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

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.

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.

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.

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.

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

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.

Ion diffusion may introduce spurious current sources in current-source density (CSD) analysis.

PubMed

Halnes, Geir; Mäki-Marttunen, Tuomo; Pettersen, Klas H; Andreassen, Ole A; Einevoll, Gaute T

2017-07-01

Current-source density (CSD) analysis is a well-established method for analyzing recorded local field potentials (LFPs), that is, the low-frequency part of extracellular potentials. Standard CSD theory is based on the assumption that all extracellular currents are purely ohmic, and thus neglects the possible impact from ionic diffusion on recorded potentials. However, it has previously been shown that in physiological conditions with large ion-concentration gradients, diffusive currents can evoke slow shifts in extracellular potentials. Using computer simulations, we here show that diffusion-evoked potential shifts can introduce errors in standard CSD analysis, and can lead to prediction of spurious current sources. Further, we here show that the diffusion-evoked prediction errors can be removed by using an improved CSD estimator which accounts for concentration-dependent effects. NEW & NOTEWORTHY Standard CSD analysis does not account for ionic diffusion. Using biophysically realistic computer simulations, we show that unaccounted-for diffusive currents can lead to the prediction of spurious current sources. This finding may be of strong interest for in vivo electrophysiologists doing extracellular recordings in general, and CSD analysis in particular. Copyright © 2017 the American Physiological Society.

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

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.

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

Diffusion from a line source

NASA Technical Reports Server (NTRS)

Burns, R. E.

1973-01-01

The problem with predicting pollutant diffusion from a line source of arbitrary geometry is treated. The concentration at the line source may be arbitrarily varied with time. Special attention is given to the meteorological inputs which act as boundary conditions for the problem, and a mixing layer of arbitrary depth is assumed. Numerical application of the derived theory indicates the combinations of meteorological parameters that may be expected to result in high pollution concentrations.

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

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).

Solute source depletion control of forward and back diffusion through low-permeability zones

NASA Astrophysics Data System (ADS)

Yang, Minjune; Annable, Michael D.; Jawitz, James W.

2016-10-01

Solute diffusive exchange between low-permeability aquitards and high-permeability aquifers acts as a significant mediator of long-term contaminant fate. Aquifer contaminants diffuse into aquitards, but as contaminant sources are depleted, aquifer concentrations decline, triggering back diffusion from aquitards. The dynamics of the contaminant source depletion, or the source strength function, controls the timing of the transition of aquitards from sinks to sources. Here, we experimentally evaluate three archetypical transient source depletion models (step-change, linear, and exponential), and we use novel analytical solutions to accurately account for dynamic aquitard-aquifer diffusive transfer. Laboratory diffusion experiments were conducted using a well-controlled flow chamber to assess solute exchange between sand aquifer and kaolinite aquitard layers. Solute concentration profiles in the aquitard were measured in situ using electrical conductivity. Back diffusion was shown to begin earlier and produce larger mass flux for rapidly depleting sources. The analytical models showed very good correspondence with measured aquifer breakthrough curves and aquitard concentration profiles. The modeling approach links source dissolution and back diffusion, enabling assessment of human exposure risk and calculation of the back diffusion initiation time, as well as the resulting plume persistence.

Solute source depletion control of forward and back diffusion through low-permeability zones.

PubMed

Yang, Minjune; Annable, Michael D; Jawitz, James W

2016-10-01

Solute diffusive exchange between low-permeability aquitards and high-permeability aquifers acts as a significant mediator of long-term contaminant fate. Aquifer contaminants diffuse into aquitards, but as contaminant sources are depleted, aquifer concentrations decline, triggering back diffusion from aquitards. The dynamics of the contaminant source depletion, or the source strength function, controls the timing of the transition of aquitards from sinks to sources. Here, we experimentally evaluate three archetypical transient source depletion models (step-change, linear, and exponential), and we use novel analytical solutions to accurately account for dynamic aquitard-aquifer diffusive transfer. Laboratory diffusion experiments were conducted using a well-controlled flow chamber to assess solute exchange between sand aquifer and kaolinite aquitard layers. Solute concentration profiles in the aquitard were measured in situ using electrical conductivity. Back diffusion was shown to begin earlier and produce larger mass flux for rapidly depleting sources. The analytical models showed very good correspondence with measured aquifer breakthrough curves and aquitard concentration profiles. The modeling approach links source dissolution and back diffusion, enabling assessment of human exposure risk and calculation of the back diffusion initiation time, as well as the resulting plume persistence. Copyright © 2016 Elsevier B.V. All rights reserved.

Application of the Approximate Bayesian Computation methods in the stochastic estimation of atmospheric contamination parameters for mobile sources

NASA Astrophysics Data System (ADS)

Kopka, Piotr; Wawrzynczak, Anna; Borysiewicz, Mieczyslaw

2016-11-01

In this paper the Bayesian methodology, known as Approximate Bayesian Computation (ABC), is applied to the problem of the atmospheric contamination source identification. The algorithm input data are on-line arriving concentrations of the released substance registered by the distributed sensors network. This paper presents the Sequential ABC algorithm in detail and tests its efficiency in estimation of probabilistic distributions of atmospheric release parameters of a mobile contamination source. The developed algorithms are tested using the data from Over-Land Atmospheric Diffusion (OLAD) field tracer experiment. The paper demonstrates estimation of seven parameters characterizing the contamination source, i.e.: contamination source starting position (x,y), the direction of the motion of the source (d), its velocity (v), release rate (q), start time of release (ts) and its duration (td). The online-arriving new concentrations dynamically update the probability distributions of search parameters. The atmospheric dispersion Second-order Closure Integrated PUFF (SCIPUFF) Model is used as the forward model to predict the concentrations at the sensors locations.

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.

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

Locating multiple diffusion sources in time varying networks from sparse observations.

PubMed

Hu, Zhao-Long; Shen, Zhesi; Cao, Shinan; Podobnik, Boris; Yang, Huijie; Wang, Wen-Xu; Lai, Ying-Cheng

2018-02-08

Data based source localization in complex networks has a broad range of applications. Despite recent progress, locating multiple diffusion sources in time varying networks remains to be an outstanding problem. Bridging structural observability and sparse signal reconstruction theories, we develop a general framework to locate diffusion sources in time varying networks based solely on sparse data from a small set of messenger nodes. A general finding is that large degree nodes produce more valuable information than small degree nodes, a result that contrasts that for static networks. Choosing large degree nodes as the messengers, we find that sparse observations from a few such nodes are often sufficient for any number of diffusion sources to be located for a variety of model and empirical networks. Counterintuitively, sources in more rapidly varying networks can be identified more readily with fewer required messenger nodes.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

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, PO Box 1207, 3430 BE Nieuwegein

2014-11-15

In this paper, a number of new 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 semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships betweenmore » heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.« less

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.

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.

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.

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

Extracting spatial information from large aperture exposures of diffuse sources

NASA Technical Reports Server (NTRS)

Clarke, J. T.; Moos, H. W.

1981-01-01

The spatial properties of large aperture exposures of diffuse emission can be used both to investigate spatial variations in the emission and to filter out camera noise in exposures of weak emission sources. Spatial imaging can be accomplished both parallel and perpendicular to dispersion with a resolution of 5-6 arc sec, and a narrow median filter running perpendicular to dispersion across a diffuse image selectively filters out point source features, such as reseaux marks and fast particle hits. Spatial information derived from observations of solar system objects is presented.

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.

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.

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.

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.

SEE rate estimation based on diffusion approximation of charge collection

NASA Astrophysics Data System (ADS)

Sogoyan, Armen V.; Chumakov, Alexander I.; Smolin, Anatoly A.

2018-03-01

The integral rectangular parallelepiped (IRPP) method remains the main approach to single event rate (SER) prediction for aerospace systems, despite the growing number of issues impairing method's validity when applied to scaled technology nodes. One of such issues is uncertainty in parameters extraction in the IRPP method, which can lead to a spread of several orders of magnitude in the subsequently calculated SER. The paper presents an alternative approach to SER estimation based on diffusion approximation of the charge collection by an IC element and geometrical interpretation of SEE cross-section. In contrast to the IRPP method, the proposed model includes only two parameters which are uniquely determined from the experimental data for normal incidence irradiation at an ion accelerator. This approach eliminates the necessity of arbitrary decisions during parameter extraction and, thus, greatly simplifies calculation procedure and increases the robustness of the forecast.

Analysis on a diffusive SIS epidemic model with logistic source

NASA Astrophysics Data System (ADS)

Li, Bo; Li, Huicong; Tong, Yachun

2017-08-01

In this paper, we are concerned with an SIS epidemic reaction-diffusion model with logistic source in spatially heterogeneous environment. We first discuss some basic properties of the parabolic system, including the uniform upper bound of solutions and global stability of the endemic equilibrium when spatial environment is homogeneous. Our primary focus is to determine the asymptotic profile of endemic equilibria (when exist) if the diffusion (migration) rate of the susceptible or infected population is small or large. Combined with the results of Li et al. (J Differ Equ 262:885-913, 2017) where the case of linear source is studied, our analysis suggests that varying total population enhances persistence of infectious disease.

Nature of the Diffuse Source and Its Central Point-like Source in SNR 0509–67.5

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

Litke, Katrina C.; Chu, You-Hua; Holmes, Abigail

We examine a diffuse emission region near the center of SNR 0509−67.5 to determine its nature. Within this diffuse region we observe a point-like source that is bright in the near-IR, but is not visible in the B and V bands. We consider an emission line observed at 6766 Å and the possibilities that it is Ly α , H α , and [O ii] λ 3727. We examine the spectral energy distribution (SED) of the source, comprised of Hubble Space Telescope B , V , I , J , and H bands in addition to Spitzer /IRAC 3.6, 4.5,more » 5.8, and 8 μ m bands. The peak of the SED is consistent with a background galaxy at z ≈ 0.8 ± 0.2 and a possible Balmer jump places the galaxy at z ≈ 0.9 ± 0.3. These SED considerations support the emission line’s identification as [O ii] λ 3727. We conclude that the diffuse source in SNR 0509−67.5 is a background galaxy at z ≈ 0.82. Furthermore, we identify the point-like source superposed near the center of the galaxy as its central bulge. Finally, we find no evidence for a surviving companion star, indicating a double-degenerate origin for SNR 0509−67.5.« less

A diffusion approach to approximating preservation probabilities for gene duplicates.

PubMed

O'Hely, Martin

2006-08-01

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

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.

An approximate stationary solution for multi-allele neutral diffusion with low mutation rates.

PubMed

Burden, Conrad J; Tang, Yurong

2016-12-01

We address the problem of determining the stationary distribution of the multi-allelic, neutral-evolution Wright-Fisher model in the diffusion limit. A full solution to this problem for an arbitrary K×K mutation rate matrix involves solving for the stationary solution of a forward Kolmogorov equation over a (K-1)-dimensional simplex, and remains intractable. In most practical situations mutations rates are slow on the scale of the diffusion limit and the solution is heavily concentrated on the corners and edges of the simplex. In this paper we present a practical approximate solution for slow mutation rates in the form of a set of line densities along the edges of the simplex. The method of solution relies on parameterising the general non-reversible rate matrix as the sum of a reversible part and a set of (K-1)(K-2)/2 independent terms corresponding to fluxes of probability along closed paths around faces of the simplex. The solution is potentially a first step in estimating non-reversible evolutionary rate matrices from observed allele frequency spectra. Copyright © 2016 Elsevier Inc. All rights reserved.

Abatement vs. treatment for efficient diffuse source water pollution management in terrestrial-marine systems.

PubMed

Roebeling, P C; Cunha, M C; Arroja, L; van Grieken, M E

2015-01-01

Marine ecosystems are affected by water pollution originating from coastal catchments. The delivery of water pollutants can be reduced through water pollution abatement as well as water pollution treatment. Hence, sustainable economic development of coastal regions requires balancing of the marginal costs from water pollution abatement and/or treatment and the associated marginal benefits from marine resource appreciation. Water pollution delivery reduction costs are, however, not equal across abatement and treatment options. In this paper, an optimal control approach is developed and applied to explore welfare maximizing rates of water pollution abatement and/or treatment for efficient diffuse source water pollution management in terrestrial-marine systems. For the case of diffuse source dissolved inorganic nitrogen water pollution in the Tully-Murray region, Queensland, Australia, (agricultural) water pollution abatement cost, (wetland) water pollution treatment cost and marine benefit functions are determined to explore welfare maximizing rates of water pollution abatement and/or treatment. Considering partial (wetland) treatment costs and positive water quality improvement benefits, results show that welfare gains can be obtained, primarily, through diffuse source water pollution abatement (improved agricultural management practices) and, to a minor extent, through diffuse source water pollution treatment (wetland restoration).

Probing the infrared counterparts of diffuse far-ultraviolet sources in the Galaxy

NASA Astrophysics Data System (ADS)

Saikia, Gautam; Shalima, P.; Gogoi, Rupjyoti; Pathak, Amit

2017-12-01

Recent availability of high quality infrared (IR) data for diffuse regions in the Galaxy and external galaxies have added to our understanding of interstellar dust. A comparison of ultraviolet (UV) and IR observations may be used to estimate absorption, scattering and thermal emission from interstellar dust. In this paper, we report IR and UV observations for selective diffuse sources in the Galaxy. Using archival mid-infrared (MIR) and far-infrared (FIR) observations from Spitzer Space Telescope, we look for counterparts of diffuse far-ultraviolet (FUV) sources observed by the Voyager, Far Ultraviolet Spectroscopic Explorer (FUSE) and Galaxy Evolution Explorer (GALEX) telescopes in the Galaxy. IR emission features at 8 μm are generally attributed to Polycyclic Aromatic Hydrocarbon (PAH) molecules, while emission at 24 μm are attributed to Very Small Grains (VSGs). The data presented here is unique and our study tries to establish a relation between various dust populations. By studying the FUV-IR correlations separately at low and high latitude locations, we have identified the grain component responsible for the diffuse FUV emission.

Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO 2 in fractured rocks

DOE PAGES

Zhou, Quanlin; Oldenburg, Curtis M.; Spangler, Lee H.; ...

2017-01-05

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheresmore » and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

Discrimination between diffuse and point sources of arsenic at Zimapán, Hidalgo state, Mexico.

PubMed

Sracek, Ondra; Armienta, María Aurora; Rodríguez, Ramiro; Villaseñor, Guadalupe

2010-01-01

There are two principal sources of arsenic in Zimapán. Point sources are linked to mining and smelting activities and especially to mine tailings. Diffuse sources are not well defined and are linked to regional flow systems in carbonate rocks. Both sources are caused by the oxidation of arsenic-rich sulfidic mineralization. Point sources are characterized by Ca-SO(4)-HCO(3) ground water type and relatively enriched values of deltaD, delta(18)O, and delta(34)S(SO(4)). Diffuse sources are characterized by Ca-Na-HCO(3) type of ground water and more depleted values of deltaD, delta(18)O, and delta(34)S(SO(4)). Values of deltaD and delta(18)O indicate similar altitude of recharge for both arsenic sources and stronger impact of evaporation for point sources in mine tailings. There are also different values of delta(34)S(SO(4)) for both sources, presumably due to different types of mineralization or isotopic zonality in deposits. In Principal Component Analysis (PCA), the principal component 1 (PC1), which describes the impact of sulfide oxidation and neutralization by the dissolution of carbonates, has higher values in samples from point sources. In spite of similar concentrations of As in ground water affected by diffuse sources and point sources (mean values 0.21 mg L(-1) and 0.31 mg L(-1), respectively, in the years from 2003 to 2008), the diffuse sources have more impact on the health of population in Zimapán. This is caused by the extraction of ground water from wells tapping regional flow system. In contrast, wells located in the proximity of mine tailings are not generally used for water supply.

Modeling deep brain stimulation: point source approximation versus realistic representation of the electrode

NASA Astrophysics Data System (ADS)

Zhang, Tianhe C.; Grill, Warren M.

2010-12-01

Deep brain stimulation (DBS) has emerged as an effective treatment for movement disorders; however, the fundamental mechanisms by which DBS works are not well understood. Computational models of DBS can provide insights into these fundamental mechanisms and typically require two steps: calculation of the electrical potentials generated by DBS and, subsequently, determination of the effects of the extracellular potentials on neurons. The objective of this study was to assess the validity of using a point source electrode to approximate the DBS electrode when calculating the thresholds and spatial distribution of activation of a surrounding population of model neurons in response to monopolar DBS. Extracellular potentials in a homogenous isotropic volume conductor were calculated using either a point current source or a geometrically accurate finite element model of the Medtronic DBS 3389 lead. These extracellular potentials were coupled to populations of model axons, and thresholds and spatial distributions were determined for different electrode geometries and axon orientations. Median threshold differences between DBS and point source electrodes for individual axons varied between -20.5% and 9.5% across all orientations, monopolar polarities and electrode geometries utilizing the DBS 3389 electrode. Differences in the percentage of axons activated at a given amplitude by the point source electrode and the DBS electrode were between -9.0% and 12.6% across all monopolar configurations tested. The differences in activation between the DBS and point source electrodes occurred primarily in regions close to conductor-insulator interfaces and around the insulating tip of the DBS electrode. The robustness of the point source approximation in modeling several special cases—tissue anisotropy, a long active electrode and bipolar stimulation—was also examined. Under the conditions considered, the point source was shown to be a valid approximation for predicting excitation

Development of a primary diffusion source of organic vapors for gas analyzer calibration

NASA Astrophysics Data System (ADS)

Lecuna, M.; Demichelis, A.; Sassi, G.; Sassi, M. P.

2018-03-01

The generation of reference mixtures of volatile organic compounds (VOCs) at trace levels (10 ppt-10 ppb) is a challenge for both environmental and clinical measurements. The calibration of gas analyzers for trace VOC measurements requires a stable and accurate source of the compound of interest. The dynamic preparation of gas mixtures by diffusion is a suitable method for fulfilling these requirements. The estimation of the uncertainty of the molar fraction of the VOC in the mixture is a key step in the metrological characterization of a dynamic generator. The performance of a dynamic generator was monitored over a wide range of operating conditions. The generation system was simulated by a model developed with computational fluid dynamics and validated against experimental data. The vapor pressure of the VOC was found to be one of the main contributors to the uncertainty of the diffusion rate and its influence at 10-70 kPa was analyzed and discussed. The air buoyancy effect and perturbations due to the weighing duration were studied. The gas carrier flow rate and the amount of liquid in the vial were found to play a role in limiting the diffusion rate. The results of sensitivity analyses were reported through an uncertainty budget for the diffusion rate. The roles of each influence quantity were discussed. A set of criteria to minimize the uncertainty contribution to the primary diffusion source (25 µg min-1) were estimated: carrier gas flow rate higher than 37.7 sml min-1, a maximum VOC liquid mass decrease in the vial of 4.8 g, a minimum residual mass of 1 g and vial weighing times of 1-3 min. With this procedure a limit uncertainty of 0.5% in the diffusion rate can be obtained for VOC mixtures at trace levels (10 ppt-10 ppb), making the developed diffusion vials a primary diffusion source with potential to become a new reference material for trace VOC analysis.

