψ in all regimes of interest, this equation can be further accurately approximated as a Helmholtz equation, with an effective relativistic "screening" scale ℓ related to the Hubble radius. We demonstrate that it is thus possible to carry out N-body simulations in the Newtonian gauge by replacing Poisson's equation with this Helmholtz equation, involving a trivial change in the Green's function kernel. Our results also motivate a simple, approximate (but very accurate) gauge transformation—δN(k )≈δsim(k )×(k2+ℓ-2)/k2 —to convert the density field δsim of standard collisionless N -body simulations (initialized in the comoving synchronous gauge) into the Newtonian gauge density δN at arbitrary times. A similar conversion can also be written in terms of particle positions. Our results can be interpreted in terms of a Jeans stability criterion induced by the expansion of the Universe. The appearance of the screening scale ℓ in the evolution of ψ , in particular, leads to a natural resolution of the "Jeans swindle" in the presence of superhorizon modes.

Cosmic ray propagation in interplanetary space

NASA Technical Reports Server (NTRS)

Voelk, H. J.

1975-01-01

The validity of the test-particle picture, the approximation of static fields, and the spatial-diffusion approximation are discussed in a general way before specific technical assumptions are introduced. It is argued that the spatial-diffusion equation for the intensity per unit energy has a much wider range of applicability than the kinetic (Fokker-Planck) equation it is derived from. This gives strong weight to the phenomenological propagation theory. The general success (and possible failure at small energies) of the phenomenological theory for the modulation of galactic cosmic rays and solar events is described. Apparent effects such as the 'free boundary' are given disproportionate weight since they establish the connection with the detailed plasma physics of the solar wind. Greatest attention is paid to the pitch-angle diffusion theory. A general theory is presented which removes the well-known secularities of the quasi-linear approximation. The possible breakdown of any pitch-angle diffusion theory at very small energies is perhaps connected with the observed 'turn up' of the spectrum at low energies. A first attempt to derive the spatial dependence of the diffusion coefficient in the solar cavity, using such a divergence free scattering theory, is described and compared with recent observations out to 5 AU.

High-throughput ab-initio dilute solute diffusion database

PubMed Central

Wu, Henry; Mayeshiba, Tam; Morgan, Dane

2016-01-01

We demonstrate automated generation of diffusion databases from high-throughput density functional theory (DFT) calculations. A total of more than 230 dilute solute diffusion systems in Mg, Al, Cu, Ni, Pd, and Pt host lattices have been determined using multi-frequency diffusion models. We apply a correction method for solute diffusion in alloys using experimental and simulated values of host self-diffusivity. We find good agreement with experimental solute diffusion data, obtaining a weighted activation barrier RMS error of 0.176 eV when excluding magnetic solutes in non-magnetic alloys. The compiled database is the largest collection of consistently calculated ab-initio solute diffusion data in the world. PMID:27434308

Effects of microwave electric fields on the translational diffusion of dipolar molecules in surface potential: A simulation study

NASA Astrophysics Data System (ADS)

Kapranov, Sergey V.; Kouzaev, Guennadi A.

2018-01-01

Variations of effective diffusion coefficient of polar molecules exposed to microwave electric fields in a surface potential are studied by solving coupled stochastic differential equations of motion with a deterministic component of the surface force. Being an essential tool for the simulation interpretation, a theoretical approach to effective diffusion in surface potential is first developed. The effective diffusion coefficient is represented as the product of the normal diffusion coefficient and potential-dependent correction function, whose temperature dependence is close to the Arrhenius form. The analytically found zero-diffusion condition defines the state of thermal equilibrium at the surface. The diffusion of a water-like dipole molecule in the potential of graphite surface is simulated in the field-free conditions and in the presence of the alternating electric fields of various magnitude intensities and frequencies. Temperature dependence of the correction function exhibits field-induced variations of the effective Lennard-Jones energy parameter. It demonstrates maximum departure from the zero-field value at certain frequencies and intensities, which is associated with variations in the rotational dynamics. A concept of the amplitude-frequency resonance put forward to interpret the simulation results is explained using a heuristic reasoning and is corroborated by semi-quantitative considerations in terms of the Dissado-Hill cluster theory of dielectric relaxation.

Scrape-off layer modeling with kinetic or diffusion description of charge-exchange atoms

NASA Astrophysics Data System (ADS)

Tokar, M. Z.

2016-12-01

Hydrogen isotope atoms, generated by charge-exchange (c-x) of neutral particles recycling from the first wall of a fusion reactor, are described either kinetically or in a diffusion approximation. In a one-dimensional (1-D) geometry, kinetic calculations are accelerated enormously by applying an approximate pass method for the assessment of integrals in the velocity space. This permits to perform an exhaustive comparison of calculations done with both approaches. The diffusion approximation is deduced directly from the velocity distribution function of c-x atoms in the limit of charge-exchanges with ions occurring much more frequently than ionization by electrons. The profiles across the flux surfaces of the plasma parameters averaged along the main part of the scrape-off layer (SOL), beyond the X-point and divertor regions, are calculated from the one-dimensional equations where parallel flows of charged particles and energy towards the divertor are taken into account as additional loss terms. It is demonstrated that the heat losses can be firmly estimated from the SOL averaged parameters only; for the particle loss the conditions in the divertor are of importance and the sensitivity of the results to the so-called "divertor impact factor" is investigated. The coupled 1-D models for neutral and charged species, with c-x atoms described either kinetically or in the diffusion approximation, are applied to assess the SOL conditions in a fusion reactor, with the input parameters from the European DEMO project. It is shown that the diffusion approximation provides practically the same profiles across the flux surfaces for the plasma density, electron, and ion temperatures, as those obtained with the kinetic description for c-x atoms. The main difference between the two approaches is observed in the characteristics of these species themselves. In particular, their energy flux onto the wall is underestimated in calculations with the diffusion approximation by 20 % - 30 % . This discrepancy can be significantly reduced if after the convergence of coupled plasma-neutral calculations, the final computation for c-x atoms is done kinetically.

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

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

Kikinzon, Evgeny; Kuznetsov, Yuri; Lipnikov, Konstatin

In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

DOE PAGES

Kikinzon, Evgeny; Kuznetsov, Yuri; Lipnikov, Konstatin; ...

2017-07-08

In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.

Halftoning Algorithms and Systems.

DTIC Science & Technology

1996-08-01

TERMS 15. NUMBER IF PAGESi. Halftoning algorithms; error diffusions ; color printing; topographic maps 16. PRICE CODE 17. SECURITY CLASSIFICATION 18...graylevels for each screen level. In the case of error diffusion algorithms, the calibration procedure using the new centering concept manifests itself as a...Novel Centering Concept for Overlapping Correction Paper / Transparency (Patent Applied 5/94)I * Applications To Error Diffusion * To Dithering (IS&T

Correction of terrestrial LiDAR intensity channel using Oren-Nayar reflectance model: An application to lithological differentiation

NASA Astrophysics Data System (ADS)

Carrea, Dario; Abellan, Antonio; Humair, Florian; Matasci, Battista; Derron, Marc-Henri; Jaboyedoff, Michel

2016-03-01

Ground-based LiDAR has been traditionally used for surveying purposes via 3D point clouds. In addition to XYZ coordinates, an intensity value is also recorded by LiDAR devices. The intensity of the backscattered signal can be a significant source of information for various applications in geosciences. Previous attempts to account for the scattering of the laser signal are usually modelled using a perfect diffuse reflection. Nevertheless, experience on natural outcrops shows that rock surfaces do not behave as perfect diffuse reflectors. The geometry (or relief) of the scanned surfaces plays a major role in the recorded intensity values. Our study proposes a new terrestrial LiDAR intensity correction, which takes into consideration the range, the incidence angle and the geometry of the scanned surfaces. The proposed correction equation combines the classical radar equation for LiDAR with the bidirectional reflectance distribution function of the Oren-Nayar model. It is based on the idea that the surface geometry can be modelled by a relief of multiple micro-facets. This model is constrained by only one tuning parameter: the standard deviation of the slope angle distribution (σslope) of micro-facets. Firstly, a series of tests have been carried out in laboratory conditions on a 2 m2 board covered by black/white matte paper (perfect diffuse reflector) and scanned at different ranges and incidence angles. Secondly, other tests were carried out on rock blocks of different lithologies and surface conditions. Those tests demonstrated that the non-perfect diffuse reflectance of rock surfaces can be practically handled by the proposed correction method. Finally, the intensity correction method was applied to a real case study, with two scans of the carbonate rock outcrop of the Dents-du-Midi (Swiss Alps), to improve the lithological identification for geological mapping purposes. After correction, the intensity values are proportional to the intrinsic material reflectance and are independent from range, incidence angle and scanned surface geometry. The corrected intensity values significantly improve the material differentiation.

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.

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

PubMed Central

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2016-01-01

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

The angular distribution of diffusely backscattered light

NASA Astrophysics Data System (ADS)

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

1997-03-01

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

Alternative derivation of an exchange-only density-functional optimized effective potential

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

Joubert, D. P.

2007-10-15

An alternative derivation of the exchange-only density-functional optimized effective potential equation is given. It is shown that the localized Hartree-Fock-common energy denominator Green's function approximation (LHF-CEDA) for the density-functional exchange potential proposed independently by Della Sala and Goerling [J. Chem. Phys. 115, 5718 (2001)] and Gritsenko and Baerends [Phys. Rev. A 64, 42506 (2001)] can be derived as an approximation to the OEP exchange potential in a similar way that the KLI approximation [Phys. Rev. A 45, 5453 (1992)] was derived. An exact expression for the correction term to the LHF-CEDA approximation can thus be found. The correction term canmore » be expressed in terms of the first-order perturbation-theory many-electron wave function shift when the Kohn-Sham Hamiltonian is subjected to a perturbation equal to the difference between the density-functional exchange potential and the Hartree-Fock nonlocal potential, expressed in terms of the Kohn-Sham orbitals. An explicit calculation shows that the density weighted mean of the correction term is zero, confirming that the LHF-CEDA approximation can be interpreted as a mean-field approximation. The corrected LHF-CEDA equation and the optimized effective potential equation are shown to be identical, with information distributed differently between terms in the equations. For a finite system the correction term falls off at least as fast as 1/r{sup 4} for large r.« less

Alternative derivation of an exchange-only density-functional optimized effective potential

NASA Astrophysics Data System (ADS)

Joubert, D. P.

2007-10-01

An alternative derivation of the exchange-only density-functional optimized effective potential equation is given. It is shown that the localized Hartree-Fock common energy denominator Green’s function approximation (LHF-CEDA) for the density-functional exchange potential proposed independently by Della Sala and Görling [J. Chem. Phys. 115, 5718 (2001)] and Gritsenko and Baerends [Phys. Rev. A 64, 42506 (2001)] can be derived as an approximation to the OEP exchange potential in a similar way that the KLI approximation [Phys. Rev. A 45, 5453 (1992)] was derived. An exact expression for the correction term to the LHF-CEDA approximation can thus be found. The correction term can be expressed in terms of the first-order perturbation-theory many-electron wave function shift when the Kohn-Sham Hamiltonian is subjected to a perturbation equal to the difference between the density-functional exchange potential and the Hartree-Fock nonlocal potential, expressed in terms of the Kohn-Sham orbitals. An explicit calculation shows that the density weighted mean of the correction term is zero, confirming that the LHF-CEDA approximation can be interpreted as a mean-field approximation. The corrected LHF-CEDA equation and the optimized effective potential equation are shown to be identical, with information distributed differently between terms in the equations. For a finite system the correction term falls off at least as fast as 1/r4 for large r .

Integrating flood modelling in a hydrological catchment model: flow approximations and spatial resolution.

NASA Astrophysics Data System (ADS)

van den Bout, Bastian; Jetten, Victor

2017-04-01

Within hydrological models, flow approximations are commonly used to reduce computation time. The validity of these approximations is strongly determined by flow height, flow velocity, the spatial resolution of the model, and by the manner in which flow routing is implemented. The assumptions of these approximations can furthermore limit emergent behavior, and influence flow behavior under space-time scaling. In this presentation, the validity and performance of the kinematic, diffusive and dynamic flow approximations are investigated for use in a catchment-based flood model. Particularly, the validity during flood events and for varying spatial resolutions is investigated. The OpenLISEM hydrological model is extended to implement these flow approximations and channel flooding based on dynamic flow. The kinematic routing uses a predefined converging flow network, the diffusive and dynamic routing uses a 2D flow solution over a DEM. The channel flow in all cases is a 1D kinematic wave approximation. The flow approximations are used to recreate measured discharge in three catchments of different size in China, Spain and Italy, among which is the hydrograph of the 2003 flood event in the Fella river basin (Italy). Furthermore, spatial resolutions are varied for the flood simulation in order to investigate the influence of spatial resolution on these flow approximations. Results show that the kinematic, diffusive and dynamic flow approximation provide least to highest accuracy, respectively, in recreating measured temporal variation of the discharge. Kinematic flow, which is commonly used in hydrological modelling, substantially over-estimates hydrological connectivity in the simulations with a spatial resolution of below 30 meters. Since spatial resolutions of models have strongly increased over the past decades, usage of routed kinematic flow should be reconsidered. In the case of flood events, spatial modelling of kinematic flow substantially over-estimates hydrological connectivity and flow concentration, leading to significant errors. The combination of diffusive or dynamic overland flow and dynamic channel flooding provides high accuracy in recreating the 2003 Fella river flood event. Finally, flow approximations substantially influenced the predictive potential of the (flash) flood model.

Metal Accretion onto White Dwarfs. I. The Approximate Approach Based on Estimates of Diffusion Timescales

NASA Astrophysics Data System (ADS)

Fontaine, G.; Brassard, P.; Dufour, P.; Tremblay, P.-E.

2015-06-01

The accretion-diffusion picture is the model par excellence for describing the presence of planetary debris polluting the atmospheres of relatively cool white dwarfs. Some important insights into the process may be derived using an approximate approach which combines static stellar models with estimates of diffusion timescales at the base of the outer convection zone or, in its absence, at the photosphere. Until recently, and to our knowledge, values of diffusion timescales in white dwarfs have all been obtained on the basis of the same physics as that developed initially by Paquette et al., including their diffusion coefficients and thermal diffusion coefficients. In view of the recent exciting discoveries of a plethora of metals (including some never seen before) polluting the atmospheres of an increasing number of cool white dwarfs, we felt that a new look at the estimates of settling timescales would be worthwhile. We thus provide improved estimates of diffusion timescales for all 27 elements from Li to Cu in the periodic table in a wide range of the surface gravity-effective temperature domain and for both DA and non-DA stars.

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue.

PubMed

Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J

2002-01-01

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.

Major diffusion leaks of clamp-on leaf cuvettes still unaccounted: how erroneous are the estimates of Farquhar et al. model parameters?

PubMed

Rodeghiero, Mirco; Niinemets, Ulo; Cescatti, Alessandro

2007-08-01

Estimates of leaf gas-exchange characteristics using standard clamp-on leaf chambers are prone to errors because of diffusion leaks. While some consideration has been given to CO(2) diffusion leaks, potential water vapour diffusion leaks through chamber gaskets have been neglected. We estimated diffusion leaks of two clamp-on Li-Cor LI-6400 (Li-Cor, Inc., Lincoln, NE, USA) leaf chambers with polymer foam gaskets and enclosing either 2 or 6 cm(2) leaf area, and conducted a sensitivity analysis of the diffusion leak effects on Farquhar et al. photosynthesis model parameters - the maximum carboxylase activity of ribulose 1 x 5-bisphosphate carboxylase/oxygenase (Rubisco) (V(cmax)), capacity for photosynthetic electron transport (J(max)) and non-photorespiratory respiration rate in light (R(d)). In addition, net assimilation rate (A(n)) versus intercellular CO(2) (C(i)) responses were measured in leaves of Mediterranean evergreen species Quercus ilex L. enclosing the whole leaf chamber in a polyvinyl fluoride bag flushed with the exhaust air of leaf chamber, thereby effectively reducing the CO(2) and water vapour gradients between ambient air and leaf chamber. For the empty chambers, average diffusion leak for CO(2), K(CO2), (molar flow rate corresponding to unit CO(2) mole fraction difference) was ca. 0.40 micromol s(-1). K(CO2) increased ca. 50% if a dead leaf was clamped between the leaf chamber. Average diffusion leak for H(2)O was ca. 5- to 10-fold larger than the diffusion leak for CO(2). Sensitivity analyses demonstrated that the consequence of a CO(2) diffusion leak was apparent enhancement of A(n) at high CO(2) mole fraction and reduction at lower CO(2) mole fraction, and overall compression of C(i) range. As the result of these modifications, Farquhar et al. model parameters were overestimated. The degree of overestimation increased in the order of V(cmax) < J(max) < R(d), and was larger for smaller chambers and for leaves with lower photosynthetic capacity, leading to overestimation of all three parameters by 70-290% for 2 cm(2), and by 10-60% for 6 cm(2) chamber. Significant diffusion corrections (5-36%) were even required for leaves with high photosynthetic capacity measured in largest chamber. Water vapour diffusion leaks further enhanced the overestimation of model parameters. For small chambers and low photosynthetic capacities, apparent C(i) was simulated to decrease with increasing A(n) because of simultaneous CO(2) and H(2)O diffusion leaks. Measurements in low photosynthetic capacity Quercus ilex leaves enclosed in 2 cm(2) leaf chamber exhibited negative apparent C(i) values at highest A(n). For the same leaves measured with the entire leaf chamber enclosed in the polyvinyl fluoride bag, C(i) and A(n) increased monotonically. While the measurements without the bag could be corrected for diffusion leaks, the required correction in A(n) and transpiration rates was 100-500%, and there was large uncertainty in Farquhar et al. model parameters derived from 'corrected'A(n)/C(i) response curves because of uncertainties in true diffusion leaks. These data demonstrate that both CO(2) and water vapour diffusion leaks need consideration in measurements with clamp-on leaf cuvettes. As plants in natural environments are often characterized by low photosynthetic capacities, cuvette designs need to be improved for reliable measurements in such species.

Utilising shade to optimize UV exposure for vitamin D

NASA Astrophysics Data System (ADS)

Turnbull, D. J.; Parisi, A. V.

2008-06-01

Numerous studies have stated that humans need to utilise full sun radiation, at certain times of the day, to assist the body in synthesising the required levels of vitamin D3. The time needed to be spent in the full sun depends on a number of factors, for example, age, skin type, latitude, solar zenith angle. Current Australian guidelines suggest exposure to approximately 1/6 to 1/3 of a minimum erythemal dose (MED), depending on age, would be appropriate to provide adequate vitamin D3 levels. The aim of the study was to determine the exposure times to diffuse solar UV to receive exposures of 1/6 and 1/3 MED for a changing solar zenith angle in order to assess the possible role that diffuse UV (scattered radiation) may play in vitamin D3 effective UV exposures (UVD3). Diffuse and global erythemal UV measurements were conducted at five minute intervals over a twelve month period for a solar zenith angle range of 4° to 80° at a latitude of 27.6° S. For a diffuse UV exposure of 1/3 MED, solar zenith angles smaller than approximately 50° can be utilised for exposure times of less than 10 min. Spectral measurements showed that, for a solar zenith angle of 40°, the UVA (315-400 nm) in the diffuse component of the solar UV is reduced by approximately 62% compared to the UVA in the global UV, whereas UVD3 wavelengths are only reduced by approximately 43%. At certain latitudes, diffuse UV under shade may play an important role in providing the human body with adequate levels of UVD3 (290-315 nm) radiation without experiencing the high levels of UVA observed in full sun.

Diffusion of Super-Gaussian Profiles

ERIC Educational Resources Information Center

Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.

2007-01-01

The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…

Large Electroweak Corrections to Vector-Boson Scattering at the Large Hadron Collider.

PubMed

Biedermann, Benedikt; Denner, Ansgar; Pellen, Mathieu

2017-06-30

For the first time full next-to-leading-order electroweak corrections to off-shell vector-boson scattering are presented. The computation features the complete matrix elements, including all nonresonant and off-shell contributions, to the electroweak process pp→μ^{+}ν_{μ}e^{+}ν_{e}jj and is fully differential. We find surprisingly large corrections, reaching -16% for the fiducial cross section, as an intrinsic feature of the vector-boson-scattering processes. We elucidate the origin of these large electroweak corrections upon using the double-pole approximation and the effective vector-boson approximation along with leading-logarithmic corrections.

Approximations for column effect in airplane wing spars

NASA Technical Reports Server (NTRS)

Warner, Edward P; Short, Mac

1927-01-01

The significance attaching to "column effect" in airplane wing spars has been increasingly realized with the passage of time, but exact computations of the corrections to bending moment curves resulting from the existence of end loads are frequently omitted because of the additional labor involved in an analysis by rigorously correct methods. The present report represents an attempt to provide for approximate column effect corrections that can be graphically or otherwise expressed so as to be applied with a minimum of labor. Curves are plotted giving approximate values of the correction factors for single and two bay trusses of varying proportions and with various relationships between axial and lateral loads. It is further shown from an analysis of those curves that rough but useful approximations can be obtained from Perry's formula for corrected bending moment, with the assumed distance between points of inflection arbitrarily modified in accordance with rules given in the report. The discussion of general rules of variation of bending stress with axial load is accompanied by a study of the best distribution of the points of support along a spar for various conditions of loading.

Potassium currents and conductance. Comparison between motor and sensory myelinated fibers.

PubMed Central

Palti, Y; Moran, N; Stämpfli, R

1980-01-01

The potassium conductance system of sensory and motor fibers from the frog Rana esculenta were studied and compared by means of the voltage clamp. The potassium ion accumulation was first estimated from the currents and reversal potentials within the framework of both a three-compartment model and diffusion-in-an-unstirred-layer model. The potassium conductance parameters were then computed using the measured currents and corrected ionic driving forces. It was found that the potassium accumulation is faster and more pronounced in sensory fibers, the voltage dependency of the potassium conductance is steeper in sensory fibers, the maximal potassium conductance, corrected for accumulation, is approximately 1.1 S/cm2 in sensory and 0.55 S/cm2 in motor fibers, and that the conductance time constants, tau n, are smaller in sensory than in motor fibers. These differences, which increase progressively with depolarization, are not detectable for depolarization of 50 mV or smaller. The interpretation of these findings in terms of different types of potassium channels as well as their implications with regard to the differences between the excitability phenomena in motor and sensory fibers are discussed. PMID:6973371

Threshold corrections to the bottom quark mass revisited

DOE PAGES

Anandakrishnan, Archana; Bryant, B. Charles; Raby, Stuart

2015-05-19

Threshold corrections to the bottom quark mass are often estimated under the approximation that tan β enhanced contributions are the most dominant. In this work we revisit this common approximation made to the estimation of the supersymmetric thresh-old corrections to the bottom quark mass. We calculate the full one-loop supersymmetric corrections to the bottom quark mass and survey a large part of the phenomenological MSSM parameter space to study the validity of considering only the tan β enhanced corrections. Our analysis demonstrates that this approximation underestimates the size of the threshold corrections by ~12.5% for most of the considered parametermore » space. We discuss the consequences for fitting the bottom quark mass and for the effective couplings to Higgses. Here, we find that it is important to consider the additional contributions when fitting the bottom quark mass but the modifications to the effective Higgs couplings are typically O(few)% for the majority of the parameter space considered.« less

Note: On the relation between Lifson-Jackson and Derrida formulas for effective diffusion coefficient

NASA Astrophysics Data System (ADS)

Kalnin, Juris R.; Berezhkovskii, Alexander M.

2013-11-01

The Lifson-Jackson formula provides the effective free diffusion coefficient for a particle diffusing in an arbitrary one-dimensional periodic potential. Its counterpart, when the underlying dynamics is described in terms of an unbiased nearest-neighbor Markovian random walk on a one-dimensional periodic lattice is given by the formula obtained by Derrida. It is shown that the latter formula can be considered as a discretized version of the Lifson-Jackson formula with correctly chosen position-dependent diffusion coefficient.

Relativistic diffusive motion in random electromagnetic fields

NASA Astrophysics Data System (ADS)

Haba, Z.

2011-08-01

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

Topographic Correction Module at Storm (TC@Storm)

NASA Astrophysics Data System (ADS)

Zaksek, K.; Cotar, K.; Veljanovski, T.; Pehani, P.; Ostir, K.

2015-04-01

Different solar position in combination with terrain slope and aspect result in different illumination of inclined surfaces. Therefore, the retrieved satellite data cannot be accurately transformed to the spectral reflectance, which depends only on the land cover. The topographic correction should remove this effect and enable further automatic processing of higher level products. The topographic correction TC@STORM was developed as a module within the SPACE-SI automatic near-real-time image processing chain STORM. It combines physical approach with the standard Minnaert method. The total irradiance is modelled as a three-component irradiance: direct (dependent on incidence angle, sun zenith angle and slope), diffuse from the sky (dependent mainly on sky-view factor), and diffuse reflected from the terrain (dependent on sky-view factor and albedo). For computation of diffuse irradiation from the sky we assume an anisotropic brightness of the sky. We iteratively estimate a linear combination from 10 different models, to provide the best results. Dependent on the data resolution, we mask shades based on radiometric (image) or geometric properties. The method was tested on RapidEye, Landsat 8, and PROBA-V data. Final results of the correction were evaluated and statistically validated based on various topography settings and land cover classes. Images show great improvements in shaded areas.

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

PubMed Central

Elcock, Adrian H.

2013-01-01

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

A computational study of Na behavior on graphene

NASA Astrophysics Data System (ADS)

Malyi, Oleksandr I.; Sopiha, Kostiantyn; Kulish, Vadym V.; Tan, Teck L.; Manzhos, Sergei; Persson, Clas

2015-04-01

We present the first ab initio and molecular dynamics study of Na adsorption and diffusion on ideal graphene that considers Na-Na interaction and dispersion forces. From density functional theory (DFT) calculations using the generalized gradient approximation (GGA), the binding energy (vs. the vacuum reference state) of -0.75 eV is higher than the cohesive energy of Na metal (E

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

PubMed

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

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

Implementation of an approximate self-energy correction scheme in the orthogonalized linear combination of atomic orbitals method of band-structure calculations

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

Gu, Z.; Ching, W.Y.