Heat source reconstruction from noisy temperature fields using a gradient anisotropic diffusion filter

NASA Astrophysics Data System (ADS)

Beitone, C.; Balandraud, X.; Delpueyo, D.; Grédiac, M.

2017-01-01

This paper presents a post-processing technique for noisy temperature maps based on a gradient anisotropic diffusion (GAD) filter in the context of heat source reconstruction. The aim is to reconstruct heat source maps from temperature maps measured using infrared (IR) thermography. Synthetic temperature fields corrupted by added noise are first considered. The GAD filter, which relies on a diffusion process, is optimized to retrieve as well as possible a heat source concentration in a two-dimensional plate. The influence of the dimensions and the intensity of the heat source concentration are discussed. The results obtained are also compared with two other types of filters: averaging filter and Gaussian derivative filter. The second part of this study presents an application for experimental temperature maps measured with an IR camera. The results demonstrate the relevancy of the GAD filter in extracting heat sources from noisy temperature fields.

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.

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.

Approximation of a radial diffusion model with a multiple-rate model for hetero-disperse particle mixtures

PubMed Central

Ju, Daeyoung; Young, Thomas M.; Ginn, Timothy R.

2012-01-01

An innovative method is proposed for approximation of the set of radial diffusion equations governing mass exchange between aqueous bulk phase and intra-particle phase for a hetero-disperse mixture of particles such as occur in suspension in surface water, in riverine/estuarine sediment beds, in soils and in aquifer materials. For this purpose the temporal variation of concentration at several uniformly distributed points within a normalized representative particle with spherical, cylindrical or planar shape is fitted with a 2-domain linear reversible mass exchange model. The approximation method is then superposed in order to generalize the model to a hetero-disperse mixture of particles. The method can reduce the computational effort needed in solving the intra-particle mass exchange of a hetero-disperse mixture of particles significantly and also the error due to the approximation is shown to be relatively small. The method is applied to describe desorption batch experiment of 1,2-Dichlorobenzene from four different soils with known particle size distributions and it could produce good agreement with experimental data. PMID:18304692

Miniaturized pulsed laser source for time-domain diffuse optics routes to wearable devices

NASA Astrophysics Data System (ADS)

Di Sieno, Laura; Nissinen, Jan; Hallman, Lauri; Martinenghi, Edoardo; Contini, Davide; Pifferi, Antonio; Kostamovaara, Juha; Mora, Alberto Dalla

2017-08-01

We validate a miniaturized pulsed laser source for use in time-domain (TD) diffuse optics, following rigorous and shared protocols for performance assessment of this class of devices. This compact source (12×6 mm2) has been previously developed for range finding applications and is able to provide short, high energy (˜100 ps, ˜0.5 nJ) optical pulses at up to 1 MHz repetition rate. Here, we start with a basic level laser characterization with an analysis of suitability of this laser for the diffuse optics application. Then, we present a TD optical system using this source and its performances in both recovering optical properties of tissue-mimicking homogeneous phantoms and in detecting localized absorption perturbations. Finally, as a proof of concept of in vivo application, we demonstrate that the system is able to detect hemodynamic changes occurring in the arm of healthy volunteers during a venous occlusion. Squeezing the laser source in a small footprint removes a key technological bottleneck that has hampered so far the realization of a miniaturized TD diffuse optics system, able to compete with already assessed continuous-wave devices in terms of size and cost, but with wider performance potentialities, as demonstrated by research over the last two decades.

Effect of the diffusion parameters on the observed γ-ray spectrum of sources and their contribution to the local all-electron spectrum: The EDGE code

NASA Astrophysics Data System (ADS)

López-Coto, R.; Hahn, J.; BenZvi, S.; Dingus, B.; Hinton, J.; Nisa, M. U.; Parsons, R. D.; Greus, F. Salesa; Zhang, H.; Zhou, H.

2018-11-01

The positron excess measured by PAMELA and AMS can only be explained if there is one or several sources injecting them. Moreover, at the highest energies, it requires the presence of nearby ( ∼ hundreds of parsecs) and middle age (maximum of ∼ hundreds of kyr) sources. Pulsars, as factories of electrons and positrons, are one of the proposed candidates to explain the origin of this excess. To calculate the contribution of these sources to the electron and positron flux at the Earth, we developed EDGE (Electron Diffusion and Gamma rays to the Earth), a code to treat the propagation of electrons and compute their diffusion from a central source with a flexible injection spectrum. Using this code, we can derive the source's gamma-ray spectrum, spatial extension, the all-electron density in space, the electron and positron flux reaching the Earth and the positron fraction measured at the Earth. We present in this paper the foundations of the code and study how different parameters affect the gamma-ray spectrum of a source and the electron flux measured at the Earth. We also studied the effect of several approximations usually performed in these studies. This code has been used to derive the results of the positron flux measured at the Earth in [1].

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Modeling diffuse sources of surface water contamination with plant protection products

NASA Astrophysics Data System (ADS)

Wendland, Sandra; Bock, Michael; Böhner, Jürgen; Lembrich, David

2015-04-01

Entries of chemical pollutants in surface waters are a serious environmental problem. Among water pollutants plant protection products (ppp) from farming practice are of major concern not only for water suppliers and environmental agencies, but also for farmers and industrial manufacturers. Lost chemicals no longer fulfill their original purpose on the field, but lead to severe damage of the environment and surface waters. Besides point-source inputs of chemical pollutants, the diffuse-source inputs from agricultural procedures play an important and not yet sufficiently studied role concerning water quality. The two most important factors for diffuse inputs are erosion and runoff. The latter usually occurs before erosion begins, and is thus often not visible in hindsight. Only if it has come to erosion, it is obvious to expect runoff in foresight at this area, too. In addition to numerous erosion models, there are also few applications to model runoff processes available. However, these conventional models utilize approximations of catchment parameters based on long-term average values or theoretically calculated concentration peaks which can only provide indications to relative amounts. Our study aims to develop and validate a simplified spatially-explicit dynamic model with high spatiotemporal resolution that enables to measure current and forecast runoff potential not only at catchment scale but field-differentiated. This method allows very precise estimations of runoff risks and supports risk reduction measures to be targeted before fields are treated. By focusing on water pathways occurring on arable land, targeted risk reduction measures like buffer strips at certain points and adapted ppp use can be taken early and pollution of rivers and other surface waters through transported pesticides, fertilizers and their products could be nearly avoided or largely minimized. Using a SAGA-based physical-parametric modeling approach, major factors influencing runoff

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.

Miniaturized pulsed laser source for time-domain diffuse optics routes to wearable devices.

PubMed

Di Sieno, Laura; Nissinen, Jan; Hallman, Lauri; Martinenghi, Edoardo; Contini, Davide; Pifferi, Antonio; Kostamovaara, Juha; Mora, Alberto Dalla

2017-08-01

We validate a miniaturized pulsed laser source for use in time-domain (TD) diffuse optics, following rigorous and shared protocols for performance assessment of this class of devices. This compact source (12×6  mm2) has been previously developed for range finding applications and is able to provide short, high energy (∼100  ps, ∼0.5  nJ) optical pulses at up to 1 MHz repetition rate. Here, we start with a basic level laser characterization with an analysis of suitability of this laser for the diffuse optics application. Then, we present a TD optical system using this source and its performances in both recovering optical properties of tissue-mimicking homogeneous phantoms and in detecting localized absorption perturbations. Finally, as a proof of concept of in vivo application, we demonstrate that the system is able to detect hemodynamic changes occurring in the arm of healthy volunteers during a venous occlusion. Squeezing the laser source in a small footprint removes a key technological bottleneck that has hampered so far the realization of a miniaturized TD diffuse optics system, able to compete with already assessed continuous-wave devices in terms of size and cost, but with wider performance potentialities, as demonstrated by research over the last two decades. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Cubic zirconia as a species permeable coating for zinc diffusion in gallium arsenide

NASA Astrophysics Data System (ADS)

Bisberg, J. E.; Dabkowski, F. P.; Chin, A. K.

1988-10-01

Diffusion of zinc into GaAs through an yttria-stabilized cubic zirconia (YSZ) passivation layer has been demonstrated with an open-tube diffusion method. Pure zinc or GaAs/Zn2As3 sources produced high quality planar p-n junctions. The YSZ layer protects the GaAs surface from excessive loss of arsenic, yet is permeable to zinc, allowing its diffusion into the semiconductor. The YSZ films, deposited by electron beam evaporation, were typically 2000 Å thick. Zinc diffusion coefficients (DT) at 650 °C in the YSZ passivated GaAs ranged from 3.6×10-10 cm2/min for the GaAs/Zn2As3 source to 1.9×10-9 cm2/min for the pure zinc source. Doping concentrations for both YSZ passivated and uncapped samples were approximately 5×1019 cm-3.

Localization of diffusion sources in complex networks with sparse observations

NASA Astrophysics Data System (ADS)

Hu, Zhao-Long; Shen, Zhesi; Tang, Chang-Bing; Xie, Bin-Bin; Lu, Jian-Feng

2018-04-01

Locating sources in a large network is of paramount importance to reduce the spreading of disruptive behavior. Based on the backward diffusion-based method and integer programming, we propose an efficient approach to locate sources in complex networks with limited observers. The results on model networks and empirical networks demonstrate that, for a certain fraction of observers, the accuracy of our method for source localization will improve as the increase of network size. Besides, compared with the previous method (the maximum-minimum method), the performance of our method is much better with a small fraction of observers, especially in heterogeneous networks. Furthermore, our method is more robust against noise environments and strategies of choosing observers.

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.

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.

Light source distribution and scattering phase function influence light transport in diffuse multi-layered media

NASA Astrophysics Data System (ADS)

Vaudelle, Fabrice; L'Huillier, Jean-Pierre; Askoura, Mohamed Lamine

2017-06-01

Red and near-Infrared light is often used as a useful diagnostic and imaging probe for highly scattering media such as biological tissues, fruits and vegetables. Part of diffusively reflected light gives interesting information related to the tissue subsurface, whereas light recorded at further distances may probe deeper into the interrogated turbid tissues. However, modelling diffusive events occurring at short source-detector distances requires to consider both the distribution of the light sources and the scattering phase functions. In this report, a modified Monte Carlo model is used to compute light transport in curved and multi-layered tissue samples which are covered with a thin and highly diffusing tissue layer. Different light source distributions (ballistic, diffuse or Lambertian) are tested with specific scattering phase functions (modified or not modified Henyey-Greenstein, Gegenbauer and Mie) to compute the amount of backscattered and transmitted light in apple and human skin structures. Comparisons between simulation results and experiments carried out with a multispectral imaging setup confirm the soundness of the theoretical strategy and may explain the role of the skin on light transport in whole and half-cut apples. Other computational results show that a Lambertian source distribution combined with a Henyey-Greenstein phase function provides a higher photon density in the stratum corneum than in the upper dermis layer. Furthermore, it is also shown that the scattering phase function may affect the shape and the magnitude of the Bidirectional Reflectance Distribution (BRDF) exhibited at the skin surface.

Locating the source of diffusion in complex networks by time-reversal backward spreading.

PubMed

Shen, Zhesi; Cao, Shinan; Wang, Wen-Xu; Di, Zengru; Stanley, H Eugene

2016-03-01

Locating the source that triggers a dynamical process is a fundamental but challenging problem in complex networks, ranging from epidemic spreading in society and on the Internet to cancer metastasis in the human body. An accurate localization of the source is inherently limited by our ability to simultaneously access the information of all nodes in a large-scale complex network. This thus raises two critical questions: how do we locate the source from incomplete information and can we achieve full localization of sources at any possible location from a given set of observable nodes. Here we develop a time-reversal backward spreading algorithm to locate the source of a diffusion-like process efficiently and propose a general locatability condition. We test the algorithm by employing epidemic spreading and consensus dynamics as typical dynamical processes and apply it to the H1N1 pandemic in China. We find that the sources can be precisely located in arbitrary networks insofar as the locatability condition is assured. Our tools greatly improve our ability to locate the source of diffusion in complex networks based on limited accessibility of nodal information. Moreover, they have implications for controlling a variety of dynamical processes taking place on complex networks, such as inhibiting epidemics, slowing the spread of rumors, pollution control, and environmental protection.

Locating the source of diffusion in complex networks by time-reversal backward spreading

NASA Astrophysics Data System (ADS)

Shen, Zhesi; Cao, Shinan; Wang, Wen-Xu; Di, Zengru; Stanley, H. Eugene

2016-03-01

Locating the source that triggers a dynamical process is a fundamental but challenging problem in complex networks, ranging from epidemic spreading in society and on the Internet to cancer metastasis in the human body. An accurate localization of the source is inherently limited by our ability to simultaneously access the information of all nodes in a large-scale complex network. This thus raises two critical questions: how do we locate the source from incomplete information and can we achieve full localization of sources at any possible location from a given set of observable nodes. Here we develop a time-reversal backward spreading algorithm to locate the source of a diffusion-like process efficiently and propose a general locatability condition. We test the algorithm by employing epidemic spreading and consensus dynamics as typical dynamical processes and apply it to the H1N1 pandemic in China. We find that the sources can be precisely located in arbitrary networks insofar as the locatability condition is assured. Our tools greatly improve our ability to locate the source of diffusion in complex networks based on limited accessibility of nodal information. Moreover, they have implications for controlling a variety of dynamical processes taking place on complex networks, such as inhibiting epidemics, slowing the spread of rumors, pollution control, and environmental protection.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Far-Infrared sources and diffuse emission in M31

NASA Technical Reports Server (NTRS)

Xu, Cong; Helou, George

1994-01-01

A study on the far-infrared (FIR) emission of M31 has been carried out with the High Resolution (HiRes) maps (approx. 1 min) derived from IRAS data. Sixty-eight FIR sources are detected in M31, which in general coincide with optical HII regions, and contribute 15, 23, 29, and 23 percent to the fluxes in 12, 25, 60, and 100 micron bands, respectively. The remaining diffuse emission, which dominates the FIR emission of M31, is studied using a dust heating model which utilizes the UV and optical photometry maps and the HI maps available in the literature. It is found that the global dust-to-gas ratio in M31 disk is 6.5 10(exp -3), very close to the dust-to-gas ratio in the solar neighborhood. There is a significant galactocentric gradient of the dust-to-HI-gas ratio, with an e-folding scale length of 9 kpc. The diffuse dust correlates tightly with the HI gas. The model indicates that the non-ionizing UV (913-4000A) radiation from massive and intermediate massive stars contributes only about 30 percent of the heating of the diffuse dust, while the optical-NIR (4000-9000A) radiation from the old stellar population is responsible for the most of the heating.

Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

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.

Comprehensive model-based prediction of micropollutants from diffuse sources in the Swiss river network

NASA Astrophysics Data System (ADS)

Strahm, Ivo; Munz, Nicole; Braun, Christian; Gälli, René; Leu, Christian; Stamm, Christian

2014-05-01

Water quality in the Swiss river network is affected by many micropollutants from a variety of diffuse sources. This study compares, for the first time, in a comprehensive manner the diffuse sources and the substance groups that contribute the most to water contamination in Swiss streams and highlights the major regions for water pollution. For this a simple but comprehensive model was developed to estimate emission from diffuse sources for the entire Swiss river network of 65 000 km. Based on emission factors the model calculates catchment specific losses to streams for more than 15 diffuse sources (such as crop lands, grassland, vineyards, fruit orchards, roads, railways, facades, roofs, green space in urban areas, landfills, etc.) and more than 130 different substances from 5 different substance groups (pesticides, biocides, heavy metals, human drugs, animal drugs). For more than 180 000 stream sections estimates of mean annual pollutant loads and mean annual concentration levels were modeled. This data was validated with a set of monitoring data and evaluated based on annual average environmental quality standards (AA-EQS). Model validation showed that the estimated mean annual concentration levels are within the range of measured data. Therefore simulations were considered as adequately robust for identifying the major sources of diffuse pollution. The analysis depicted that in Switzerland widespread pollution of streams can be expected. Along more than 18 000 km of the river network one or more simulated substances has a concentration exceeding the AA-EQS. In single stream sections it could be more than 50 different substances. Moreover, the simulations showed that in two-thirds of small streams (Strahler order 1 and 2) at least one AA-EQS is always exceeded. The highest number of substances exceeding the AA-EQS are in areas with large fractions of arable cropping, vineyards and fruit orchards. Urban areas are also of concern even without considering

Evaluation of diffusion coefficients by means of an approximate steady-state condition in sedimentation velocity distributions.

PubMed

Scott, David J; Harding, Stephen E; Winzor, Donald J

2015-12-01

This investigation examined the feasibility of manipulating the rotor speed in sedimentation velocity experiments to spontaneously generate an approximate steady-state condition where the extent of diffusional spreading is matched exactly by the boundary sharpening arising from negative s-c dependence. Simulated sedimentation velocity distributions based on the sedimentation characteristics for a purified mucin preparation were used to illustrate a simple procedure for determining the diffusion coefficient from such steady-state distributions in situations where the concentration dependence of the sedimentation coefficient, s = s(0)/(1 + Kc), was quantified in terms of the limiting sedimentation coefficient as c → 0 (s(0)) and the concentration coefficient (K). Those simulations established that spontaneous generation of the approximate steady state could well be a feature of sedimentation velocity distributions for many unstructured polymer systems because the requirement that Kcoω(2)s(0)/D be between 46 and 183 cm(-2) is not unduly restrictive. Although spontaneous generation of the approximate steady state is also a theoretical prediction for structured macromolecular solutes exhibiting linear concentration dependence of the sedimentation coefficient, s = s(0)(1 - kc), the required value of k is far too large for any practical advantage to be taken of this approach with globular proteins. Copyright © 2015 Elsevier Inc. All rights reserved.

Evaluation of dual-source parallel RF excitation for diffusion-weighted whole-body MR imaging with background body signal suppression at 3.0 T.

PubMed

Mürtz, Petra; Kaschner, Marius; Träber, Frank; Kukuk, Guido M; Büdenbender, Sarah M; Skowasch, Dirk; Gieseke, Jürgen; Schild, Hans H; Willinek, Winfried A

2012-11-01

To evaluate the use of dual-source parallel RF excitation (TX) for diffusion-weighted whole-body MRI with background body signal suppression (DWIBS) at 3.0 T. Forty consecutive patients were examined on a clinical 3.0-T MRI system using a diffusion-weighted (DW) spin-echo echo-planar imaging sequence with a combination of short TI inversion recovery and slice-selective gradient reversal fat suppression. DWIBS of the neck (n=5), thorax (n=8), abdomen (n=6) and pelvis (n=21) was performed both with TX (2:56 min) and with standard single-source RF excitation (4:37 min). The quality of DW images and reconstructed inverted maximum intensity projections was visually judged by two readers (blinded to acquisition technique). Signal homogeneity and fat suppression were scored as "improved", "equal", "worse" or "ambiguous". Moreover, the apparent diffusion coefficient (ADC) values were measured in muscles, urinary bladder, lymph nodes and lesions. By the use of TX, signal homogeneity was "improved" in 25/40 and "equal" in 15/40 cases. Fat suppression was "improved" in 17/40 and "equal" in 23/40 cases. These improvements were statistically significant (p<0.001, Wilcoxon signed-rank test). In five patients, fluid-related dielectric shading was present, which improved remarkably. The ADC values did not significantly differ for the two RF excitation methods (p=0.630 over all data, pairwise Student's t-test). Dual-source parallel RF excitation improved image quality of DWIBS at 3.0 T with respect to signal homogeneity and fat suppression, reduced scan time by approximately one-third, and did not influence the measured ADC values. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Revisiting the diffusion approximation to estimate evolutionary rates of gene family diversification.

PubMed

Gjini, Erida; Haydon, Daniel T; David Barry, J; Cobbold, Christina A

2014-01-21

Genetic diversity in multigene families is shaped by multiple processes, including gene conversion and point mutation. Because multi-gene families are involved in crucial traits of organisms, quantifying the rates of their genetic diversification is important. With increasing availability of genomic data, there is a growing need for quantitative approaches that integrate the molecular evolution of gene families with their higher-scale function. In this study, we integrate a stochastic simulation framework with population genetics theory, namely the diffusion approximation, to investigate the dynamics of genetic diversification in a gene family. Duplicated genes can diverge and encode new functions as a result of point mutation, and become more similar through gene conversion. To model the evolution of pairwise identity in a multigene family, we first consider all conversion and mutation events in a discrete manner, keeping track of their details and times of occurrence; second we consider only the infinitesimal effect of these processes on pairwise identity accounting for random sampling of genes and positions. The purely stochastic approach is closer to biological reality and is based on many explicit parameters, such as conversion tract length and family size, but is more challenging analytically. The population genetics approach is an approximation accounting implicitly for point mutation and gene conversion, only in terms of per-site average probabilities. Comparison of these two approaches across a range of parameter combinations reveals that they are not entirely equivalent, but that for certain relevant regimes they do match. As an application of this modelling framework, we consider the distribution of nucleotide identity among VSG genes of African trypanosomes, representing the most prominent example of a multi-gene family mediating parasite antigenic variation and within-host immune evasion. © 2013 Published by Elsevier Ltd. All rights reserved.

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

sfDM: Open-Source Software for Temporal Analysis and Visualization of Brain Tumor Diffusion MR Using Serial Functional Diffusion Mapping.

PubMed

Ceschin, Rafael; Panigrahy, Ashok; Gopalakrishnan, Vanathi

2015-01-01

A major challenge in the diagnosis and treatment of brain tumors is tissue heterogeneity leading to mixed treatment response. Additionally, they are often difficult or at very high risk for biopsy, further hindering the clinical management process. To overcome this, novel advanced imaging methods are increasingly being adapted clinically to identify useful noninvasive biomarkers capable of disease stage characterization and treatment response prediction. One promising technique is called functional diffusion mapping (fDM), which uses diffusion-weighted imaging (DWI) to generate parametric maps between two imaging time points in order to identify significant voxel-wise changes in water diffusion within the tumor tissue. Here we introduce serial functional diffusion mapping (sfDM), an extension of existing fDM methods, to analyze the entire tumor diffusion profile along the temporal course of the disease. sfDM provides the tools necessary to analyze a tumor data set in the context of spatiotemporal parametric mapping: the image registration pipeline, biomarker extraction, and visualization tools. We present the general workflow of the pipeline, along with a typical use case for the software. sfDM is written in Python and is freely available as an open-source package under the Berkley Software Distribution (BSD) license to promote transparency and reproducibility.

Numerical Simulation of the Diffusion Processes in Nanoelectrode Arrays Using an Axial Neighbor Symmetry Approximation.

PubMed

Peinetti, Ana Sol; Gilardoni, Rodrigo S; Mizrahi, Martín; Requejo, Felix G; González, Graciela A; Battaglini, Fernando

2016-06-07

Nanoelectrode arrays have introduced a complete new battery of devices with fascinating electrocatalytic, sensitivity, and selectivity properties. To understand and predict the electrochemical response of these arrays, a theoretical framework is needed. Cyclic voltammetry is a well-fitted experimental technique to understand the undergoing diffusion and kinetics processes. Previous works describing microelectrode arrays have exploited the interelectrode distance to simulate its behavior as the summation of individual electrodes. This approach becomes limited when the size of the electrodes decreases to the nanometer scale due to their strong radial effect with the consequent overlapping of the diffusional fields. In this work, we present a computational model able to simulate the electrochemical behavior of arrays working either as the summation of individual electrodes or being affected by the overlapping of the diffusional fields without previous considerations. Our computational model relays in dividing a regular electrode array in cells. In each of them, there is a central electrode surrounded by neighbor electrodes; these neighbor electrodes are transformed in a ring maintaining the same active electrode area than the summation of the closest neighbor electrodes. Using this axial neighbor symmetry approximation, the problem acquires a cylindrical symmetry, being applicable to any diffusion pattern. The model is validated against micro- and nanoelectrode arrays showing its ability to predict their behavior and therefore to be used as a designing tool.

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Comparison of flat cleaved and cylindrical diffusing fibers as treatment sources for interstitial photodynamic therapy.

PubMed

Baran, Timothy M; Foster, Thomas H

2014-02-01

For interstitial photodynamic therapy (iPDT) of bulky tumors, careful treatment planning is required in order to ensure that a therapeutic dose is delivered to the tumor, while minimizing damage to surrounding normal tissue. In clinical contexts, iPDT has typically been performed with either flat cleaved or cylindrical diffusing optical fibers as light sources. Here, the authors directly compare these two source geometries in terms of the number of fibers and duration of treatment required to deliver a prescribed light dose to a tumor volume. Treatment planning software for iPDT was developed based on graphics processing unit enhanced Monte Carlo simulations. This software was used to optimize the number of fibers, total energy delivered by each fiber, and the position of individual fibers in order to deliver a target light dose (D90) to 90% of the tumor volume. Treatment plans were developed using both flat cleaved and cylindrical diffusing fibers, based on tissue volumes derived from CT data from a head and neck cancer patient. Plans were created for four cases: fixed energy per fiber, fixed number of fibers, and in cases where both or neither of these factors were fixed. When the number of source fibers was fixed at eight, treatment plans based on flat cleaved fibers required each to deliver 7180-8080 J in order to deposit 90 J/cm(2) in 90% of the tumor volume. For diffusers, each fiber was required to deliver 2270-2350 J (333-1178 J/cm) in order to achieve this same result. For the case of fibers delivering a fixed 900 J, 13 diffusers or 19 flat cleaved fibers at a spacing of 1 cm were required to deliver the desired dose. With energy per fiber fixed at 2400 J and the number of fibers fixed at eight, diffuser fibers delivered the desired dose to 93% of the tumor volume, while flat cleaved fibers delivered this dose to 79%. With both energy and number of fibers allowed to vary, six diffusers delivering 3485-3600 J were required, compared to ten flat cleaved

Diffusion approximation with polarization and resonance effects for the modelling of seismic waves in strongly scattering small-scale media

NASA Astrophysics Data System (ADS)

Margerin, Ludovic

2013-01-01

This paper presents an analytical study of the multiple scattering of seismic waves by a collection of randomly distributed point scatterers. The theory assumes that the energy envelopes are smooth, but does not require perturbations to be small, thereby allowing the modelling of strong, resonant scattering. The correlation tensor of seismic coda waves recorded at a three-component sensor is decomposed into a sum of eigenmodes of the elastodynamic multiple scattering (Bethe-Salpeter) equation. For a general moment tensor excitation, a total number of four modes is necessary to describe the transport of seismic waves polarization. Their spatio-temporal dependence is given in closed analytical form. Two additional modes transporting exclusively shear polarizations may be excited by antisymmetric moment tensor sources only. The general solution converges towards an equipartition mixture of diffusing P and S waves which allows the retrieval of the local Green's function from coda waves. The equipartition time is obtained analytically and the impact of absorption on Green's function reconstruction is discussed. The process of depolarization of multiply scattered waves and the resulting loss of information is illustrated for various seismic sources. It is shown that coda waves may be used to characterize the source mechanism up to lapse times of the order of a few mean free times only. In the case of resonant scatterers, a formula for the diffusivity of seismic waves incorporating the effect of energy entrapment inside the scatterers is obtained. Application of the theory to high-contrast media demonstrates that coda waves are more sensitive to slow rather than fast velocity anomalies by several orders of magnitude. Resonant scattering appears as an attractive physical phenomenon to explain the small values of the diffusion constant of seismic waves reported in volcanic areas.

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

PubMed

Watanabe, Hayafumi

2014-01-01

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

Product diffusion through on-demand information-seeking behaviour.

PubMed

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

2018-02-01

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

Product diffusion through on-demand information-seeking behaviour

PubMed Central

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

2018-01-01

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

Directed Thermal Diffusions through Metamaterial Source Illusion with Homogeneous Natural Media

PubMed Central

Xu, Guoqiang; Zhang, Haochun; Jin, Liang

2018-01-01

Owing to the utilization of transformation optics, many significant research and development achievements have expanded the applications of illusion devices into thermal fields. However, most of the current studies on relevant thermal illusions used to reshape the thermal fields are dependent of certain pre-designed geometric profiles with complicated conductivity configurations. In this paper, we propose a methodology for designing a new class of thermal source illusion devices for achieving directed thermal diffusions with natural homogeneous media. The employments of the space rotations in the linear transformation processes allow the directed thermal diffusions to be independent of the geometric profiles, and the utilization of natural homogeneous media improve the feasibility. Four schemes, with fewer types of homogeneous media filling the functional regions, are demonstrated in transient states. The expected performances are observed in each scheme. The related performance are analyzed by comparing the thermal distribution characteristics and the illusion effectiveness on the measured lines. The findings obtained in this paper see applications in the development of directed diffusions with minimal thermal loss, used in novel “multi-beam” thermal generation, thermal lenses, solar receivers, and waveguide. PMID:29671833

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

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

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1975-10-01

The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P$sub 1$) in up to three- dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First- order perturbation analysis capability is available at the macroscopic cross section level. (auth)

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

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

Du, Qiang, E-mail: jyanghkbu@gmail.com; Yang, Jiang, E-mail: qd2125@columbia.edu

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simplemore » ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.« less

Implementation of cost-effective diffuse light source mechanism to reduce specular reflection and halo effects for resistor-image processing

NASA Astrophysics Data System (ADS)

Chen, Yung-Sheng; Wang, Jeng-Yau

2015-09-01

Light source plays a significant role to acquire a qualified image from objects for facilitating the image processing and pattern recognition. For objects possessing specular surface, the phenomena of reflection and halo appearing in the acquired image will increase the difficulty of information processing. Such a situation may be improved by the assistance of valuable diffuse light source. Consider reading resistor via computer vision, due to the resistor's specular reflective surface it will face with a severe non-uniform luminous intensity on image yielding a higher error rate in recognition without a well-controlled light source. A measurement system including mainly a digital microscope embedded in a replaceable diffuse cover, a ring-type LED embedded onto a small pad carrying a resistor for evaluation, and Arduino microcontrollers connected with PC, is presented in this paper. Several replaceable cost-effective diffuse covers made by paper bowl, cup and box inside pasted with white paper are presented for reducing specular reflection and halo effects and compared with a commercial diffuse some. The ring-type LED can be flexibly configured to be a full or partial lighting based on the application. For each self-made diffuse cover, a set of resistors with 4 or 5 color bands are captured via digital microscope for experiments. The signal-to-noise ratio from the segmented resistor-image is used for performance evaluation. The detected principal axis of resistor body is used for the partial LED configuration to further improve the lighting condition. Experimental results confirm that the proposed mechanism can not only evaluate the cost-effective diffuse light source but also be extended as an automatic recognition system for resistor reading.

Comparison of flat cleaved and cylindrical diffusing fibers as treatment sources for interstitial photodynamic therapy

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

Baran, Timothy M., E-mail: timothy.baran@rochester.edu; Foster, Thomas H.

Purpose: For interstitial photodynamic therapy (iPDT) of bulky tumors, careful treatment planning is required in order to ensure that a therapeutic dose is delivered to the tumor, while minimizing damage to surrounding normal tissue. In clinical contexts, iPDT has typically been performed with either flat cleaved or cylindrical diffusing optical fibers as light sources. Here, the authors directly compare these two source geometries in terms of the number of fibers and duration of treatment required to deliver a prescribed light dose to a tumor volume. Methods: Treatment planning software for iPDT was developed based on graphics processing unit enhanced Montemore » Carlo simulations. This software was used to optimize the number of fibers, total energy delivered by each fiber, and the position of individual fibers in order to deliver a target light dose (D{sub 90}) to 90% of the tumor volume. Treatment plans were developed using both flat cleaved and cylindrical diffusing fibers, based on tissue volumes derived from CT data from a head and neck cancer patient. Plans were created for four cases: fixed energy per fiber, fixed number of fibers, and in cases where both or neither of these factors were fixed. Results: When the number of source fibers was fixed at eight, treatment plans based on flat cleaved fibers required each to deliver 7180–8080 J in order to deposit 90 J/cm{sup 2} in 90% of the tumor volume. For diffusers, each fiber was required to deliver 2270–2350 J (333–1178 J/cm) in order to achieve this same result. For the case of fibers delivering a fixed 900 J, 13 diffusers or 19 flat cleaved fibers at a spacing of 1 cm were required to deliver the desired dose. With energy per fiber fixed at 2400 J and the number of fibers fixed at eight, diffuser fibers delivered the desired dose to 93% of the tumor volume, while flat cleaved fibers delivered this dose to 79%. With both energy and number of fibers allowed to vary, six diffusers delivering 3485�

Approximate Seismic Diffusive Models of Near-Receiver Geology: Applications from Lab Scale to Field

NASA Astrophysics Data System (ADS)

King, Thomas; Benson, Philip; De Siena, Luca; Vinciguerra, Sergio

2017-04-01

This paper presents a novel and simple method of seismic envelope analysis that can be applied at multiple scales, e.g. field, m to km scale and laboratory, mm to cm scale, and utilises the diffusive approximation of the seismic wavefield (Wegler, 2003). Coefficient values for diffusion and attenuation are obtained from seismic coda energies and are used to describe the rate at which seismic energy is scattered and attenuated into the local medium around a receiver. Values are acquired by performing a linear least squares inversion of coda energies calculated in successive time windows along a seismic trace. Acoustic emission data were taken from piezoelectric transducers (PZT) with typical resonance frequency of 1-5MHz glued around rock samples during deformation laboratory experiments carried out using a servo-controlled triaxial testing machine, where a shear/damage zone is generated under compression after the nucleation, growth and coalescence of microcracks. Passive field data were collected from conventional geophones during the 2004-2008 eruption of Mount St. Helens volcano (MSH), USA where a sudden reawakening of the volcanic activity and a new dome growth has occurred. The laboratory study shows a strong correlation between variations of the coefficients over time and the increase of differential stress as the experiment progresses. The field study links structural variations present in the near-surface geology, including those seen in previous geophysical studies of the area, to these same coefficients. Both studies show a correlation between frequency and structural feature size, i.e. landslide slip-planes and microcracks, with higher frequencies being much more sensitive to smaller scale features and vice-versa.

Exploration of diffuse and discrete sources of acid mine drainage to a headwater mountain stream in Colorado, USA

USGS Publications Warehouse

Johnston, Allison; Runkel, Robert L.; Navarre-Sitchler, Alexis; Singha, Kamini

2017-01-01

We investigated the impact of acid mine drainage (AMD) contamination from the Minnesota Mine, an inactive gold and silver mine, on Lion Creek, a headwater mountain stream near Empire, Colorado. The objective was to map the sources of AMD contamination, including discrete sources visible at the surface and diffuse inputs that were not readily apparent. This was achieved using geochemical sampling, in-stream and in-seep fluid electrical conductivity (EC) logging, and electrical resistivity imaging (ERI) of the subsurface. The low pH of the AMD-impacted water correlated to high fluid EC values that served as a target for the ERI. From ERI, we identified two likely sources of diffuse contamination entering the stream: (1) the subsurface extent of two seepage faces visible on the surface, and (2) rainfall runoff washing salts deposited on the streambank and in a tailings pile on the east bank of Lion Creek. Additionally, rainfall leaching through the tailings pile is a potential diffuse source of contamination if the subsurface beneath the tailings pile is hydraulically connected with the stream. In-stream fluid EC was lowest when stream discharge was highest in early summer and then increased throughout the summer as stream discharge decreased, indicating that the concentration of dissolved solids in the stream is largely controlled by mixing of groundwater and snowmelt. Total dissolved solids (TDS) load is greatest in early summer and displays a large diel signal. Identification of diffuse sources and variability in TDS load through time should allow for more targeted remediation options.

Combining land use information and small stream sampling with PCR-based methods for better characterization of diffuse sources of human fecal pollution.