Based on the Sterne-Inkson model for the self-energy correction to the single-particle energy in the local-density approximation (LDA), we have implemented an approximate energy-dependent and [bold k]-dependent [ital GW] correction scheme to the orthogonalized linear combination of atomic orbital-based local-density calculation for insulators. In contrast to the approach of Jenkins, Srivastava, and Inkson, we evaluate the on-site exchange integrals using the LDA Bloch functions throughout the Brillouin zone. By using a [bold k]-weighted band gap [ital E][sub [ital g

Diffusion amid random overlapping obstacles: Similarities, invariants, approximations

PubMed Central

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

2011-01-01

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

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Probing the structural and dynamical properties of liquid water with models including non-local electron correlation

NASA Astrophysics Data System (ADS)

Del Ben, Mauro; Hutter, Jürg; VandeVondele, Joost

2015-08-01

Water is a ubiquitous liquid that displays a wide range of anomalous properties and has a delicate structure that challenges experiment and simulation alike. The various intermolecular interactions that play an important role, such as repulsion, polarization, hydrogen bonding, and van der Waals interactions, are often difficult to reproduce faithfully in atomistic models. Here, electronic structure theories including all these interactions at equal footing, which requires the inclusion of non-local electron correlation, are used to describe structure and dynamics of bulk liquid water. Isobaric-isothermal (NpT) ensemble simulations based on the Random Phase Approximation (RPA) yield excellent density (0.994 g/ml) and fair radial distribution functions, while various other density functional approximations produce scattered results (0.8-1.2 g/ml). Molecular dynamics simulation in the microcanonical (NVE) ensemble based on Møller-Plesset perturbation theory (MP2) yields dynamical properties in the condensed phase, namely, the infrared spectrum and diffusion constant. At the MP2 and RPA levels of theory, ice is correctly predicted to float on water, resolving one of the anomalies as resulting from a delicate balance between van der Waals and hydrogen bonding interactions. For several properties, obtaining quantitative agreement with experiment requires correction for nuclear quantum effects (NQEs), highlighting their importance, for structure, dynamics, and electronic properties. A computed NQE shift of 0.6 eV for the band gap and absorption spectrum illustrates the latter. Giving access to both structure and dynamics of condensed phase systems, non-local electron correlation will increasingly be used to study systems where weak interactions are of paramount importance.

A fluorescence correlation spectroscopy study of the diffusion of an organic dye in the gel phase and fluid phase of a single lipid vesicle.

PubMed

Ghosh, Subhadip; Adhikari, Aniruddha; Sen Mojumdar, Supratik; Bhattacharyya, Kankan

2010-05-06

The mobility of the organic dye DCM (4-dicyanomethylene-2-methyl-6-p-dimethyl aminostyryl-4H-pyran) in the gel and fluid phases of a lipid vesicle is studied by fluorescence correlation spectroscopy (FCS). Using FCS, translational diffusion of DCM is determined in the gel phase and fluid phase of a single lipid vesicle adhered to a glass surface. The size of a lipid vesicle (average diameter approximately 100 nm) is smaller than the diffraction limited spot size (approximately 250 nm) of the microscope. Thus, the vesicle is confined within the laser focus. Three lipid vesicles (1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC)) having different gel transition temperatures (-1, 23, and 41 degrees C, respectively) were studied. The diffusion coefficient of the dye DCM in bulk water is approximately 300 microm(2)/s. In the lipid vesicle, the average D(t) decreases markedly to approximately 5 microm(2)/s (approximately 60 times) in the gel phase (for DPPC at 20 degrees C) and 40 microm(2)/s ( approximately 8 times) in the fluid phase (for DLPC at 20 degrees C). This clearly demonstrates higher mobility in the fluid phase compared with the gel phase of a lipid. It is observed that the D(t) values vary from lipid to lipid and there is a distribution of D(t) values. The diffusion of the hydrophobic dye DCM (D(t) approximately 5 microm(2)/s) in the DPPC vesicle is found to be 8 times smaller than that of a hydrophilic anioinic dye C343 (D(t) approximately 40 microm(2)/s). This is attributed to different locations of the hydrophobic (DCM) and hydrophilic (C343) dyes.

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

reaction- diffusion equation is a difficult problem in analysis that will not be addressed here. Errors will also arise from numerically approx solutions to...the ODEs. When comparing the approximate solution to actual reaction- diffusion systems found in nature, we must also take into account errors that...

Quantum close coupling calculation of transport and relaxation properties for Hg-H2 system

NASA Astrophysics Data System (ADS)

Nemati-Kande, Ebrahim; Maghari, Ali

2016-11-01

Quantum mechanical close coupling calculation of the state-to-state transport and relaxation cross sections have been done for Hg-H2 molecular system using a high-level ab initio potential energy surface. Rotationally averaged cross sections were also calculated to obtain the energy dependent Senftleben-Beenakker cross sections at the energy range of 0.005-25,000 cm-1. Boltzmann averaging of the energy dependent Senftleben-Beenakker cross sections showed the temperature dependency over a wide temperature range of 50-2500 K. Interaction viscosity and diffusion coefficients were also calculated using close coupling cross sections and full classical Mason-Monchick approximation. The results were compared with each other and with the available experimental data. It was found that Mason-Monchick approximation for viscosity is more reliable than diffusion coefficient. Furthermore, from the comparison of the experimental diffusion coefficients with the result of the close coupling and Mason-Monchick approximation, it was found that the Hg-H2 potential energy surface used in this work can reliably predict diffusion coefficient data.

Diffusion of strongly magnetized cosmic ray particles in a turbulent medium

NASA Technical Reports Server (NTRS)

Ptuskin, V. S.

1985-01-01

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

The diffusion approximation. An application to radiative transfer in clouds

NASA Technical Reports Server (NTRS)

Arduini, R. F.; Barkstrom, B. R.

1976-01-01

It is shown how the radiative transfer equation reduces to the diffusion equation. To keep the mathematics as simple as possible, the approximation is applied to a cylindrical cloud of radius R and height h. The diffusion equation separates in cylindrical coordinates and, in a sample calculation, the solution is evaluated for a range of cloud radii with cloud heights of 0.5 km and 1.0 km. The simplicity of the method and the speed with which solutions are obtained give it potential as a tool with which to study the effects of finite-sized clouds on the albedo of the earth-atmosphere system.

Effects of EPI distortion correction pipelines on the connectome in Parkinson's Disease

NASA Astrophysics Data System (ADS)

Galvis, Justin; Mezher, Adam F.; Ragothaman, Anjanibhargavi; Villalon-Reina, Julio E.; Fletcher, P. Thomas; Thompson, Paul M.; Prasad, Gautam

2016-03-01

Echo-planar imaging (EPI) is commonly used for diffusion-weighted imaging (DWI) but is susceptible to nonlinear geometric distortions arising from inhomogeneities in the static magnetic field. These inhomogeneities can be measured and corrected using a fieldmap image acquired during the scanning process. In studies where the fieldmap image is not collected, these distortions can be corrected, to some extent, by nonlinearly registering the diffusion image to a corresponding anatomical image, either a T1- or T2-weighted image. Here we compared two EPI distortion correction pipelines, both based on nonlinear registration, which were optimized for the particular weighting of the structural image registration target. The first pipeline used a 3D nonlinear registration to a T1-weighted target, while the second pipeline used a 1D nonlinear registration to a T2-weighted target. We assessed each pipeline in its ability to characterize high-level measures of brain connectivity in Parkinson's disease (PD) in 189 individuals (58 healthy controls, 131 people with PD) from the Parkinson's Progression Markers Initiative (PPMI) dataset. We computed a structural connectome (connectivity map) for each participant using regions of interest from a cortical parcellation combined with DWI-based whole-brain tractography. We evaluated test-retest reliability of the connectome for each EPI distortion correction pipeline using a second diffusion scan acquired directly after the participants' first. Finally, we used support vector machine (SVM) classification to assess how accurately each pipeline classified PD versus healthy controls using each participants' structural connectome.

[Palliative surgical correction of respiratory insufficiency in diffusive pulmonary emphysema].

PubMed

Gorbunkov, S D; Varlamov, V V; Cherny, S M; Lukina, O V; Kiryukhina, L D; Romanikhin, A I; Zinchenko, A V; Akopov, A L

To analyze early postoperative period in patients with diffuse pulmonary emphysema after palliative surgical correction of respiratory failure. The study included 196 patients who underwent bullectomy (n=111) and surgical reduction of pulmonary volume (n=85). Overall morbidity and mortality were 40.8% and 12.2% respectively. Among patients older than 60 years these values were significantly higher (58.0% and 22.6% respectively). It was shown that age over 60 years is associated with high risk of complications and mortality after excision of large and giant bulls. In patients <60 years morbidity is comparable after bullectomy and surgical reduction of pulmonary volume. Selection of patients for palliative surgical correction of respiratory failure is generally corresponded to that for lung transplantation. However, these methods should be considered complementary rather competing.

Super-Arrhenius diffusion in an undercooled binary Lennard-Jones liquid results from a quantifiable correlation effect.

PubMed

de Souza, Vanessa K; Wales, David J

2006-02-10

On short time scales an underlying Arrhenius temperature dependence of the diffusion constant can be extracted from the fragile, super-Arrhenius diffusion of a binary Lennard-Jones mixture. This Arrhenius diffusion is related to the true super-Arrhenius behavior by a factor that depends on the average angle between steps in successive time windows. The correction factor accounts for the fact that on average, successive displacements are negatively correlated, and this effect can therefore be linked directly with the higher apparent activation energy for diffusion at low temperature.

Hybrid Monte Carlo-Diffusion Method For Light Propagation in Tissue With a Low-Scattering Region

NASA Astrophysics Data System (ADS)

Hayashi, Toshiyuki; Kashio, Yoshihiko; Okada, Eiji

2003-06-01

The heterogeneity of the tissues in a head, especially the low-scattering cerebrospinal fluid (CSF) layer surrounding the brain has previously been shown to strongly affect light propagation in the brain. The radiosity-diffusion method, in which the light propagation in the CSF layer is assumed to obey the radiosity theory, has been employed to predict the light propagation in head models. Although the CSF layer is assumed to be a nonscattering region in the radiosity-diffusion method, fine arachnoid trabeculae cause faint scattering in the CSF layer in real heads. A novel approach, the hybrid Monte Carlo-diffusion method, is proposed to calculate the head models, including the low-scattering region in which the light propagation does not obey neither the diffusion approximation nor the radiosity theory. The light propagation in the high-scattering region is calculated by means of the diffusion approximation solved by the finite-element method and that in the low-scattering region is predicted by the Monte Carlo method. The intensity and mean time of flight of the detected light for the head model with a low-scattering CSF layer calculated by the hybrid method agreed well with those by the Monte Carlo method, whereas the results calculated by means of the diffusion approximation included considerable error caused by the effect of the CSF layer. In the hybrid method, the time-consuming Monte Carlo calculation is employed only for the thin CSF layer, and hence, the computation time of the hybrid method is dramatically shorter than that of the Monte Carlo method.

Hybrid Monte Carlo-diffusion method for light propagation in tissue with a low-scattering region.

PubMed

Hayashi, Toshiyuki; Kashio, Yoshihiko; Okada, Eiji

2003-06-01

The heterogeneity of the tissues in a head, especially the low-scattering cerebrospinal fluid (CSF) layer surrounding the brain has previously been shown to strongly affect light propagation in the brain. The radiosity-diffusion method, in which the light propagation in the CSF layer is assumed to obey the radiosity theory, has been employed to predict the light propagation in head models. Although the CSF layer is assumed to be a nonscattering region in the radiosity-diffusion method, fine arachnoid trabeculae cause faint scattering in the CSF layer in real heads. A novel approach, the hybrid Monte Carlo-diffusion method, is proposed to calculate the head models, including the low-scattering region in which the light propagation does not obey neither the diffusion approximation nor the radiosity theory. The light propagation in the high-scattering region is calculated by means of the diffusion approximation solved by the finite-element method and that in the low-scattering region is predicted by the Monte Carlo method. The intensity and mean time of flight of the detected light for the head model with a low-scattering CSF layer calculated by the hybrid method agreed well with those by the Monte Carlo method, whereas the results calculated by means of the diffusion approximation included considerable error caused by the effect of the CSF layer. In the hybrid method, the time-consuming Monte Carlo calculation is employed only for the thin CSF layer, and hence, the computation time of the hybrid method is dramatically shorter than that of the Monte Carlo method.

An approximate analysis of the diffusing flow in a self-controlled heat pipe.

NASA Technical Reports Server (NTRS)

Somogyi, D.; Yen, H. H.

1973-01-01

Constant-density two-dimensional axisymmetric equations are presented for the diffusing flow of a class of self-controlled heat pipes. The analysis is restricted to the vapor space. Condensation of the vapor is related to its mass fraction at the wall by the gas kinetic formula. The Karman-Pohlhausen integral method is applied to obtain approximate solutions. Solutions are presented for a water heat pipe with neon control gas.

On the acceleration of charged particles at relativistic shock fronts

NASA Technical Reports Server (NTRS)

Kirk, J. G.; Schneider, P.

1987-01-01

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.

Dispersion in Rectangular Networks: Effective Diffusivity and Large-Deviation Rate Function

NASA Astrophysics Data System (ADS)

Tzella, Alexandra; Vanneste, Jacques

2016-09-01

The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply, and urban pollution. Motivated by this, we develop a large-deviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time t ≫1 . This theory provides an approximation for the concentration that remains valid for large distances from the center of mass, specifically for distances up to O (t ) and thus much beyond the O (t1 /2) range where a standard Gaussian approximation holds. A byproduct of the approach is a closed-form expression for the effective diffusivity tensor that governs this Gaussian approximation. Monte Carlo simulations of Brownian particles confirm the large-deviation results and demonstrate their effectiveness in describing the scalar distribution when t is only moderately large.

Methodology and apparatus for diffuse photon imaging

DOEpatents

Feng, S.C.; Zeng, F.; Zhao, H.L.

1997-12-09

Non-invasive near infrared optical medical imaging devices for both hematoma detection in the brain and early tumor detection in the breast is achieved using image reconstruction which allows a mapping of the position dependent contrast diffusive propagation constants, which are related to the optical absorption coefficient and scattering coefficient in the tissue, at near infrared wavelengths. Spatial resolutions in the range of 5 mm for adult brain sizes and breast sizes can be achieved. The image reconstruction utilizes WKB approximation on most probable diffusion paths which has as lowest order approximation the straight line-of-sight between the plurality of sources and the plurality of detectors. The WKB approximation yields a set of linear equations in which the contrast optical absorption coefficients are the unknowns and for which signals can be generated to produce a pixel map of the contrast optical resolution of the scanned tissue. 58 figs.

Methodology and apparatus for diffuse photon mimaging

DOEpatents

Feng, Shechao C.; Zeng, Fanan; Zhao, Hui-Lin

1997-12-09

Non-invasive near infrared optical medical imaging devices for both hematoma detection in the brain and early tumor detection in the breast is achieved using image reconstruction which allows a mapping of the position dependent contrast diffusive propagation constants, which are related to the optical absorption coefficient and scattering coefficient in the tissue, at near infrared wavelengths. Spatial resolutions in the range of 5 mm for adult brain sizes and breast sizes can be achieved. The image reconstruction utilizes WKB approximation on most probable diffusion paths which has as lowest order approximation the straight line-of-sight between the plurality of sources and the plurality of detectors. The WKB approximation yields a set of linear equations in which the contrast optical absorption coefficients are the unknowns and for which signals can be generated to produce a pixel map of the contrast optical resolution of the scanned tissue.

Multishot cartesian turbo spin-echo diffusion imaging using iterative POCSMUSE Reconstruction.

PubMed

Zhang, Zhe; Zhang, Bing; Li, Ming; Liang, Xue; Chen, Xiaodong; Liu, Renyuan; Zhang, Xin; Guo, Hua

2017-07-01

To report a diffusion imaging technique insensitive to off-resonance artifacts and motion-induced ghost artifacts using multishot Cartesian turbo spin-echo (TSE) acquisition and iterative POCS-based reconstruction of multiplexed sensitivity encoded magnetic resonance imaging (MRI) (POCSMUSE) for phase correction. Phase insensitive diffusion preparation was used to deal with the violation of the Carr-Purcell-Meiboom-Gill (CPMG) conditions of TSE diffusion-weighted imaging (DWI), followed by a multishot Cartesian TSE readout for data acquisition. An iterative diffusion phase correction method, iterative POCSMUSE, was developed and implemented to eliminate the ghost artifacts in multishot TSE DWI. The in vivo human brain diffusion images (from one healthy volunteer and 10 patients) using multishot Cartesian TSE were acquired at 3T and reconstructed using iterative POCSMUSE, and compared with single-shot and multishot echo-planar imaging (EPI) results. These images were evaluated by two radiologists using visual scores (considering both image quality and distortion levels) from 1 to 5. The proposed iterative POCSMUSE reconstruction was able to correct the ghost artifacts in multishot DWI. The ghost-to-signal ratio of TSE DWI using iterative POCSMUSE (0.0174 ± 0.0024) was significantly (P < 0.0005) smaller than using POCSMUSE (0.0253 ± 0.0040). The image scores of multishot TSE DWI were significantly higher than single-shot (P = 0.004 and 0.006 from two reviewers) and multishot (P = 0.008 and 0.004 from two reviewers) EPI-based methods. The proposed multishot Cartesian TSE DWI using iterative POCSMUSE reconstruction can provide high-quality diffusion images insensitive to motion-induced ghost artifacts and off-resonance related artifacts such as chemical shifts and susceptibility-induced image distortions. 1 Technical Efficacy: Stage 1 J. MAGN. RESON. IMAGING 2017;46:167-174. © 2016 International Society for Magnetic Resonance in Medicine.

A Comparison Between Modeled and Measured Clear-Sky Radiative Shortwave Fluxes in Arctic Environments, with Special Emphasis on Diffuse Radiation

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

Barnard, James C.; Flynn, Donna M.

2002-10-08

The ability of the SBDART radiative transfer model to predict clear-sky diffuse and direct normal broadband shortwave irradiances is investigated. Model calculations of these quantities are compared with data from the Atmospheric Radiation Measurement (ARM) program’s Southern Great Plains (SGP) and North Slope of Alaska (NSA) sites. The model tends to consistently underestimate the direct normal irradiances at both sites by about 1%. In regards to clear-sky diffuse irradiance, the model overestimates this quantity at the SGP site in a manner similar to what has been observed in other studies (Halthore and Schwartz, 2000). The difference between the diffuse SBDARTmore » calculations and Halthore and Schwartz’s MODTRAN calculations is very small, thus demonstrating that SBDART performs similarly to MODTRAN. SBDART is then applied to the NSA site, and here it is found that the discrepancy between the model calculations and corrected diffuse measurements (corrected for daytime offsets, Dutton et al., 2001) is 0.4 W/m2 when averaged over the 12 cases considered here. Two cases of diffuse measurements from a shaded “black and white” pyranometer are also compared with the calculations and the discrepancy is again minimal. Thus, it appears as if the “diffuse discrepancy” that exists at the SGP site does not exist at the NSA sites. We cannot yet explain why the model predicts diffuse radiation well at one site but not at the other.« less

Vacancies and Vacancy-Mediated Self Diffusion in Cr 2 O 3 : A First-Principles Study

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

Medasani, Bharat; Sushko, Maria L.; Rosso, Kevin M.

Charged and neutral vacancies and vacancy mediated self diffusion in alpha-Cr2O3 were investigated using first principles density functional theory (DFT) and periodic supercell formalism. The vacancy formation energies of charged defects were calculated using the electrostatic finite-size corrections to account for electrostatic interactions between supercells and the corrections for the bandgap underestimation in DFT. Calculations predict that neutral oxygen (O) vacancies are predominant in chromium (Cr)-rich conditions and Cr vacancies with -2 charge state are the dominant defects in O-rich conditions. The charge transition levels of both O and Cr vacancies are deep within the bandgap indicating the stability ofmore » these defects. Transport calculations indicate that vacancy mediated diffusion along the basal plane has lower energy barriers for both O and Cr ions. The most favorable vacancy mediated self diffusion processes correspond to the diffusion of Cr ion in 3+ charge state and O ion in 2- state, respectively. Our calculations reveal that Cr triple defects comprised of Cr in octahedral interstitial sites with two adjacent Cr vacancies along the c-axis have a lower formation energy compared to that of charged Cr vacancies. The formation of such triple defects facilitate Cr self diffusion along the c-axis.« less

Spatial homogenization methods for pin-by-pin neutron transport calculations

NASA Astrophysics Data System (ADS)

Kozlowski, Tomasz

For practical reactor core applications low-order transport approximations such as SP3 have been shown to provide sufficient accuracy for both static and transient calculations with considerably less computational expense than the discrete ordinate or the full spherical harmonics methods. These methods have been applied in several core simulators where homogenization was performed at the level of the pin cell. One of the principal problems has been to recover the error introduced by pin-cell homogenization. Two basic approaches to treat pin-cell homogenization error have been proposed: Superhomogenization (SPH) factors and Pin-Cell Discontinuity Factors (PDF). These methods are based on well established Equivalence Theory and Generalized Equivalence Theory to generate appropriate group constants. These methods are able to treat all sources of error together, allowing even few-group diffusion with one mesh per cell to reproduce the reference solution. A detailed investigation and consistent comparison of both homogenization techniques showed potential of PDF approach to improve accuracy of core calculation, but also reveal its limitation. In principle, the method is applicable only for the boundary conditions at which it was created, i.e. for boundary conditions considered during the homogenization process---normally zero current. Therefore, there exists a need to improve this method, making it more general and environment independent. The goal of proposed general homogenization technique is to create a function that is able to correctly predict the appropriate correction factor with only homogeneous information available, i.e. a function based on heterogeneous solution that could approximate PDFs using homogeneous solution. It has been shown that the PDF can be well approximated by least-square polynomial fit of non-dimensional heterogeneous solution and later used for PDF prediction using homogeneous solution. This shows a promise for PDF prediction for off-reference conditions, such as during reactor transients which provide conditions that can not typically be anticipated a priori.

Diffusion Modeling of Cooling Rates of Relict Olivine in Semarkona Chondrules

NASA Astrophysics Data System (ADS)

Hewins, R. H.; Ganguly, J.; Mariani, E.

2009-03-01

Diffusive exchange profiles between relict olivine and melt-grown olivine in Semarkona Type IIA chondrules were oriented by EBSD to correct D. Results for Fe-Mg (D from Dohmen) and Cr (Ito and Ganguly) are concordant at 300°-400°C/hr.

Influence of Coupled Radiation and Ablation on the Aerothermodynamic Environment of Planetary Entry Vehicles

NASA Technical Reports Server (NTRS)

Johnston, Christopher O.; Gnoffo, Peter A.; Mazaheri, Alireza

2013-01-01

A review of recently published coupled radiation and ablation capabilities involving the simulation of hypersonic flowfields relevant to Earth, Mars, or Venus entry is presented. The three fundamental mechanisms of radiation coupling are identified as radiative cooling, precursor photochemistry, and ablation-radiation interaction. The impact of these mechanisms are shown to be significant for a 3 m radius sphere entering Earth at hypothetical Mars return conditions (approximately 15 km/s). To estimate the influence precursor absorption on the radiative flux for a wide range of conditions, a simplified approach is developed that requires only the non-precursor solution. Details of a developed coupled ablation approach, which is capable of treating both massively ablating flowfields in the sublimation regime and weakly ablating diffusion Climited oxidation cases, are presented. A review of the two primary uncoupled ablation approximations, identified as the blowing correction and film coefficient approximations, is made and their impact for Earth and Mars entries is shown to be significant for recession and convective heating predictions. Fully coupled ablation and radiation simulations are presented for the Mars return sphere throughout its entire trajectory. Applying to the Mars return sphere the Pioneer- Venus heritage carbon phenolic heatshield, which has properties available in the open literature, the differences between steady state ablation and coupling to a material response code are shown to be significant.

High-temperature high-pressure properties of silica from Quantum Monte Carlo and Density Functional Perturbation Theory

NASA Astrophysics Data System (ADS)

Cohen, R. E.; Driver, K.; Wu, Z.; Militzer, B.; Rios, P. L.; Towler, M.; Needs, R.

2009-03-01

We have used diffusion quantum Monte Carlo (DMC) with the CASINO code with thermal free energies from phonons computed using density functional perturbation theory (DFPT) with the ABINIT code to obtain phase transition curves and thermal equations of state of silica phases under pressure. We obtain excellent agreement with experiments for the metastable phase transition from quartz to stishovite. The local density approximation (LDA) incorrectly gives stishovite as the ground state. The generalized gradient approximation (GGA) correctly gives quartz as the ground state, but does worse than LDA for the equations of state. DMC, variational quantum Monte Carlo (VMC), and DFT all give good results for the ferroelastic transition of stishovite to the CaCl2 structure, and LDA or the WC exchange correlation potentials give good results within a given silica phase. The δV and δH from the CaCl2 structure to α-PbO2 is small, giving uncertainly in the theoretical transition pressure. It is interesting that DFT has trouble with silica transitions, although the electronic structures of silica are insulating, simple closed-shell with ionic/covalent bonding. It seems like the errors in DFT are from not precisely giving the ion sizes.

Photon migration in non-scattering tissue and the effects on image reconstruction

NASA Astrophysics Data System (ADS)

Dehghani, H.; Delpy, D. T.; Arridge, S. R.

1999-12-01

Photon propagation in tissue can be calculated using the relationship described by the transport equation. For scattering tissue this relationship is often simplified and expressed in terms of the diffusion approximation. This approximation, however, is not valid for non-scattering regions, for example cerebrospinal fluid (CSF) below the skull. This study looks at the effects of a thin clear layer in a simple model representing the head and examines its effect on image reconstruction. Specifically, boundary photon intensities (total number of photons exiting at a point on the boundary due to a source input at another point on the boundary) are calculated using the transport equation and compared with data calculated using the diffusion approximation for both non-scattering and scattering regions. The effect of non-scattering regions on the calculated boundary photon intensities is presented together with the advantages and restrictions of the transport code used. Reconstructed images are then presented where the forward problem is solved using the transport equation for a simple two-dimensional system containing a non-scattering ring and the inverse problem is solved using the diffusion approximation to the transport equation.

Self-diffusion in a system of interacting Langevin particles

NASA Astrophysics Data System (ADS)

Dean, D. S.; Lefèvre, A.

2004-06-01

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

Magnetospheric Multiscale Observations of the Electron Diffusion Region of Large Guide Field Magnetic Reconnection

NASA Technical Reports Server (NTRS)

Eriksson, S.; Wilder, F. D.; Ergun, R. E.; Schwartz, S. J.; Cassak, P. A.; Burch, J. L.; Chen, Li-Jen; Torbert, R. B.; Phan, T. D.; Lavraud, B.;

Light diffusion in N-layered turbid media: steady-state domain.

PubMed

Liemert, André; Kienle, Alwin

2010-01-01

We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.

Local error estimates for adaptive simulation of the Reaction–Diffusion Master Equation via operator splitting

PubMed Central

Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda

2015-01-01

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity. PMID:26865735

Local error estimates for adaptive simulation of the Reaction-Diffusion Master Equation via operator splitting.

PubMed

Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda

2014-06-01

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity.

Towards a comprehensive framework for movement and distortion correction of diffusion MR images: Within volume movement.

PubMed

Andersson, Jesper L R; Graham, Mark S; Drobnjak, Ivana; Zhang, Hui; Filippini, Nicola; Bastiani, Matteo

2017-05-15

Most motion correction methods work by aligning a set of volumes together, or to a volume that represents a reference location. These are based on an implicit assumption that the subject remains motionless during the several seconds it takes to acquire all slices in a volume, and that any movement occurs in the brief moment between acquiring the last slice of one volume and the first slice of the next. This is clearly an approximation that can be more or less good depending on how long it takes to acquire one volume and in how rapidly the subject moves. In this paper we present a method that increases the temporal resolution of the motion correction by modelling movement as a piecewise continous function over time. This intra-volume movement correction is implemented within a previously presented framework that simultaneously estimates distortions, movement and movement-induced signal dropout. We validate the method on highly realistic simulated data containing all of these effects. It is demonstrated that we can estimate the true movement with high accuracy, and that scalar parameters derived from the data, such as fractional anisotropy, are estimated with greater fidelity when data has been corrected for intra-volume movement. Importantly, we also show that the difference in fidelity between data affected by different amounts of movement is much reduced when taking intra-volume movement into account. Additional validation was performed on data from a healthy volunteer scanned when lying still and when performing deliberate movements. We show an increased correspondence between the "still" and the "movement" data when the latter is corrected for intra-volume movement. Finally we demonstrate a big reduction in the telltale signs of intra-volume movement in data acquired on elderly subjects. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Extrapolation-Based References Improve Motion and Eddy-Current Correction of High B-Value DWI Data: Application in Parkinson's Disease Dementia.