PubMed

Peed, Lindsay A; Nietch, Christopher T; Kelty, Catherine A; Meckes, Mark; Mooney, Thomas; Sivaganesan, Mano; Shanks, Orin C

2011-07-01

Diffuse sources of human fecal pollution allow for the direct discharge of waste into receiving waters with minimal or no treatment. Traditional culture-based methods are commonly used to characterize fecal pollution in ambient waters, however these methods do not discern between human and other animal sources of fecal pollution making it difficult to identify diffuse pollution sources. Human-associated quantitative real-time PCR (qPCR) methods in combination with low-order headwatershed sampling, precipitation information, and high-resolution geographic information system land use data can be useful for identifying diffuse source of human fecal pollution in receiving waters. To test this assertion, this study monitored nine headwatersheds over a two-year period potentially impacted by faulty septic systems and leaky sanitary sewer lines. Human fecal pollution was measured using three different human-associated qPCR methods and a positive significant correlation was seen between abundance of human-associated genetic markers and septic systems following wet weather events. In contrast, a negative correlation was observed with sanitary sewer line densities suggesting septic systems are the predominant diffuse source of human fecal pollution in the study area. These results demonstrate the advantages of combining water sampling, climate information, land-use computer-based modeling, and molecular biology disciplines to better characterize diffuse sources of human fecal pollution in environmental waters.

Diffuse Gamma Rays Galactic and Extragalactic Diffuse Emission

NASA Technical Reports Server (NTRS)

Moskalenko, Igor V.; Strong, Andrew W.; Reimer, Olaf

2004-01-01

Diffuse gamma rays consist of several components: truly diffuse emission from the interstellar medium, the extragalactic background, whose origin is not firmly established yet, and the contribution from unresolved and faint Galactic point sources. One approach to unravel these components is to study the diffuse emission from the interstellar medium, which traces the interactions of high energy particles with interstellar gas and radiation fields. Because of its origin such emission is potentially able to reveal much about the sources and propagation of cosmic rays. The extragalactic background, if reliably determined, can be used in cosmological and blazar studies. Studying the derived average spectrum of faint Galactic sources may be able to give a clue to the nature of the emitting objects.

Modelled isotopic fractionation and transient diffusive release of methane from potential subsurface sources on Mars

NASA Astrophysics Data System (ADS)

Stevens, Adam H.; Patel, Manish R.; Lewis, Stephen R.

2017-01-01

We calculate transport timescales of martian methane and investigate the effect of potential release mechanisms into the atmosphere using a numerical model that includes both Fickian and Knudsen diffusion. The incorporation of Knudsen diffusion, which improves on a Fickian description of transport given the low permeability of the martian regolith, means that transport timescales from sources collocated with a putative martian water table are very long, up to several million martian years. Transport timescales also mean that any temporally varying source process, even in the shallow subsurface, would not result in a significant, observable variation in atmospheric methane concentration since changes resulting from small variations in flux would be rapidly obscured by atmospheric transport. This means that a short-lived 'plume' of methane, as detected by Mumma et al. (2009) and Webster et al. (2014), cannot be reconciled with diffusive transport from any reasonable depth and instead must invoke alternative processes such as fracturing or convective plumes. It is shown that transport through the martian regolith will cause a significant change in the isotopic composition of the gas, meaning that methane release from depth will produce an isotopic signature in the atmosphere that could be significantly different than the source composition. The deeper the source, the greater the change, and the change in methane composition in both δ13C and δD approaches -1000 ‰ for sources at a depth greater than around 1 km. This means that signatures of specific sources, in particular the methane produced by biogenesis that is generally depleted in 13CH4 and CH3D, could be obscured. We find that an abiogenic source of methane could therefore display an isotopic fractionation consistent with that expected for biogenic source processes if the source was at sufficient depth. The only unambiguous inference that can be made from measurements of methane isotopes alone is a measured �

Approximation of effective moisture-diffusion coefficient to characterize performance of a barrier coating

NASA Astrophysics Data System (ADS)

Nagai, Shingo

2013-11-01

We report estimation of the effective diffusion coefficient of moisture through a barrier coating to develop an encapsulation technology for the thin-film electronics industry. This investigation targeted a silicon oxide (SiOx) film that was deposited on a plastic substrate by a large-process-area web coater. Using the finite difference method based on diffusion theory, our estimation of the effective diffusion coefficient of a SiOx film corresponded to that of bulk glass that was previously reported. This result suggested that the low diffusivities of barrier films can be obtained on a mass-production level in the factory. In this investigation, experimental observations and mathematical confirmation revealed the limit of the water vapor transmission rate on the single barrier coating.

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.

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

PubMed

Boitard, Simon; Loisel, Patrice

2007-05-01

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

Algorithms and analytical solutions for rapidly approximating long-term dispersion from line and area sources

NASA Astrophysics Data System (ADS)

Barrett, Steven R. H.; Britter, Rex E.

Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105-8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean

Fgf8 morphogen gradient forms by a source-sink mechanism with freely diffusing molecules.

PubMed

Yu, Shuizi Rachel; Burkhardt, Markus; Nowak, Matthias; Ries, Jonas; Petrásek, Zdenek; Scholpp, Steffen; Schwille, Petra; Brand, Michael

2009-09-24

It is widely accepted that tissue differentiation and morphogenesis in multicellular organisms are regulated by tightly controlled concentration gradients of morphogens. How exactly these gradients are formed, however, remains unclear. Here we show that Fgf8 morphogen gradients in living zebrafish embryos are established and maintained by two essential factors: fast, free diffusion of single molecules away from the source through extracellular space, and a sink function of the receiving cells, regulated by receptor-mediated endocytosis. Evidence is provided by directly examining single molecules of Fgf8 in living tissue by fluorescence correlation spectroscopy, quantifying their local mobility and concentration with high precision. By changing the degree of uptake of Fgf8 into its target cells, we are able to alter the shape of the Fgf8 gradient. Our results demonstrate that a freely diffusing morphogen can set up concentration gradients in a complex multicellular tissue by a simple source-sink mechanism.

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

PubMed Central

Orio, Patricio; Soudry, Daniel

2012-01-01

Background The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled gating particles, while the DA was modeled using uncoupled gating particles. Implementations of DA with coupled particles, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. Main Contributions We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable – allowing an easy, transparent and efficient DA implementation, avoiding unnecessary approximations. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods, except when

Using hybrid implicit Monte Carlo diffusion to simulate gray radiation hydrodynamics

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

Cleveland, Mathew A., E-mail: cleveland7@llnl.gov; Gentile, Nick

This work describes how to couple a hybrid Implicit Monte Carlo Diffusion (HIMCD) method with a Lagrangian hydrodynamics code to evaluate the coupled radiation hydrodynamics equations. This HIMCD method dynamically applies Implicit Monte Carlo Diffusion (IMD) [1] to regions of a problem that are opaque and diffusive while applying standard Implicit Monte Carlo (IMC) [2] to regions where the diffusion approximation is invalid. We show that this method significantly improves the computational efficiency as compared to a standard IMC/Hydrodynamics solver, when optically thick diffusive material is present, while maintaining accuracy. Two test cases are used to demonstrate the accuracy andmore » performance of HIMCD as compared to IMC and IMD. The first is the Lowrie semi-analytic diffusive shock [3]. The second is a simple test case where the source radiation streams through optically thin material and heats a thick diffusive region of material causing it to rapidly expand. We found that HIMCD proves to be accurate, robust, and computationally efficient for these test problems.« less

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.

Diffusive-convective physical vapor transport of PbTe from a Te-rich solid source

NASA Technical Reports Server (NTRS)

Zoutendyk, J.; Akutagawa, W.

1982-01-01

Crystal growth of PbTe by physical vapor transport (sublimation) in a closed ampoule is governed by the vapor species in thermal equilibrium with the solid compound. Deviations from stoichiometry in the source material cause diffusion limitation of the transport rate, which can be modified by natural (gravity-driven) convection. Mass-transport experiments have been performed using Te-rich material wherein sublimation rates have been measured in order to study the effects of natural convection in diffusion-limited vapor transport. Linear velocities for both crystal growth and evaporation (back sublimation) have been measured for transport in the direction of gravity, horizontally, and opposite to gravity. The experimental results are discussed in terms of both the one-dimensional diffusive-advective model and current, more sophisticated theory which includes natural convection. There is some evidence that convection effects from radial temperature gradients and solutal density gradients have been observed.

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.

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

Approximating high angular resolution apparent diffusion coefficient profiles using spherical harmonics under BiGaussian assumption

NASA Astrophysics Data System (ADS)

Cao, Ning; Liang, Xuwei; Zhuang, Qi; Zhang, Jun

2009-02-01

Magnetic Resonance Imaging (MRI) techniques have achieved much importance in providing visual and quantitative information of human body. Diffusion MRI is the only non-invasive tool to obtain information of the neural fiber networks of the human brain. The traditional Diffusion Tensor Imaging (DTI) is only capable of characterizing Gaussian diffusion. High Angular Resolution Diffusion Imaging (HARDI) extends its ability to model more complex diffusion processes. Spherical harmonic series truncated to a certain degree is used in recent studies to describe the measured non-Gaussian Apparent Diffusion Coefficient (ADC) profile. In this study, we use the sampling theorem on band-limited spherical harmonics to choose a suitable degree to truncate the spherical harmonic series in the sense of Signal-to-Noise Ratio (SNR), and use Monte Carlo integration to compute the spherical harmonic transform of human brain data obtained from icosahedral schema.

Moist, Double-diffusive convection

NASA Astrophysics Data System (ADS)

Oishi, Jeffrey; Burns, Keaton; Brown, Ben; Lecoanet, Daniel; Vasil, Geoffrey

2017-11-01

Double-diffusive convection occurs when the competition between stabilizing and a destabilizing buoyancy source is mediated by a difference in the diffusivity of each source. Such convection is important in a wide variety of astrophysical and geophysical flows. However, in giant planets, double-diffusive convection occurs in regions where condensation of important components of the atmosphere occurs. Here, we present preliminary calculations of moist, double-diffusive convection using the Dedalus pseudospectral framework. Using a simple model for phase change, we verify growth rates for moist double diffusive convection from linear calculations and report on preliminary relationships between the ability to form liquid phase and the resulting Nusselt number in nonlinear simulations.

Advection-diffusion model for the simulation of air pollution distribution from a point source emission

NASA Astrophysics Data System (ADS)

Ulfah, S.; Awalludin, S. A.; Wahidin

2018-01-01

Advection-diffusion model is one of the mathematical models, which can be used to understand the distribution of air pollutant in the atmosphere. It uses the 2D advection-diffusion model with time-dependent to simulate air pollution distribution in order to find out whether the pollutants are more concentrated at ground level or near the source of emission under particular atmospheric conditions such as stable, unstable, and neutral conditions. Wind profile, eddy diffusivity, and temperature are considered in the model as parameters. The model is solved by using explicit finite difference method, which is then visualized by a computer program developed using Lazarus programming software. The results show that the atmospheric conditions alone influencing the level of concentration of pollutants is not conclusive as the parameters in the model have their own effect on each atmospheric condition.

HIREGS observations of the Galactic center and Galactic plane: Separation of the diffuse Galactic hard X-ray continuum from the point source spectra

NASA Technical Reports Server (NTRS)

Boggs, S. E.; Lin, R. P.; Coburn, W.; Feffer, P.; Pelling, R. M.; Schroeder, P.; Slassi-Sennou, S.

1997-01-01

The balloon-borne high resolution gamma ray and X-ray germanium spectrometer (HIREGS) was used to observe the Galactic center and two positions along the Galactic plane from Antarctica in January 1995. For its flight, the collimators were configured to measure the Galactic diffuse hard X-ray continuum between 20 and 200 keV by directly measuring the point source contributions to the wide field of view flux for subtraction. The hard X-ray spectra of GX 1+4 and GRO J1655-40 were measured with the diffuse continuum subtracted off. The analysis technique for source separation is discussed and the preliminary separated spectra for these point sources and the Galactic diffuse emission are presented.

Effects of the approximations of light propagation on quantitative photoacoustic tomography using two-dimensional photon diffusion equation and linearization

NASA Astrophysics Data System (ADS)

Okawa, Shinpei; Hirasawa, Takeshi; Kushibiki, Toshihiro; Ishihara, Miya

2017-12-01

Quantitative photoacoustic tomography (QPAT) employing a light propagation model will play an important role in medical diagnoses by quantifying the concentration of hemoglobin or a contrast agent. However, QPAT by the light propagation model with the three-dimensional (3D) radiative transfer equation (RTE) requires a huge computational load in the iterative forward calculations involved in the updating process to reconstruct the absorption coefficient. The approximations of the light propagation improve the efficiency of the image reconstruction for the QPAT. In this study, we compared the 3D/two-dimensional (2D) photon diffusion equation (PDE) approximating 3D RTE with the Monte Carlo simulation based on 3D RTE. Then, the errors in a 2D PDE-based linearized image reconstruction caused by the approximations were quantitatively demonstrated and discussed in the numerical simulations. It was clearly observed that the approximations affected the reconstructed absorption coefficient. The 2D PDE-based linearized algorithm succeeded in the image reconstruction of the region with a large absorption coefficient in the 3D phantom. The value reconstructed in the phantom experiment agreed with that in the numerical simulation, so that it was validated that the numerical simulation of the image reconstruction predicted the relationship between the true absorption coefficient of the target in the 3D medium and the reconstructed value with the 2D PDE-based linearized algorithm. Moreover, the the true absorption coefficient in 3D medium was estimated from the 2D reconstructed image on the basis of the prediction by the numerical simulation. The estimation was successful in the phantom experiment, although some limitations were revealed.

Point-source and diffuse high-energy neutrino emission from Type IIn supernovae

NASA Astrophysics Data System (ADS)

Petropoulou, M.; Coenders, S.; Vasilopoulos, G.; Kamble, A.; Sironi, L.

2017-09-01

Type IIn supernovae (SNe), a rare subclass of core collapse SNe, explode in dense circumstellar media that have been modified by the SNe progenitors at their last evolutionary stages. The interaction of the freely expanding SN ejecta with the circumstellar medium gives rise to a shock wave propagating in the dense SN environment, which may accelerate protons to multi-PeV energies. Inelastic proton-proton collisions between the shock-accelerated protons and those of the circumstellar medium lead to multimessenger signatures. Here, we evaluate the possible neutrino signal of Type IIn SNe and compare with IceCube observations. We employ a Monte Carlo method for the calculation of the diffuse neutrino emission from the SN IIn class to account for the spread in their properties. The cumulative neutrino emission is found to be ˜10 per cent of the observed IceCube neutrino flux above 60 TeV. Type IIn SNe would be the dominant component of the diffuse astrophysical flux, only if 4 per cent of all core collapse SNe were of this type and 20-30 per cent of the shock energy was channeled to accelerated protons. Lower values of the acceleration efficiency are accessible by the observation of a single Type IIn SN as a neutrino point source with IceCube using up-going muon neutrinos. Such an identification is possible in the first year following the SN shock breakout for sources within 20 Mpc.

An extended galactic population of low-luminosity x-ray sources (CVs?) and the diffuse x-ray background

NASA Technical Reports Server (NTRS)

Maoz, Eyal; Grindlay, Jonathan E.

1995-01-01

The incompatibility of the properties of the X-ray background (XRB) with active galactic nuclei (AGNs) contributing approximately greater than 60% at energies of a few keV has often been interpreted as being due to a substantial contribution of a new population of yet unrecognized X-ray sources. The existence of such population has been recently suggested also by an analysis of very deep ROSAT observations which revealed a considerable excess of faint X-ray sources over that expected from QSO evolution models, and that the average spectrum of the resolved sources becomes harder with decreasing flux limit. These sources could be extragalactic in origin, but if they make a substantial contribution to the XRB then they must exhibit much weaker clustering than galaxies or QSOs in order to be consistent with the stringent constraints on source clustering imposed by autocorrelation analyses of the unresolved XRB. We investigate the possibility that the indicated new population of X-ray sources is Galactic in origin. Examining spherical halo and thick disk distributions, we derive the allowed properties of such populations which would resolve the discrepancy found in the number counts of faint sources and be consistent with observational constraints on the total background intensity, the XRB anisotropy, the number of unidentified bright sources, the Galaxy's total X-ray luminosity, and with the results of fluctuation analyses of the unresolved XRB. We find that a flattened Galactic halo (or a thick disk) distribution with a scale height of a few kpc is consistent with all the above requirements. The typical X-ray luminosity of the sources is approximately equal to 10(exp 30-31)ergs/s in the 0.5-2 keV band, the number density of sources in the solar vicinity is approximately 10(exp -4.5)pc(exp -3), their total number in the Galaxy is approximately 10(exp 8.5), and their total contribution to the Galaxy's X-ray luminosity is approximately 10(exp 39) ergs/s. We discuss the

Diffusion approximation-based simulation of stochastic ion channels: which method to use?

PubMed Central

Pezo, Danilo; Soudry, Daniel; Orio, Patricio

2014-01-01

To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie's method for Markov Chains (MC) simulation is highly accurate, yet it becomes computationally intensive in the regime of a high number of channels. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA). Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties—such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Goldwyn et al., 2011; Linaro et al., 2011; Dangerfield et al., 2012; Orio and Soudry, 2012; Schmandt and Galán, 2012; Güler, 2013; Huang et al., 2013a), comparing all of them in a set of numerical simulations that assess numerical accuracy and computational efficiency on three different models: (1) the original Hodgkin and Huxley model, (2) a model with faster sodium channels, and (3) a multi-compartmental model inspired in granular cells. We conclude that for a low number of channels (usually below 1000 per simulated compartment) one should use MC—which is the fastest and most accurate method. For a high number of channels, we recommend using the method by Orio and Soudry (2012), possibly combined with the method by Schmandt and Galán (2012) for increased speed and slightly reduced accuracy. Consequently, MC modeling may be the best method for detailed multicompartment neuron models—in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels. PMID:25404914

Sources of dioxins in the United Kingdom: the steel industry and other sources.

PubMed

Anderson, David R; Fisher, Raymond

2002-01-01

Several countries have compiled national inventories of dioxin (polychlorinated dibenzo-p-dioxin [PCDD] and polychlorinated dibenzofuran [PCDF]) releases that detail annual mass emission estimates for regulated sources. High temperature processes, such as commercial waste incineration and iron ore sintering used in the production of iron and steel, have been identified as point sources of dioxins. Other important releases of dioxins are from various diffuse sources such as bonfire burning and domestic heating. The PCDD/F inventory for emissions to air in the UK has decreased significantly from 1995 to 1998 because of reduced emissions from waste incinerators which now generally operate at waste gas stack emissions of 1 ng I-TEQ/Nm3 or below. The iron ore sintering process is the only noteworthy source of PCDD/Fs at integrated iron and steelworks operated by Corus (formerly British Steel plc) in the UK. The mean waste gas stack PCDD/F concentration for this process is 1,2 ng I-TEQ/Nm3 based on 94 measurements and it has been estimated that this results in an annual mass release of approximately 38 g I-TEQ per annum. Diffuse sources now form a major contribution to the UK inventory as PCDD/Fs from regulated sources have decreased, for example, the annual celebration of Bonfire Night on 5th November in the UK causes an estimated release of 30 g I-TEQ, similar to that emitted by five sinter plants in the UK.