PubMed

Nilsson, Markus; Szczepankiewicz, Filip; van Westen, Danielle; Hansson, Oskar

2015-01-01

Conventional motion and eddy-current correction, where each diffusion-weighted volume is registered to a non diffusion-weighted reference, suffers from poor accuracy for high b-value data. An alternative approach is to extrapolate reference volumes from low b-value data. We aim to compare the performance of conventional and extrapolation-based correction of diffusional kurtosis imaging (DKI) data, and to demonstrate the impact of the correction approach on group comparison studies. DKI was performed in patients with Parkinson's disease dementia (PDD), and healthy age-matched controls, using b-values of up to 2750 s/mm2. The accuracy of conventional and extrapolation-based correction methods was investigated. Parameters from DTI and DKI were compared between patients and controls in the cingulum and the anterior thalamic projection tract. Conventional correction resulted in systematic registration errors for high b-value data. The extrapolation-based methods did not exhibit such errors, yielding more accurate tractography and up to 50% lower standard deviation in DKI metrics. Statistically significant differences were found between patients and controls when using the extrapolation-based motion correction that were not detected when using the conventional method. We recommend that conventional motion and eddy-current correction should be abandoned for high b-value data in favour of more accurate methods using extrapolation-based references.

Critical decay exponent of the pair contact process with diffusion

NASA Astrophysics Data System (ADS)

Park, Su-Chan

2014-11-01

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

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

Kaufman, H.R.

Bohm diffusion has been found to be approximately valid for many plasmas in strong magnetic fields. Assuming Bohm diffusion describes electron diffusion directly (H. R. Kaufman, AIAA J. {bold 23}, 78 (1985)), with an equal ion loss possible from the ambipolar field that is generated (F. F. Chen, {ital Introduction} {ital to} {ital Plasma} {ital Physics} (Plenum, New York, 1974), p. 169), an order-of-magnitude analysis can show why such electron diffusion should be expected.

Self and transport diffusivity of CO2 in the metal-organic framework MIL-47(V) explored by quasi-elastic neutron scattering experiments and molecular dynamics simulations.

PubMed

Salles, Fabrice; Jobic, Hervé; Devic, Thomas; Llewellyn, Philip L; Serre, Christian; Férey, Gérard; Maurin, Guillaume

2010-01-26

Quasi-elastic neutron scattering measurements are combined with molecular dynamics simulations to determine the self-diffusivity, corrected diffusivity, and transport diffusivity of CO(2) in the metal-organic framework MIL-47(V) (MIL = Materials Institut Lavoisier) over a wide range of loading. The force field used for describing the host/guest interactions is first validated on the thermodynamics of the MIL-47(V)/CO(2) system, prior to being transferred to the investigations of the dynamics. A decreasing profile is then deduced for D(s) and D(o) whereas D(t) presents a non monotonous evolution with a slight decrease at low loading followed by a sharp increase at higher loading. Such decrease of D(t) which has never been evidenced in any microporous systems comes from the atypical evolution of the thermodynamic correction factor that reaches values below 1 at low loading. This implies that, due to intermolecular interactions, the CO(2) molecules in MIL-47(V) do not behave like an ideal gas. Further, molecular simulations enabled us to elucidate unambiguously a 3D diffusion mechanism within the pores of MIL-47(V).

Simulation of temperature distribution in tumor Photothermal treatment

NASA Astrophysics Data System (ADS)

Zhang, Xiyang; Qiu, Shaoping; Wu, Shulian; Li, Zhifang; Li, Hui

2018-02-01

The light transmission in biological tissue and the optical properties of biological tissue are important research contents of biomedical photonics. It is of great theoretical and practical significance in medical diagnosis and light therapy of disease. In this paper, the temperature feedback-controller was presented for monitoring photothermal treatment in realtime. Two-dimensional Monte Carlo (MC) and diffuse approximation were compared and analyzed. The results demonstrated that diffuse approximation using extrapolated boundary conditions by finite element method is a good approximation to MC simulation. Then in order to minimize thermal damage, real-time temperature monitoring was appraised by proportional-integral-differential (PID) controller in the process of photothermal treatment.

Some Fundamental Issues of Mathematical Simulation in Biology

NASA Astrophysics Data System (ADS)

Razzhevaikin, V. N.

2018-02-01

Some directions of simulation in biology leading to original formulations of mathematical problems are overviewed. Two of them are discussed in detail: the correct solvability of first-order linear equations with unbounded coefficients and the construction of a reaction-diffusion equation with nonlinear diffusion for a model of genetic wave propagation.

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

Improved solar models constructed with a formulation of convection for stellar structure and evolution calculations without the mixing-length theory approximations

NASA Technical Reports Server (NTRS)

Lydon, Thomas J.; Fox, Peter A.; Sofia, Sabatino

1993-01-01

We have updated a previous attempt to incorporate within a solar model a treatment of convection based upon numerical simulations of convection rather than mixing-length theory (MLT). We have modified our formulation of convection for a better treatment of the kinetic energy flux. Our solar model has been updated to include a complete range of OPAL opacities, the Debye-Hueckel correction to the equation of state, helium diffusion due to gravitational settling, and atmospheres by Kurucz. We construct a series of models using both MLT and our revised formulation of convection and the compared results to measurements of the solar radius, the solar luminosity, and the depth of the solar convection zone as inferred from helioseismology. We find X(solar) = 0.702 +/- 0.005, Y(solar) = 0.278 +/- 0.005, and Z(solar) = 0.0193 +/- 0.0005.

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

NASA Technical Reports Server (NTRS)

Campbell, Joel

2007-01-01

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Probabilistic vs. non-probabilistic approaches to the neurobiology of perceptual decision-making

PubMed Central

Drugowitsch, Jan; Pouget, Alexandre

2012-01-01

Optimal binary perceptual decision making requires accumulation of evidence in the form of a probability distribution that specifies the probability of the choices being correct given the evidence so far. Reward rates can then be maximized by stopping the accumulation when the confidence about either option reaches a threshold. Behavioral and neuronal evidence suggests that humans and animals follow such a probabilitistic decision strategy, although its neural implementation has yet to be fully characterized. Here we show that that diffusion decision models and attractor network models provide an approximation to the optimal strategy only under certain circumstances. In particular, neither model type is sufficiently flexible to encode the reliability of both the momentary and the accumulated evidence, which is a pre-requisite to accumulate evidence of time-varying reliability. Probabilistic population codes, in contrast, can encode these quantities and, as a consequence, have the potential to implement the optimal strategy accurately. PMID:22884815

The SMM model as a boundary value problem using the discrete diffusion equation.

PubMed

Campbell, Joel

2007-12-01

A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

The validity of flow approximations when simulating catchment-integrated flash floods

NASA Astrophysics Data System (ADS)

Bout, B.; Jetten, V. G.

2018-01-01

Within hydrological models, flow approximations are commonly used to reduce computation time. The validity of these approximations is strongly determined by flow height, flow velocity and the spatial resolution of the model. In this presentation, the validity and performance of the kinematic, diffusive and dynamic flow approximations are investigated for use in a catchment-based flood model. Particularly, the validity during flood events and for varying spatial resolutions is investigated. The OpenLISEM hydrological model is extended to implement both these flow approximations and channel flooding based on dynamic flow. The flow approximations are used to recreate measured discharge in three catchments, among which is the hydrograph of the 2003 flood event in the Fella river basin. Furthermore, spatial resolutions are varied for the flood simulation in order to investigate the influence of spatial resolution on these flow approximations. Results show that the kinematic, diffusive and dynamic flow approximation provide least to highest accuracy, respectively, in recreating measured discharge. Kinematic flow, which is commonly used in hydrological modelling, substantially over-estimates hydrological connectivity in the simulations with a spatial resolution of below 30 m. Since spatial resolutions of models have strongly increased over the past decades, usage of routed kinematic flow should be reconsidered. The combination of diffusive or dynamic overland flow and dynamic channel flooding provides high accuracy in recreating the 2003 Fella river flood event. Finally, in the case of flood events, spatial modelling of kinematic flow substantially over-estimates hydrological connectivity and flow concentration since pressure forces are removed, leading to significant errors.

Population genetics inference for longitudinally-sampled mutants under strong selection.

PubMed

Lacerda, Miguel; Seoighe, Cathal

2014-11-01

Longitudinal allele frequency data are becoming increasingly prevalent. Such samples permit statistical inference of the population genetics parameters that influence the fate of mutant variants. To infer these parameters by maximum likelihood, the mutant frequency is often assumed to evolve according to the Wright-Fisher model. For computational reasons, this discrete model is commonly approximated by a diffusion process that requires the assumption that the forces of natural selection and mutation are weak. This assumption is not always appropriate. For example, mutations that impart drug resistance in pathogens may evolve under strong selective pressure. Here, we present an alternative approximation to the mutant-frequency distribution that does not make any assumptions about the magnitude of selection or mutation and is much more computationally efficient than the standard diffusion approximation. Simulation studies are used to compare the performance of our method to that of the Wright-Fisher and Gaussian diffusion approximations. For large populations, our method is found to provide a much better approximation to the mutant-frequency distribution when selection is strong, while all three methods perform comparably when selection is weak. Importantly, maximum-likelihood estimates of the selection coefficient are severely attenuated when selection is strong under the two diffusion models, but not when our method is used. This is further demonstrated with an application to mutant-frequency data from an experimental study of bacteriophage evolution. We therefore recommend our method for estimating the selection coefficient when the effective population size is too large to utilize the discrete Wright-Fisher model. Copyright © 2014 by the Genetics Society of America.

Multispecies lottery competition: a diffusion analysis

USGS Publications Warehouse

Hatfield, J.S.; Chesson, P.L.; Tuljapurkar, S.; Caswell, H.

1997-01-01

The lottery model is a stochastic competition model designed for space-limited communities of sedentary organisms. Examples of such communities include coral reef fishes, aquatic sessile organisms, and many plant communities. Explicit conditions for the coexistence of two species and the stationary distribution of the two-species model were determined previously using an approximation with a diffusion process. In this chapter, a diffusion approximation is presented for the multispecies model for communities of two or more species, and a stage-structured model is investigated. The stage-structured model would be more reasonable for communities of long-lived species such as trees in a forest in which recruitment and death rates depend on the age or stage of the individuals.

Elimination of single-beam substitution error in diffuse reflectance measurements using an integrating sphere.

PubMed

Vidovic, Luka; Majaron, Boris

2014-02-01

Diffuse reflectance spectra (DRS) of biological samples are commonly measured using an integrating sphere (IS). To account for the incident light spectrum, measurement begins by placing a highly reflective white standard against the IS sample opening and collecting the reflected light. After replacing the white standard with the test sample of interest, DRS of the latter is determined as the ratio of the two values at each involved wavelength. However, such a substitution may alter the fluence rate inside the IS. This leads to distortion of measured DRS, which is known as single-beam substitution error (SBSE). Barring the use of more complex experimental setups, the literature states that only approximate corrections of the SBSE are possible, e.g., by using look-up tables generated with calibrated low-reflectivity standards. We present a practical method for elimination of SBSE when using IS equipped with an additional reference port. Two additional measurements performed at this port enable a rigorous elimination of SBSE. Our experimental characterization of SBSE is replicated by theoretical derivation. This offers an alternative possibility of computational removal of SBSE based on advance characterization of a specific DRS setup. The influence of SBSE on quantitative analysis of DRS is illustrated in one application example.

Conceptual Design Study of a Closed Brayton Cycle Turbogenerator for Space Power Thermal-To-Electric Conversion System

NASA Technical Reports Server (NTRS)

Hansen, Jeff L.

2000-01-01

A conceptual design study was completed for a 360 kW Helium-Xenon closed Brayton cycle turbogenerator. The selected configuration is comprised of a single-shaft gas turbine engine coupled directly to a high-speed generator. The engine turbomachinery includes a 2.5:1 pressure ratio compression system with an inlet corrected flow of 0.44 kg/sec. The single centrifugal stage impeller discharges into a scroll via a vaned diffuser. The scroll routes the air into the cold side sector of the recuperator. The hot gas exits a nuclear reactor radiator at 1300 K and enters the turbine via a single-vaned scroll. The hot gases are expanded through the turbine and then diffused before entering the hot side sector of the recuperator. The single shaft design is supported by air bearings. The high efficiency shaft mounted permanent magnet generator produces an output of 370 kW at a speed of 60,000 rpm. The total weight of the turbogenerator is estimated to be only 123 kg (less than 5% of the total power plant) and has a volume of approximately 0.11 cubic meters. This turbogenerator is a key element in achieving the 40 to 45% overall power plant thermal efficiency.

Distributed modeling of diffusive solute transport in peritoneal dialysis.

PubMed

Waniewski, Jacek

2002-01-01

The diffusive transport between blood and an ex-tissue medium (dialysis fluid) is evaluated using a mathematical model that takes into account the (quasicontinuous) distribution of capillaries within the tissue at various distances from the tissue surface, and includes diffusive-convective transport through the capillary wall and lymphatic absorption from the tissue. General formulas for solute penetration depth, lambda, and for the diffusive mass transport coefficient for the transport between blood and dialysis fluid, K(BD), are provided in terms of local transport coefficients for capillary wall, tissue, and lymphatic absorption. For pure diffusive transport between blood and dialysis fluid and thick tissue layers (i.e., if the solute penetration depth is much lower than the tissue thickness) these formulas yield previously known expressions. It is shown that apparent tissue layers, with widths lambdaTBL and lambdaT, respectively, may be defined according to the values of local transport parameters in such a way that K(BD) is equal to the solute clearance K(TBL) from the tissue by blood and lymph for a layer with width lambdaTBL or to the solute clearance K(T) from blood to dialysate by diffusion through the tissue layer with width lambdaT. For tissue layers with width much higher than the penetration depth: lambdaT approximately = lambdaTBL approximately = lambda. These characteristic width lengths depend on the transport parameters (and thus on the size) of solutes. Effective blood flow, which may be related to the exchange of the solute between blood and dialysate, is defined using an analogy to the extraction/absorption coefficients for blood-tissue exchange. Various approximations for the distributed model formula for diffusive mass transport coefficient (K(BD)) are possible. The appropriate range for their application is obtained from the general formula.

An inverse moisture diffusion algorithm for the determination of diffusion coefficient

Treesearch

Jen Y. Liu; William T. Simpson; Steve P. Verrill

2000-01-01

The finite difference approximation is applied to estimate the moisture-dependent diffusion coefficient by utilizing test data of isothermal moisture desorption in northern red oak (Quercus rubra). The test data contain moisture distributions at discrete locations across the thickness of specimens, which coincides with the radial direction of northern red oak, and at...

An inverse moisture diffusion algorithm for the determination of diffusion coefficient

Treesearch

Jen Y. Liu; William T. Simpson; Steve P. Verrill

2001-01-01

The finite difference approximation is applied to estimate the moisture-dependent diffusion coefficient by utilizing test data of isothermal moisture desorption in northern red oak (Quercus rubra). The test data contain moisture distributions at discrete locations across the thickness of specimens, which coincides with the radial direction of northern red oak, and at...

Pattern formations and optimal packing.

PubMed

Mityushev, Vladimir

2016-04-01

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

Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source.

PubMed

Kienle, A; Patterson, M S

1997-09-01

We investigate theoretically the errors in determining the reduced scattering and absorption coefficients of semi-infinite turbid media from frequency-domain reflectance measurements made at small distances between the source and the detector(s). The errors are due to the uncertainties in the measurement of the phase, the modulation and the steady-state reflectance as well as to the diffusion approximation which is used as a theoretical model to describe light propagation in tissue. Configurations using one and two detectors are examined for the measurement of the phase and the modulation and for the measurement of the phase and the steady-state reflectance. Three solutions of the diffusion equation are investigated. We show that measurements of the phase and the steady-state reflectance at two different distances are best suited for the determination of the optical properties close to the source. For this arrangement the errors in the absorption coefficient due to typical uncertainties in the measurement are greater than those resulting from the application of the diffusion approximation at a modulation frequency of 200 MHz. A Monte Carlo approach is also examined; this avoids the errors due to the diffusion approximation.

A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

PubMed

Thygesen, Uffe Høgsbro

2016-03-01

We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when the chemical gradients grow increasingly steep. The dispersal becomes anisotropic in steep gradients, with larger dispersal across the gradient than along the gradient. In contrast to one-dimensional settings, strong bias increases dispersal. We next include Brownian rotation in the model and find that, in limit of high chemotactic sensitivity, the chemotactic drift is 64% of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation. The proposed technique for obtaining diffusion approximations is conceptually and computationally simple, and applicable also when statistics of the motion is obtained empirically or through Monte Carlo simulation of the motion.

The importance of correcting for signal drift in diffusion MRI.

PubMed

Vos, Sjoerd B; Tax, Chantal M W; Luijten, Peter R; Ourselin, Sebastien; Leemans, Alexander; Froeling, Martijn

2017-01-01

To investigate previously unreported effects of signal drift as a result of temporal scanner instability on diffusion MRI data analysis and to propose a method to correct this signal drift. We investigated the signal magnitude of non-diffusion-weighted EPI volumes in a series of diffusion-weighted imaging experiments to determine whether signal magnitude changes over time. Different scan protocols and scanners from multiple vendors were used to verify this on phantom data, and the effects on diffusion kurtosis tensor estimation in phantom and in vivo data were quantified. Scalar metrics (eigenvalues, fractional anisotropy, mean diffusivity, mean kurtosis) and directional information (first eigenvectors and tractography) were investigated. Signal drift, a global signal decrease with subsequently acquired images in the scan, was observed in phantom data on all three scanners, with varying magnitudes up to 5% in a 15-min scan. The signal drift has a noticeable effect on the estimation of diffusion parameters. All investigated quantitative parameters as well as tractography were affected by this artifactual signal decrease during the scan. By interspersing the non-diffusion-weighted images throughout the session, the signal decrease can be estimated and compensated for before data analysis; minimizing the detrimental effects on subsequent MRI analyses. Magn Reson Med 77:285-299, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

Estimation of biomedical optical properties by simultaneous use of diffuse reflectometry and photothermal radiometry: investigation of light propagation models

NASA Astrophysics Data System (ADS)

Fonseca, E. S. R.; de Jesus, M. E. P.

2007-07-01

The estimation of optical properties of highly turbid and opaque biological tissue is a difficult task since conventional purely optical methods rapidly loose sensitivity as the mean photon path length decreases. Photothermal methods, such as pulsed or frequency domain photothermal radiometry (FD-PTR), on the other hand, show remarkable sensitivity in experimental conditions that produce very feeble optical signals. Photothermal Radiometry is primarily sensitive to absorption coefficient yielding considerably higher estimation errors on scattering coefficients. Conversely, purely optical methods such as Local Diffuse Reflectance (LDR) depend mainly on the scattering coefficient and yield much better estimates of this parameter. Therefore, at moderate transport albedos, the combination of photothermal and reflectance methods can improve considerably the sensitivity of detection of tissue optical properties. The authors have recently proposed a novel method that combines FD-PTR with LDR, aimed at improving sensitivity on the determination of both optical properties. Signal analysis was performed by global fitting the experimental data to forward models based on Monte-Carlo simulations. Although this approach is accurate, the associated computational burden often limits its use as a forward model. Therefore, the application of analytical models based on the diffusion approximation offers a faster alternative. In this work, we propose the calculation of the diffuse reflectance and the fluence rate profiles under the δ-P I approximation. This approach is known to approximate fluence rate expressions better close to collimated sources and boundaries than the standard diffusion approximation (SDA). We extend this study to the calculation of the diffuse reflectance profiles. The ability of the δ-P I based model to provide good estimates of the absorption, scattering and anisotropy coefficients is tested against Monte-Carlo simulations over a wide range of scattering to absorption ratios. Experimental validation of the proposed method is accomplished by a set of measurements on solid absorbing and scattering phantoms.

Effect of the scattering delay on time-dependent photon migration in turbid media.

PubMed

Yaroslavsky, I V; Yaroslavsky, A N; Tuchin, V V; Schwarzmaier, H J

1997-09-01

We modified the diffusion approximation of the time-dependent radiative transfer equation to account for a finite scattering delay time. Under the usual assumptions of the diffusion approximation, the effect of the scattering delay leads to a simple renormalization of the light velocity that appears in the diffusion equation. Accuracy of the model was evaluated by comparison with Monte Carlo simulations in the frequency domain for a semi-infinite geometry. A good agreement is demonstrated for both matched and mismatched boundary conditions when the distance from the source is sufficiently large. The modified diffusion model predicts that the neglect of the scattering delay when the optical properties of the turbid material are derived from normalized frequency- or time-domain measurements should result in an underestimation of the absorption coefficient and an overestimation of the transport coefficient. These observations are consistent with the published experimental data.

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

PubMed

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

1979-10-01

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

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.

On Large Time Behavior and Selection Principle for a Diffusive Carr-Penrose Model

NASA Astrophysics Data System (ADS)

Conlon, Joseph G.; Dabkowski, Michael; Wu, Jingchen

2016-04-01

This paper is concerned with the study of a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. A main subject of interest is to understand how the presence of diffusion acts as a selection principle, which singles out a particular self-similar solution of the linear LSW model as determining the large time behavior of the diffusive model. A selection principle is rigorously proven for a model which is a semiclassical approximation to the diffusive model. Upper bounds on the rate of coarsening are also obtained for the full diffusive model.

Diffusion scrubber-ion chromatography for the measurement of trace levels of atmospheric HCl

NASA Astrophysics Data System (ADS)

Lindgren, Per F.

A diffusion scrubber-ion chromatographic (DS-IC) instrument has been characterized and employed for the measurement of trace levels of gaseous HCl in the atmosphere. The instrument operates with a temporal resolution of 5 min and the detection limit is estimated to be 5 pptv. Collection efficiencies for HCl with two identical diffusion scrubbers were 28±2% and 20±2%, respectively, at a sampling flow rate of 2 SLPM. Instrument response decreases with increased relative humidity. An equation, correction factor=2.45 × 10 -7 × %r.h 3 + 1.00, is used to correct for the relative humidity dependency. The instrument was tested in ambient air studies by measuring background mixing ratios between 0.02 and 0.5 ppbv at a suburban sampling site. Calibration of the instrument was carried out with a novel source of gaseous HCl based on sublimation of ammonium chloride.

Impact of mesophyll diffusion on estimated global land CO 2 fertilization

DOE PAGES

Sun, Ying; Gu, Lianhong; Dickinson, Robert E.; ...

2014-10-13

In C 3 plants, CO 2 concentrations drop considerably along mesophyll diffusion pathways from substomatal cavities to chloroplasts where CO 2 assimilation occurs. Global carbon cycle models have not explicitly represented this internal drawdown and so overestimate CO 2 available for carboxylation and underestimate photosynthetic responsiveness to atmospheric CO 2. An explicit consideration of mesophyll diffusion increases the modeled cumulative CO 2 fertilization effect (CFE) for global gross primary production (GPP) from 915 PgC to 1057 PgC for the period of 1901 to 2010. This increase represents a 16% correction, large enough to explain the persistent overestimation of growth ratesmore » of historical atmospheric CO 2 by Earth System Models. Without this correction, the CFE for global GPP is underestimated by 0.05 PgC yr -1ppm -1. This finding implies that the contemporary terrestrial biosphere is more CO 2-limited than previously thought.« less

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress

NASA Astrophysics Data System (ADS)

Tchitchekova, Deyana S.; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-01

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ˜3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation. The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied. The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Morphology Effect on Proton Dynamics in Nafion® 117 and Sulfonated Polyether Ether Ketone

NASA Astrophysics Data System (ADS)

Leong, Jun Xing; Diño, Wilson Agerico; Ahmad, Azizan; Daud, Wan Ramli Wan; Kasai, Hideaki

2016-09-01

We report results of our experimental and theoretical studies on the dynamics of proton conductivity in Nafion® 117 and self-fabricated sulfonated polyether ether ketone (SPEEK) membranes. Knowing that the presence of water molecules in the diffusion process results in a lower energy barrier, we determined the diffusion barriers and corresponding tunneling probabilities of Nafion® 117 and SPEEK system using a simple theoretical model that excludes the medium (water molecules) in the initial calculations. We then propose an equation that relates the membrane conductivity to the tunneling probability. We recover the effect of the medium by introducing a correction term into the proposed equation, which takes into account the effect of the proton diffusion distance and the hydration level. We have also experimentally verified that the proposed equation correctly explain the difference in conductivity between Nafion® 117 and SPEEK. We found that membranes that are to be operated in low hydration environments (high temperatures) need to be designed with short diffusion distances to enhance and maintain high conductivity.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress.

PubMed

Tchitchekova, Deyana S; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-21

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ∼3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

Measurement of absorbed dose with a bone-equivalent extrapolation chamber.

PubMed

DeBlois, François; Abdel-Rahman, Wamied; Seuntjens, Jan P; Podgorsak, Ervin B

2002-03-01

A hybrid phantom-embedded extrapolation chamber (PEEC) made of Solid Water and bone-equivalent material was used for determining absorbed dose in a bone-equivalent phantom irradiated with clinical radiation beams (cobalt-60 gamma rays; 6 and 18 MV x rays; and 9 and 15 MeV electrons). The dose was determined with the Spencer-Attix cavity theory, using ionization gradient measurements and an indirect determination of the chamber air-mass through measurements of chamber capacitance. The collected charge was corrected for ionic recombination and diffusion in the chamber air volume following the standard two-voltage technique. Due to the hybrid chamber design, correction factors accounting for scatter deficit and electrode composition were determined and applied in the dose equation to obtain absorbed dose in bone for the equivalent homogeneous bone phantom. Correction factors for graphite electrodes were calculated with Monte Carlo techniques and the calculated results were verified through relative air cavity dose measurements for three different polarizing electrode materials: graphite, steel, and brass in conjunction with a graphite collecting electrode. Scatter deficit, due mainly to loss of lateral scatter in the hybrid chamber, reduces the dose to the air cavity in the hybrid PEEC in comparison with full bone PEEC by 0.7% to approximately 2% depending on beam quality and energy. In megavoltage photon and electron beams, graphite electrodes do not affect the dose measurement in the Solid Water PEEC but decrease the cavity dose by up to 5% in the bone-equivalent PEEC even for very thin graphite electrodes (<0.0025 cm). In conjunction with appropriate correction factors determined with Monte Carlo techniques, the uncalibrated hybrid PEEC can be used for measuring absorbed dose in bone material to within 2% for high-energy photon and electron beams.

Magnetotelluric investigation of the geothermal anomaly in Hailin, Mudanjiang, northeastern China

NASA Astrophysics Data System (ADS)

Zhang, Lili; Hao, Tianyao; Xiao, Qibin; Wang, Jie; Zhou, Liang; Qi, Min; Cui, Xiangpan; Cai, Ningxiao

2015-07-01

To study the occurrence conditions and locations of geothermal bodies in Hailin, Mudanjiang, northeastern China, we conducted a magnetotelluric investigation to delineate the electrical conductivity structure of the area on three parallel profiles. The area to the west of the Mudanjiang Fault lies in the Hailang sag of the Ning'an Basin. The data were processed using the mutual reference technique, static shift correction, and structural strike and dimensionality analysis based on tensor decomposition. Moreover, a modified anisotropic-diffusion-based method was used to suppress noise for the magnetotelluric time series data. This method retains the advantages of conventional anisotropic diffusion and is superior in its discrimination ability. The method is characteristic not only of the inherited features such as intra-region smoothing and edge preservation, but also of the adaptive selection of the diffusion coefficient. Data analysis revealed that the electrical resistivity structure can be approximated by a two-dimensional characterization. Two-dimensional inversion and rendering visualization show that a highly resistive granite basement is covered with conductive sedimentary layers and that a relatively low-resistivity anomalous structure with a resistivity of approximately 100-600 Ω·m is imbedded in the high-resistivity background. The anomalous structure has a narrow top and a wide bottom (the bottom depth is at least 3500 m). The shape and electrical features of the structure indicate favorable storage space for hot subsurface water. Fault activities and magma intrusion may result in the fractures of the basement, which are filled with hot water and thus produce the relatively low resistivity. Based on a comprehensive analysis, we infer that the structure is indicative of a geothermal reservoir. An exploratory well drilled near the structure confirms the occurrence of high temperatures. Several geological factors (cap rock, basement, and major faults) determine the favorable geothermal conditions of the reservoir. Large areas of granite form the major thermal source for the study area. The Mudanjiang and Hailang River Faults and their subsidiary faults provide another heat source and movement channels.

General relativistic corrections to the weak lensing convergence power spectrum

NASA Astrophysics Data System (ADS)

Giblin, John T.; Mertens, James B.; Starkman, Glenn D.; Zentner, Andrew R.

2017-11-01

We compute the weak lensing convergence power spectrum, Cℓκκ, in a dust-filled universe using fully nonlinear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and partially utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, ℓ˜2 - 3 , and percent-level corrections at intermediate angular scales of ℓ˜20 - 30 .

Estimation of Mesospheric Densities at Low Latitudes Using the Kunming Meteor Radar Together With SABER Temperatures

NASA Astrophysics Data System (ADS)

Yi, Wen; Xue, Xianghui; Reid, Iain M.; Younger, Joel P.; Chen, Jinsong; Chen, Tingdi; Li, Na

2018-04-01

Neutral mesospheric densities at a low latitude have been derived during April 2011 to December 2014 using data from the Kunming meteor radar in China (25.6°N, 103.8°E). The daily mean density at 90 km was estimated using the ambipolar diffusion coefficients from the meteor radar and temperatures from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument. The seasonal variations of the meteor radar-derived density are consistent with the density from the Mass Spectrometer and Incoherent Scatter (MSIS) model, show a dominant annual variation, with a maximum during winter, and a minimum during summer. A simple linear model was used to separate the effects of atmospheric density and the meteor velocity on the meteor radar peak detection height. We find that a 1 km/s difference in the vertical meteor velocity yields a change of approximately 0.42 km in peak height. The strong correlation between the meteor radar density and the velocity-corrected peak height indicates that the meteor radar density estimates accurately reflect changes in neutral atmospheric density and that meteor peak detection heights, when adjusted for meteoroid velocity, can serve as a convenient tool for measuring density variations around the mesopause. A comparison of the ambipolar diffusion coefficient and peak height observed simultaneously by two co-located meteor radars indicates that the relative errors of the daily mean ambipolar diffusion coefficient and peak height should be less than 5% and 6%, respectively, and that the absolute error of the peak height is less than 0.2 km.

Adaptive optics system performance approximations for atmospheric turbulence correction

NASA Astrophysics Data System (ADS)

Tyson, Robert K.

1990-10-01

Analysis of adaptive optics system behavior often can be reduced to a few approximations and scaling laws. For atmospheric turbulence correction, the deformable mirror (DM) fitting error is most often used to determine a priori the interactuator spacing and the total number of correction zones required. This paper examines the mirror fitting error in terms of its most commonly used exponential form. The explicit constant in the error term is dependent on deformable mirror influence function shape and actuator geometry. The method of least squares fitting of discrete influence functions to the turbulent wavefront is compared to the linear spatial filtering approximation of system performance. It is found that the spatial filtering method overstimates the correctability of the adaptive optics system by a small amount. By evaluating fitting error for a number of DM configurations, actuator geometries, and influence functions, fitting error constants verify some earlier investigations.

Radiative transfer in dusty nebulae. III - The effects of dust albedo

NASA Technical Reports Server (NTRS)

Petrosian, V.; Dana, R. A.

1980-01-01

The effects of an albedo of internal dust, such as ionization structure and temperature of dust grain, were studied by the quasi-diffusion method with an iterative technique for solving the radiative heat transfer equations. It was found that the generalized on-the-spot approximation solution is adequate for most astrophysical applications for a zero albedo; for a nonzero albedo, the Eddington approximation is more accurate. The albedo increases the average energy of the diffuse photons, increasing the ionization level of hydrogen and heavy elements if the Eddington approximation is applied; the dust thermal gradient is reduced so that the infrared spectrum approaches blackbody spectrum with an increasing albedo.

Analytic non-Maxwellian electron velocity distribution function in a Hall discharge plasma

NASA Astrophysics Data System (ADS)

Shagayda, Andrey; Tarasov, Alexey

2017-10-01

The electron velocity distribution function in the low-pressure discharges with the crossed electric and magnetic fields, which occur in magnetrons, plasma accelerators, and Hall thrusters with a closed electron drift, is not Maxwellian. A deviation from equilibrium is caused by a large electron mean free path relative to the Larmor radius and the size of the discharge channel. In this study, we derived in the relaxation approximation the analytical expression of the electron velocity distribution function in a weakly ionized Lorentz plasma with the crossed electric and magnetic fields in the presence of the electron density and temperature gradients in the direction of the electric field. The solution was obtained in the stationary approximation far from boundary surfaces, when diffusion and mobility are determined by the classical effective collision frequency of electrons with ions and atoms. The moments of the distribution function including the average velocity, the stress tensor, and the heat flux were calculated and compared with the classical hydrodynamic expressions. It was shown that a kinetic correction to the drift velocity stems from a contribution of the off-diagonal component of the stress tensor. This correction becomes essential if the drift velocity in the crossed electric and magnetic fields would be comparable to the thermal velocity of electrons. The electron temperature has three different components at a nonzero effective collision frequency and two different components in the limit when the collision frequency tends to zero. It is shown that, in the presence of ionization collisions, the components of the heat flux have additives that are not related to the temperature gradient, and arise because of the electron drift.

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1994-01-01

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Ballistic-diffusive approximation for the thermal dynamics of metallic nanoparticles in nanocomposite materials

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

Shirdel-Havar, A. H., E-mail: Amir.hushang.shirdel@gmail.com; Masoudian Saadabad, R.

2015-03-21

Based on ballistic-diffusive approximation, a method is presented to model heat transfer in nanocomposites containing metal nanoparticles. This method provides analytical expression for the temperature dynamics of metallic nanoparticles embedded in a dielectric medium. In this study, nanoparticles are considered as spherical shells, so that Boltzmann equation is solved using ballistic-diffusive approximation to calculate the electron and lattice thermal dynamics in gold nanoparticles, while thermal exchange between the particles is taken into account. The model was used to investigate the influence of particle size and metal concentration of the medium on the electron and lattice thermal dynamics. It is shownmore » that these two parameters are crucial in determining the nanocomposite thermal behavior. Our results showed that the heat transfer rate from nanoparticles to the matrix decreases as the nanoparticle size increases. On the other hand, increasing the metal concentration of the medium can also decrease the heat transfer rate.« less

New Monte Carlo model of cylindrical diffusing fibers illustrates axially heterogeneous fluorescence detection: simulation and experimental validation

PubMed Central

Baran, Timothy M.; Foster, Thomas H.

2011-01-01

We present a new Monte Carlo model of cylindrical diffusing fibers that is implemented with a graphics processing unit. Unlike previously published models that approximate the diffuser as a linear array of point sources, this model is based on the construction of these fibers. This allows for accurate determination of fluence distributions and modeling of fluorescence generation and collection. We demonstrate that our model generates fluence profiles similar to a linear array of point sources, but reveals axially heterogeneous fluorescence detection. With axially homogeneous excitation fluence, approximately 90% of detected fluorescence is collected by the proximal third of the diffuser for μs'/μa = 8 in the tissue and 70 to 88% is collected in this region for μs'/μa = 80. Increased fluorescence detection by the distal end of the diffuser relative to the center section is also demonstrated. Validation of these results was performed by creating phantoms consisting of layered fluorescent regions. Diffusers were inserted into these layered phantoms and fluorescence spectra were collected. Fits to these spectra show quantitative agreement between simulated fluorescence collection sensitivities and experimental results. These results will be applicable to the use of diffusers as detectors for dosimetry in interstitial photodynamic therapy. PMID:21895311

Slow-roll corrections in multi-field inflation: a separate universes approach

NASA Astrophysics Data System (ADS)

Karčiauskas, Mindaugas; Kohri, Kazunori; Mori, Taro; White, Jonathan

2018-05-01

In view of cosmological parameters being measured to ever higher precision, theoretical predictions must also be computed to an equally high level of precision. In this work we investigate the impact on such predictions of relaxing some of the simplifying assumptions often used in these computations. In particular, we investigate the importance of slow-roll corrections in the computation of multi-field inflation observables, such as the amplitude of the scalar spectrum Pζ, its spectral tilt ns, the tensor-to-scalar ratio r and the non-Gaussianity parameter fNL. To this end we use the separate universes approach and δ N formalism, which allows us to consider slow-roll corrections to the non-Gaussianity of the primordial curvature perturbation as well as corrections to its two-point statistics. In the context of the δ N expansion, we divide slow-roll corrections into two categories: those associated with calculating the correlation functions of the field perturbations on the initial flat hypersurface and those associated with determining the derivatives of the e-folding number with respect to the field values on the initial flat hypersurface. Using the results of Nakamura & Stewart '96, corrections of the first kind can be written in a compact form. Corrections of the second kind arise from using different levels of slow-roll approximation in solving for the super-horizon evolution, which in turn corresponds to using different levels of slow-roll approximation in the background equations of motion. We consider four different levels of approximation and apply the results to a few example models. The various approximations are also compared to exact numerical solutions.

Analyzing the errors of DFT approximations for compressed water systems

NASA Astrophysics Data System (ADS)

Alfè, D.; Bartók, A. P.; Csányi, G.; Gillan, M. J.

2014-07-01

We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm3 where the experimental pressure is 15 kilobars; second, thermal samples of compressed water clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mEh ≃ 15 meV/monomer for the liquid and the clusters.

Analyzing the errors of DFT approximations for compressed water systems

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

Alfè, D.; London Centre for Nanotechnology, UCL, London WC1H 0AH; Thomas Young Centre, UCL, London WC1H 0AH

We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm{sup 3} where the experimental pressure is 15 kilobars; second, thermal samples of compressed watermore » clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mE{sub h} ≃ 15 meV/monomer for the liquid and the clusters.« less

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media

NASA Technical Reports Server (NTRS)

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

2001-01-01

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.

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.

Evidence for equivalence of diffusion processes of passive scalar and magnetic fields in anisotropic Navier-Stokes turbulence.

PubMed

Jurčišinová, E; Jurčišin, M

2017-05-01

The influence of the uniaxial small-scale anisotropy on the kinematic magnetohydrodynamic turbulence is investigated by using the field theoretic renormalization group technique in the one-loop approximation of a perturbation theory. The infrared stable fixed point of the renormalization group equations, which drives the scaling properties of the model in the inertial range, is investigated as the function of the anisotropy parameters and it is shown that, at least at the one-loop level of approximation, the diffusion processes of the weak passive magnetic field in the anisotropically driven kinematic magnetohydrodynamic turbulence are completely equivalent to the corresponding diffusion processes of passively advected scalar fields in the anisotropic Navier-Stokes turbulent environments.

Anomalous current in diffusive ferromagnetic Josephson junctions

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Practical and adequate approach to modeling light propagation in an adult head with low-scattering regions by use of diffusion theory.

PubMed

Koyama, Tatsuya; Iwasaki, Atsushi; Ogoshi, Yosuke; Okada, Eiji

2005-04-10

A practical and adequate approach to modeling light propagation in an adult head with a low-scattering cerebrospinal fluid (CSF) region by use of diffusion theory was investigated. The diffusion approximation does not hold in a nonscattering or low-scattering regions. The hybrid radiosity-diffusion method was adopted to model the light propagation in the head with a nonscattering region. In the hybrid method the geometry of the nonscattering region is acquired as a priori information. In reality, low-level scattering occurs in the CSF region and may reduce the error caused by the diffusion approximation. The partial optical path length and the spatial sensitivity profile calculated by the finite-element method agree well with those calculated by the Monte Carlo method in the case in which the transport scattering coefficient of the CSF layer is greater than 0.3 mm(-1). Because it is feasible to assume that the transport scattering coefficient of a CSF layer is 0.3 mm(-1), it is practical to adopt diffusion theory to the modeling of light propagation in an adult head as an alternative to the hybrid method.

Practical and adequate approach to modeling light propagation in an adult head with low-scattering regions by use of diffusion theory

NASA Astrophysics Data System (ADS)

Koyama, Tatsuya; Iwasaki, Atsushi; Ogoshi, Yosuke; Okada, Eiji

2005-04-01

A practical and adequate approach to modeling light propagation in an adult head with a low-scattering cerebrospinal fluid (CSF) region by use of diffusion theory was investigated. The diffusion approximation does not hold in a nonscattering or low-scattering regions. The hybrid radiosity-diffusion method was adopted to model the light propagation in the head with a nonscattering region. In the hybrid method the geometry of the nonscattering region is acquired as a priori information. In reality, low-level scattering occurs in the CSF region and may reduce the error caused by the diffusion approximation. The partial optical path length and the spatial sensitivity profile calculated by the finite-element method agree well with those calculated by the Monte Carlo method in the case in which the transport scattering coefficient of the CSF layer is greater than 0.3 mm^-1. Because it is feasible to assume that the transport scattering coefficient of a CSF layer is 0.3 mm^-1, it is practical to adopt diffusion theory to the modeling of light propagation in an adult head as an alternative to the hybrid method.

Infrared diffuse interstellar bands

NASA Astrophysics Data System (ADS)

Galazutdinov, G. A.; Lee, Jae-Joon; Han, Inwoo; Lee, Byeong-Cheol; Valyavin, G.; Krełowski, J.

2017-05-01

We present high-resolution (R ˜ 45 000) profiles of 14 diffuse interstellar bands in the ˜1.45 to ˜2.45 μm range based on spectra obtained with the Immersion Grating INfrared Spectrograph at the McDonald Observatory. The revised list of diffuse bands with accurately estimated rest wavelengths includes six new features. The diffuse band at 15 268.2 Å demonstrates a very symmetric profile shape and thus can serve as a reference for finding the 'interstellar correction' to the rest wavelength frame in the H range, which suffers from a lack of known atomic/molecular lines.

Relative Roles of Gap Junction Channels and Cytoplasm in Cell-to-Cell Diffusion of Fluorescent Tracers

NASA Astrophysics Data System (ADS)

Safranyos, Richard G. A.; Caveney, Stanley; Miller, James G.; Petersen, Nils O.

1987-04-01

Intercellular (tissue) diffusion of molecules requires cytoplasmic diffusion and diffusion through gap junctional (or cell-to-cell) channels. The rates of tissue and cytoplasmic diffusion of fluorescent tracers, expressed as an effective diffusion coefficient, De, and a cytoplasmic diffusion coefficient, Dcyt, have been measured among the developing epidermal cells of a larval beetle, Tenebrio molitor L., to determine the contribution of the junctional channels to intercellular diffusion. Tracer diffusion was measured by injecting fluorescent tracers into cells and quantitating the rate of subsequent spread into adjacent cells. Cytoplasmic diffusion was determined by fluorescence photobleaching. These experiments show that gap junctional channels constitute approximately 70-80% of the total cell-to-cell resistance to the diffusion of organic tracers at high concentrations in this tissue. At low concentrations, however, the binding of tracer to cytoplasm slows down the cytoplasmic diffusion, which may limit intercellular diffusion.

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.

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

DOE PAGES

Grout, Ray; Kolla, Hemanth; Minion, Michael; ...

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. Here, we demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

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

Grout, Ray; Kolla, Hemanth; Minion, Michael

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited tomore » recovering from soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual on the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehen- sive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

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

Grout, Ray; Kolla, Hemanth; Minion, Michael

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Anomalous diffusion of single metal atoms on a graphene oxide support

DOE PAGES

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

2017-04-21

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

Validation of DWI pre-processing procedures for reliable differentiation between human brain gliomas.

PubMed

Vellmer, Sebastian; Tonoyan, Aram S; Suter, Dieter; Pronin, Igor N; Maximov, Ivan I

2018-02-01

Diffusion magnetic resonance imaging (dMRI) is a powerful tool in clinical applications, in particular, in oncology screening. dMRI demonstrated its benefit and efficiency in the localisation and detection of different types of human brain tumours. Clinical dMRI data suffer from multiple artefacts such as motion and eddy-current distortions, contamination by noise, outliers etc. In order to increase the image quality of the derived diffusion scalar metrics and the accuracy of the subsequent data analysis, various pre-processing approaches are actively developed and used. In the present work we assess the effect of different pre-processing procedures such as a noise correction, different smoothing algorithms and spatial interpolation of raw diffusion data, with respect to the accuracy of brain glioma differentiation. As a set of sensitive biomarkers of the glioma malignancy grades we chose the derived scalar metrics from diffusion and kurtosis tensor imaging as well as the neurite orientation dispersion and density imaging (NODDI) biophysical model. Our results show that the application of noise correction, anisotropic diffusion filtering, and cubic-order spline interpolation resulted in the highest sensitivity and specificity for glioma malignancy grading. Thus, these pre-processing steps are recommended for the statistical analysis in brain tumour studies. Copyright © 2017. Published by Elsevier GmbH.

Study of weak corrections to Drell-Yan, top-quark pair, and dijet production at high energies with MCFM

DOE PAGES

Campbell, John M.; Wackeroth, Doreen; Zhou, Jia

2016-11-29

Electroweak (EW) corrections can be enhanced at high energies due to the soft or collinear radiation of virtual and real W and Z bosons that result in Sudakov-like corrections of the form αmore » $$l\\atop{W}$$log n(Q 2/M2$$\\atop{W,Z}$$), where α W=α/(4π sin 2θ W) and n ≤ 2l-1. The inclusion of EW corrections in predictions for hadron colliders is, therefore, especially important when searching for signals of possible new physics in distributions probing the kinematic regime Q 2>>M$$2\\atop{V}$$. Next-to-leading order (NLO) EW corrections should also be taken into account when their size [O(α)] is comparable to that of QCD corrections at next-to-next-to-leading order (NNLO) [O(α$$2\\atop{s}$$)]. To this end, we have implemented the NLO weak corrections to the neutral-current Drell-Yan process, top-quark pair production and dijet production in the parton-level Monte Carlo program MCFM. This enables a combined study with the corresponding QCD corrections at NLO and NNLO. We provide both the full NLO weak corrections and their Sudakov approximation since the latter is often used for a fast evaluation of weak effects at high energies and can be extended to higher orders. Finally, with both the exact and approximate results at hand, the validity of the Sudakov approximation can be readily quantified.« less

Scattering of laser light - more than just smoke and mirrors

NASA Technical Reports Server (NTRS)

Davis, Anthony B.; Love, Stephen; Cahalan, Robert

2004-01-01

A short course on off-beam cloud lidar is given. Specific topics addressed include: motivation and goal of off-beam cloud lidar; diffusion physics; numeric amalysis; and validity of the diffusion approximation. A demo of the process is included.

Strongly anomalous diffusion in sheared magnetic configurations

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

Vanden Eijnden, E.; Balescu, R.

1996-03-01

The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface {ital x}=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface {ital x}=0. Due to the shear, the diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly non-Gaussian. The reference surface acts likemore » an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of the first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded that the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium. {copyright} {ital 1996 American Institute of Physics.}« less

Finite Difference Formulation for Prediction of Water Pollution

NASA Astrophysics Data System (ADS)

Johari, Hanani; Rusli, Nursalasawati; Yahya, Zainab

2018-03-01

Water is an important component of the earth. Human being and living organisms are demand for the quality of water. Human activity is one of the causes of the water pollution. The pollution happened give bad effect to the physical and characteristic of water contents. It is not practical to monitor all aspects of water flow and transport distribution. So, in order to help people to access to the polluted area, a prediction of water pollution concentration must be modelled. This study proposed a one-dimensional advection diffusion equation for predicting the water pollution concentration transport. The numerical modelling will be produced in order to predict the transportation of water pollution concentration. In order to approximate the advection diffusion equation, the implicit Crank Nicolson is used. For the purpose of the simulation, the boundary condition and initial condition, the spatial steps and time steps as well as the approximations of the advection diffusion equation have been encoded. The results of one dimensional advection diffusion equation have successfully been used to predict the transportation of water pollution concentration by manipulating the velocity and diffusion parameters.

Time delay of critical images in the vicinity of cusp point of gravitational-lens systems

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Zhdanov, V.

2016-12-01

We consider approximate analytical formulas for time-delays of critical images of a point source in the neighborhood of a cusp-caustic. We discuss zero, first and second approximations in powers of a parameter that defines the proximity of the source to the cusp. These formulas link the time delay with characteristics of the lens potential. The formula of zero approximation was obtained by Congdon, Keeton & Nordgren (MNRAS, 2008). In case of a general lens potential we derived first order correction thereto. If the potential is symmetric with respect to the cusp axis, then this correction is identically equal to zero. For this case, we obtained second order correction. The relations found are illustrated by a simple model example.

Characterization and Performance of the Suomi-NPP VIIRS Solar Diffuser Stability Monitor

NASA Technical Reports Server (NTRS)

Fulbright, Jon P.; Ning, Lei; Kwofu, Chiang; Xiaoxiong, Xiong

2012-01-01

We describe the on-orbit characterization and performance of the Solar Diffuser Stability Monitor (SDSM) on-board Suomi-NPP/VIIRS. This description includes the observing procedure of each SDSM event, the algorithms used to generate the Solar Diffuser degradation corrective factors, and the results for the mission to date. We will also compare the performance of the VIIRS SDSM and SD to the similar components operating on the MODIS instrument on the EOS Terra and Aqua satellites

3D early embryogenesis image filtering by nonlinear partial differential equations.

PubMed

Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O

2010-08-01

We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which are artificially connected due to acquisition error intrinsically linked to physics of LSM. In all studied aspects it turned out that the nonlinear diffusion filter which is called geodesic mean curvature flow (GMCF) has the best performance. Copyright 2010 Elsevier B.V. All rights reserved.

A HIGHWAY MODEL FOR THE ADVECTION, DIFFUSION AND CHEMICAL REACTION OF POLLUTANTS RELEASED BY AUTOMOBILES: PART I. ADVECTION AND DIFFUSION OF SF6 TRACER GAS

EPA Science Inventory

A two-dimensional, finite-difference model simulating a highway has been developed which is able to handle linear and nonlinear chemical reactions. Transport of the pollutants is accomplished by use of an upstream-flux-corrected algorithm developed at the Naval Research Laborator...

The True Color of Yogi: An Accurate Method for Removing Diffuse Illumination from Multispectral Images of Mars

NASA Technical Reports Server (NTRS)

Stoker, Carol R.; Rages, Kathy

2002-01-01

We correct spectra of Yogi to remove diffuse illumination and show that the part of Yogi facing the wind is less red than other faces of the rock. Our method eliminates ambiguity in interpreting spectra obtained under Mars illumination conditions. Additional information is contained in the original extended abstract.

The Role of Hypothetico-Deductive Reasoning and Physical Analogues of Molecular Interactions in Conceptual Change.

ERIC Educational Resources Information Center

Lawson, Anton E.; And Others

1993-01-01

The experimental/analogy group scored significantly higher than the control group on a posttest question that required the definition of diffusion (n=77 community college students). Hypothetico-deductive reasoning skill was significantly related to correct application of the diffusion concept to a change from the misapplication of the polarity and…

A Method of Correcting for Tilt From Horizontal in Downwelling Shortwave Irradiance Measurements on Moving Platforms

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

Long, Charles N.; Bucholtz, Anthony; Jonsson, Haf

2010-04-14

Significant errors occur in downwelling shortwave irradiance measurements made on moving platforms due to tilt from horizontal because, when the sun is not completely blocked by overhead cloud, the downwelling shortwave irradiance has a prominent directional component from the direct sun. A-priori knowledge of the partitioning between the direct and diffuse components of the total shortwave irradiance is needed to properly apply a correction for tilt. This partitioning information can be adequately provided using a newly available commercial radiometer that produces reasonable measurements of the total and diffuse shortwave irradiance, and by subtraction the direct shortwave irradiance, with no movingmore » parts and regardless of azimuthal orientation. We have developed methodologies for determining the constant pitch and roll offsets of the radiometers for aircraft applications, and for applying a tilt correction to the total shortwave irradiance data. Results suggest that the methodology is for tilt up to +/-10°, with 90% of the data corrected to within 10 Wm-2 at least for clear-sky data. Without a proper tilt correction, even data limited to 5° of tilt as is typical current practice still exhibits large errors, greater than 100 Wm-2 in some cases. Given the low cost, low weight, and low power consumption of the SPN1 total and diffuse radiometer, opportunities previously excluded for moving platform measurements such as small Unmanned Aerial Vehicles and solar powered buoys now become feasible using our methodology. The increase in measurement accuracy is important, given current concerns over long-term climate variability and change especially over the 70% of the Earth’s surface covered by ocean where long-term records of these measurements are sorely needed and must be made on ships and buoys.« less

Corrective action investigation plan for Corrective Action Unit Number 423: Building 03-60 Underground Discharge Point, Tonopah Test Range, Nevada

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

NONE

1997-10-27

This Corrective Action Investigation Plan (CAIP) contains the environmental sample collection objectives and the criteria for conducting site investigation activities at Corrective Action Unit (CAU) Number 423, the Building 03-60 Underground Discharge Point (UDP), which is located in Area 3 at the Tonopah Test Range (TTR). The TTR, part of the Nellis Air Force Range, is approximately 225 kilometers (140 miles) northwest of Las Vegas, Nevada. CAU Number 423 is comprised of only one Corrective Action Site (CAS) which includes the Building 03-60 UDP and an associated discharge line extending from Building 03-60 to a point approximately 73 meters (240more » feet) northwest. The UDP was used between approximately 1965 and 1990 to dispose of waste fluids from the Building 03-60 automotive maintenance shop. It is likely that soils surrounding the UDP have been impacted by oil, grease, cleaning supplies and solvents as well as waste motor oil and other automotive fluids released from the UDP.« less

All-electron quasiparticle self-consistent GW band structures for SrTiO 3 including lattice polarization corrections in different phases

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

Bhandari, Churna; van Schilfgaarde, Mark; Kotani, Takao

The electronic band structure of SrTiO3 is investigated in the all-electron quasiparticle self-consistent GW (QSGW) approximation. Unlike previous pseudopotential-based QSGW or single-shot G0W0 calculations, the gap is found to be significantly overestimated compared to experiment. After putting in a correction for the underestimate of the screening by the random phase approximation in terms of a 0.8Σ approach, the gap is still overestimated. The 0.8Σ approach is discussed and justified in terms of various recent literature results including electron-hole corrections. Adding a lattice polarization correction (LPC) in the q→0 limit for the screening of W, agreement with experiment is recovered. Themore » LPC is alternatively estimated using a polaron model. Here, we apply our approach to the cubic and tetragonal phases as well as a hypothetical layered postperovskite structure and find that the local density approximation (LDA) to GW gap correction is almost independent of structure.« less

All-electron quasiparticle self-consistent GW band structures for SrTiO 3 including lattice polarization corrections in different phases

DOE PAGES

Bhandari, Churna; van Schilfgaarde, Mark; Kotani, Takao; ...