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.

Application of a simplified calculation for full-wave microtremor H/ V spectral ratio based on the diffuse field approximation to identify underground velocity structures

NASA Astrophysics Data System (ADS)

Wu, Hao; Masaki, Kazuaki; Irikura, Kojiro; Sánchez-Sesma, Francisco José

2017-12-01

Under the diffuse field approximation, the full-wave (FW) microtremor H/ V spectral ratio ( H/ V) is modeled as the square root of the ratio of the sum of imaginary parts of the Green's function of the horizontal components to that of the vertical one. For a given layered medium, the FW H/ V can be well approximated with only surface waves (SW) H/ V of the "cap-layered" medium which consists of the given layered medium and a new larger velocity half-space (cap layer) at large depth. Because the contribution of surface waves can be simply obtained by the residue theorem, the computation of SW H/ V of cap-layered medium is faster than that of FW H/ V evaluated by discrete wavenumber method and contour integration method. The simplified computation of SW H/ V was then applied to identify the underground velocity structures at six KiK-net strong-motion stations. The inverted underground velocity structures were used to evaluate FW H/ Vs which were consistent with the SW H/ Vs of corresponding cap-layered media. The previous study on surface waves H/ Vs proposed with the distributed surface sources assumption and a fixed Rayleigh-to-Love waves amplitude ratio for horizontal motions showed a good agreement with the SW H/ Vs of our study. The consistency between observed and theoretical spectral ratios, such as the earthquake motions of H/ V spectral ratio and spectral ratio of horizontal motions between surface and bottom of borehole, indicated that the underground velocity structures identified from SW H/ V of cap-layered medium were well resolved by the new method.[Figure not available: see fulltext.

Diffusion with chemical reaction: An attempt to explain number density anomalies in experiments involving alkali vapor

NASA Technical Reports Server (NTRS)

Snow, W. L.

1974-01-01

The mutual diffusion of two reacting gases is examined which takes place in a bath of inert gas atoms. Solutions are obtained between concentric spheres, each sphere acting as a source for one of the reactants. The calculational model is used to illustrate severe number density gradients observed in absorption experiments with alkali vapor. Severe gradients result when sq root k/D R is approximately 5 where k, D, and R are respectively the second order rate constant, the multicomponent diffusion constant, and the geometrical dimension of the experiment.

Diffuse gamma-ray emission from self-confined cosmic rays around Galactic sources

NASA Astrophysics Data System (ADS)

D'Angelo, Marta; Morlino, Giovanni; Amato, Elena; Blasi, Pasquale

2018-02-01

The propagation of particles accelerated at supernova remnant shocks and escaping the parent remnants is likely to proceed in a strongly non-linear regime, due to the efficient self-generation of Alfvén waves excited through streaming instability near the sources. Depending on the amount of neutral hydrogen present in the regions around the sites of supernova explosions, cosmic rays may accumulate an appreciable grammage in the same regions and get self-confined for non-negligible times, which in turn results in an enhanced rate of production of secondaries. Here we calculate the contribution to the diffuse gamma-ray background due to the overlap along lines of sight of several of these extended haloes as due to pion production induced by self-confined cosmic rays. We find that if the density of neutrals is low, the haloes can account for a substantial fraction of the diffuse emission observed by Fermi-Large Area Telescope (LAT), depending on the orientation of the line of sight with respect to the direction of the Galactic Centre.

Distinguishing Betwen Effects of Local Inputs (Contaminated Sediments, Point Sources) and Upstream Diffuse Nonpoint Source Input: Refinement of a Watershed Development Index for New England

EPA Science Inventory

Assessment tools are being developed to predict diffuse NPS effects from watershed development and distinguish these from local impacts (point sources, contaminated sediments). Using EMAP data from the New England Wadeable Stream Survey and two state datasets (CT, ME), we are de...

Multispecies diffusion models: A study of uranyl species diffusion

NASA Astrophysics Data System (ADS)

Liu, Chongxuan; Shang, Jianying; Zachara, John M.

2011-12-01

Rigorous numerical description of multispecies diffusion requires coupling of species, charge, and aqueous and surface complexation reactions that collectively affect diffusive fluxes. The applicability of a fully coupled diffusion model is, however, often constrained by the availability of species self-diffusion coefficients, as well as by computational complication in imposing charge conservation. In this study, several diffusion models with variable complexity in charge and species coupling were formulated and compared to describe reactive multispecies diffusion in groundwater. Diffusion of uranyl [U(VI)] species was used as an example in demonstrating the effectiveness of the models in describing multispecies diffusion. Numerical simulations found that a diffusion model with a single, common diffusion coefficient for all species was sufficient to describe multispecies U(VI) diffusion under a steady state condition of major chemical composition, but not under transient chemical conditions. Simulations revealed that for multispecies U(VI) diffusion under transient chemical conditions, a fully coupled diffusion model could be well approximated by a component-based diffusion model when the diffusion coefficient for each chemical component was properly selected. The component-based diffusion model considers the difference in diffusion coefficients between chemical components, but not between the species within each chemical component. This treatment significantly enhanced computational efficiency at the expense of minor charge conservation. The charge balance in the component-based diffusion model can be enforced, if necessary, by adding a secondary migration term resulting from model simplification. The effect of ion activity coefficient gradients on multispecies diffusion is also discussed. The diffusion models were applied to describe U(VI) diffusive mass transfer in intragranular domains in two sediments collected from U.S. Department of Energy's Hanford 300A

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

Modeling the reversible, diffusive sink effect in response to transient contaminant sources.

PubMed

Zhao, D; Little, J C; Hodgson, A T

2002-09-01

A physically based diffusion model is used to evaluate the sink effect of diffusion-controlled indoor materials and to predict the transient contaminant concentration in indoor air in response to several time-varying contaminant sources. For simplicity, it is assumed the predominant indoor material is a homogeneous slab, initially free of contaminant, and the air within the room is well mixed. The model enables transient volatile organic compound (VOC) concentrations to be predicted based on the material/air partition coefficient (K) and the material-phase diffusion coefficient (D) of the sink. Model predictions are made for three scenarios, each mimicking a realistic situation in a building. Styrene, phenol, and naphthalene are used as representative VOCs. A styrene butadiene rubber (SBR) backed carpet, vinyl flooring (VF), and a polyurethane foam (PUF) carpet cushion are considered as typical indoor sinks. In scenarios involving a sinusoidal VOC input and a double exponential decaying input, the model predicts the sink has a modest impact for SBR/styrene, but the effect increases for VF/phenol and PUF/naphthalene. In contrast, for an episodic chemical spill, SBR is predicted to reduce the peak styrene concentration considerably. A parametric study reveals for systems involving a large equilibrium constant (K), the kinetic constant (D) will govern the shape of the resulting gasphase concentration profile. On the other hand, for systems with a relaxed mass transfer resistance, K will dominate the profile.

Analytical close-to-source investigation for an isotropic point source in an unbounded, anisotropically scattering medium

NASA Astrophysics Data System (ADS)

Rinzema, Kees; ten Bosch, Jaap J.; Ferwerda, Hedzer A.; Hoenders, Bernhard J.

1995-01-01

The diffusion approximation, which is often used to describe the propagation of light in biological tissues, is only good at a sufficient distance from sources and boundaries. Light- tissue interaction is however most intense in the region close to the source. It would therefore be interesting to study this region more closely. Although scattering in biological tissues is predominantly forward peaked, explicit solutions to the transport equation have only been obtained in the case of isotropic scattering. Particularly, for the case of an isotropic point source in an unbounded, isotropically scattering medium the solution is well known. We show that this problem can also be solved analytically if the scattering is no longer isotropic, while everything else remains the same.

Survey of upper band chorus and ECH waves: Implications for the diffuse aurora

NASA Astrophysics Data System (ADS)

Meredith, Nigel; Horne, Richard; Thorne, Richard; Anderson, Roger

2010-05-01

The origin of the diffuse aurora has been a source of controversy for many years. More recently the question has taken a new significance in view of the associated changes in atmospheric chemistry which may affect the middle atmosphere. Here we use CRRES data to assess the importance of upper band chorus and electron cyclotron harmonic (ECH) waves in the production of the diffuse aurora. Both wave modes increase with increasing geomagnetic activity, suggesting they are related to periods of enhanced convection and/or substorm activity. They are confined to the near-equatorial region which excludes the pre-noon sector from the wave survey. During active conditions intense ECH waves and upper band chorus, with amplitudes exceeding 1 mVm-1, are observed in the region 4 < L < 7 from 2100 to 0600 MLT approximately 20% and 6% of the time respectively. This suggests that both wave modes can put electrons on strong diffusion, but only during active conditions and not at all local times. Scattering rates fall below the strong diffusion limit at other times when the wave amplitudes are weaker. Fluxes of low energy electrons (100 eV < E < 30 keV) also increase with increasing geomagnetic activity in approximately the same region of geospace as the waves, suggesting that these electrons are responsible for the generation of the waves. The patterns of the upper band chorus, ECH waves and low energy electrons are similar to the global morphology of the diffuse aurora, suggesting that both wave modes play significant roles in the production of the diffuse aurora.

Diffusion barriers

NASA Technical Reports Server (NTRS)

Nicolet, M. A.

1983-01-01

The choice of the metallic film for the contact to a semiconductor device is discussed. One way to try to stabilize a contact is by interposing a thin film of a material that has low diffusivity for the atoms in question. This thin film application is known as a diffusion barrier. Three types of barriers can be distinguished. The stuffed barrier derives its low atomic diffusivity to impurities that concentrate along the extended defects of a polycrystalline layer. Sacrificial barriers exploit the fact that some (elemental) thin films react in a laterally uniform and reproducible fashion. Sacrificial barriers have the advantage that the point of their failure is predictable. Passive barriers are those most closely approximating an ideal barrier. The most-studied case is that of sputtered TiN films. Stuffed barriers may be viewed as passive barriers whose low diffusivity material extends along the defects of the polycrystalline host.

Fast computation of quadrupole and hexadecapole approximations in microlensing with a single point-source evaluation

NASA Astrophysics Data System (ADS)

Cassan, Arnaud

2017-07-01

The exoplanet detection rate from gravitational microlensing has grown significantly in recent years thanks to a great enhancement of resources and improved observational strategy. Current observatories include ground-based wide-field and/or robotic world-wide networks of telescopes, as well as space-based observatories such as satellites Spitzer or Kepler/K2. This results in a large quantity of data to be processed and analysed, which is a challenge for modelling codes because of the complexity of the parameter space to be explored and the intensive computations required to evaluate the models. In this work, I present a method that allows to compute the quadrupole and hexadecapole approximations of the finite-source magnification with more efficiency than previously available codes, with routines about six times and four times faster, respectively. The quadrupole takes just about twice the time of a point-source evaluation, which advocates for generalizing its use to large portions of the light curves. The corresponding routines are available as open-source python codes.

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…

Impacts by point and diffuse micropollutant sources on the stream water quality at catchment scale

NASA Astrophysics Data System (ADS)

Petersen, M. F.; Eriksson, E.; Binning, P. J.; Bjerg, P. L.

2012-04-01

The water quality of surface waters is threatened by multiple anthropogenic pollutants and the large variety of pollutants challenges the monitoring and assessment of the water quality. The aim of this study was to characterize and quantify both point and diffuse sources of micropollutants impacting the water quality of a stream at catchment scale. Grindsted stream in western Jutland, Denmark was used as a study site. The stream passes both urban and agricultural areas and is impacted by severe groundwater contamination in Grindsted city. Along a 12 km reach of Grindsted stream, the potential pollution sources were identified including a pharmaceutical factory site with a contaminated old drainage ditch, two waste deposits, a wastewater treatment plant, overflow structures, fish farms, industrial discharges and diffuse agricultural and urban sources. Six water samples were collected along the stream and analyzed for general water quality parameters, inorganic constituents, pesticides, sulfonamides, chlorinated solvents, BTEXs, and paracetamol and ibuprofen. The latter two groups were not detected. The general water quality showed typical conditions for a stream in western Jutland. Minor impacts by releases of organic matter and nutrients were found after the fish farms and the waste water treatment plant. Nickel was found at concentrations 5.8 - 8.8 μg/l. Nine pesticides and metabolites of both agricultural and urban use were detected along the stream; among these were the two most frequently detected and some rarely detected pesticides in Danish water courses. The concentrations were generally consistent with other findings in Danish streams and in the range 0.01 - 0.09 μg/l; except for metribuzin-diketo that showed high concentrations up to 0.74 μg/l. The groundwater contamination at the pharmaceutical factory site, the drainage ditch and the waste deposits is similar in composition containing among others sulfonamides and chlorinated solvents (including vinyl

In vivo time-gated diffuse correlation spectroscopy at quasi-null source-detector separation.

PubMed

Pagliazzi, M; Sekar, S Konugolu Venkata; Di Sieno, L; Colombo, L; Durduran, T; Contini, D; Torricelli, A; Pifferi, A; Mora, A Dalla

2018-06-01

We demonstrate time domain diffuse correlation spectroscopy at quasi-null source-detector separation by using a fast time-gated single-photon avalanche diode without the need of time-tagging electronics. This approach allows for increased photon collection, simplified real-time instrumentation, and reduced probe dimensions. Depth discriminating, quasi-null distance measurement of blood flow in a human subject is presented. We envision the miniaturization and integration of matrices of optical sensors of increased spatial resolution and the enhancement of the contrast of local blood flow changes.

The Fermi Large Area Telescope Thrid Gamma-ray Source Catalog

NASA Astrophysics Data System (ADS)

Stephens, Thomas E.; Ballet, Jean; Burnett, Toby; Cavazzuti, Elisabetta; Digel, Seth William; Fermi LAT Collaboration

2015-01-01

We present an overview of the third Fermi Large Area Telescope source catalog (3FGL) of sources in the 100 MeV - 300 GeV range. Based on the first four years of science data from the Fermi Gamma-ray Space Telescope mission, it is the deepest yet in this energy range. Relative to the 2FGL catalog (Nolan et al. 2012, ApJS 199, 31), the 3FGL catalog incorporates twice as much data as well as a number of analysis improvements, including improved calibrations at the event reconstruction level, an updated model for Galactic diffuse gamma-ray emission, a refined procedure for source detection, and improved methods for associating LAT sources with potential counterparts at other wavelengths. The 3FGL catalog includes 3033 sources, with source location regions, spectral properties, and monthly light curves for each. For approximately one-third of the sources we have not found counterparts at other wavelengths. More than 1100 of the identified or associated sources are active galaxies of the blazar class; several other classes of non-blazar active galaxies are also represented in the 3FGL. Pulsars represent the largest Galactic source class. From source counts of Galactic sources we estimate the contribution of unresolved sources to the Galactic diffuse emission.

Anisotropies in the Diffuse Gamma-Ray Background Measured by the Fermi LAT

NASA Technical Reports Server (NTRS)

Ferrara, E. C.; McEnery, J. E.; Troja, E.

2012-01-01

The contribution of unresolved sources to the diffuse gamma-ray background could induce anisotropies in this emission on small angular scales. We analyze the angular power spectrum of the diffuse emission measured by the Fermi LAT at Galactic latitudes absolute value of b > 30 deg in four energy bins spanning 1 to 50 GeV. At multipoles l >= 155, corresponding to angular scales approx < 2 deg, angular power above the photon noise level is detected at > 99.99% CL in the 1-2 GeV, 2- 5 GeV, and 5- 10 GeV energy bins, and at > 99% CL at 10-50 GeV. Within each energy bin the measured angular power takes approximately the same value at all multipoles l >= 155, suggesting that it originates from the contribution of one or more unclustered source populations. The amplitude of the angular power normalized to the mean intensity in each energy bin is consistent with a constant value at all energies, C(sub p) / (I)(exp 2) = 9.05 +/- 0.84 x 10(exp -6) sr, while the energy dependence of C(sub p) is consistent with the anisotropy arising from one or more source populations with power-law photon spectra with spectral index Gamma (sub s) = 2.40 +/- 0.07. We discuss the implications of the measured angular power for gamma-ray source populations that may provide a contribution to the diffuse gamma-ray background.

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

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

Repetitively pulsed UV radiation source based on a run-away electron preionised diffuse discharge in nitrogen

NASA Astrophysics Data System (ADS)

Baksht, E. Kh; Burachenko, A. G.; Lomaev, M. I.; Panchenko, A. N.; Tarasenko, V. F.

2015-04-01

An extended repetitively pulsed source of spontaneous UV radiation is fabricated, which may also be used for producing laser radiation. Voltage pulses with an incident wave amplitude of up to 30 kV, a half-amplitude duration of ~4 ns and a rise time of ~2.5 ns are applied to a gap with a nonuniform electric field. For an excitation region length of 35 cm and a nitrogen pressure of 30 - 760 Torr, a diffusive discharge up to a pulse repetition rate of 2 kHz is produced without using an additional system for gap preionisation. An investigation is made of the plasma of the run-away electron preionised diffuse discharge. Using a CCD camera it is found that the dense diffused plasma fills the gap in a time shorter than 1 ns. X-ray radiation is recorded from behind the foil anode throughout the pressure range under study; a supershort avalanche electron beam is recorded by the collector electrode at pressures below 100 Torr.

Martian CH(4): sources, flux, and detection.