2018-01-23

The electronic band structure of SrTiO3 is investigated in the all-electron quasiparticle self-consistent GW (QSGW) approximation. Unlike previous pseudopotential-based QSGW or single-shot G0W0 calculations, the gap is found to be significantly overestimated compared to experiment. After putting in a correction for the underestimate of the screening by the random phase approximation in terms of a 0.8Σ approach, the gap is still overestimated. The 0.8Σ approach is discussed and justified in terms of various recent literature results including electron-hole corrections. Adding a lattice polarization correction (LPC) in the q→0 limit for the screening of W, agreement with experiment is recovered. Themore » LPC is alternatively estimated using a polaron model. Here, we apply our approach to the cubic and tetragonal phases as well as a hypothetical layered postperovskite structure and find that the local density approximation (LDA) to GW gap correction is almost independent of structure.« less

Breakdown of the single-exchange approximation in third-order symmetry-adapted perturbation theory.

PubMed

Lao, Ka Un; Herbert, John M

2012-03-22

We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for (E(exch-ind)((30))), based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a "hybrid" SAPT approach, in which a dimer Hartree-Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange-induction formulas that go beyond the SEA. © 2012 American Chemical Society

SeaWiFS long-term solar diffuser reflectance trend analysis

NASA Astrophysics Data System (ADS)

Eplee, Robert E., Jr.; Patt, Frederick S.; Barnes, Robert A.; McClain, Charles R.

2006-08-01

The NASA Ocean Biology Processing Group's Calibration and Validation (Cal/Val) Team implemented daily solar calibrations of SeaWiFS to look for step-function changes in the instrument response and has used these calibrations to supplement the monthly lunar calibrations in monitoring the radiometric stability of SeaWiFS during its first year of on-orbit operations. The Team has undertaken an analysis of the mission-long solar calibration time series, with the lunar-derived radiometric corrections over time applied, to assess the long-term degradation of the solar diffuser reflectance over nine years on orbit. The SeaWiFS diffuser is an aluminum plate coated with YB71 paint. The bidirectional reflectance distribution function of the diffuser was not fully characterized before launch, so the Cal/Val Team has implemented a regression of the solar incidence angles and the drift in the node of the satellite's orbit against the diffuser time series to correct for solar incidence angle effects. An exponential function with a time constant of 200 days yields the best fit to the diffuser time series. The decrease in diffuser reflectance over the mission is wavelength-dependent, ranging from 9% in the blue (412 nm) to 5% in the red and near infrared (670-865 nm). The degradation of diffuser reflctance is similar to that observed for SeaWiFS radiometric response itself from lunar calibration time series for bands 1-5 (412-555 nm), though the magnitude of the change is four times larger for the diffuser. Evidently, the same optical degradation process has affected both the telescope optics and the solar diffuser in the blue and green. The Cal/Val Team has developed a methodology for computing the signal-to-noise ratio (SNR) for SeaWiFS on orbit from the diffuser time series. The on-orbit change in the SNR for each band over the nine-year mission is less than 7%. The on-orbit performance of the SeaWiFS solar diffuser should offer insight into the long-term on-orbit performance of solar diffusers on other instruments, such as MODIS, VIIRS, and ABI.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

Effect of Impurities on O and Al Boundary Diffusion in Alumina: Application Alumina Scale Growth in Alloys

DTIC Science & Technology

2012-01-24

of Ni alone enhances transport by approximately a factor of 2 relative to undoped alumina. The diffusive transport of chromium in both pure and Y...doped fine-grained alumina has been investigated over the temperature range 1250 -1650 C. From a quantitative assessment of the chromium diffusion...diffusion of chromium in both undoped and Y-doped fine-grained alumina has been investigated. In this work, Cr + was employed as a plausible substitute

SENSIT.FOR: A program for sensitometric reduction

NASA Astrophysics Data System (ADS)

Maury, A.; Marchal, J.

1984-09-01

A FORTRAN program for sensitometric evaluation of processes involved in hypering astronomical plates was written. It contains subroutines for full or quick description of the operation being done; choice of type of sensitogram; creation of 16 subfiles in the scan; density filtering; correction for area; specular PDS to diffuse ISO density calibration; and fog correction.

A Fast Hyperspectral Vector Radiative Transfer Model in UV to IR spectral bands

NASA Astrophysics Data System (ADS)

Ding, J.; Yang, P.; Sun, B.; Kattawar, G. W.; Platnick, S. E.; Meyer, K.; Wang, C.

2016-12-01

We develop a fast hyperspectral vector radiative transfer model with a spectral range from UV to IR with 5 nm resolutions. This model can simulate top of the atmosphere (TOA) diffuse radiance and polarized reflectance by considering gas absorption, Rayleigh scattering, and aerosol and cloud scattering. The absorption component considers several major atmospheric absorbers such as water vapor, CO2, O3, and O2 including both line and continuum absorptions. A regression-based method is used to parameterize the layer effective optical thickness for each gas, which substantially increases the computation efficiency for absorption while maintaining high accuracy. This method is over 500 times faster than the existing line-by-line method. The scattering component uses the successive order of scattering (SOS) method. For Rayleigh scattering, convergence is fast due to the small optical thickness of atmospheric gases. For cloud and aerosol layers, a small-angle approximation method is used in SOS calculations. The scattering process is divided into two parts, a forward part and a diffuse part. The scattering in the small-angle range in the forward direction is approximated as forward scattering. A cloud or aerosol layer is divided into thin layers. As the ray propagates through each thin layer, a portion diverges as diffuse radiation, while the remainder continues propagating in forward direction. The computed diffuse radiance is the sum of all of the diffuse parts. The small-angle approximation makes the SOS calculation converge rapidly even in a thick cloud layer.

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

NASA Astrophysics Data System (ADS)

Nec, Yana

2018-01-01

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

Optical tomography in the presence of void regions

PubMed

Dehghani; Arridge; Schweiger; Delpy

2000-09-01

There is a growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in the use of this technique for obtaining tomographic images of the neonatal head, with the view of determining the levels of oxygenated and deoxygenated blood within the brain. Owing to computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region location; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases in which there exists a nonscattering region. We present reconstructed images of objects that contain a nonscattering region within a diffusive material. Here the forward data is calculated with the radiosity-diffusion model, and the inverse problem is solved with either the radiosity-diffusion model or the diffusion-only model. The reconstructed images show that even in the presence of only a thin nonscattering layer, a diffusion-only reconstruction will fail. When a radiosity-diffusion model is used for image reconstruction, together with a priori information about the position of the nonscattering region, the quality of the reconstructed image is considerably improved. The accuracy of the reconstructed images depends largely on the position of the anomaly with respect to the nonscattering region as well as the thickness of the nonscattering region.

Self-diffusion in dense granular shear flows.

PubMed

Utter, Brian; Behringer, R P

2004-03-01

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

Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions

NASA Astrophysics Data System (ADS)

Chebotarev, Alexander Yu.; Grenkin, Gleb V.; Kovtanyuk, Andrey E.; Botkin, Nikolai D.; Hoffmann, Karl-Heinz

2018-04-01

The paper is concerned with a problem of diffraction type. The study starts with equations of complex (radiative and conductive) heat transfer in a multicomponent domain with Fresnel matching conditions at the interfaces. Applying the diffusion, P1, approximation yields a pair of coupled nonlinear PDEs describing the radiation intensity and temperature for each component of the domain. Matching conditions for these PDEs, imposed at the interfaces between the domain components, are derived. The unique solvability of the obtained problem is proven, and numerical experiments are conducted.

Dissolution and solubility behavior of fenofibrate in sodium lauryl sulfate solutions.

PubMed

Granero, Gladys E; Ramachandran, Chandrasekharan; Amidon, Gordon L

2005-10-01

The solubility of fenofibrate in pH 6.8 McIlvaine buffers containing varying concentrations of sodium lauryl sulfate was determined. The dissolution behavior of fenofibrate was also examined in the same solutions with rotating disk experiments. It was observed that the enhancement in intrinsic dissolution rate was approximately 500-fold and the enhancement in solubility was approximately 2000-fold in a pH 6.8 buffer containing 2% (w/v) sodium lauryl sulfate compared to that in buffer alone. The micellar solubilization equilibrium coefficient (k*) was estimated from the solubility data and found to be 30884+/-213 L/mol. The diffusivity for the free solute, 7.15x10(-6) cm2/s, was calculated using Schroeder's additive molal volume estimates and Hayduk-Laurie correlation. The diffusivity of the drug-loaded micelle, estimated from the experimental solubility and dissolution data and the calculated value for free solute diffusivity, was 0.86x10(-6) cm2/s. Thus, the much lower enhancement in dissolution of fenofibrate compared to its enhancement in solubility in surfactant solutions appears to be consistent with the contribution to the total transport due to enhanced micellar solubilization as well as a large decrease (approximately 8-fold) in the diffusivity of the drug-loaded micelle.

Stormtime transport of ring current and radiation belt ions

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, L. R.; Gorney, David J.

1993-01-01

This is an investigation of stormtime particle transport that leads to formation of the ring current. Our method is to trace the guiding-center motion of representative ions (having selected first adiabatic invariants mu) in response to model substorm-associated impulses in the convection electric field. We compare our simulation results qualitatively with existing analytically tractable idealizations of particle transport (direct convective access and radial diffusion) in order to assess the limits of validity of these approximations. For mu approximately less than 10 MeV/G (E approximately less than 10 keV at L equivalent to 3) the ion drift period on the final (ring-current) drift shell of interest (L equivalent to 3) exceeds the duration of the main phase of our model storm, and we find that the transport of ions to this drift shell is appropriately idealized as direct convective access, typically from open drift paths. Ion transport to a final closed drift path from an open (plasma-sheet) drift trajectory is possible for those portions of that drift path that lie outside the mean stormtime separatrix between closed and open drift trajectories, For mu approximately 10-25 MeV/G (110 keV approximately less than E approximately less than 280 keV at L equivalent to 3) the drift period at L equivalent to 3 is comparable to the postulated 3-hr duration of the storm, and the mode of transport is transitional between direct convective access and transport that resembles radial diffusion. (This particle population is transitional between the ring current and radiation belt). For mu approximately greater than 25 MeV/G (radiation-belt ions having E approximately greater than 280 keV at L equivalent to 3) the ion drift period is considerably shorter than the main phase of a typical storm, and ions gain access to the ring-current region essentially via radial diffusion. By computing the mean and mean-square cumulative changes in 1/L among (in this case) 12 representative ions equally spaced in drift time around the steady-state drift shell of interest (L equivalent to 3), we have estimated (from both our forward and our time-reversed simulations) the time-integrated radial-diffusion coefficients D(sup sim)(sub LL) for particles having selected values of mu approximately greater than 15 MeV/G. The results agree surprisingly well with the predictions (D(sup ql)(sub LL)) of quasilinear radial diffusion theory, despite the rather brief duration (approximately 3 hrs) of our model storm and despite the extreme variability (with frequency) of the spectral-density function that characterizes the applied electric field during our model storm. As expected, the values of D(sup sim)(sub LL) deduced (respectively) from our forward and time-reversed simulations agree even better with each other and with D(sup sim)(sub LL) when the impulse amplitudes which characterize the individual substorms of our model storm are systematically reduced.

Virtual Excitation and Multiple Scattering Correction Terms to the Neutron Index of Refraction for Hydrogen.

PubMed

Schoen, K; Snow, W M; Kaiser, H; Werner, S A

2005-01-01

The neutron index of refraction is generally derived theoretically in the Fermi approximation. However, the Fermi approximation neglects the effects of the binding of the nuclei of a material as well as multiple scattering. Calculations by Nowak introduced correction terms to the neutron index of refraction that are quadratic in the scattering length and of order 10(-3) fm for hydrogen and deuterium. These correction terms produce a small shift in the final value for the coherent scattering length of H2 in a recent neutron interferometry experiment.

Entanglement renormalization, quantum error correction, and bulk causality

NASA Astrophysics Data System (ADS)

Kim, Isaac H.; Kastoryano, Michael J.

2017-04-01

Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progres-sively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.

On basis set superposition error corrected stabilization energies for large n-body clusters.

PubMed

Walczak, Katarzyna; Friedrich, Joachim; Dolg, Michael

2011-10-07

In this contribution, we propose an approximate basis set superposition error (BSSE) correction scheme for the site-site function counterpoise and for the Valiron-Mayer function counterpoise correction of second order to account for the basis set superposition error in clusters with a large number of subunits. The accuracy of the proposed scheme has been investigated for a water cluster series at the CCSD(T), CCSD, MP2, and self-consistent field levels of theory using Dunning's correlation consistent basis sets. The BSSE corrected stabilization energies for a series of water clusters are presented. A study regarding the possible savings with respect to computational resources has been carried out as well as a monitoring of the basis set dependence of the approximate BSSE corrections. © 2011 American Institute of Physics

Integral imaging based light field display with enhanced viewing resolution using holographic diffuser

NASA Astrophysics Data System (ADS)

Yan, Zhiqiang; Yan, Xingpeng; Jiang, Xiaoyu; Gao, Hui; Wen, Jun

2017-11-01

An integral imaging based light field display method is proposed by use of holographic diffuser, and enhanced viewing resolution is gained over conventional integral imaging systems. The holographic diffuser is fabricated with controlled diffusion characteristics, which interpolates the discrete light field of the reconstructed points to approximate the original light field. The viewing resolution can thus be improved and independent of the limitation imposed by Nyquist sampling frequency. An integral imaging system with low Nyquist sampling frequency is constructed, and reconstructed scenes of high viewing resolution using holographic diffuser are demonstrated, verifying the feasibility of the method.

Utilising shade to optimize UV exposure for vitamin D

NASA Astrophysics Data System (ADS)

Turnbull, D. J.; Parisi, A. V.

2008-01-01

Numerous studies have stated that humans need to utilise full sun radiation, at certain times of the day, to assist the body in synthesising the required levels of vitamin D3. The time needed to be spent in the full sun depends on a number of factors, for example, age, skin type, latitude, solar zenith angle. Current Australian guidelines suggest exposure to approximately 1/6 to 1/3 of a minimum erythemal dose (MED), depending on age, would be appropriate to provide adequate vitamin D3 levels. The aim of the study was to determine the exposure times to diffuse solar UV to receive exposures of 1/6 and 1/3 MED for a changing solar zenith angle in order to assess the possible role that diffuse UV (scattered radiation) may play in vitamin D3 effective UV exposures (UVD3). Diffuse and global erythemal UV measurements were conducted at five minute intervals over a twelve month period for a solar zenith angle range of 4° to 80° at a latitude of 27.6° S. For diffuse UV exposures of 1/6 and 1/3 MED, solar zenith angles smaller than 60° and 50° respectively can be utilised for exposure times of less than 10 min. Spectral measurements showed that, for a solar zenith angle of 40°, the UVA (315-400 nm) in the diffuse component of the solar UV is reduced by approximately 62% compared to the UVA in the global UV, whereas UVD3 wavelengths are only reduced by approximately 43%. At certain latitudes, diffuse UV under shade may play an important role in providing the human body with adequate levels of UVD3 (290-330 nm) radiation without experiencing the high levels of damaging UVA observed in full sun.

Approximate Analytical Time-Dependent Solutions to Describe Large-Amplitude Local Calcium Transients in the Presence of Buffers

PubMed Central

Mironova, Lidia A.; Mironov, Sergej L.

2008-01-01

Local Ca2+ signaling controls many neuronal functions, which is often achieved through spatial localization of Ca2+ signals. These nanodomains are formed due to combined effects of Ca2+ diffusion and binding to the cytoplasmic buffers. In this article we derived simple analytical expressions to describe Ca2+ diffusion in the presence of mobile and immobile buffers. A nonlinear character of the reaction-diffusion problem was circumvented by introducing a logarithmic approximation of the concentration term. The obtained formulas reproduce free Ca2+ levels up to 50 μM and their changes in the millisecond range. Derived equations can be useful to predict spatiotemporal profiles of large-amplitude [Ca2+] transients, which participate in various physiological processes. PMID:17872951

Nonequilibrium Fluctuations and Enhanced Diffusion of a Driven Particle in a Dense Environment

NASA Astrophysics Data System (ADS)

Illien, Pierre; Bénichou, Olivier; Oshanin, Gleb; Sarracino, Alessandro; Voituriez, Raphaël

2018-05-01

We study the diffusion of a tracer particle driven out of equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the tracer induced by both the crowding interactions and the external driving. We finally consider the high-density and low-density limits of the model and show that our approximation scheme becomes exact in these limits.

Low Noise in a Diffusion-Cooled Hot-Electron Mixer at 2.5 THz

NASA Technical Reports Server (NTRS)

Karasik, B. S.; Gaidis, M. C.; McGrath, W. R.; Bumble, B.; LeDuc, H. G.

1997-01-01

The noise performance of a Nb hot-electron bolometer mixer at 2.5 THz has been investigated. The devices are fabricated from a 12-nm-thick Nb film, and have a 0.30 micrometer x 0.15 micrometer in-plane size, thus exploiting diffusion as the electron cooling mechanism. The rf coupling was provided by a twin-slot planar antenna on an elliptical Si lens. The experimentally measured double sideband noise temperature of the receiver was as low as 2750 +/- 250 K with an estimated mixer noise temperature of approximately equal 900 K. The mixer bandwidth derived from both noise bandwidth and IF impedance measurements was approximately equal 1.4 GHz. These results demonstrate the low-noise operation of the diffusion-cooled bolometer mixer above 2 THz.

A minimalistic approach to static and dynamic electron correlations: Amending generalized valence bond method with extended random phase approximation correlation correction

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

Chatterjee, Koushik; Jawulski, Konrad; Pastorczak, Ewa

A perfect-pairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples ofmore » systems of diverse electronic structures, we show that the resulting ERPA-GVB method greatly improves upon the GVB model. ERPA-GVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPA-GVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play.« less

On proton excitation of forbidden lines in positive ions

NASA Astrophysics Data System (ADS)

Burgess, Alan; Tully, John A.

2005-08-01

The semi-classical impact parameter approximations used by Bahcall and Wolf and by Bely and Faucher, for proton excitation of electric quadrupole transitions in positive ions, both fail at high energies, giving cross sections which do not fall off correctly as constant/E. This is in contrast with the pioneering example of Seaton for Fe+13 and of Reid and Schwarz for S+3, both of whom achieve the correct functional form, but do not ensure the correct constant of proportionality. By combining the Born and semi-classical approximations one can obtain cross sections which have the full correct behaviour as E → ∞, and hence, rate coefficients which have the correct high temperature behaviour (~C/T1/2 with the correct value of C). We provide a computer program for calculating these. An error in Faucher's derivation of the Born formula is also discussed.

A Correction for the Epsilon Approximate Test in Repeated Measures Designs with Two or More Independent Groups.

ERIC Educational Resources Information Center

Lecoutre, Bruno

1991-01-01

The routine epsilon approximate test in repeated measures designs when the condition of circularity is unfulfilled uses an erroneous formula in the case of two or more groups. Because this may lead to underestimation of the deviation from circularity when the subject number is small, a correction is proposed. (Author/SLD)

Messages Do Diffuse Faster than Messengers: Reconciling Disparate Estimates of the Morphogen Bicoid Diffusion Coefficient

PubMed Central

Sigaut, Lorena; Pearson, John E.; Colman-Lerner, Alejandro; Ponce Dawson, Silvina

2014-01-01

The gradient of Bicoid (Bcd) is key for the establishment of the anterior-posterior axis in Drosophila embryos. The gradient properties are compatible with the SDD model in which Bcd is synthesized at the anterior pole and then diffuses into the embryo and is degraded with a characteristic time. Within this model, the Bcd diffusion coefficient is critical to set the timescale of gradient formation. This coefficient has been measured using two optical techniques, Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Correlation Spectroscopy (FCS), obtaining estimates in which the FCS value is an order of magnitude larger than the FRAP one. This discrepancy raises the following questions: which estimate is "correct''; what is the reason for the disparity; and can the SDD model explain Bcd gradient formation within the experimentally observed times? In this paper, we use a simple biophysical model in which Bcd diffuses and interacts with binding sites to show that both the FRAP and the FCS estimates may be correct and compatible with the observed timescale of gradient formation. The discrepancy arises from the fact that FCS and FRAP report on different effective (concentration dependent) diffusion coefficients, one of which describes the spreading rate of the individual Bcd molecules (the messengers) and the other one that of their concentration (the message). The latter is the one that is more relevant for the gradient establishment and is compatible with its formation within the experimentally observed times. PMID:24901638

Broadening of polymer chromatographic signals: Analysis, quantification and correction through effective diffusion coefficients.

PubMed

Suárez, Inmaculada; Coto, Baudilio

2015-08-14

Average molecular weights and polydispersity indexes are some of the most important parameters considered in the polymer characterization. Usually, gel permeation chromatography (GPC) and multi angle light scattering (MALS) are used for this determination, but GPC values are overestimated due to the dispersion introduced by the column separation. Several procedures were proposed to correct such effect usually involving more complex calibration processes. In this work, a new method of calculation has been considered including diffusion effects. An equation for the concentration profile due to diffusion effects along the GPC column was considered to be a Fickian function and polystyrene narrow standards were used to determine effective diffusion coefficients. The molecular weight distribution function of mono and poly disperse polymers was interpreted as a sum of several Fickian functions representing a sample formed by only few kind of polymer chains with specific molecular weight and diffusion coefficient. Proposed model accurately fit the concentration profile along the whole elution time range as checked by the computed standard deviation. Molecular weights obtained by this new method are similar to those obtained by MALS or traditional GPC while polydispersity index values are intermediate between those obtained by the traditional GPC combined to Universal Calibration method and the MALS method. Values for Pearson and Lin coefficients shows improvement in the correlation of polydispersity index values determined by GPC and MALS methods when diffusion coefficients and new methods are used. Copyright © 2015 Elsevier B.V. All rights reserved.

Messages do diffuse faster than messengers: reconciling disparate estimates of the morphogen bicoid diffusion coefficient.

PubMed

Sigaut, Lorena; Pearson, John E; Colman-Lerner, Alejandro; Ponce Dawson, Silvina

2014-06-01

The gradient of Bicoid (Bcd) is key for the establishment of the anterior-posterior axis in Drosophila embryos. The gradient properties are compatible with the SDD model in which Bcd is synthesized at the anterior pole and then diffuses into the embryo and is degraded with a characteristic time. Within this model, the Bcd diffusion coefficient is critical to set the timescale of gradient formation. This coefficient has been measured using two optical techniques, Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Correlation Spectroscopy (FCS), obtaining estimates in which the FCS value is an order of magnitude larger than the FRAP one. This discrepancy raises the following questions: which estimate is "correct''; what is the reason for the disparity; and can the SDD model explain Bcd gradient formation within the experimentally observed times? In this paper, we use a simple biophysical model in which Bcd diffuses and interacts with binding sites to show that both the FRAP and the FCS estimates may be correct and compatible with the observed timescale of gradient formation. The discrepancy arises from the fact that FCS and FRAP report on different effective (concentration dependent) diffusion coefficients, one of which describes the spreading rate of the individual Bcd molecules (the messengers) and the other one that of their concentration (the message). The latter is the one that is more relevant for the gradient establishment and is compatible with its formation within the experimentally observed times.

Conservation laws in the quantum Hall Liouvillian theory and its generalizations

NASA Astrophysics Data System (ADS)

Moore, Joel E.

2003-06-01

It is known that the localization length scaling of noninteracting electrons near the quantum Hall plateau transition can be described in a theory of the bosonic density operators, with no reference to the underlying fermions. The resulting "Liouvillian" theory has a U(1|1) global supersymmetry as well as a hierarchy of geometric conservation laws related to the noncommutative geometry of the lowest Landau level (LLL). Approximations to the Liouvillian theory contain quite different physics from standard approximations to the underlying fermionic theory. Mean-field and large- N generalizations of the Liouvillian are shown to describe problems of noninteracting bosons that enlarge the U(1|1) supersymmetry to U(1|1)× SO( N) or U(1|1)× SU( N). These noninteracting bosonic problems are studied numerically for 2⩽ N⩽8 by Monte Carlo simulation and compared to the original N=1 Liouvillian theory. The N>1 generalizations preserve the first two of the hierarchy of geometric conservation laws, leading to logarithmic corrections at order 1/ N to the diffusive large- N limit, but do not preserve the remaining conservation laws. The emergence of nontrivial scaling at the plateau transition, in the Liouvillian approach, is shown to depend sensitively on the unusual geometry of Landau levels.

Kinetics of binary nucleation of vapors in size and composition space.

PubMed

Fisenko, Sergey P; Wilemski, Gerald

2004-11-01

We reformulate the kinetic description of binary nucleation in the gas phase using two natural independent variables: the total number of molecules g and the molar composition x of the cluster. The resulting kinetic equation can be viewed as a two-dimensional Fokker-Planck equation describing the simultaneous Brownian motion of the clusters in size and composition space. Explicit expressions for the Brownian diffusion coefficients in cluster size and composition space are obtained. For characterization of binary nucleation in gases three criteria are established. These criteria establish the relative importance of the rate processes in cluster size and composition space for different gas phase conditions and types of liquid mixtures. The equilibrium distribution function of the clusters is determined in terms of the variables g and x. We obtain an approximate analytical solution for the steady-state binary nucleation rate that has the correct limit in the transition to unary nucleation. To further illustrate our description, the nonequilibrium steady-state cluster concentrations are found by numerically solving the reformulated kinetic equation. For the reformulated transient problem, the relaxation or induction time for binary nucleation was calculated using Galerkin's method. This relaxation time is affected by processes in both size and composition space, but the contributions from each process can be separated only approximately.

Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model

NASA Technical Reports Server (NTRS)

Sommer, T. P.; So, R. M. C.; Zhang, H. S.

1993-01-01

A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies.