PubMed

Onstott, T C; McGown, D; Kessler, J; Lollar, B Sherwood; Lehmann, K K; Clifford, S M

2006-04-01

Recent observations have detected trace amounts of CH(4) heterogeneously distributed in the martian atmosphere, which indicated a subsurface CH(4) flux of ~2 x 10(5) to 2 x 10(9) cm(2) s(1). Four different origins for this CH(4) were considered: (1) volcanogenic; (2) sublimation of hydrate- rich ice; (3) diffusive transport through hydrate-saturated cryosphere; and (4) microbial CH(4) generation above the cryosphere. A diffusive flux model of the martian crust for He, H(2), and CH(4) was developed based upon measurements of deep fracture water samples from South Africa. This model distinguishes between abiogenic and microbial CH(4) sources based upon their isotopic composition, and couples microbial CH(4) production to H(2) generation by H(2)O radiolysis. For a He flux of approximately 10(5) cm(2) s(1) this model yields an abiogenic CH(4) flux and a microbial CH(4) flux of approximately 10(6) and approximately 10(9) cm(2) s(1), respectively. This flux will only reach the martian surface if CH(4) hydrate is saturated in the cryosphere; otherwise it will be captured within the cryosphere. The sublimation of a hydrate-rich cryosphere could generate the observed CH(4) flux, whereas microbial CH(4) production in a hypersaline environment above the hydrate stability zone only seems capable of supplying approximately 10(5) cm(2) s(1) of CH(4). The model predicts that He/H(2)/CH(4)/C(2)H(6) abundances and the C and H isotopic values of CH(4) and the C isotopic composition of C(2)H(6) could reveal the different sources. Cavity ring-down spectrometers represent the instrument type that would be most capable of performing the C and H measurements of CH(4) on near future rover missions and pinpointing the cause and source of the CH(4) emissions.

A combined kick-out and dissociative diffusion mechanism of grown-in Be in InGaAs and InGaAsP. A new finite difference-Bairstow method for solution of the diffusion equations

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

Koumetz, Serge D., E-mail: Serge.Koumetz@univ-rouen.fr; Martin, Patrick; Murray, Hugues

Experimental results on the diffusion of grown-in beryllium (Be) in indium gallium arsenide (In{sub 0.53}Ga{sub 0.47}As) and indium gallium arsenide phosphide (In{sub 0.73}Ga{sub 0.27}As{sub 0.58}P{sub 0.42}) gas source molecular beam epitaxy alloys lattice-matched to indium phosphide (InP) can be successfully explained in terms of a combined kick-out and dissociative diffusion mechanism, involving neutral Be interstitials (Be{sub i}{sup 0}), singly positively charged gallium (Ga), indium (In) self-interstitials (I{sub III}{sup +}) and singly positively charged Ga, In vacancies (V{sub III}{sup +}). A new numerical method of solution to the system of diffusion equations, based on the finite difference approximations and Bairstow's method,more » is proposed.« less

Bayesian estimation of a source term of radiation release with approximately known nuclide ratios

NASA Astrophysics Data System (ADS)

Tichý, Ondřej; Šmídl, Václav; Hofman, Radek

2016-04-01

We are concerned with estimation of a source term in case of an accidental release from a known location, e.g. a power plant. Usually, the source term of an accidental release of radiation comprises of a mixture of nuclide. The gamma dose rate measurements do not provide a direct information on the source term composition. However, physical properties of respective nuclide (deposition properties, decay half-life) can be used when uncertain information on nuclide ratios is available, e.g. from known reactor inventory. The proposed method is based on linear inverse model where the observation vector y arise as a linear combination y = Mx of a source-receptor-sensitivity (SRS) matrix M and the source term x. The task is to estimate the unknown source term x. The problem is ill-conditioned and further regularization is needed to obtain a reasonable solution. In this contribution, we assume that nuclide ratios of the release is known with some degree of uncertainty. This knowledge is used to form the prior covariance matrix of the source term x. Due to uncertainty in the ratios the diagonal elements of the covariance matrix are considered to be unknown. Positivity of the source term estimate is guaranteed by using multivariate truncated Gaussian distribution. Following Bayesian approach, we estimate all parameters of the model from the data so that y, M, and known ratios are the only inputs of the method. Since the inference of the model is intractable, we follow the Variational Bayes method yielding an iterative algorithm for estimation of all model parameters. Performance of the method is studied on simulated 6 hour power plant release where 3 nuclide are released and 2 nuclide ratios are approximately known. The comparison with method with unknown nuclide ratios will be given to prove the usefulness of the proposed approach. This research is supported by EEA/Norwegian Financial Mechanism under project MSMT-28477/2014 Source-Term Determination of Radionuclide Releases

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

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.

Simulation of Bacillus subtilis biofilm growth on agar plate by diffusion-reaction based continuum model

NASA Astrophysics Data System (ADS)

Zhang, Xianlong; Wang, Xiaoling; Nie, Kai; Li, Mingpeng; Sun, Qingping

2016-08-01

Various species of bacteria form highly organized spatially-structured aggregates known as biofilms. To understand how microenvironments impact biofilm growth dynamics, we propose a diffusion-reaction continuum model to simulate the formation of Bacillus subtilis biofilm on an agar plate. The extended finite element method combined with level set method are employed to perform the simulation, numerical results show the quantitative relationship between colony morphologies and nutrient depletion over time. Considering that the production of polysaccharide in wild-type cells may enhance biofilm spreading on the agar plate, we inoculate mutant colony incapable of producing polysaccharide to verify our results. Predictions of the glutamate source biofilm’s shape parameters agree with the experimental mutant colony better than that of glycerol source biofilm, suggesting that glutamate is rate limiting nutrient for Bacillus subtilis biofilm growth on agar plate, and the diffusion-limited is a better description to the experiment. In addition, we find that the diffusion time scale is of the same magnitude as growth process, and the common-employed quasi-steady approximation is not applicable here.

Simulation of Bacillus subtilis biofilm growth on agar plate by diffusion-reaction based continuum model.

PubMed

Zhang, Xianlong; Wang, Xiaoling; Nie, Kai; Li, Mingpeng; Sun, Qingping

2016-07-19

Various species of bacteria form highly organized spatially-structured aggregates known as biofilms. To understand how microenvironments impact biofilm growth dynamics, we propose a diffusion-reaction continuum model to simulate the formation of Bacillus subtilis biofilm on an agar plate. The extended finite element method combined with level set method are employed to perform the simulation, numerical results show the quantitative relationship between colony morphologies and nutrient depletion over time. Considering that the production of polysaccharide in wild-type cells may enhance biofilm spreading on the agar plate, we inoculate mutant colony incapable of producing polysaccharide to verify our results. Predictions of the glutamate source biofilm's shape parameters agree with the experimental mutant colony better than that of glycerol source biofilm, suggesting that glutamate is rate limiting nutrient for Bacillus subtilis biofilm growth on agar plate, and the diffusion-limited is a better description to the experiment. In addition, we find that the diffusion time scale is of the same magnitude as growth process, and the common-employed quasi-steady approximation is not applicable here.

Controllable uncertain opinion diffusion under confidence bound and unpredicted diffusion probability

NASA Astrophysics Data System (ADS)

Yan, Fuhan; Li, Zhaofeng; Jiang, Yichuan

2016-05-01

The issues of modeling and analyzing diffusion in social networks have been extensively studied in the last few decades. Recently, many studies focus on uncertain diffusion process. The uncertainty of diffusion process means that the diffusion probability is unpredicted because of some complex factors. For instance, the variety of individuals' opinions is an important factor that can cause uncertainty of diffusion probability. In detail, the difference between opinions can influence the diffusion probability, and then the evolution of opinions will cause the uncertainty of diffusion probability. It is known that controlling the diffusion process is important in the context of viral marketing and political propaganda. However, previous methods are hardly feasible to control the uncertain diffusion process of individual opinion. In this paper, we present suitable strategy to control this diffusion process based on the approximate estimation of the uncertain factors. We formulate a model in which the diffusion probability is influenced by the distance between opinions, and briefly discuss the properties of the diffusion model. Then, we present an optimization problem at the background of voting to show how to control this uncertain diffusion process. In detail, it is assumed that each individual can choose one of the two candidates or abstention based on his/her opinion. Then, we present strategy to set suitable initiators and their opinions so that the advantage of one candidate will be maximized at the end of diffusion. The results show that traditional influence maximization algorithms are not applicable to this problem, and our algorithm can achieve expected performance.

Multifrequency VLA observations of PKS 0745 - 191 - The archetypal 'cooling flow' radio source?

NASA Technical Reports Server (NTRS)

Baum, S. A.; O'Dea, C. P.

1991-01-01

Ninety-, 20-, 6- and 2-cm VLA observations of the high-radio-luminosity cooling-flow radio source PKS 0745 - 191 are presented. The radio source was found to have a core with a very steep spectrum (alpha is approximately -1.5) and diffuse emission with an even steeper spectrum (alpha is approximately -1.5 to -2.3) without clear indications of the jets, hotspots, or double lobes found in the other radio sources of comparable luminosity. It is inferred that the energy to power the radio source comes from the central engine, but the source's structure may be heavily influenced by the past history of the galaxy and the inflowing intracluster medium. It is shown that, while the radio source is energetically unimportant for the cluster as a whole, it is important on the scale of the cooling flow. The mere existence of cosmic rays and magnetic fields within a substantial fraction of the volume inside the cooling radius has important consequences for cooling-flow models.

The Approximate Bayesian Computation methods in the localization of the atmospheric contamination source

NASA Astrophysics Data System (ADS)

Kopka, P.; Wawrzynczak, A.; Borysiewicz, M.

2015-09-01

In many areas of application, a central problem is a solution to the inverse problem, especially estimation of the unknown model parameters to model the underlying dynamics of a physical system precisely. In this situation, the Bayesian inference is a powerful tool to combine observed data with prior knowledge to gain the probability distribution of searched parameters. We have applied the modern methodology named Sequential Approximate Bayesian Computation (S-ABC) to the problem of tracing the atmospheric contaminant source. The ABC is technique commonly used in the Bayesian analysis of complex models and dynamic system. Sequential methods can significantly increase the efficiency of the ABC. In the presented algorithm, the input data are the on-line arriving concentrations of released substance registered by distributed sensor network from OVER-LAND ATMOSPHERIC DISPERSION (OLAD) experiment. The algorithm output are the probability distributions of a contamination source parameters i.e. its particular location, release rate, speed and direction of the movement, start time and duration. The stochastic approach presented in this paper is completely general and can be used in other fields where the parameters of the model bet fitted to the observable data should be found.

Modeling of Diffuse-Diffuse Photon Coupling via a Nonscattering Region: a Comparative Study

NASA Astrophysics Data System (ADS)

Lee, Jae Hoon; Kim, Seunghwan; Kim, Youn Tae

2004-06-01

It is well established that diffusion approximation is valid for light propagation in highly scattering media, but it breaks down in nonscattering regions. The previous methods that manipulate nonscattering regions are essentially boundary-to-boundary coupling (BBC) methods through a nonscattering void region based on the radiosity theory. We present a boundary-to-interior coupling (BIC) method. BIC is based on the fact that the collimated pencil beam incident on the medium can be replaced by an isotropic point source positioned at one reduced scattering length inside the medium from an illuminated point. A similar replacement is possible for the nondiffuse lights that enter the diffuse medium through the void, and it is formulated as the BIC method. We implemented both coupling methods using the finite element method (FEM) and tested for the circle with a void gap and for a four-layer adult head model. For mean time of flight, the BIC shows better agreement with Monte Carlo (MC) simulation results than BBC. For intensity, BIC shows a comparable match with MC data compared with that of BBC. The effect of absorption of the clear layer in the adult head model was investigated. Both mean time and intensity decrease as absorption of the clear layer increases.

Modeling of diffuse-diffuse photon coupling via a nonscattering region: a comparative study.

PubMed

Lee, Jae Hoon; Kim, Seunghwan; Kim, Youn Tae

2004-06-20

It is well established that diffusion approximation is valid for light propagation in highly scattering media, but it breaks down in nonscattering regions. The previous methods that manipulate nonscattering regions are essentially boundary-to-boundary coupling (BBC) methods through a nonscattering void region based on the radiosity theory. We present a boundary-to-interior coupling (BIC) method. BIC is based on the fact that the collimated pencil beam incident on the medium can be replaced by an isotropic point source positioned at one reduced scattering length inside the medium from an illuminated point. A similar replacement is possible for the nondiffuse lights that enter the diffuse medium through the void, and it is formulated as the BIC method. We implemented both coupling methods using the finite element method (FEM) and tested for the circle with a void gap and for a four-layer adult head model. For mean time of flight, the BIC shows better agreement with Monte Carlo (MC) simulation results than BBC. For intensity, BIC shows a comparable match with MC data compared with that of BBC. The effect of absorption of the clear layer in the adult head model was investigated. Both mean time and intensity decrease as absorption of the clear layer increases.

Single-layer model to predict the source/sink behavior of diffusion-controlled building materials.

PubMed

Kumar, Deept; Little, John C

2003-09-01

Building materials may act as both sources of and sinks forvolatile organic compounds (VOCs) in indoor air. A strategy to characterize the rate of absorption and desorption of VOCs by diffusion-controlled building materials is validated. A previously developed model that predicts mass transfer between a flat slab of material and the well-mixed air within a chamber or room is extended. The generalized model allows a nonuniform initial material-phase concentration and a transient influent gas-phase concentration to be simultaneously considered. An analytical solution to the more general model is developed. Experimental data are obtained by placing samples of vinyl flooring inside a small stainless steel chamber and exposing them to absorption/desorption cycles of n-dodecane and phenol. Measured values for the material-air partition coefficient and the material-phase diffusion coefficient were obtained previously in a series of completely independent experiments. The a priori model predictions are in close agreement with the observed experimental data.

Approximate supernova remnant dynamics with cosmic ray production

NASA Technical Reports Server (NTRS)

Voelk, H. J.; Drury, L. O.; Dorfi, E. A.

1985-01-01

Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probably sources of Cosmic Rays. Recent shock acceleration models treating the Cosmic Rays (CR's) as test particles nb a prescribed Supernova Remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the Interstellar Medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation.

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).

Anisotropies in the diffuse gamma-ray background measured by the Fermi LAT

DOE PAGES

Ackermann, M.; Ajello, M.; Albert, A.; ...

2012-04-23

The contribution of unresolved sources to the diffuse gamma-ray background could induce anisotropies in this emission on small angular scales. Here, we analyze the angular power spectrum of the diffuse emission measured by the Fermi Large Area Telescope at Galactic latitudes | b | > 30 ° in four energy bins spanning 1–50 GeV. At multipoles ℓ ≥ 155 , corresponding to angular scales ≲ 2 ° , angular power above the photon noise level is detected at > 99.99 % confidence level in the 1–2 GeV, 2–5 GeV, and 5–10 GeV energy bins, and at > 99 % confidencemore » level at 10–50 GeV. Within each energy bin the measured angular power takes approximately the same value at all multipoles ℓ ≥ 155 , suggesting that it originates from the contribution of one or more unclustered source populations. Furthermore, the amplitude of the angular power normalized to the mean intensity in each energy bin is consistent with a constant value at all energies, C P / < I > 2 = 9.05 ± 0.84 × 10 - 6 sr , while the energy dependence of C P is consistent with the anisotropy arising from one or more source populations with power-law photon spectra with spectral index Γ s = 2.40 ± 0.07 . We also discuss the implications of the measured angular power for gamma-ray source populations that may provide a contribution to the diffuse gamma-ray background.« less

Repetitively pulsed UV radiation source based on a run-away electron preionised diffuse discharge in nitrogen

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

Baksht, E Kh; Burachenko, A G; Lomaev, M I

2015-04-30

An extended repetitively pulsed source of spontaneous UV radiation is fabricated, which may also be used for producing laser radiation. Voltage pulses with an incident wave amplitude of up to 30 kV, a half-amplitude duration of ∼4 ns and a rise time of ∼2.5 ns are applied to a gap with a nonuniform electric field. For an excitation region length of 35 cm and a nitrogen pressure of 30 – 760 Torr, a diffusive discharge up to a pulse repetition rate of 2 kHz is produced without using an additional system for gap preionisation. An investigation is made of themore » plasma of the run-away electron preionised diffuse discharge. Using a CCD camera it is found that the dense diffused plasma fills the gap in a time shorter than 1 ns. X-ray radiation is recorded from behind the foil anode throughout the pressure range under study; a supershort avalanche electron beam is recorded by the collector electrode at pressures below 100 Torr. (laser applications and other topics in quantum electronics)« less

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.

Laser induced heat source distribution in bio-tissues

NASA Astrophysics Data System (ADS)

Li, Xiaoxia; Fan, Shifu; Zhao, Youquan

2006-09-01

During numerical simulation of laser and tissue thermal interaction, the light fluence rate distribution should be formularized and constituted to the source term in the heat transfer equation. Usually the solution of light irradiative transport equation is given in extreme conditions such as full absorption (Lambert-Beer Law), full scattering (Lubelka-Munk theory), most scattering (Diffusion Approximation) et al. But in specific conditions, these solutions will induce different errors. The usually used Monte Carlo simulation (MCS) is more universal and exact but has difficulty to deal with dynamic parameter and fast simulation. Its area partition pattern has limits when applying FEM (finite element method) to solve the bio-heat transfer partial differential coefficient equation. Laser heat source plots of above methods showed much difference with MCS. In order to solve this problem, through analyzing different optical actions such as reflection, scattering and absorption on the laser induced heat generation in bio-tissue, a new attempt was made out which combined the modified beam broaden model and the diffusion approximation model. First the scattering coefficient was replaced by reduced scattering coefficient in the beam broaden model, which is more reasonable when scattering was treated as anisotropic scattering. Secondly the attenuation coefficient was replaced by effective attenuation coefficient in scattering dominating turbid bio-tissue. The computation results of the modified method were compared with Monte Carlo simulation and showed the model provided reasonable predictions of heat source term distribution than past methods. Such a research is useful for explaining the physical characteristics of heat source in the heat transfer equation, establishing effective photo-thermal model, and providing theory contrast for related laser medicine experiments.