Quantitative Microplate-Based Respirometry with Correction for Oxygen Diffusion

PubMed Central

2009-01-01

Respirometry using modified cell culture microplates offers an increase in throughput and a decrease in biological material required for each assay. Plate based respirometers are susceptible to a range of diffusion phenomena; as O2 is consumed by the specimen, atmospheric O2 leaks into the measurement volume. Oxygen also dissolves in and diffuses passively through the polystyrene commonly used as a microplate material. Consequently the walls of such respirometer chambers are not just permeable to O2 but also store substantial amounts of gas. O2 flux between the walls and the measurement volume biases the measured oxygen consumption rate depending on the actual [O2] gradient. We describe a compartment model-based correction algorithm to deconvolute the biological oxygen consumption rate from the measured [O2]. We optimize the algorithm to work with the Seahorse XF24 extracellular flux analyzer. The correction algorithm is biologically validated using mouse cortical synaptosomes and liver mitochondria attached to XF24 V7 cell culture microplates, and by comparison to classical Clark electrode oxygraph measurements. The algorithm increases the useful range of oxygen consumption rates, the temporal resolution, and durations of measurements. The algorithm is presented in a general format and is therefore applicable to other respirometer systems. PMID:19555051

Asymptotic, multigroup flux reconstruction and consistent discontinuity factors

DOE PAGES

Trahan, Travis J.; Larsen, Edward W.

2015-05-12

Recent theoretical work has led to an asymptotically derived expression for reconstructing the neutron flux from lattice functions and multigroup diffusion solutions. The leading-order asymptotic term is the standard expression for flux reconstruction, i.e., it is the product of a shape function, obtained through a lattice calculation, and the multigroup diffusion solution. The first-order asymptotic correction term is significant only where the gradient of the diffusion solution is not small. Inclusion of this first-order correction term can significantly improve the accuracy of the reconstructed flux. One may define discontinuity factors (DFs) to make certain angular moments of the reconstructed fluxmore » continuous across interfaces between assemblies in 1-D. Indeed, the standard assembly discontinuity factors make the zeroth moment (scalar flux) of the reconstructed flux continuous. The inclusion of the correction term in the flux reconstruction provides an additional degree of freedom that can be used to make two angular moments of the reconstructed flux continuous across interfaces by using current DFs in addition to flux DFs. Thus, numerical results demonstrate that using flux and current DFs together can be more accurate than using only flux DFs, and that making the second angular moment continuous can be more accurate than making the zeroth moment continuous.« less

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.

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

PubMed

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

2008-01-01

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

SeaWiFS long-term solar diffuser reflectance and sensor noise analyses.

PubMed

Eplee, Robert E; Patt, Frederick S; Barnes, Robert A; McClain, Charles R

2007-02-10

The NASA Ocean Biology Processing Group's Calibration and Validation (Cal/Val) team has undertaken an analysis of the mission-long Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) solar calibration time series to assess the long-term degradation of the solar diffuser reflectance over 9 years on orbit. The SeaWiFS diffuser is an aluminum plate coated with YB71 paint. The bidirectional reflectance distribution function of the diffuser was not fully characterized before launch, so the Cal/Val team has implemented a regression of the solar incidence angles and the drift in the node of the satellite's orbit against the diffuser time series to correct for solar incidence angle effects. An exponential function with a time constant of 200 days yields the best fit to the diffuser time series. The decrease in diffuser reflectance over the mission is wavelength dependent, ranging from 9% in the blue (412 nm) to 5% in the red and near infrared (670-865 nm). The Cal/Val team has developed a methodology for computing the signal-to-noise ratio (SNR) for SeaWiFS on orbit from the diffuser time series corrected for both the varying solar incidence angles and the diffuser reflectance degradation. A sensor noise model is used to compare on-orbit SNRs computed for radiances reflected from the diffuser with prelaunch SNRs measured at typical radiances specified for the instrument. To within the uncertainties in the measurements, the SNRs for SeaWiFS have not changed over the mission. The on-orbit performance of the SeaWiFS solar diffuser should offer insight into the long-term on-orbit performance of solar diffusers on other instruments, such as the Moderate-Resolution Imaging Spectrometer [currently flying on the Earth Observing System (EOS) Terra and Aqua satellites], the Visible and Infrared Radiometer Suite [scheduled to fly on the NASA National Polar-orbiting Operational Environmental Satellite System (NPOESS) and NPOESS Preparatory Project (NPP) satellites] and the Advanced Baseline Imager [scheduled to fly on the National Oceanic and Atmospheric Administration Geostationary Environmental Operational Satellite Series R (GOES-R) satellites].

SeaWiFS long-term solar diffuser reflectance and sensor noise analyses

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

Eplee, Robert E. Jr.; Patt, Frederick S.; Barnes, Robert A.

The NASA Ocean Biology Processing Group's Calibration and Validation(Cal/Val) team has undertaken an analysis of the mission-long Sea-Viewing Wide Field-of-View Sensor (SeaWiFS)solar calibration time series to assess the long-term degradation of the solar diffuser reflectance over 9 years on orbit. The SeaWiFS diffuser is an aluminum plate coated with YB71 paint. The bidirectional reflectance distribution function of the diffuser was not fully characterized before launch,so the Cal/Val team has implemented a regression of the solar incidence angles and the drift in the node of the satellite's orbit against the diffuser time series to correct for solar incidence angle effects. Anmore » exponential function with a time constant of 200 days yields the best fit to the diffuser time series.The decrease in diffuser reflectance over the mission is wavelength dependent,ranging from 9% in the blue(412 nm) to 5% in the red and near infrared(670-865 nm). The Cal/Val team has developed a methodology for computing the signal-to-noise ratio (SNR) for SeaWiFS on orbit from the diffuser time series corrected for both the varying solar incidence angles and the diffuser reflectance degradation. A sensor noise model is used to compare on-orbit SNRs computed for radiances reflected from the diffuser with prelaunch SNRs measured at typical radiances specified for the instrument. To within the uncertainties in the measurements, the SNRs for SeaWiFS have not changed over the mission. The on-orbit performance of the SeaWiFS solar diffuser should offer insight into the long-term on-orbit performance of solar diffusers on other instruments, such as the Moderate-Resolution Imaging Spectrometer [currently flying on the Earth Observing System (EOS) Terra and Aqua satellites], the Visible and Infrared Radiometer Suite [scheduled to fly on the NASA National Polar-orbiting Operational Environmental Satellite System (NPOESS) and NPOESS Preparatory Project (NPP) satellites] and the Advanced Baseline Imager [scheduled to fly on the National Oceanic and Atmospheric Administration Geostationary Environmental Operational Satellite Series R (GOES-R) satellites].« less

SeaWiFS long-term solar diffuser reflectance and sensor noise analyses

NASA Astrophysics Data System (ADS)

Eplee, Robert E., Jr.; Patt, Frederick S.; Barnes, Robert A.; McClain, Charles R.

2007-02-01

The NASA Ocean Biology Processing Group's Calibration and Validation (Cal/Val) team has undertaken an analysis of the mission-long Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) solar calibration time series to assess the long-term degradation of the solar diffuser reflectance over 9 years on orbit. The SeaWiFS diffuser is an aluminum plate coated with YB71 paint. The bidirectional reflectance distribution function of the diffuser was not fully characterized before launch, so the Cal/Val team has implemented a regression of the solar incidence angles and the drift in the node of the satellite's orbit against the diffuser time series to correct for solar incidence angle effects. An exponential function with a time constant of 200 days yields the best fit to the diffuser time series. The decrease in diffuser reflectance over the mission is wavelength dependent, ranging from 9% in the blue (412 nm) to 5% in the red and near infrared (670-865 nm). The Cal/Val team has developed a methodology for computing the signal-to-noise ratio (SNR) for SeaWiFS on orbit from the diffuser time series corrected for both the varying solar incidence angles and the diffuser reflectance degradation. A sensor noise model is used to compare on-orbit SNRs computed for radiances reflected from the diffuser with prelaunch SNRs measured at typical radiances specified for the instrument. To within the uncertainties in the measurements, the SNRs for SeaWiFS have not changed over the mission. The on-orbit performance of the SeaWiFS solar diffuser should offer insight into the long-term on-orbit performance of solar diffusers on other instruments, such as the Moderate-Resolution Imaging Spectrometer [currently flying on the Earth Observing System (EOS) Terra and Aqua satellites], the Visible and Infrared Radiometer Suite [scheduled to fly on the NASA National Polar-orbiting Operational Environmental Satellite System (NPOESS) and NPOESS Preparatory Project (NPP) satellites] and the Advanced Baseline Imager [scheduled to fly on the National Oceanic and Atmospheric Administration Geostationary Environmental Operational Satellite Series R (GOES-R) satellites].

Using a Quasipotential Transformation for Modeling Diffusion Media inPolymer-Electrolyte Fuel Cells

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

Weber, Adam Z.; Newman, John

2008-08-29

In this paper, a quasipotential approach along with conformal mapping is used to model the diffusion media of a polymer-electrolyte fuel cell. This method provides a series solution that is grid independent and only requires integration along a single boundary to solve the problem. The approach accounts for nonisothermal phenomena, two-phase flow, correct placement of the electronic potential boundary condition, and multilayer media. The method is applied to a cathode diffusion medium to explore the interplay between water and thermal management and performance, the impact of the rib-to-channel ratio, and the existence of diffusion under the rib and flooding phenomena.

Elevated Temperature Creep Deformation in Solid Solution <001> NiAL-3.6Ti Single Crystals

NASA Technical Reports Server (NTRS)

Whittenberger, J. Daniel; Noebe, Ronald D.; Darolia, Ram

2003-01-01

The 1100 to 1500 K slow plastic strain rate compressive properties of <001> oriented NiAl-3.6Ti single crystals have been measured, and the results suggests that two deformation processes exist. While the intermediate temperature/faster strain rate mechanism is uncertain, plastic flow at elevated temperature/slower strain rates in NiAl-3.6Ti appears to be controlled by solute drag as described by the Cottrell-Jaswon solute drag model for gliding b = a(sub 0)<101> dislocations. While the calculated activation energy of deformation is much higher (approximately 480 kJ/mol) than the activation energy for diffusion (approximately 290 kJ/mol) used in the Cottrell-Jaswon creep model, a forced temperature compensated - power law fit using the activation energy for diffusion was able to adequately (greater than 90%) predict the observed creep properties. Thus we conclude that the rejection of a diffusion controlled mechanism can not be simply based on a large numerical difference between the activation energies for deformation and diffusion.

Homogenization of a Directed Dispersal Model for Animal Movement in a Heterogeneous Environment.

PubMed

Yurk, Brian P

2016-10-01

The dispersal patterns of animals moving through heterogeneous environments have important ecological and epidemiological consequences. In this work, we apply the method of homogenization to analyze an advection-diffusion (AD) model of directed movement in a one-dimensional environment in which the scale of the heterogeneity is small relative to the spatial scale of interest. We show that the large (slow) scale behavior is described by a constant-coefficient diffusion equation under certain assumptions about the fast-scale advection velocity, and we determine a formula for the slow-scale diffusion coefficient in terms of the fast-scale parameters. We extend the homogenization result to predict invasion speeds for an advection-diffusion-reaction (ADR) model with directed dispersal. For periodic environments, the homogenization approximation of the solution of the AD model compares favorably with numerical simulations. Invasion speed approximations for the ADR model also compare favorably with numerical simulations when the spatial period is sufficiently small.

Elimination of Spurious Fractional Charges in Dissociating Molecules by Correcting the Shape of Approximate Kohn-Sham Potentials.

PubMed

Komsa, Darya N; Staroverov, Viktor N

2016-11-08

Standard density-functional approximations often incorrectly predict that heteronuclear diatomic molecules dissociate into fractionally charged atoms. We demonstrate that these spurious charges can be eliminated by adapting the shape-correction method for Kohn-Sham potentials that was originally introduced to improve Rydberg excitation energies [ Phys. Rev. Lett. 2012 , 108 , 253005 ]. Specifically, we show that if a suitably determined fraction of electron charge is added to or removed from a frontier Kohn-Sham orbital level, the approximate Kohn-Sham potential of a stretched molecule self-corrects by developing a semblance of step structure; if this potential is used to obtain the electron density of the neutral molecule, charge delocalization is blocked and spurious fractional charges disappear beyond a certain internuclear distance.

The Harrison Diffusion Kinetics Regimes in Solute Grain Boundary Diffusion

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

Belova, Irina; Fiedler, T; Kulkarni, Nagraj S

2012-01-01

Knowledge of the limits of the principal Harrison kinetics regimes (Type-A, B and C) for grain boundary diffusion is very important for the correct analysis of the depth profiles in a tracer diffusion experiment. These regimes for self-diffusion have been extensively studied in the past by making use of the phenomenological Lattice Monte Carlo (LMC) method with the result that the limits are now well established. The relationship of those self-diffusion limits to the corresponding ones for solute diffusion in the presence of solute segregation to the grain boundaries remains unclear. In the present study, the influence of solute segregationmore » on the limits is investigated with the LMC method for the well-known parallel grain boundary slab model by showing the equivalence of two diffusion models. It is shown which diffusion parameters are useful for identifying the limits of the Harrison kinetics regimes for solute grain boundary diffusion. It is also shown how the measured segregation factor from the diffusion experiment in the Harrison Type-B kinetics regime may differ from the global segregation factor.« less

Pyridine adsorption and diffusion on Pt(111) investigated with density functional theory

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

Kolsbjerg, Esben L.; Groves, Michael N.; Hammer, Bjørk, E-mail: hammer@phys.au.dk

2016-04-28

The adsorption, diffusion, and dissociation of pyridine, C{sub 5}H{sub 5}N, on Pt(111) are investigated with van der Waals-corrected density functional theory. An elaborate search for local minima in the adsorption potential energy landscape reveals that the intact pyridine adsorbs with the aromatic ring parallel to the surface. Piecewise interconnections of the local minima in the energy landscape reveal that the most favourable diffusion path for pyridine has a barrier of 0.53 eV. In the preferred path, the pyridine remains parallel to the surface while performing small single rotational steps with a carbon-carbon double bond hinged above a single Pt atom.more » The origin of the diffusion pathway is discussed in terms of the C{sub 2}–Pt π-bond being stronger than the corresponding CN–Pt π-bond. The energy barrier and reaction enthalpy for dehydrogenation of adsorbed pyridine into an adsorbed, upright bound α-pyridyl species are calculated to 0.71 eV and 0.18 eV, respectively (both zero-point energy corrected). The calculations are used to rationalize previous experimental observations from the literature for pyridine on Pt(111).« less

New Solution of Diffusion-Advection Equation for Cosmic-Ray Transport Using Ultradistributions

NASA Astrophysics Data System (ADS)

Rocca, M. C.; Plastino, A. R.; Plastino, A.; Ferri, G. L.; de Paoli, A.

2015-11-01

In this paper we exactly solve the diffusion-advection equation (DAE) for cosmic-ray transport. For such a purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for the DAE. From the ensuing solution, we obtain several approximations as limiting cases of various situations of physical and astrophysical interest. One of them involves Solar cosmic-rays' diffusion.

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

NASA Astrophysics Data System (ADS)

Batistić, Benjamin; Robnik, Marko

2011-09-01

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

A sun-crown-sensor model and adapted C-correction logic for topographic correction of high resolution forest imagery

NASA Astrophysics Data System (ADS)

Fan, Yuanchao; Koukal, Tatjana; Weisberg, Peter J.

2014-10-01

Canopy shadowing mediated by topography is an important source of radiometric distortion on remote sensing images of rugged terrain. Topographic correction based on the sun-canopy-sensor (SCS) model significantly improved over those based on the sun-terrain-sensor (STS) model for surfaces with high forest canopy cover, because the SCS model considers and preserves the geotropic nature of trees. The SCS model accounts for sub-pixel canopy shadowing effects and normalizes the sunlit canopy area within a pixel. However, it does not account for mutual shadowing between neighboring pixels. Pixel-to-pixel shadowing is especially apparent for fine resolution satellite images in which individual tree crowns are resolved. This paper proposes a new topographic correction model: the sun-crown-sensor (SCnS) model based on high-resolution satellite imagery (IKONOS) and high-precision LiDAR digital elevation model. An improvement on the C-correction logic with a radiance partitioning method to address the effects of diffuse irradiance is also introduced (SCnS + C). In addition, we incorporate a weighting variable, based on pixel shadow fraction, on the direct and diffuse radiance portions to enhance the retrieval of at-sensor radiance and reflectance of highly shadowed tree pixels and form another variety of SCnS model (SCnS + W). Model evaluation with IKONOS test data showed that the new SCnS model outperformed the STS and SCS models in quantifying the correlation between terrain-regulated illumination factor and at-sensor radiance. Our adapted C-correction logic based on the sun-crown-sensor geometry and radiance partitioning better represented the general additive effects of diffuse radiation than C parameters derived from the STS or SCS models. The weighting factor Wt also significantly enhanced correction results by reducing within-class standard deviation and balancing the mean pixel radiance between sunlit and shaded slopes. We analyzed these improvements with model comparison on the red and near infrared bands. The advantages of SCnS + C and SCnS + W on both bands are expected to facilitate forest classification and change detection applications.

2-D Modeling of Nanoscale MOSFETs: Non-Equilibrium Green's Function Approach

NASA Technical Reports Server (NTRS)

Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan

2001-01-01

We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Electron-electron interaction is treated within Hartree approximation by solving NEGF and Poisson equations self-consistently. For the calculations presented here, parallelization is performed by distributing the solution of NEGF equations to various processors, energy wise. We present simulation of the "benchmark" MIT 25nm and 90nm MOSFETs and compare our results to those from the drift-diffusion simulator and the quantum-corrected results available. In the 25nm MOSFET, the channel length is less than ten times the electron wavelength, and the electron scattering time is comparable to its transit time. Our main results are: (1) Simulated drain subthreshold current characteristics are shown, where the potential profiles are calculated self-consistently by the corresponding simulation methods. The current predicted by our quantum simulation has smaller subthreshold slope of the Vg dependence which results in higher threshold voltage. (2) When gate oxide thickness is less than 2 nm, gate oxide leakage is a primary factor which determines off-current of a MOSFET (3) Using our 2-D NEGF simulator, we found several ways to drastically decrease oxide leakage current without compromising drive current. (4) Quantum mechanically calculated electron density is much smaller than the background doping density in the poly silicon gate region near oxide interface. This creates an additional effective gate voltage. Different ways to. include this effect approximately will be discussed.

Effects of convergent diffusion and charge transfer kinetics on the diffusion layer thickness of spherical micro- and nanoelectrodes.

PubMed

Molina, A; Laborda, E; González, J; Compton, R G

2013-05-21

Nuances of the linear diffusion layer approximation are examined for slow charge transfer reactions at (hemi)spherical micro- and nanoelectrodes. This approximation is widely employed in Electrochemistry to evaluate the extent of electrolyte solution perturbed by the electrode process, which is essential to the understanding of the effects arising from thin-layer diffusion, convergent diffusion, convection, coupled chemical reactions and the double layer. The concept was well established for fast charge transfer processes at macroelectrodes, but remains unclear under other conditions such that a thorough assessment of its meaning was necessary. In a previous publication [A. Molina, J. González, E. Laborda and R. G. Compton, Phys. Chem. Chem. Phys., 2013, 15, 2381-2388] we shed some light on the influence of the reversibility degree. In the present work, the meaning of the diffusion layer thickness is investigated when very small electrodes are employed and so the contribution of convergent diffusion to the mass transport is very important. An analytical expression is given to calculate the linear diffusion layer thickness at (hemi)spherical electrodes and its behaviour is studied for a wide range of conditions of reversibility (from reversible to fully-irreversible processes) and electrode size (from macro- to nano-electrodes). Rigorous analytical solutions are deduced for true concentration profiles, surface concentrations, linear diffusion layer thickness and current densities when a potential pulse is applied at (hemi)spherical electrodes. The expressions for the magnitudes mentioned above are valid for electrodes of any size (including (hemi)spherical nanoelectrodes) and for any degree of reversibility, provided that mass transport occurs exclusively via diffusion. The variation of the above with the electrode size, applied potential and charge transfer kinetics is studied.

Macro-microscopic mass formulae and nuclear mass predictions

NASA Astrophysics Data System (ADS)

Royer, G.; Guilbaud, M.; Onillon, A.

2010-12-01

Different mass formulae derived from the liquid drop model and the pairing and shell energies of the Thomas-Fermi model have been studied and compared. They include or not the diffuseness correction to the Coulomb energy, the charge exchange correction term, the curvature energy, different forms of the Wigner term and powers of the relative neutron excess I=(N-Z)/A. Their coefficients have been determined by a least square fitting procedure to 2027 experimental atomic masses (G. Audi et al. (2003) [1]). The Coulomb diffuseness correction Z/A term or the charge exchange correction Z/A term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately but their coefficients are very unstable. The different fits lead to a surface energy coefficient of around 17-18 MeV. A large equivalent rms radius ( r=1.22-1.24 fm) or a shorter central radius may be used. An rms deviation of 0.54 MeV can be reached between the experimental and theoretical masses. The remaining differences come probably mainly from the determination of the shell and pairing energies. Mass predictions of selected expressions have been compared to 161 new experimental masses and the correct agreement allows to provide extrapolations to masses of 656 selected exotic nuclei.

Accelerating EPI distortion correction by utilizing a modern GPU-based parallel computation.

PubMed

Yang, Yao-Hao; Huang, Teng-Yi; Wang, Fu-Nien; Chuang, Tzu-Chao; Chen, Nan-Kuei

2013-04-01

The combination of phase demodulation and field mapping is a practical method to correct echo planar imaging (EPI) geometric distortion. However, since phase dispersion accumulates in each phase-encoding step, the calculation complexity of phase modulation is Ny-fold higher than conventional image reconstructions. Thus, correcting EPI images via phase demodulation is generally a time-consuming task. Parallel computing by employing general-purpose calculations on graphics processing units (GPU) can accelerate scientific computing if the algorithm is parallelized. This study proposes a method that incorporates the GPU-based technique into phase demodulation calculations to reduce computation time. The proposed parallel algorithm was applied to a PROPELLER-EPI diffusion tensor data set. The GPU-based phase demodulation method reduced the EPI distortion correctly, and accelerated the computation. The total reconstruction time of the 16-slice PROPELLER-EPI diffusion tensor images with matrix size of 128 × 128 was reduced from 1,754 seconds to 101 seconds by utilizing the parallelized 4-GPU program. GPU computing is a promising method to accelerate EPI geometric correction. The resulting reduction in computation time of phase demodulation should accelerate postprocessing for studies performed with EPI, and should effectuate the PROPELLER-EPI technique for clinical practice. Copyright © 2011 by the American Society of Neuroimaging.

Inverse Compton Scattering in Mildly Relativistic Plasma

NASA Technical Reports Server (NTRS)

Molnar, S. M.; Birkinshaw, M.

1998-01-01

We investigated the effect of inverse Compton scattering in mildly relativistic static and moving plasmas with low optical depth using Monte Carlo simulations, and calculated the Sunyaev-Zel'dovich effect in the cosmic background radiation. Our semi-analytic method is based on a separation of photon diffusion in frequency and real space. We use Monte Carlo simulation to derive the intensity and frequency of the scattered photons for a monochromatic incoming radiation. The outgoing spectrum is determined by integrating over the spectrum of the incoming radiation using the intensity to determine the correct weight. This method makes it possible to study the emerging radiation as a function of frequency and direction. As a first application we have studied the effects of finite optical depth and gas infall on the Sunyaev-Zel'dovich effect (not possible with the extended Kompaneets equation) and discuss the parameter range in which the Boltzmann equation and its expansions can be used. For high temperature clusters (k(sub B)T(sub e) greater than or approximately equal to 15 keV) relativistic corrections based on a fifth order expansion of the extended Kompaneets equation seriously underestimate the Sunyaev-Zel'dovich effect at high frequencies. The contribution from plasma infall is less important for reasonable velocities. We give a convenient analytical expression for the dependence of the cross-over frequency on temperature, optical depth, and gas infall speed. Optical depth effects are often more important than relativistic corrections, and should be taken into account for high-precision work, but are smaller than the typical kinematic effect from cluster radial velocities.

Contribution of HI-bearing ultra-diffuse galaxies to the cosmic number density of galaxies

NASA Astrophysics Data System (ADS)

Jones, M. G.; Papastergis, E.; Pandya, V.; Leisman, L.; Romanowsky, A. J.; Yung, L. Y. A.; Somerville, R. S.; Adams, E. A. K.

2018-06-01

We estimate the cosmic number density of the recently identified class of HI-bearing ultra-diffuse sources (HUDs) based on the completeness limits of the ALFALFA survey. These objects have HI masses approximately in the range 8.5 < logMHI/M⊙ < 9.5, average r-band surface brightnesses fainter than 24 mag arcsec-2, half-light radii greater than 1.5 kpc, and are separated from neighbours by at least 350 kpc. In this work we demonstrate that they contribute at most 6% of the population of HI-bearing dwarfs detected by ALFALFA (with similar HI masses), have a total cosmic number density of (1.5 ± 0.6) × 10-3 Mpc-3, and an HI mass density of (6.0 ± 0.8) × 105 M⊙ Mpc-3. We estimate that this is similar to the total cosmic number density of ultra-diffuse galaxies (UDGs) in groups and clusters, and conclude that the relation between the number of UDGs hosted in a halo and the halo mass must have a break below M200 1012 M⊙ in order to account for the abundance of HUDs in the field. The distribution of the velocity widths of HUDs rises steeply towards low values, indicating a preference for slow rotation rates compared to the global HI-rich dwarf population. These objects were already included in previous measurements of the HI mass function, but have been absent from measurements of the galaxy stellar mass function owing to their low surface brightness. However, we estimate that due to their low number density the inclusion of HUDs would constitute a correction of less than 1%. Comparison with the Santa Cruz semi-analytic model shows that it produces HI-rich central UDGs that have similar colours to HUDs, but that these UDGs are currently produced in a much greater number. While previous results from this sample have favoured formation scenarios where HUDs form in high spin-parameter halos, comparisons with recent results which invoke that formation mechanism reveal that this model produces an order of magnitude more field UDGs than we observe in the HUD population, and these have an occurrence rate (relative to other dwarfs) that is approximately double what we observe. In addition, the colours of HUDs are bluer than predicted, although we suspect this is due to a systematic problem in reproducing the star formation histories of low-mass galaxies rather than being specific to the ultra-diffuse nature of these sources.

Transverse thermal conductivity of porous materials made from aligned nano- and microcylindrical pores

NASA Astrophysics Data System (ADS)

Prasher, Ravi

2006-09-01

Nanoporous and microporous materials made from aligned cylindrical pores play important roles in present technologies and will play even bigger roles in future technologies. The insight into the phonon thermal conductivity of these materials is important and relevant in many technologies and applications. Since the mean free path of phonons can be comparable to the pore size and interpore distance, diffusion-approximation based effective medium models cannot be used to predict the thermal conductivity of these materials. Strictly speaking, the Boltzmann transport equation (BTE) must be solved to capture the ballistic nature of thermal transport; however, solving BTE in such a complex network of pores is impractical. As an alternative, we propose an approximate ballistic-diffusive microscopic effective medium model for predicting the thermal conductivity of phonons in two-dimensional nanoporous and microporous materials made from aligned cylindrical pores. The model captures the size effects due to the pore diameter and the interpore distance and reduces to diffusion-approximation based models for macroporous materials. The results are in good agreement with experimental data.