Search for diffuse neutrino flux from astrophysical sources with MACRO

NASA Astrophysics Data System (ADS)

MACRO Collaboration; Ambrosio, M.; Antolini, R.; Auriemma, G.; Bakari, D.; Baldini, A.; Barbarino, G. C.; Barish, B. C.; Battistoni, G.; Becherini, Y.; Bellotti, R.; Bemporad, C.; Bernardini, P.; Bilokon, H.; Bloise, C.; Bower, C.; Brigida, M.; Bussino, S.; Cafagna, F.; Calicchio, M.; Campana, D.; Carboni, M.; Caruso, R.; Cecchini, S.; Cei, F.; Chiarella, V.; Choudhary, B. C.; Coutu, S.; Cozzi, M.; de Cataldo, G.; Dekhissi, H.; de Marzo, C.; de Mitri, I.; Derkaoui, J.; de Vincenzi, M.; di Credico, A.; Erriquez, O.; Favuzzi, C.; Forti, C.; Fusco, P.; Giacomelli, G.; Giannini, G.; Giglietto, N.; Giorgini, M.; Grassi, M.; Grillo, A.; Guarino, F.; Gustavino, C.; Habig, A.; Hanson, K.; Heinz, R.; Iarocci, E.; Katsavounidis, E.; Katsavounidis, I.; Kearns, E.; Kim, H.; Kyriazopoulou, S.; Lamanna, E.; Lane, C.; Levin, D. S.; Lipari, P.; Longley, N. P.; Longo, M. J.; Loparco, F.; Maaroufi, F.; Mancarella, G.; Mandrioli, G.; Margiotta, A.; Marini, A.; Martello, D.; Marzari-Chiesa, A.; Mazziotta, M. N.; Michael, D. G.; Monacelli, P.; Montaruli, T.; Monteno, M.; Mufson, S.; Musser, J.; Nicolò, D.; Nolty, R.; Orth, C.; Osteria, G.; Palamara, O.; Patera, V.; Patrizii, L.; Pazzi, R.; Peck, C. W.; Perrone, L.; Petrera, S.; Pistilli, P.; Popa, V.; Rainò, A.; Reynoldson, J.; Ronga, F.; Rrhioua, A.; Satriano, C.; Scapparone, E.; Scholberg, K.; Sciubba, A.; Serra, P.; Sioli, M.; Sirri, G.; Sitta, M.; Spinelli, P.; Spinetti, M.; Spurio, M.; Steinberg, R.; Stone, J. L.; Sulak, L. R.; Surdo, A.; Tarlè, G.; Togo, V.; Vakili, M.; Walter, C. W.; Webb, R.

2003-04-01

Many galactic and extragalactic astrophysical sources are currently considered promising candidates as high-energy neutrino emitters. Astrophysical neutrinos can be detected as upward-going muons produced in charged-current interactions with the medium surrounding the detector. The expected neutrino fluxes from various models start to dominate on the atmospheric neutrino background at neutrino energies above some tens of TeV. We present the results of a search for an excess of high-energy upward-going muons among the sample of data collected by MACRO during ~5.8 years of effective running time. No significant evidence for this signal was found. As a consequence, an upper limit on the flux of upward-going muons from high-energy neutrinos was set at the level of 1.7×10-14 cm-2s-1sr-1. The corresponding upper limit for the diffuse neutrino flux was evaluated assuming a neutrino power law spectrum. Our result was compared with theoretical predictions and upper limits from other experiments.

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

Single Crystal Diffuse Neutron Scattering

DOE PAGES

Welberry, Richard; Whitfield, Ross

2018-01-11

Diffuse neutron scattering has become a valuable tool for investigating local structure in materials ranging from organic molecular crystals containing only light atoms to piezo-ceramics that frequently contain heavy elements. Although neutron sources will never be able to compete with X-rays in terms of the available flux the special properties of neutrons, viz. the ability to explore inelastic scattering events, the fact that scattering lengths do not vary systematically with atomic number and their ability to scatter from magnetic moments, provides strong motivation for developing neutron diffuse scattering methods. Here, we compare three different instruments that have been used bymore » us to collect neutron diffuse scattering data. Two of these are on a spallation source and one on a reactor source.« less

Single Crystal Diffuse Neutron Scattering

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

Welberry, Richard; Whitfield, Ross

Diffuse neutron scattering has become a valuable tool for investigating local structure in materials ranging from organic molecular crystals containing only light atoms to piezo-ceramics that frequently contain heavy elements. Although neutron sources will never be able to compete with X-rays in terms of the available flux the special properties of neutrons, viz. the ability to explore inelastic scattering events, the fact that scattering lengths do not vary systematically with atomic number and their ability to scatter from magnetic moments, provides strong motivation for developing neutron diffuse scattering methods. Here, we compare three different instruments that have been used bymore » us to collect neutron diffuse scattering data. Two of these are on a spallation source and one on a reactor source.« less

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Glass diffusion source for constraining BSF region of a solar cell

DOEpatents

Lesk, I.A.; Pryor, R.A.; Coleman, M.G.

1982-08-27

The present invention is directed to a method of fabricating a solar cell comprising simultaneous diffusion of the p and n dopant materials into the solar cell substrate. The simultaneous diffusion process is preceded by deposition of a capping layer impervious to doping by thermal diffusion processes.

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.…

Simultaneous Determination of Thermal Conductivity and Thermal Diffusivity of Food and Agricultural Materials Using a Transient Plane-Source Method

USDA-ARS?s Scientific Manuscript database

Thermal conductivity and thermal diffusivity are two important physical properties essential for designing any food engineering processes. Recently a new transient plane-source method was developed to measure a variety of materials, but its application in foods has not been documented. Therefore, ...

Design and evaluation of an imaging spectrophotometer incorporating a uniform light source.

PubMed

Noble, S D; Brown, R B; Crowe, T G

2012-03-01

Accounting for light that is diffusely scattered from a surface is one of the practical challenges in reflectance measurement. Integrating spheres are commonly used for this purpose in point measurements of reflectance and transmittance. This solution is not directly applicable to a spectral imaging application for which diffuse reflectance measurements are desired. In this paper, an imaging spectrophotometer design is presented that employs a uniform light source to provide diffuse illumination. This creates the inverse measurement geometry to the directional illumination/diffuse reflectance mode typically used for point measurements. The final system had a spectral range between 400 and 1000 nm with a 5.2 nm resolution, a field of view of approximately 0.5 m by 0.5 m, and millimeter spatial resolution. Testing results indicate illumination uniformity typically exceeding 95% and reflectance precision better than 1.7%.

Sucrose diffusion in aqueous solution

PubMed Central

Murray, Benjamin J.

2016-01-01

The diffusion of sugar in aqueous solution is important both in nature and in technological applications, yet measurements of diffusion coefficients at low water content are scarce. We report directly measured sucrose diffusion coefficients in aqueous solution. Our technique utilises a Raman isotope tracer method to monitor the diffusion of non-deuterated and deuterated sucrose across a boundary between the two aqueous solutions. At a water activity of 0.4 (equivalent to 90 wt% sucrose) at room temperature, the diffusion coefficient of sucrose was determined to be approximately four orders of magnitude smaller than that of water in the same material. Using literature viscosity data, we show that, although inappropriate for the prediction of water diffusion, the Stokes–Einstein equation works well for predicting sucrose diffusion under the conditions studied. As well as providing information of importance to the fundamental understanding of diffusion in binary solutions, these data have technological, pharmaceutical and medical implications, for example in cryopreservation. Moreover, in the atmosphere, slow organic diffusion may have important implications for aerosol growth, chemistry and evaporation, where processes may be limited by the inability of a molecule to diffuse between the bulk and the surface of a particle. PMID:27364512

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.

destiny: diffusion maps for large-scale single-cell data in R.

PubMed

Angerer, Philipp; Haghverdi, Laleh; Büttner, Maren; Theis, Fabian J; Marr, Carsten; Buettner, Florian

2016-04-15

: Diffusion maps are a spectral method for non-linear dimension reduction and have recently been adapted for the visualization of single-cell expression data. Here we present destiny, an efficient R implementation of the diffusion map algorithm. Our package includes a single-cell specific noise model allowing for missing and censored values. In contrast to previous implementations, we further present an efficient nearest-neighbour approximation that allows for the processing of hundreds of thousands of cells and a functionality for projecting new data on existing diffusion maps. We exemplarily apply destiny to a recent time-resolved mass cytometry dataset of cellular reprogramming. destiny is an open-source R/Bioconductor package "bioconductor.org/packages/destiny" also available at www.helmholtz-muenchen.de/icb/destiny A detailed vignette describing functions and workflows is provided with the package. carsten.marr@helmholtz-muenchen.de or f.buettner@helmholtz-muenchen.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Instrumentation in Diffuse Optical Imaging

PubMed Central

Zhang, Xiaofeng

2014-01-01

Diffuse optical imaging is highly versatile and has a very broad range of applications in biology and medicine. It covers diffuse optical tomography, fluorescence diffuse optical tomography, bioluminescence, and a number of other new imaging methods. These methods of diffuse optical imaging have diversified instrument configurations but share the same core physical principle – light propagation in highly diffusive media, i.e., the biological tissue. In this review, the author summarizes the latest development in instrumentation and methodology available to diffuse optical imaging in terms of system architecture, light source, photo-detection, spectral separation, signal modulation, and lastly imaging contrast. PMID:24860804

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

Partially Coherent Scattering in Stellar Chromospheres. Part 4; Analytic Wing Approximations

NASA Technical Reports Server (NTRS)

Gayley, K. G.

1993-01-01

Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas. The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series.

Catchment Models and Management Tools for diffuse Contaminants (Sediment, Phosphorus and Pesticides): DIFFUSE Project

NASA Astrophysics Data System (ADS)

Mockler, Eva; Reaney, Simeon; Mellander, Per-Erik; Wade, Andrew; Collins, Adrian; Arheimer, Berit; Bruen, Michael

2017-04-01

The agricultural sector is the most common suspected source of nutrient pollution in Irish rivers. However, it is also often the most difficult source to characterise due to its predominantly diffuse nature. Particulate phosphorus in surface water and dissolved phosphorus in groundwater are of particular concern in Irish water bodies. Hence the further development of models and indices to assess diffuse sources of contaminants are required for use by the Irish Environmental Protection Agency (EPA) to provide support for river basin planning. Understanding connectivity in the landscape is a vital component of characterising the source-pathway-receptor relationships for water-borne contaminants, and hence is a priority in this research. The DIFFUSE Project will focus on connectivity modelling and incorporation of connectivity into sediment, nutrient and pesticide risk mapping. The Irish approach to understanding and managing natural water bodies has developed substantially in recent years assisted by outputs from multiple research projects, including modelling and analysis tools developed during the Pathways and CatchmentTools projects. These include the Pollution Impact Potential (PIP) maps, which are an example of research output that is used by the EPA to support catchment management. The PIP maps integrate an understanding of the pollution pressures and mobilisation pathways and, using the source-pathways-receptor model, provide a scientific basis for evaluation of mitigation measures. These maps indicate the potential risk posed by nitrate and phosphate from diffuse agricultural sources to surface and groundwater receptors and delineate critical source areas (CSAs) as a means of facilitating the targeting of mitigation measures. Building on this previous research, the DIFFUSE Project will develop revised and new catchment managements tools focused on connectivity, sediment, phosphorus and pesticides. The DIFFUSE project will strive to identify the state

Diffuse radiation

NASA Technical Reports Server (NTRS)

1981-01-01

A diffuse celestial radiation which is isotropic at least on a course scale were measured from the soft X-ray region to about 150 MeV, at which energy the intensity falls below that of the galactic emission for most galactic latitudes. The spectral shape, the intensity, and the established degree of isotropy of this diffuse radiation already place severe constraints on the possible explanations for this radiation. Among the extragalactic theories, the more promising explanations of the isotropic diffuse emission appear to be radiation from exceptional galaxies from matter antimatter annihilation at the boundaries of superclusters of galaxies of matter and antimatter in baryon symmetric big bang models. Other possible sources for extragalactic diffuse gamma radiation are discussed and include normal galaxies, clusters of galaxies, primordial cosmic rays interacting with intergalactic matter, primordial black holes, and cosmic ray leakage from galaxies.

An experimental study of solid source diffusion by spin on dopants and its application for minimal silicon-on-insulator CMOS fabrication

NASA Astrophysics Data System (ADS)

Liu, Yongxun; Koga, Kazuhiro; Khumpuang, Sommawan; Nagao, Masayoshi; Matsukawa, Takashi; Hara, Shiro

2017-06-01

Solid source diffusions of phosphorus (P) and boron (B) into the half-inch (12.5 mm) minimal silicon (Si) wafers by spin on dopants (SOD) have been systematically investigated and the physical-vapor-deposited (PVD) titanium nitride (TiN) metal gate minimal silicon-on-insulator (SOI) complementary metal-oxide-semiconductor (CMOS) field-effect transistors (FETs) have successfully been fabricated using the developed SOD thermal diffusion technique. It was experimentally confirmed that a low temperature oxidation (LTO) process which depresses a boron silicide layer formation is effective way to remove boron-glass in a diluted hydrofluoric acid (DHF) solution. It was also found that top Si layer thickness of SOI wafers is reduced in the SOD thermal diffusion process because of its consumption by thermal oxidation owing to the oxygen atoms included in SOD films, which should be carefully considered in the ultrathin SOI device fabrication. Moreover, normal operations of the fabricated minimal PVD-TiN metal gate SOI-CMOS inverters, static random access memory (SRAM) cells and ring oscillators have been demonstrated. These circuit level results indicate that no remarkable particles and interface traps were introduced onto the minimal wafers during the device fabrication, and the developed solid source diffusion by SOD is useful for the fabrication of functional logic gate minimal SOI-CMOS integrated circuits.

High-grade glioma diffusive modeling using statistical tissue information and diffusion tensors extracted from atlases.

PubMed

Roniotis, Alexandros; Manikis, Georgios C; Sakkalis, Vangelis; Zervakis, Michalis E; Karatzanis, Ioannis; Marias, Kostas

2012-03-01

Glioma, especially glioblastoma, is a leading cause of brain cancer fatality involving highly invasive and neoplastic growth. Diffusive models of glioma growth use variations of the diffusion-reaction equation in order to simulate the invasive patterns of glioma cells by approximating the spatiotemporal change of glioma cell concentration. The most advanced diffusive models take into consideration the heterogeneous velocity of glioma in gray and white matter, by using two different discrete diffusion coefficients in these areas. Moreover, by using diffusion tensor imaging (DTI), they simulate the anisotropic migration of glioma cells, which is facilitated along white fibers, assuming diffusion tensors with different diffusion coefficients along each candidate direction of growth. Our study extends this concept by fully exploiting the proportions of white and gray matter extracted by normal brain atlases, rather than discretizing diffusion coefficients. Moreover, the proportions of white and gray matter, as well as the diffusion tensors, are extracted by the respective atlases; thus, no DTI processing is needed. Finally, we applied this novel glioma growth model on real data and the results indicate that prognostication rates can be improved. © 2012 IEEE

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.

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.

Diffuse Optical Tomography for Brain Imaging: Continuous Wave Instrumentation and Linear Analysis Methods

NASA Astrophysics Data System (ADS)

Giacometti, Paolo; Diamond, Solomon G.

Diffuse optical tomography (DOT) is a functional brain imaging technique that measures cerebral blood oxygenation and blood volume changes. This technique is particularly useful in human neuroimaging measurements because of the coupling between neural and hemodynamic activity in the brain. DOT is a multichannel imaging extension of near-infrared spectroscopy (NIRS). NIRS uses laser sources and light detectors on the scalp to obtain noninvasive hemodynamic measurements from spectroscopic analysis of the remitted light. This review explains how NIRS data analysis is performed using a combination of the modified Beer-Lambert law (MBLL) and the diffusion approximation to the radiative transport equation (RTE). Laser diodes, photodiode detectors, and optical terminals that contact the scalp are the main components in most NIRS systems. Placing multiple sources and detectors over the surface of the scalp allows for tomographic reconstructions that extend the individual measurements of NIRS into DOT. Mathematically arranging the DOT measurements into a linear system of equations that can be inverted provides a way to obtain tomographic reconstructions of hemodynamics in the brain.

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...

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.

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.

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.

Back-Projection Imaging of extended, diffuse seismic sources in volcanic and hydrothermal systems

NASA Astrophysics Data System (ADS)

Kelly, C. L.; Lawrence, J. F.; Beroza, G. C.

2017-12-01

Volcanic and hydrothermal systems exhibit a wide range of seismicity that is directly linked to fluid and volatile activity in the subsurface and that can be indicative of imminent hazardous activity. Seismograms recorded near volcanic and hydrothermal systems typically contain "noisy" records, but in fact, these complex signals are generated by many overlapping low-magnitude displacements and pressure changes at depth. Unfortunately, excluding times of high-magnitude eruptive activity that typically occur infrequently relative to the length of a system's entire eruption cycle, these signals often have very low signal-to-noise ratios and are difficult to identify and study using established seismic analysis techniques (i.e. phase-picking, template matching). Arrays of short-period and broadband seismic sensors are proven tools for monitoring short- and long-term changes in volcanic and hydrothermal systems. Time-reversal techniques (i.e. back-projection) that are improved by additional seismic observations have been successfully applied to locating volcano-seismic sources recorded by dense sensor arrays. We present results from a new computationally efficient back-projection method that allows us to image the evolution of extended, diffuse sources of volcanic and hydrothermal seismicity. We correlate short time-window seismograms from receiver-pairs to find coherent signals and propagate them back in time to potential source locations in a 3D subsurface model. The strength of coherent seismic signal associated with any potential source-receiver-receiver geometry is equal to the correlation of the short time-windows of seismic records at appropriate time lags as determined by the velocity structure and ray paths. We stack (sum) all short time-window correlations from all receiver-pairs to determine the cumulative coherence of signals at each potential source location. Through stacking, coherent signals from extended and/or repeating sources of short-period energy

Plume persistence caused by back diffusion from thin clay layers in a sand aquifer following TCE source-zone hydraulic isolation.

PubMed

Parker, Beth L; Chapman, Steven W; Guilbeault, Martin A

2008-11-14

This paper concludes that back diffusion from one or a few thin clayey beds in a sand aquifer can cause contaminant persistence above MCLs in a sand aquifer long after the source zone initially causing the plume is isolated or removed. This conclusion is based on an intensive case study of a TCE contaminated site in Florida, with the processes evaluated using numerical modeling. At this site, the TCE DNAPL zone formed decades ago, and was hydraulically isolated by means of an innovative system performing groundwater extraction, treatment and re-injection. Treated water is re-injected in a row of injection wells situated a short distance downgradient of the extraction wells, creating a clean-water displacement front to efficiently flush the downgradient plume. This scheme avoids the creation of stagnation zones typical of most groundwater pump-and-treat systems, thereby minimizing the time for aquifer flushing and therefore downgradient cleanup. The system began operation in August 2002 and although the performance monitoring shows substantial declines in concentrations, detectable levels of TCE and degradation products persist downgradient of the re-injection wells, long after the TCE should have disappeared based on calculations assuming a nearly homogenous sand aquifer. Three hypotheses were assessed for this plume persistence: 1) incomplete source-zone capture, 2) DNAPL occurrence downgradient of the re-injection wells, and 3) back diffusion from one or more thin clay beds in the aquifer. After careful consideration, the first two hypotheses were eliminated, leaving back diffusion as the only plausible hypothesis, supported by detailed measurements of VOC concentrations within and near the clay beds and also by numerical model simulations that closely represent the field site hydrogeologic conditions. The model was also used to simulate a more generalized, hypothetical situation where more thin clayey beds occur in a sand aquifer with an underlying aquitard

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.