Fermi-Compton scattering due to magnetopause surface fluctuations in Jupiter's magnetospheric cavity

NASA Technical Reports Server (NTRS)

Barbosa, D. D.

1981-01-01

The effects of boundary surface fluctuations on a spectrum of electromagnetic radiation trapped in a high Q (quality) cavity are considered. Undulating walls introduce small frequency shifts at reflection to the radiation, and it is argued that the process is entirely analogous to both Fermi (particle) acceleration and inverse Compton scattering. A Fokker-Planck formalism is pursued; it yields a diffusion equation in frequency for which the Green's function and steady-state solutions are found. Applying this analysis to the Jovian continuum radiation discovered by Voyager spacecraft, it is suggested that characteristic diffusion times are greater than 1 year, and that in order to account for the steep frequency spectra observed, an unidentified loss mechanism must operate in the cavity with a decay time constant approximately equal to the characteristic diffusion time divided by 28. A radiator-reactor model of the cavity is investigated to provide an estimate for the intrinsic luminosity of the low frequency (approximately 100 Hz) continuum source whose power is approximately 7 x 10 to the 6th W.

Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results.

PubMed

Martelli, F; Contini, D; Taddeucci, A; Zaccanti, G

1997-07-01

In our companion paper we presented a model to describe photon migration through a diffusing slab. The model, developed for a homogeneous slab, is based on the diffusion approximation and is able to take into account reflection at the boundaries resulting from the refractive index mismatch. In this paper the predictions of the model are compared with solutions of the radiative transfer equation obtained by Monte Carlo simulations in order to determine the applicability limits of the approximated theory in different physical conditions. A fitting procedure, carried out with the optical properties as fitting parameters, is used to check the application of the model to the inverse problem. The results show that significant errors can be made if the effect of the refractive index mismatch is not properly taken into account. Errors are more important when measurements of transmittance are used. The effects of using a receiver with a limited angular field of view and the angular distribution of the radiation that emerges from the slab have also been investigated.

Determining Enzyme Activity by Radial Diffusion

ERIC Educational Resources Information Center

Davis, Bill D.

1977-01-01

Discusses advantages of radial diffusion assay in determining presence of enzyme and/or rough approximation of amount of enzyme activities. Procedures are included for the preparation of starch-agar plates, and the application and determination of enzyme. Techniques using plant materials (homogenates, tissues, ungerminated embryos, and seedlings)…

Self-diffusivity and interdiffusivity of molten aluminum-copper alloys under pressure, derived from molecular dynamics.

PubMed

Rudd, Robert E; Cabot, William H; Caspersen, Kyle J; Greenough, Jeffrey A; Richards, David F; Streitz, Frederick H; Miller, Paul L

2012-03-01

We use molecular dynamics (MD) to simulate diffusion in molten aluminum-copper (AlCu) alloys. The self-diffusivities and Maxwell-Stefan diffusivities are calculated for AlCu mixtures using the Green-Kubo formulas at temperatures from 1000 to 4000 K and pressures from 0 to 25 GPa, along with additional points at higher temperatures and pressures. The diffusivities are corrected for finite-size effects. The Maxwell-Stefan diffusivity is compared to the diffusivity calculated from the self-diffusivities using a generalization of the Darken equation. We find that the effects of cross-correlation are small. Using the calculated self-diffusivities, we have assessed whether dilute hard-sphere and dilute Lennard-Jones models apply to the molten mixture. Neither of the two dilute gas diffusivities describes the diffusivity in molten Al and Cu. We report generalized analytic models for the self-diffusivities and interdiffusivity (mutual diffusivity) that fit the MD results well. The MD-derived transport coefficients are in good agreement with the available experimental data. We also report MD calculations of the viscosity and an analytic fit to those results. The ionic thermal conductivity is discussed briefly.

Self-diffusivity and interdiffusivity of molten aluminum-copper alloys under pressure, derived from molecular dynamics

NASA Astrophysics Data System (ADS)

Rudd, Robert E.; Cabot, William H.; Caspersen, Kyle J.; Greenough, Jeffrey A.; Richards, David F.; Streitz, Frederick H.; Miller, Paul L.

2012-03-01

We use molecular dynamics (MD) to simulate diffusion in molten aluminum-copper (AlCu) alloys. The self-diffusivities and Maxwell-Stefan diffusivities are calculated for AlCu mixtures using the Green-Kubo formulas at temperatures from 1000 to 4000 K and pressures from 0 to 25 GPa, along with additional points at higher temperatures and pressures. The diffusivities are corrected for finite-size effects. The Maxwell-Stefan diffusivity is compared to the diffusivity calculated from the self-diffusivities using a generalization of the Darken equation. We find that the effects of cross-correlation are small. Using the calculated self-diffusivities, we have assessed whether dilute hard-sphere and dilute Lennard-Jones models apply to the molten mixture. Neither of the two dilute gas diffusivities describes the diffusivity in molten Al and Cu. We report generalized analytic models for the self-diffusivities and interdiffusivity (mutual diffusivity) that fit the MD results well. The MD-derived transport coefficients are in good agreement with the available experimental data. We also report MD calculations of the viscosity and an analytic fit to those results. The ionic thermal conductivity is discussed briefly.

COSMIC MICROWAVE BACKGROUND POLARIZATION AND TEMPERATURE POWER SPECTRA ESTIMATION USING LINEAR COMBINATION OF WMAP 5 YEAR MAPS

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

Samal, Pramoda Kumar; Jain, Pankaj; Saha, Rajib

We estimate cosmic microwave background (CMB) polarization and temperature power spectra using Wilkinson Microwave Anisotropy Probe (WMAP) 5 year foreground contaminated maps. The power spectrum is estimated by using a model-independent method, which does not utilize directly the diffuse foreground templates nor the detector noise model. The method essentially consists of two steps: (1) removal of diffuse foregrounds contamination by making linear combination of individual maps in harmonic space and (2) cross-correlation of foreground cleaned maps to minimize detector noise bias. For the temperature power spectrum we also estimate and subtract residual unresolved point source contamination in the cross-power spectrummore » using the point source model provided by the WMAP science team. Our TT, TE, and EE power spectra are in good agreement with the published results of the WMAP science team. We perform detailed numerical simulations to test for bias in our procedure. We find that the bias is small in almost all cases. A negative bias at low l in TT power spectrum has been pointed out in an earlier publication. We find that the bias-corrected quadrupole power (l(l + 1)C{sub l} /2{pi}) is 532 {mu}K{sup 2}, approximately 2.5 times the estimate (213.4 {mu}K{sup 2}) made by the WMAP team.« less

Effects of image distortions originating from susceptibility variations and concomitant fields on diffusion MRI tractography results

PubMed Central

Irfanoglu, M. Okan; Walker, Lindsay; Sarlls, Joelle; Marenco, Stefano; Pierpaoli, Carlo

2013-01-01

In this work we investigate the effects of echo planar imaging (EPI) distortions on diffusion tensor imaging (DTI) based fiber tractography results. We propose a simple experimental framework that would enable assessing the effects of EPI distortions on the accuracy and reproducibility of fiber tractography from a pilot study on a few subjects. We compare trajectories computed from two diffusion datasets collected on each subject that are identical except for the orientation of phase encode direction, either right–left (RL) or anterior–posterior (AP). We define metrics to assess potential discrepancies between RL and AP trajectories in association, commissural, and projection pathways. Results from measurements on a 3 Tesla clinical scanner indicated that the effects of EPI distortions on computed fiber trajectories are statistically significant and large in magnitude, potentially leading to erroneous inferences about brain connectivity. The correction of EPI distortion using an image-based registration approach showed a significant improvement in tract consistency and accuracy. Although obtained in the context of a DTI experiment, our findings are generally applicable to all EPI-based diffusion MRI tractography investigations, including high angular resolution (HARDI) methods. On the basis of our findings, we recommend adding an EPI distortion correction step to the diffusion MRI processing pipeline if the output is to be used for fiber tractography. PMID:22401760

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

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

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients.

PubMed

Chen, Weitian; Sica, Christopher T; Meyer, Craig H

2008-11-01

Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method.

Nonergodicity of microfine binary systems

NASA Astrophysics Data System (ADS)

Son, L. D.; Sidorov, V. E.; Popel', P. S.; Shul'gin, D. B.

2016-02-01

The correction to the equation of state that is related to the nonergodicity of diffusion dynamics is discussed for a binary solid solution with a limited solubility. It is asserted that, apart from standard thermodynamic variables (temperature, volume, concentration), this correction should be taken into account in the form of the average local chemical potential fluctuations associated with microheterogeneity in order to plot a phase diagram. It is shown that a low value of this correction lowers the miscibility gap and that this gap splits when this correction increases. This situation is discussed for eutectic systems and Ga-Pb, Fe-Cu, and Cu-Zr alloys.

An Approximate Markov Model for the Wright-Fisher Diffusion and Its Application to Time Series Data.

PubMed

Ferrer-Admetlla, Anna; Leuenberger, Christoph; Jensen, Jeffrey D; Wegmann, Daniel

2016-06-01

The joint and accurate inference of selection and demography from genetic data is considered a particularly challenging question in population genetics, since both process may lead to very similar patterns of genetic diversity. However, additional information for disentangling these effects may be obtained by observing changes in allele frequencies over multiple time points. Such data are common in experimental evolution studies, as well as in the comparison of ancient and contemporary samples. Leveraging this information, however, has been computationally challenging, particularly when considering multilocus data sets. To overcome these issues, we introduce a novel, discrete approximation for diffusion processes, termed mean transition time approximation, which preserves the long-term behavior of the underlying continuous diffusion process. We then derive this approximation for the particular case of inferring selection and demography from time series data under the classic Wright-Fisher model and demonstrate that our approximation is well suited to describe allele trajectories through time, even when only a few states are used. We then develop a Bayesian inference approach to jointly infer the population size and locus-specific selection coefficients with high accuracy and further extend this model to also infer the rates of sequencing errors and mutations. We finally apply our approach to recent experimental data on the evolution of drug resistance in influenza virus, identifying likely targets of selection and finding evidence for much larger viral population sizes than previously reported. Copyright © 2016 by the Genetics Society of America.

Vibrational spectroscopy of water in hydrated lipid multi-bilayers. II. Two-dimensional infrared and peak shift observables within different theoretical approximations.

PubMed

Gruenbaum, Scott M; Pieniazek, Piotr A; Skinner, J L

2011-10-28

In a previous report, we calculated the infrared absorption spectrum and both the isotropic and anisotropic pump-probe signals for the OD stretch of isotopically dilute water in dilauroylphosphatidylcholine (DLPC) multi-bilayers as a function of the lipid hydration level. These results were then compared to recent experimental measurements and are in generally good agreement. In this paper, we will further investigate the structure and dynamics of hydration water using molecular dynamics simulations and calculations of the two-dimensional infrared and vibrational echo peak shift observables for hydration water in DLPC membranes. These observables have not yet been measured experimentally, but future comparisons may provide insight into spectral diffusion processes and hydration water heterogeneity. We find that at low hydration levels the motion of water molecules inside the lipid membrane is significantly arrested, resulting in very slow spectral diffusion. At higher hydration levels, spectral diffusion is more rapid, but still slower than in bulk water. We also investigate the effects of several common approximations on the calculation of spectroscopic observables by computing these observables within multiple levels of theory. The impact of these approximations on the resulting spectra affects our interpretation of these measurements and reveals that, for example, the cumulant approximation, which may be valid for certain systems, is not a good approximation for a highly heterogeneous environment such as hydration water in lipid multi-bilayers.

A quantitative comparison of two methods to correct eddy current-induced distortions in DT-MRI.

PubMed

Muñoz Maniega, Susana; Bastin, Mark E; Armitage, Paul A

2007-04-01

Eddy current-induced geometric distortions of single-shot, diffusion-weighted, echo-planar (DW-EP) images are a major confounding factor to the accurate determination of water diffusion parameters in diffusion tensor MRI (DT-MRI). Previously, it has been suggested that these geometric distortions can be removed from brain DW-EP images using affine transformations determined from phantom calibration experiments using iterative cross-correlation (ICC). Since this approach was first described, a number of image-based registration methods have become available that can also correct eddy current-induced distortions in DW-EP images. However, as yet no study has investigated whether separate eddy current calibration or image-based registration provides the most accurate way of removing these artefacts from DT-MRI data. Here we compare how ICC phantom calibration and affine FLIRT (http://www.fmrib.ox.ac.uk), a popular image-based multi-modal registration method that can correct both eddy current-induced distortions and bulk subject motion, perform when registering DW-EP images acquired with different slice thicknesses (2.8 and 5 mm) and b-values (1000 and 3000 s/mm(2)). With the use of consistency testing, it was found that ICC was a more robust algorithm for correcting eddy current-induced distortions than affine FLIRT, especially at high b-value and small slice thickness. In addition, principal component analysis demonstrated that the combination of ICC phantom calibration (to remove eddy current-induced distortions) with rigid body FLIRT (to remove bulk subject motion) provided a more accurate registration of DT-MRI data than that achieved by affine FLIRT.

Corrections beyond the leading order in π{sup 0} → e{sup +}e{sup −} process

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

Husek, T.; Kampf, K.; Novotný, J.

2016-01-22

We briefly summarize experimental and theoretical results on the rare decay π{sup 0} → e{sup +}e{sup −}. Two-loop QED corrections are reviewed and the bremsstrahlung contribution beyond the soft-photon approximation is analytically calculated. Using the leading logarithm approximation, the possible contribution of QCD corrections is estimated. The complete result can be used to fit the value of the contact interaction coupling χ{sup (r)} to the recent KTeV experiment with the result χ{sup (r)}(M{sub ρ}) = 4.5±1.0.

Determination of the charge of relativistic heavy nuclei from emulsion tracks

NASA Technical Reports Server (NTRS)

Morgan, S. H., Jr.; Eby, P. B.

1971-01-01

The number of delta rays with energies between 50 and 150 keV that are produced by heavy nuclei in emulsions is calculated. The Z(2) dependence predicted by the first Born approximation is corrected by a direct calculation of the Mott exact phase-shift scattering cross section. Comparisons are made with corrections predicted by the second Born approximation. When the phase-shift results are applied to the problem of charge identification, corrections of up to 4 units of charge for 1.457-GeV/nucleon nuclei with charge Z = 75 are found.

Multiscale Modeling of Diffusion in a Crowded Environment.

PubMed

Meinecke, Lina

2017-11-01

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space-dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size, and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.

Spatial variability of the Arctic Ocean's double-diffusive staircase

NASA Astrophysics Data System (ADS)

Shibley, N. C.; Timmermans, M.-L.; Carpenter, J. R.; Toole, J. M.

2017-02-01

The Arctic Ocean thermohaline stratification frequently exhibits a staircase structure overlying the Atlantic Water Layer that can be attributed to the diffusive form of double-diffusive convection. The staircase consists of multiple layers of O(1) m in thickness separated by sharp interfaces, across which temperature and salinity change abruptly. Through a detailed analysis of Ice-Tethered Profiler measurements from 2004 to 2013, the double-diffusive staircase structure is characterized across the entire Arctic Ocean. We demonstrate how the large-scale Arctic Ocean circulation influences the small-scale staircase properties. These staircase properties (layer thicknesses and temperature and salinity jumps across interfaces) are examined in relation to a bulk vertical density ratio spanning the staircase stratification. We show that the Lomonosov Ridge serves as an approximate boundary between regions of low density ratio (approximately 3-4) on the Eurasian side and higher density ratio (approximately 6-7) on the Canadian side. We find that the Eurasian Basin staircase is characterized by fewer, thinner layers than that in the Canadian Basin, although the margins of all basins are characterized by relatively thin layers and the absence of a well-defined staircase. A double-diffusive 4/3 flux law parametrization is used to estimate vertical heat fluxes in the Canadian Basin to be O(0.1) W m-2. It is shown that the 4/3 flux law may not be an appropriate representation of heat fluxes through the Eurasian Basin staircase. Here molecular heat fluxes are estimated to be between O(0.01) and O(0.1) W m-2. However, many uncertainties remain about the exact nature of these fluxes.

Microgravity nucleation and particle coagulation experiments support

NASA Technical Reports Server (NTRS)

Lilleleht, L. U.; Ferguson, F. T.

1987-01-01

A preliminary model for diffusion between concentric hemispheres was adapted to the cylindrical geometry of a microgravity nucleation apparatus, and extended to include the effects of radiation and conduction through the containment walls. Computer programs were developed to calculate first the temperature distribution and then the evolving concentration field using a finite difference formulation of the transient diffusion and radiation processes. The following estimations are made: (1) it takes approximately 35 minutes to establish a steady temperature field; (2) magnesium vapors released into the argon environment at the steady temperature distribution will reach a maximum supersaturation ratio of approximately 10,000 in the 20-second period at a distance of 15 cm from the source of vapors; and (3) approximately 750W electrical power will be required to maintain steady operating temperatures within the chamber.

Laser Spot Detection Based on Reaction Diffusion.

PubMed

Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J M; Dormido, Raquel; Duro, Natividad

2016-03-01

Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.

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.

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.

Benchmarking the pseudopotential and fixed-node approximations in diffusion Monte Carlo calculations of molecules and solids

DOE PAGES

Nazarov, Roman; Shulenburger, Luke; Morales, Miguel A.; ...

2016-03-28

We performed diffusion Monte Carlo (DMC) calculations of the spectroscopic properties of a large set of molecules, assessing the effect of different approximations. In systems containing elements with large atomic numbers, we show that the errors associated with the use of nonlocal mean-field-based pseudopotentials in DMC calculations can be significant and may surpass the fixed-node error. In conclusion, we suggest practical guidelines for reducing these pseudopotential errors, which allow us to obtain DMC-computed spectroscopic parameters of molecules and equation of state properties of solids in excellent agreement with experiment.

Benchmarking the pseudopotential and fixed-node approximations in diffusion Monte Carlo calculations of molecules and solids

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

Nazarov, Roman; Shulenburger, Luke; Morales, Miguel A.

We performed diffusion Monte Carlo (DMC) calculations of the spectroscopic properties of a large set of molecules, assessing the effect of different approximations. In systems containing elements with large atomic numbers, we show that the errors associated with the use of nonlocal mean-field-based pseudopotentials in DMC calculations can be significant and may surpass the fixed-node error. In conclusion, we suggest practical guidelines for reducing these pseudopotential errors, which allow us to obtain DMC-computed spectroscopic parameters of molecules and equation of state properties of solids in excellent agreement with experiment.

A new frequency domain analytical solution of a cascade of diffusive channels for flood routing

NASA Astrophysics Data System (ADS)

Cimorelli, Luigi; Cozzolino, Luca; Della Morte, Renata; Pianese, Domenico; Singh, Vijay P.

2015-04-01

Simplified flood propagation models are often employed in practical applications for hydraulic and hydrologic analyses. In this paper, we present a new numerical method for the solution of the Linear Parabolic Approximation (LPA) of the De Saint Venant equations (DSVEs), accounting for the space variation of model parameters and the imposition of appropriate downstream boundary conditions. The new model is based on the analytical solution of a cascade of linear diffusive channels in the Laplace Transform domain. The time domain solutions are obtained using a Fourier series approximation of the Laplace Inversion formula. The new Inverse Laplace Transform Diffusive Flood Routing model (ILTDFR) can be used as a building block for the construction of real-time flood forecasting models or in optimization models, because it is unconditionally stable and allows fast and fairly precise computation.

Error analysis and correction of discrete solutions from finite element codes

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Stein, P. A.; Knight, N. F., Jr.; Reissner, J. E.

1984-01-01

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

A method of bias correction for maximal reliability with dichotomous measures.

PubMed

Penev, Spiridon; Raykov, Tenko

2010-02-01

This paper is concerned with the reliability of weighted combinations of a given set of dichotomous measures. Maximal reliability for such measures has been discussed in the past, but the pertinent estimator exhibits a considerable bias and mean squared error for moderate sample sizes. We examine this bias, propose a procedure for bias correction, and develop a more accurate asymptotic confidence interval for the resulting estimator. In most empirically relevant cases, the bias correction and mean squared error correction can be performed simultaneously. We propose an approximate (asymptotic) confidence interval for the maximal reliability coefficient, discuss the implementation of this estimator, and investigate the mean squared error of the associated asymptotic approximation. We illustrate the proposed methods using a numerical example.

Expanding the calculation of activation volumes: Self-diffusion in liquid water

NASA Astrophysics Data System (ADS)

Piskulich, Zeke A.; Mesele, Oluwaseun O.; Thompson, Ward H.

2018-04-01

A general method for calculating the dependence of dynamical time scales on macroscopic thermodynamic variables from a single set of simulations is presented. The approach is applied to the pressure dependence of the self-diffusion coefficient of liquid water as a particularly useful illustration. It is shown how the activation volume associated with diffusion can be obtained directly from simulations at a single pressure, avoiding approximations that are typically invoked.

Optimization of the Inverse Algorithm for Estimating the Optical Properties of Biological Materials Using Spatially-resolved Diffuse Reflectance Technique

USDA-ARS?s Scientific Manuscript database

Determination of the optical properties from intact biological materials based on diffusion approximation theory is a complicated inverse problem, and it requires proper implementation of inverse algorithm, instrumentation, and experiment. This work was aimed at optimizing the procedure of estimatin...

Turboprop+: enhanced Turboprop diffusion-weighted imaging with a new phase correction.

PubMed

Lee, Chu-Yu; Li, Zhiqiang; Pipe, James G; Debbins, Josef P

2013-08-01

Faster periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) diffusion-weighted imaging acquisitions, such as Turboprop and X-prop, remain subject to phase errors inherent to a gradient echo readout, which ultimately limits the applied turbo factor (number of gradient echoes between each pair of radiofrequency refocusing pulses) and, thus, scan time reductions. This study introduces a new phase correction to Turboprop, called Turboprop+. This technique employs calibration blades, which generate 2-D phase error maps and are rotated in accordance with the data blades, to correct phase errors arising from off-resonance and system imperfections. The results demonstrate that with a small increase in scan time for collecting calibration blades, Turboprop+ had a superior immunity to the off-resonance-related artifacts when compared to standard Turboprop and recently proposed X-prop with the high turbo factor (turbo factor = 7). Thus, low specific absorption rate and short scan time can be achieved in Turboprop+ using a high turbo factor, whereas off-resonance related artifacts are minimized. © 2012 Wiley Periodicals, Inc.

General Model of Hindered Diffusion.

PubMed

Eloul, Shaltiel; Compton, Richard G

2016-11-03

The diffusion of a particle from bulk solution is slowed as it moves close to an adsorbing surface. A general model is reported that is easily applied by theoreticians and experimentalists. Specifically, it is shown here that in general and regardless of the space size, the magnitude of the effect of hindered diffusion on the flux is a property of the diffusion layer thickness. We explain and approximate the effect. Predictions of concentration profiles show that a "hindered diffusion layer" is formed near the adsorbing surface within the diffusion layer, observed even when the particle radius is just a 0.1% of the diffusion layer thickness. In particular, we focus on modern electrochemistry processes involving with impact of particles with either ultrasmall electrodes or particles in convective systems. The concept of the "hindered diffusion layer" is generally important for example in recent biophysical models of particles diffusion to small targets.

Diffusion of Redox-Sensitive Elements in Basalt at Different Oxygen Fugacities

NASA Technical Reports Server (NTRS)

Szumila, I.; Trail, D.; Danielson, L. R.

2017-01-01

The terrestrial planets and moons of our solar system have differentiated over a range of oxygen fugacity conditions. Basalts formed from magmas on the Earth cover a range of more oxidized states (from approximately IW (iron wustite) plus 2 to approximately FMQ (fayalite-magnetite-quartz) plus 3) than crustal rocks from Mars (IW to approximately IW plus 3), and basalts from the Moon are more reduced than both, ranging from IW to IW minus 2. The small body Vesta differentiated around IW minus 4. Characterization of redox sensitive elements' diffusivities will offer insight into behavior of these elements as a function of f (fugacity of) O2 for these planetary bodies. Here, we report a systematic study of the diffusion of redox-sensitive elements in basaltic melts with varying oxygen fugacities (fO2) for trace elements, V, Nb, W, Mo, La, Ce, Pr, Sm, Eu, Gd, Ta, and W. Since fO2 is an intensive variable that is different for the reservoirs of various planets and moons in our solar system, it is important to characterize how changes in redox states will affect diffusion. We conducted experiments in a piston cylinder device at 1300 degrees Centigrade and 1 gigapascal, at the University of Rochester and NASA Johnson Space Center. We buffered some experiments at Ru-RuO2 (FMQ plus 6.00), and conducted other experiments within either a graphite or Mo capsule, which corresponds to fO2s of either FMQ minus1.2, or FMQ minus 3.00, respectively. Characterizing the diffusivities of redox sensitive elements at different fO2s is important because some elements, like Eu, have varying valence states, such as Eu (sup 2 plus) and Eu (sup 3 plus). Differences in charge and ion radii may lead to differences in diffusivities within silicate melts. This could, lead to formation of a Eu anomaly by diffusion, the magnitude of which may be controlled by the fO2. Characterization of trace element diffusion is also important in understanding trace element fractionation. We found, during the course of our investigation, that not only did the diffusivities of the redox sensitive elements change with fO2, but that the diffusivities of all other analyzed elements also changed. This indicates that not only do changes in valence influence trace elements diffusivities but that the structure of melt may have changed with varying oxygen fugacity, probably due to changes in the speciation of the major element Fe.

Online quantitative analysis of multispectral images of human body tissues

NASA Astrophysics Data System (ADS)

Lisenko, S. A.

2013-08-01

A method is developed for online monitoring of structural and morphological parameters of biological tissues (haemoglobin concentration, degree of blood oxygenation, average diameter of capillaries and the parameter characterising the average size of tissue scatterers), which involves multispectral tissue imaging, image normalisation to one of its spectral layers and determination of unknown parameters based on their stable regression relation with the spectral characteristics of the normalised image. Regression is obtained by simulating numerically the diffuse reflectance spectrum of the tissue by the Monte Carlo method at a wide variation of model parameters. The correctness of the model calculations is confirmed by the good agreement with the experimental data. The error of the method is estimated under conditions of general variability of structural and morphological parameters of the tissue. The method developed is compared with the traditional methods of interpretation of multispectral images of biological tissues, based on the solution of the inverse problem for each pixel of the image in the approximation of different analytical models.

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

Fleury, Pierre; Uzan, Jean-Philippe; Larena, Julien, E-mail: fleury@iap.fr, E-mail: j.larena@ru.ac.za, E-mail: uzan@iap.fr

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing usmore » to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integration of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.« less

The theory of stochastic cosmological lensing

NASA Astrophysics Data System (ADS)

Fleury, Pierre; Larena, Julien; Uzan, Jean-Philippe

2015-11-01

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integration of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.

Numerical simulations of crystal growth in a transdermal drug delivery system

NASA Astrophysics Data System (ADS)

Zeng, Jianming; Jacob, Karl I.; Tikare, Veena

2004-02-01

Grain growth by precipitation and Ostwald ripening in an unstressed matrix of a dissolved crystallizable component was simulated using a kinetic Monte Carlo model. This model was used previously to study Ostwald ripening in the high crystallizable component regime and was shown to correctly simulate solution, diffusion and precipitation. In this study, the same model with modifications was applied to the low crystallizable regime of interest to the transdermal drug delivery system (TDS) community. We demonstrate the model's utility by simulating precipitation and grain growth during isothermal storage at different supersaturation conditions. The simulation results provide a first approximation for the crystallization occurring in TDS. It has been reported that for relatively higher temperature growth of drug crystals in TDS occurs only in the middle third of the polymer layer. The results from the simulations support these findings that crystal growth is limited to the middle third of the region, where the availability of crystallizable components is the highest, for cluster growth at relatively high temperature.

Non-invasive method for quantitative evaluation of exogenous compound deposition on skin.

PubMed

Stamatas, Georgios N; Wu, Jeff; Kollias, Nikiforos

2002-02-01

Topical application of active compounds on skin is common to both pharmaceutical and cosmetic industries. Quantification of the concentration of a compound deposited on the skin is important in determining the optimum formulation to deliver the pharmaceutical or cosmetic benefit. The most commonly used techniques to date are either invasive or not easily reproducible. In this study, we have developed a noninvasive alternative to these techniques based on spectrofluorimetry. A mathematical model based on diffusion approximation theory is utilized to correct fluorescence measurements for the attenuation caused by endogenous skin chromophore absorption. The limitation is that the compound of interest has to be either fluorescent itself or fluorescently labeled. We used the method to detect topically applied salicylic acid. Based on the mathematical model a calibration curve was constructed that is independent of endogenous chromophore concentration. We utilized the method to localize salicylic acid in epidermis and to follow its dynamics over a period of 3 d.

Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix

NASA Astrophysics Data System (ADS)

Palanisamy, Duraivelan; den Otter, Wouter K.

2018-05-01

We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.

[Identification of special quality eggs with NIR spectroscopy technology based on symbol entropy feature extraction method].

PubMed

Zhao, Yong; Hong, Wen-Xue

2011-11-01

Fast, nondestructive and accurate identification of special quality eggs is an urgent problem. The present paper proposed a new feature extraction method based on symbol entropy to identify near infrared spectroscopy of special quality eggs. The authors selected normal eggs, free range eggs, selenium-enriched eggs and zinc-enriched eggs as research objects and measured the near-infrared diffuse reflectance spectra in the range of 12 000-4 000 cm(-1). Raw spectra were symbolically represented with aggregation approximation algorithm and symbolic entropy was extracted as feature vector. An error-correcting output codes multiclass support vector machine classifier was designed to identify the spectrum. Symbolic entropy feature is robust when parameter changed and the highest recognition rate reaches up to 100%. The results show that the identification method of special quality eggs using near-infrared is feasible and the symbol entropy can be used as a new feature extraction method of near-infrared spectra.

Deformations of a pre-stretched elastic membrane driven by non-uniform electroosmotic flow

NASA Astrophysics Data System (ADS)

Bercovici, Moran; Boyko, Evgeniy; Gat, Amir

2016-11-01

We study viscous-elastic dynamics of fluid confined between a rigid plate and a pre-stretched elastic membrane subjected to non-uniform electroosmotic flow, and focus on the case of a finite-size membrane clamped at its boundaries. Considering small deformations of a strongly pre-stretched membrane, and applying the lubrication approximation for the flow, we derive a linearized leading-order non-homogenous 4th order diffusion equation governing the deformation and pressure fields. We derive a time-dependent Green's function for a rectangular domain, and use it to obtain several basic solutions for the cases of constant and time varying electric fields. In addition, defining an asymptotic expansion where the small parameter is the ratio of the induced to prescribed tension, we obtain a set of four one-way coupled equations providing a first order correction for the deformation field. Funded by the European Research Council (ERC) under the Horizon 2020 Research and Innovation Programme, Grant agreement No. 678734 (MetamorphChip).

The Chandra M10l Megasecond: Diffuse Emission

NASA Technical Reports Server (NTRS)

Kuntz, K. D.; Snowden, S. L.

2009-01-01

Because MIOl is nearly face-on, it provides an excellent laboratory in which to study the distribution of X-ray emitting gas in a typical late-type spiral galaxy. We obtained a Chandra observation with a cumulative exposure of roughly 1 Ms to study the diffuse X-ray emission in MlOl. The bulk of the X-ray emission is correlated with the star formation traced by the FUV emission. The global FUV/Xray correlation is non-linear (the X-ray surface brightness is roughly proportional to the square root of the FUV surface brightness) and the small-scale correlation is poor, probably due to the delay between the FUV emission and the X-ray production ill star-forming regions. The X-ray emission contains only minor contributions from unresolved stars (approximates less than 3%), unresolved X-ray point sources (approximates less than 4%), and individual supernova remnants (approximates 3%). The global spectrum of the diffuse emission can be reasonably well fitted with a three component thermal model, but the fitted temperatures are not unique; many distributions of emission measure can produce the same temperatures when observed with the current CCD energy resolution. The spectrum of the diffuse emission depends on the environment; regions with higher X-ray surface brightnesses have relatively stronger hard components, but there is no significant evidence that the temperatures of the emitting components increase with surface brightness.

Use of corrected centrifugal sudden approximations for the calculation of effective cross sections. II. The N sub 2 --He system

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

Thachuk, M.; McCourt, F.R.W.

1991-09-15

A series of centrifugal sudden (CS) and infinite-order sudden (IOS) approximations together with their corrected versions, respectively, the corrected centrifugal sudden (CCS) and corrected infinite-order sudden (CIOS) approximations, originally introduced by McLenithan and Secrest (J. Chem. Phys. {bold 80}, 2480 (1987)), have been compared with the close-coupled (CC) method for the N{sub 2}--He interaction. This extends previous work using the H{sub 2}--He system (J. Chem. Phys. {bold 93}, 3931 (1990)) to an interaction which is more anisotropic and more classical in nature. A set of eleven energy dependent cross sections, including both relaxation and production types, has been calculated usingmore » the {ital LF}- and {ital LA}-labeling schemes for the CS approximation, as well as the {ital KI}-, {ital KF}-, {ital KA}-, and {ital KM}-labeling schemes for the IOS approximation. The latter scheme is defined as {ital KM}={ital K}=max({ital k}{sub {ital j}},{ital k}{sub {ital j}{sub {ital I}}}). Further, a number of temperature dependent cross sections formed from thermal averages of the above set have also been compared at 100 and 200 K. These comparisons have shown that the CS approximation produced accurate results for relaxation type cross sections regardless of the {ital L}-labeling scheme chosen, but inaccurate results for production type cross sections. Further, except for one particular cross section, the CCS approximation did not generally improve the accuracy of the CS results using either the {ital LF}- or {ital LA}-labeling schemes. The accuracy of the IOS results vary greatly between the cross sections with the most accurate values given by the {ital KM}-labeling scheme. The CIOS approximation generally increases the accuracy of the corresponding IOS results but does not completely eliminate the errors associated with them.« less

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).

Intermediate boundary conditions for LOD, ADI and approximate factorization methods

NASA Technical Reports Server (NTRS)

Leveque, R. J.

1985-01-01

A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.

Efficient kinetic Monte Carlo method for reaction-diffusion problems with spatially varying annihilation rates

NASA Astrophysics Data System (ADS)

Schwarz, Karsten; Rieger, Heiko

2013-03-01

We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.

Second-order singular pertubative theory for gravitational lenses

NASA Astrophysics Data System (ADS)

Alard, C.

2018-03-01

The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second-order expansion is considered as a small correction to the first-order expansion. Using this approach, it is demonstrated that in practice the second-order expansion is reducible to a first order expansion via a re-definition of the first-order pertubative fields. Even if in usual applications the second-order correction is small the reducibility of the second-order expansion to the first-order expansion indicates a potential degeneracy issue. In general, this degeneracy is hard to break. A useful and simple second-order approximation is the thin source approximation, which offers a direct estimation of the correction. The practical application of the corrections derived in this paper is illustrated by using an elliptical NFW lens model. The second-order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude, it is clear that for accurate modelization of gravitational lenses using the perturbative method the second-order perturbative expansion should be considered. In particular, an evaluation of the degeneracy due to the second-order term should be performed, for which the thin source approximation is particularly useful.

Diffusion tensor imaging (DTI) with retrospective motion correction for large-scale pediatric imaging.

PubMed

Holdsworth, Samantha J; Aksoy, Murat; Newbould, Rexford D; Yeom, Kristen; Van, Anh T; Ooi, Melvyn B; Barnes, Patrick D; Bammer, Roland; Skare, Stefan

2012-10-01

To develop and implement a clinical DTI technique suitable for the pediatric setting that retrospectively corrects for large motion without the need for rescanning and/or reacquisition strategies, and to deliver high-quality DTI images (both in the presence and absence of large motion) using procedures that reduce image noise and artifacts. We implemented an in-house built generalized autocalibrating partially parallel acquisitions (GRAPPA)-accelerated diffusion tensor (DT) echo-planar imaging (EPI) sequence at 1.5T and 3T on 1600 patients between 1 month and 18 years old. To reconstruct the data, we developed a fully automated tailored reconstruction software that selects the best GRAPPA and ghost calibration weights; does 3D rigid-body realignment with importance weighting; and employs phase correction and complex averaging to lower Rician noise and reduce phase artifacts. For select cases we investigated the use of an additional volume rejection criterion and b-matrix correction for large motion. The DTI image reconstruction procedures developed here were extremely robust in correcting for motion, failing on only three subjects, while providing the radiologists high-quality data for routine evaluation. This work suggests that, apart from the rare instance of continuous motion throughout the scan, high-quality DTI brain data can be acquired using our proposed integrated sequence and reconstruction that uses a retrospective approach to motion correction. In addition, we demonstrate a substantial improvement in overall image quality by combining phase correction with complex averaging, which reduces the Rician noise that biases noisy data. Copyright © 2012 Wiley Periodicals, Inc.

Efficient gradient calibration based on diffusion MRI.

PubMed

Teh, Irvin; Maguire, Mahon L; Schneider, Jürgen E

2017-01-01

To propose a method for calibrating gradient systems and correcting gradient nonlinearities based on diffusion MRI measurements. The gradient scaling in x, y, and z were first offset by up to 5% from precalibrated values to simulate a poorly calibrated system. Diffusion MRI data were acquired in a phantom filled with cyclooctane, and corrections for gradient scaling errors and nonlinearity were determined. The calibration was assessed with diffusion tensor imaging and independently validated with high resolution anatomical MRI of a second structured phantom. The errors in apparent diffusion coefficients along orthogonal axes ranged from -9.2% ± 0.4% to + 8.8% ± 0.7% before calibration and -0.5% ± 0.4% to + 0.8% ± 0.3% after calibration. Concurrently, fractional anisotropy decreased from 0.14 ± 0.03 to 0.03 ± 0.01. Errors in geometric measurements in x, y and z ranged from -5.5% to + 4.5% precalibration and were likewise reduced to -0.97% to + 0.23% postcalibration. Image distortions from gradient nonlinearity were markedly reduced. Periodic gradient calibration is an integral part of quality assurance in MRI. The proposed approach is both accurate and efficient, can be setup with readily available materials, and improves accuracy in both anatomical and diffusion MRI to within ±1%. Magn Reson Med 77:170-179, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. © 2016 Wiley Periodicals, Inc.

Efficient gradient calibration based on diffusion MRI

PubMed Central

Teh, Irvin; Maguire, Mahon L.

2016-01-01

Purpose To propose a method for calibrating gradient systems and correcting gradient nonlinearities based on diffusion MRI measurements. Methods The gradient scaling in x, y, and z were first offset by up to 5% from precalibrated values to simulate a poorly calibrated system. Diffusion MRI data were acquired in a phantom filled with cyclooctane, and corrections for gradient scaling errors and nonlinearity were determined. The calibration was assessed with diffusion tensor imaging and independently validated with high resolution anatomical MRI of a second structured phantom. Results The errors in apparent diffusion coefficients along orthogonal axes ranged from −9.2% ± 0.4% to + 8.8% ± 0.7% before calibration and −0.5% ± 0.4% to + 0.8% ± 0.3% after calibration. Concurrently, fractional anisotropy decreased from 0.14 ± 0.03 to 0.03 ± 0.01. Errors in geometric measurements in x, y and z ranged from −5.5% to + 4.5% precalibration and were likewise reduced to −0.97% to + 0.23% postcalibration. Image distortions from gradient nonlinearity were markedly reduced. Conclusion Periodic gradient calibration is an integral part of quality assurance in MRI. The proposed approach is both accurate and efficient, can be setup with readily available materials, and improves accuracy in both anatomical and diffusion MRI to within ±1%. Magn Reson Med 77:170–179, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. PMID:26749277

Joint correction of Nyquist artifact and minuscule motion-induced aliasing artifact in interleaved diffusion weighted EPI data using a composite two-dimensional phase correction procedure

PubMed Central

Chang, Hing-Chiu; Chen, Nan-kuei

2016-01-01

Diffusion-weighted imaging (DWI) obtained with interleaved echo-planar imaging (EPI) pulse sequence has great potential of characterizing brain tissue properties at high spatial-resolution. However, interleaved EPI based DWI data may be corrupted by various types of aliasing artifacts. First, inconsistencies in k-space data obtained with opposite readout gradient polarities result in Nyquist artifact, which is usually reduced with 1D phase correction in post-processing. When there exist eddy current cross terms (e.g., in oblique-plane EPI), 2D phase correction is needed to effectively reduce Nyquist artifact. Second, minuscule motion induced phase inconsistencies in interleaved DWI scans result in image-domain aliasing artifact, which can be removed with reconstruction procedures that take shot-to-shot phase variations into consideration. In existing interleaved DWI reconstruction procedures, Nyquist artifact and minuscule motion-induced aliasing artifact are typically removed subsequently in two stages. Although the two-stage phase correction generally performs well for non-oblique plane EPI data obtained from well-calibrated system, the residual artifacts may still be pronounced in oblique-plane EPI data or when there exist eddy current cross terms. To address this challenge, here we report a new composite 2D phase correction procedure, which effective removes Nyquist artifact and minuscule motion induced aliasing artifact jointly in a single step. Our experimental results demonstrate that the new 2D phase correction method can much more effectively reduce artifacts in interleaved EPI based DWI data as compared with the existing two-stage artifact correction procedures. The new method robustly enables high-resolution DWI, and should prove highly valuable for clinical uses and research studies of DWI. PMID:27114342

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

NASA Astrophysics Data System (ADS)

McEvoy, Erica L.

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

Physarum machines: encapsulating reaction-diffusion to compute spanning tree

NASA Astrophysics Data System (ADS)

Adamatzky, Andrew

2007-12-01

The Physarum machine is a biological computing device, which employs plasmodium of Physarum polycephalum as an unconventional computing substrate. A reaction-diffusion computer is a chemical computing device that computes by propagating diffusive or excitation wave fronts. Reaction-diffusion computers, despite being computationally universal machines, are unable to construct certain classes of proximity graphs without the assistance of an external computing device. I demonstrate that the problem can be solved if the reaction-diffusion system is enclosed in a membrane with few ‘growth points’, sites guiding the pattern propagation. Experimental approximation of spanning trees by P. polycephalum slime mold demonstrates the feasibility of the approach. Findings provided advance theory of reaction-diffusion computation by enriching it with ideas of slime mold computation.

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.

Advanced diffusion MRI and biomarkers in the central nervous system: a new approach.

PubMed

Martín Noguerol, T; Martínez Barbero, J P

The introduction of diffusion-weighted sequences has revolutionized the detection and characterization of central nervous system (CNS) disease. Nevertheless, the assessment of diffusion studies of the CNS is often limited to qualitative estimation. Moreover, the pathophysiological complexity of the different entities that affect the CNS cannot always be correctly explained through classical models. The development of new models for the analysis of diffusion sequences provides numerous parameters that enable a quantitative approach to both diagnosis and prognosis as well as to monitoring the response to treatment; these parameters can be considered potential biomarkers of health and disease. In this update, we review the physical bases underlying diffusion studies and diffusion tensor imaging, advanced models for their analysis (intravoxel coherent motion and kurtosis), and the biological significance of the parameters derived. Copyright © 2017 SERAM. Publicado por Elsevier España, S.L.U. All rights reserved.

The use of a standardized gray reference card in dental photography to correct the effects of five commonly used diffusers on the color of 40 extracted human teeth.

PubMed

Hein, Sascha; Zangl, Michael

2016-01-01

The aim of this in vitro study was to investigate the color changes of human teeth caused by five different diffuser materials commonly used in dental photography, as well as software influence, and to confirm whether the use of a standardized gray reference card is effective in correcting these color changes during digital postproduction. Forty extracted human teeth were obtained from a specialized oral surgery practice in Cham, Germany. Five commonly used diffuser materials were chosen to be investigated, which included: polyethylene (PET), White Frost photographic paper, LumiQuest polyamide (nylon) material, 80 gsm white printing paper, and 3M linear polarizing filter sheet used for cross polarization. A digital single-lens reflex camera (Canon EOS 5D MKII) was used, together with a twin flash suitable for macrophotography (Canon MT-24EX Macro Twin Lite). Images were tethered into Adobe Lightroom CC using the RAW format. A standardized gray reference card (WhiBal, Michael Tapes Design) was used for exposure calibration and white balancing. Classic Color Me- ter software (Ricci Adams, version 1.6 (122)) was used to obtain CIE L*a*b* values of the specimens before and after white balancing and exposure correction. All diffusers caused visually perceivable color changes on the extracted teeth: White Frost (ΔE* 1.24; sd 0.47), 80 gsm printing paper (ΔE* 2.94; sd 0.35), LumiQuest polyamide (ΔE* 3.68; sd 0.54), PET (ΔE* 6.55; sd 0.41), and 3M linear polarizing filter sheet (ΔE* 7.58; sd 1.00). The use of a standardized gray reference card (WhiBal) could correct these values below the visually perceivable threshold: White Frost (ΔE* 0.58; sd 0.36), 80 gsm printing paper (ΔE* 0.93; sd 0.54), LumiQuest polyamide (ΔE* 0.66; sd 0.58), PET (ΔE* 0.59; sd 0.33), and 3M linear polarizing filter sheet (ΔE* 0.53; sd 0.42). The use of a standardized gray reference card with specified CIE L*a*b* values should be considered when diffusers are used in dental photography in order to reveal the color of preoperative situations (ie, shade documentation) and document postoperative results accurately.

Diffusion of Siderophile Elements in Iron Meteorites

NASA Astrophysics Data System (ADS)

Watson, H. C.; Watson, E. B.

2001-12-01

Preliminary results for diffusion of siderophile elements (Cu, Os, Pd, Re, Os, and Mo) in an iron meteorite analog were obtained at 1400° C and 1GPa from diffusion couple experiments in a piston-cylinder apparatus. Alloys were prepared by synthesizing mixtures of pure metal powders. The alloys were made from a 90 wt% Fe and 10 wt% Ni base mixture, and approximately 1wt% of the various siderophile elements was added (individually) to the same base mixture to make the doped alloys. The powders were packed in pre-drilled holes (~1 mm dia. by 8 mm deep) in MgO cylinders, and run in a piston cylinder apparatus at 1400° C and 1GPa for 48 hours. The resulting homogeneous alloys were then sectioned into wafers approximately 1mm thick, and the faces were polished to prepare for the diffusion experiments. A diffusion couple experiment was conducted by mating a pure alloy wafer and a doped wafer, and placing the couple into an MgO capsule for pressurization and heating in the piston cylinder. The duration of the diffusion experiments ranged from 33 hours to 72 hours. Upon run completion, the diffusion couples were extracted, sectioned lengthwise, and polished for analysis. Diffusion profiles were measured using an electron microprobe. From these experiments it was found that at 1400° C and 1GPa the diffusion coefficient of Os is 1.6E-14 m2/s, the diffusion coefficient of Re is 2.8E-14 m2/s, for Pd it is 9.2E-14 m2/s, for Cu it is 1.2E-13 m2/s, and for Mo it is 2.3E-13 m2/s. These preliminary results raise the possibility that significant diffusive fraction of siderophile elements may occur in metal-silicate systems that fail to equilibrate fully, or under disequilibrium crystallization in pure metal systems.

Singleshot T1 Mapping using Simultaneous Acquisitions of Spin- and STimulated-Echo Planar Imaging (2D ss-SESTEPI)

PubMed Central

Shi, Xianfeng; Kim, Seong-Eun; Jeong, Eun-Kee

2011-01-01

The conventional stimulated-echo NMR sequence only measures the longitudinal component, while discarding the transverse component, after tipping up the prepared magnetization. This transverse magnetization can be used to measure a spin-echo, in addition to the stimulated-echo. 2D ss-SESTEPI is an EPI-based singleshot imaging technique that simultaneously acquires a spin-echo-planar image (SEPI) and a stimulated-echo-planar image (STEPI) after a single RF excitation. The magnitudes of SEPI and STEPI differ by T1 decay and diffusion weighting for perfect 90° RF, and thus can be used to rapidly measure T1. However, the spatial variation of B1 amplitude induces un-even splitting of the transverse magnetization for SEPI and STEPI within the imaging FOV. Correction for B1 inhomogeneity is therefore critical for 2D ss-SESTEPI to be used for T1 measurement. We developed a method for B1 inhomogeneity correction by acquiring an additional STEPI with minimal mixing time, calculating the difference between the spin-echo and the stimulated-echo and multiplying the STEPI by the inverse functional map. Diffusion-induced decay is corrected by measuring the average diffusivity during the prescanning. Rapid singleshot T1 mapping may be useful for various applications, such as dynamic T1 mapping for real-time estimation of the concentration of contrast agent in DCE-MRI. PMID:20564579

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*

PubMed Central

BARMPOUTIS, ANGELOS; JEFFREY, HO; VEMURI, BABA C.

2012-01-01

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space P02m of 2mth-order symmetric positive semi-definite tensors is known to be a convex cone, enforcing positivity constraint directly on P02m is usually not straightforward computationally because there is no known analytic description of P02m for m > 1. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone P02m for the cases 0 < m < 3, and presenting an explicit characterization of the approximation Σ2m ⊂ Ω2m for m ≥ 1, using the subset Ω2m⊂P02m of semi-definite tensors that can be written as a sum of squares of tensors of order m. Furthermore, we show that this approximation leads to a non-negative linear least-squares (NNLS) optimization problem with the complexity that equals the number of generators in Σ2m. Finally, we experimentally validate the proposed approach and we present an application for computing 2mth-order diffusion tensors from Diffusion Weighted Magnetic Resonance Images. PMID:23285313

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.

A symmetrical image encryption scheme in wavelet and time domain

NASA Astrophysics Data System (ADS)

Luo, Yuling; Du, Minghui; Liu, Junxiu

2015-02-01

There has been an increasing concern for effective storages and secure transactions of multimedia information over the Internet. Then a great variety of encryption schemes have been proposed to ensure the information security while transmitting, but most of current approaches are designed to diffuse the data only in spatial domain which result in reducing storage efficiency. A lightweight image encryption strategy based on chaos is proposed in this paper. The encryption process is designed in transform domain. The original image is decomposed into approximation and detail components using integer wavelet transform (IWT); then as the more important component of the image, the approximation coefficients are diffused by secret keys generated from a spatiotemporal chaotic system followed by inverse IWT to construct the diffused image; finally a plain permutation is performed for diffusion image by the Logistic mapping in order to reduce the correlation between adjacent pixels further. Experimental results and performance analysis demonstrate the proposed scheme is an efficient, secure and robust encryption mechanism and it realizes effective coding compression to satisfy desirable storage.

Resolving power for the diffusion orientation distribution function.

PubMed

Jensen, Jens H; Helpern, Joseph A

2016-08-01

The diffusion orientation distribution function (dODF) is primarily used for white matter fiber tractography. Here the resolving power of the dODF is investigated for a simple diffusion model of two intersecting axonal fiber bundles. The resolving power for the dODF is evaluated using the Sparrow criterion. This is determined for the exact dODF and also for q-space imaging (QSI), q-ball, and kurtosis approximations. Based on theoretical and numerical calculations, the resolving power is found to depend on the eigenvalues of the diffusion model and on the degree of radial weighting for the dODF. The resolving powers of the QSI and q-ball dODFs improve with increased b-value. The kurtosis dODF has a resolving power similar to that of the exact dODF. The dODFs, whether exact or approximate, have finite resolving powers that limit their sensitivity to fiber crossings. The resolving powers for the different dODFs considered here provide convenient benchmarks for assessing and comparing their performance. Magn Reson Med 76:679-688, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Valuing options in shot noise market

NASA Astrophysics Data System (ADS)

Laskin, Nick

2018-07-01

A new exactly solvable option pricing model has been introduced and elaborated. It is assumed that a stock price follows a Geometric shot noise process. An arbitrage-free integro-differential option pricing equation has been obtained and solved. The new Greeks have been analytically calculated. It has been shown that in diffusion approximation the developed option pricing model incorporates the well-known Black-Scholes equation and its solution. The stochastic dynamic origin of the Black-Scholes volatility has been uncovered. To model the observed market stock price patterns consisting of high frequency small magnitude and low frequency large magnitude jumps, the superposition of two Geometric shot noises has been implemented. A new generalized option pricing equation has been obtained and its exact solution was found. Merton's jump-diffusion formula for option price was recovered in diffusion approximation. Despite the non-Gaussian nature of probability distributions involved, the new option pricing model has the same degree of analytical tractability as the Black-Scholes model and the Merton jump-diffusion model. This attractive feature allows one to derive exact formulas to value options and option related instruments in the market with jump-like price patterns.

Inexpensive Meter for Total Solar Radiation

NASA Technical Reports Server (NTRS)

Laue, E. G.

1987-01-01

Pyranometer containing solar cells measures combined intensity of direct light from Sun and diffuse light from sky. Instrument includes polyethylene dome that diffuses entering light so output of light detectors does not vary significantly with changing angle of Sun during day. Not to be calibrated for response of each detector to Sun angle, and sensor outputs not corrected separately before summed and integrated. Aids in deciding on proper time to harvest crops.

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Kinetic and Mechanism Study of Vanadium Acid Leaching from Black Shale Using Microwave Heating Method

NASA Astrophysics Data System (ADS)

Wang, Jing-peng; Zhang, Yi-min; Huang, Jing; Liu, Tao

2018-04-01

The leaching kinetics of the vanadium leaching process were investigated by the comparison of microwave heating and conventional heating methods. Microwave heating with CaF2 had a synergistic effect and improved the vanadium leaching efficiency. In contrast to conventional heating leaching, microwave heating accelerated the vanadium leaching rate by approximately 1-3% and by approximately 15% when CaF2 was also used. The kinetics analysis showed that the calculated activation energy decreased in the microwave heating method in the presence and absence of CaF2. The control procedure of leaching also changed from a chemical reaction control step to a mixed chemical diffusion control step upon the addition of CaF2. Microwave heating was shown to be suitable for leaching systems with diffusion or mixed chemical diffusion control steps when the target mineral does not have a microwave absorbing ability.