Isotope effect of mercury diffusion in air

PubMed Central

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

2014-01-01

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

Isotope effect of mercury diffusion in air.

PubMed

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

2014-01-01

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

Theoretical Interpretation of the Measurement of Diffusion Parameters with Pulsed Neutron Source; INTERPRETAZIONE TEORICA DELLE MISURE DI PARAMETRI DI DIFFUSIONE COL METODO DELLE SORGENTI NEUTRONICHE PULSATE

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

Boffi, V.C.; Molinari, V.G.; Parks, D.E.

1962-05-01

Features of the pulsed neution source theory connected with the measurement of diffusion parameters are discussed. Various analytical procedures for determining the decay constant of the fully thermalized neutron flux are compared. The problem of the diffusion coefficient definition is also considered in some detail. (auth)

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.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

Implications of matrix diffusion on 1,4-dioxane persistence at contaminated groundwater sites.

PubMed

Adamson, David T; de Blanc, Phillip C; Farhat, Shahla K; Newell, Charles J

2016-08-15

Management of groundwater sites impacted by 1,4-dioxane can be challenging due to its migration potential and perceived recalcitrance. This study examined the extent to which 1,4-dioxane's persistence was subject to diffusion of mass into and out of lower-permeability zones relative to co-released chlorinated solvents. Two different release scenarios were evaluated within a two-layer aquifer system using an analytical modeling approach. The first scenario simulated a 1,4-dioxane and 1,1,1-TCA source zone where spent solvent was released. The period when 1,4-dioxane was actively loading the low-permeability layer within the source zone was estimated to be <3years due to its high effective solubility. While this was approximately an order-of-magnitude shorter than the loading period for 1,1,1-TCA, the mass of 1,4-dioxane stored within the low-permeability zone at the end of the simulation period (26kg) was larger than that predicted for 1,1,1-TCA (17kg). Even 80years after release, the aqueous 1,4-dioxane concentration was still several orders-of-magnitude higher than potentially-applicable criteria. Within the downgradient plume, diffusion contributed to higher concentrations and enhanced penetration of 1,4-dioxane into the low-permeability zones relative to 1,1,1-TCA. In the second scenario, elevated 1,4-dioxane concentrations were predicted at a site impacted by migration of a weak source from an upgradient site. Plume cutoff was beneficial because it could be implemented in time to prevent further loading of the low-permeability zone at the downgradient site. Overall, this study documented that 1,4-dioxane within transmissive portions of the source zone is quickly depleted due to characteristics that favor both diffusion-based storage and groundwater transport, leaving little mass to treat using conventional means. Furthermore, the results highlight the differences between 1,4-dioxane and chlorinated solvent source zones, suggesting that back diffusion of 1

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

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

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

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

Stress, deformation and diffusion interactions in solids - A simulation study

NASA Astrophysics Data System (ADS)

Fischer, F. D.; Svoboda, J.

2015-05-01

Equations of diffusion treated in the frame of Manning's concept, are completed by equations for generation/annihilation of vacancies at non-ideal sources and sinks, by conservation laws, by equations for generation of an eigenstrain state and by a strain-stress analysis. The stress-deformation-diffusion interactions are demonstrated on the evolution of a diffusion couple consisting of two thin layers of different chemical composition forming a free-standing plate without external loading. The equations are solved for different material parameters represented by the values of diffusion coefficients of individual components and by the intensity of sources and sinks for vacancies. The results of simulations indicate that for low intensity of sources and sinks for vacancies a significant eigenstress state can develop and the interdiffusion process is slowed down. For high intensity of sources and sinks for vacancies a significant eigenstrain state can develop and the eigenstress state quickly relaxes. If the difference in the diffusion coefficients of individual components is high, then the intensity of sources and sinks for vacancies influences the interdiffusion process considerably. For such systems their description only by diffusion coefficients is insufficient and must be completed by a microstructure characterization.

Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: Insights into spectral vanishing viscosity

NASA Astrophysics Data System (ADS)

Moura, R. C.; Sherwin, S. J.; Peiró, J.

2016-02-01

This study addresses linear dispersion-diffusion analysis for the spectral/hp continuous Galerkin (CG) formulation in one dimension. First, numerical dispersion and diffusion curves are obtained for the advection-diffusion problem and the role of multiple eigencurves peculiar to spectral/hp methods is discussed. From the eigencurves' behaviour, we observe that CG might feature potentially undesirable non-smooth dispersion/diffusion characteristics for under-resolved simulations of problems strongly dominated by either convection or diffusion. Subsequently, the linear advection equation augmented with spectral vanishing viscosity (SVV) is analysed. Dispersion and diffusion characteristics of CG with SVV-based stabilization are verified to display similar non-smooth features in flow regions where convection is much stronger than dissipation or vice-versa, owing to a dependency of the standard SVV operator on a local Péclet number. First a modification is proposed to the traditional SVV scaling that enforces a globally constant Péclet number so as to avoid the previous issues. In addition, a new SVV kernel function is suggested and shown to provide a more regular behaviour for the eigencurves along with a consistent increase in resolution power for higher-order discretizations, as measured by the extent of the wavenumber range where numerical errors are negligible. The dissipation characteristics of CG with the SVV modifications suggested are then verified to be broadly equivalent to those obtained through upwinding in the discontinuous Galerkin (DG) scheme. Nevertheless, for the kernel function proposed, the full upwind DG scheme is found to have a slightly higher resolution power for the same dissipation levels. These results show that improved CG-SVV characteristics can be pursued via different kernel functions with the aid of optimization algorithms.

Channels That Cooperatively Service a Data Stream and Voice Messages. II. Diffusion Approximations.

DTIC Science & Technology

1979-11-01

Leoczky, Profegsr J 2 ’ "-Carnegie-Mellon University D -1 " Gaver, Professor Department of Operations Research Reviewed by: Released by: Michael G...ered) REPORT DOCUMENTATION PAGE BFRE CNSTRUTINOR ~I4 REPORT-9Nu 2 . GOVT ACCESSION No. 3 RECIPIENT’S CATALOG NUMBER 4TITLE (and Sbtile) TPOFP0 ED...approximations valid for the extreme but realistic case in which n/p is large, and none give a Wiener approximation. 2 Rather than focus on this simple

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.

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.

Transient plane source (tps) sensors for simultaneous measurements of thermal conductivity and thermal diffusivity of insulators, fluids and conductors

NASA Astrophysics Data System (ADS)

Maqsood, Asghari; Anis-ur-Rehman, M.

2013-12-01

Thermal conductivity and thermal diffusivity are two important physical properties for designing any food engineering processes1. The knowledge of thermal properties of the elements, compounds and different materials in many industrial applications is a requirement for their final functionality. Transient plane source (tps) sensors are reported2 to be useful for the simultaneous measurement of thermal conductivity, thermal diffusivity and volumetric heat capacity of insulators, conductor liquids3 and high-TC superconductors4. The tps-sensor consists of a resistive element in the shape of double spiral made of 10 micrometer thick Ni-foils covered on both sides with 25 micrometer thick Kapton. This sensor acts both as a heat source and a resistance thermometer for recording the time dependent temperature increase. From the knowledge of the temperature co-efficient of the metal spiral, the temperature increase of the sensor can be determined precisely by placing the sensor in between two surfaces of the same material under test. This temperature increase is then related to the thermal conductivity, thermal diffusivity and volumetric heat capacity by simple relations2,5. The tps-sensor has been used to measure thermal conductivities from 0.001 Wm-1K-1to 600 Wm-1K-1 and temperature ranges covered from 77K- 1000K. This talk gives the design, advantages and limitations of the tpl-sensor along with its applications to the measurementof thermal properties in a variety of materials.

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

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

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

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.

Optical processing furnace with quartz muffle and diffuser plate

DOEpatents

Sopori, Bhushan L.

1995-01-01

An optical furnace for annealing a process wafer comprising a source of optical energy, a quartz muffle having a door to hold the wafer for processing, and a quartz diffuser plate to diffuse the light impinging on the quartz muffle; a feedback system with a light sensor located in the door or wall of the muffle is also provided for controlling the source of optical energy. The quartz for the diffuser plate is surface etched (to give the quartz diffusive qualities) in the furnace during a high intensity burn-in process.

Aseismic Slip of a Thin Slab Due to a Fluid Source

NASA Astrophysics Data System (ADS)

Aubin, P. W.; Viesca, R. C.

2017-12-01

We explore the effects of an increase of pore pressure on the frictional interface along the base of a thin slab. The thin slab approximation corresponds to a layer overriding a substrate in which variations along the layer's length occur over distances much greater than the layer thickness. We consider deformation that may be in-plane or anti-plane, but approximately uniform in depth, such that spatial variations of displacement (and hence, slip) occur only along one direction parallel to the interface. Such a thin-sheet model may well represent the deformation of landslides and glacial ice streams, and also serves as a first-pass for fault systems, which, while better represented by elastic half-spaces in frictional contact, nonetheless show qualitatively similar behavior. We consider that the friction coefficient at the layer's interface remains (approximately) constant, and that aseismic slip is initiated by a (line) source of fluid at constant pressure, with one-dimensional diffusion parallel to the interface. As posed, the problem yields a self-similar expansion of slip, whose extent grows proportionally to (α * t)^(1/2) (where α is the hydraulic diffusivity) and can either lag behind or outpace the fluid diffusion front. The problem is controlled by a single parameter, accounting for the friction coefficient and the initial (pre-injection) states of stress and pore pressure. The problem solution consists of the self-similar slip profile and the coefficient of proportionality for the crack-front motion. Within the problem parameter range, two end-member scenarios result: one in which the initial level of shear stress on the interface is close to the value of the pre-injection strength (critically stressed) or another in which fluid pressure is just enough to induce slip (marginally pressurized). For the critically stressed and marginally pressurized cases, the aseismic slip front lies far ahead or far behind, respectively, the fluid diffusion front. We find

Scanning, non-contact, hybrid broadband diffuse optical spectroscopy and diffuse correlation spectroscopy system.

PubMed

Johansson, Johannes D; Mireles, Miguel; Morales-Dalmau, Jordi; Farzam, Parisa; Martínez-Lozano, Mar; Casanovas, Oriol; Durduran, Turgut

2016-02-01

A scanning system for small animal imaging using non-contact, hybrid broadband diffuse optical spectroscopy (ncDOS) and diffuse correlation spectroscopy (ncDCS) is presented. The ncDOS uses a two-dimensional spectrophotometer retrieving broadband (610-900 nm) spectral information from up to fifty-seven source-detector distances between 2 and 5 mm. The ncDCS data is simultaneously acquired from four source-detector pairs. The sample is scanned in two dimensions while tracking variations in height. The system has been validated with liquid phantoms, demonstrated in vivo on a human fingertip during an arm cuff occlusion and on a group of mice with xenoimplanted renal cell carcinoma.

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.

Artificial neural networks for retrieving absorption and reduced scattering spectra from frequency-domain diffuse reflectance spectroscopy at short source-detector separation

PubMed Central

Chen, Yu-Wen; Chen, Chien-Chih; Huang, Po-Jung; Tseng, Sheng-Hao

2016-01-01

Diffuse reflectance spectroscopy (DRS) based on the frequency-domain (FD) technique has been employed to investigate the optical properties of deep tissues such as breast and brain using source to detector separation up to 40 mm. Due to the modeling and system limitations, efficient and precise determination of turbid sample optical properties from the FD diffuse reflectance acquired at a source-detector separation (SDS) of around 1 mm has not been demonstrated. In this study, we revealed that at SDS of 1 mm, acquiring FD diffuse reflectance at multiple frequencies is necessary for alleviating the influence of inevitable measurement uncertainty on the optical property recovery accuracy. Furthermore, we developed artificial neural networks (ANNs) trained by Monte Carlo simulation generated databases that were capable of efficiently determining FD reflectance at multiple frequencies. The ANNs could work in conjunction with a least-square optimization algorithm to rapidly (within 1 second), accurately (within 10%) quantify the sample optical properties from FD reflectance measured at SDS of 1 mm. In addition, we demonstrated that incorporating the steady-state apparatus into the FD DRS system with 1 mm SDS would enable obtaining broadband absorption and reduced scattering spectra of turbid samples in the wavelength range from 650 to 1000 nm. PMID:27446671

A comparison of Fick and Maxwell-Stefan diffusion formulations in PEMFC gas diffusion layers

NASA Astrophysics Data System (ADS)

Lindstrom, Michael; Wetton, Brian

2017-01-01

This paper explores the mathematical formulations of Fick and Maxwell-Stefan diffusion in the context of polymer electrolyte membrane fuel cell cathode gas diffusion layers. The simple Fick law with a diagonal diffusion matrix is an approximation of Maxwell-Stefan. Formulations of diffusion combined with mass-averaged Darcy flow are considered for three component gases. For this application, the formulations can be compared computationally in a simple, one dimensional setting. Despite the models' seemingly different structure, it is observed that the predictions of the formulations are very similar on the cathode when air is used as oxidant. The two formulations give quite different results when the Nitrogen in the air oxidant is replaced by helium (this is often done as a diagnostic for fuel cells designs). The two formulations also give quite different results for the anode with a dilute Hydrogen stream. These results give direction to when Maxwell-Stefan diffusion, which is more complicated to implement computationally in many codes, should be used in fuel cell simulations.

Optimal approximation of harmonic growth clusters by orthogonal polynomials

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

Teodorescu, Razvan

2008-01-01

Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoreticaI model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows), to the granular dynamics of hard spheres, and even diffusion-limited aggregation. Although a complete solution for the continuum case exists, efficient approximations of the boundary evolution are very useful due to their practical applications. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel is discussed, as well as relations to potential theory.

Field-scale forward and back diffusion through low-permeability zones

NASA Astrophysics Data System (ADS)

Yang, Minjune; Annable, Michael D.; Jawitz, James W.

2017-07-01

Understanding the effects of back diffusion of groundwater contaminants from low-permeability zones to aquifers is critical to making site management decisions related to remedial actions. Here, we combine aquifer and aquitard data to develop recommended site characterization strategies using a three-stage classification of plume life cycle based on the solute origins: aquifer source zone dissolution, source zone dissolution combined with back diffusion from an aquitard, and only back diffusion. We use measured aquitard concentration profile data from three field sites to identify signature shapes that are characteristic of these three stages. We find good fits to the measured data with analytical solutions that include the effects of advection and forward and back diffusion through low-permeability zones, and linearly and exponentially decreasing flux resulting from source dissolution in the aquifer. Aquifer contaminant time series data at monitoring wells from a mature site were well described using analytical solutions representing the combined case of source zone and back diffusion, while data from a site where the source had been isolated were well described solely by back diffusion. The modeling approach presented in this study is designed to enable site managers to implement appropriate remediation technologies at a proper timing for high- and low-permeability zones, considering estimated plume life cycle.

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

NASA Astrophysics Data System (ADS)

Shi, Fan; Lowe, Mike; Craster, Richard

2017-06-01

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

J1649+2635: A Grand-Design Spiral with a Large Double-Lobed Radio Source

NASA Technical Reports Server (NTRS)

Mao, Minnie Y.; Owen, Frazer; Duffin, Ryan; Keel, Bill; Lacy, Mark; Momjian, Emmanuel; Morrison, Glenn; Mroczkowski, Tony; Neff, Susan; Norris, Ray P.;

The Linear Mixing Approximation for Planetary Ices

NASA Astrophysics Data System (ADS)

Bethkenhagen, M.; Meyer, E. R.; Hamel, S.; Nettelmann, N.; French, M.; Scheibe, L.; Ticknor, C.; Collins, L. A.; Kress, J. D.; Fortney, J. J.; Redmer, R.

2017-12-01

We investigate the validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices, which are thought to dominate the interior of the ice giant planets Uranus and Neptune. For that purpose we perform density functional theory molecular dynamics simulations using the VASP code.[1] In particular, we compute 1:1 binary mixtures of water, ammonia, and methane, as well as their 2:1:4 ternary mixture at pressure-temperature conditions typical for the interior of Uranus and Neptune.[2,3] In addition, a new ab initio EOS for methane is presented. The linear mixing approximation is verified for the conditions present inside Uranus ranging up to 10 Mbar based on the comprehensive EOS data set. We also calculate the diffusion coefficients for the ternary mixture along different Uranus interior profiles and compare them to the values of the pure compounds. We find that deviations of the linear mixing approximation from the real mixture are generally small; for the EOS they fall within about 4% uncertainty while the diffusion coefficients deviate up to 20% . The EOS of planetary ices are applied to adiabatic models of Uranus. It turns out that a deep interior of almost pure ices is consistent with the gravity field data, in which case the planet becomes rather cold (T core ˜ 4000 K). [1] G. Kresse and J. Hafner, Physical Review B 47, 558 (1993). [2] R. Redmer, T.R. Mattsson, N. Nettelmann and M. French, Icarus 211, 798 (2011). [3] N. Nettelmann, K. Wang, J. J. Fortney, S. Hamel, S. Yellamilli, M. Bethkenhagen and R. Redmer, Icarus 275, 107 (2016).

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.

Light distribution modulated diffuse reflectance spectroscopy.

PubMed

Huang, Pin-Yuan; Chien, Chun-Yu; Sheu, Chia-Rong; Chen, Yu-Wen; Tseng, Sheng-Hao

2016-06-01

Typically, a diffuse reflectance spectroscopy (DRS) system employing a continuous wave light source would need to acquire diffuse reflectances measured at multiple source-detector separations for determining the absorption and reduced scattering coefficients of turbid samples. This results in a multi-fiber probe structure and an indefinite probing depth. Here we present a novel DRS method that can utilize a few diffuse reflectances measured at one source-detector separation for recovering the optical properties of samples. The core of innovation is a liquid crystal (LC) cell whose scattering property can be modulated by the bias voltage. By placing the LC cell between the light source and the sample, the spatial distribution of light in the sample can be varied as the scattering property of the LC cell modulated by the bias voltage, and this would induce intensity variation of the collected diffuse reflectance. From a series of Monte Carlo simulations and phantom measurements, we found that this new light distribution modulated DRS (LDM DRS) system was capable of accurately recover the absorption and scattering coefficients of turbid samples and its probing depth only varied by less than 3% over the full bias voltage variation range. Our results suggest that this LDM DRS platform could be developed to various low-cost, efficient, and compact systems for in-vivo superficial tissue investigation.

Light distribution modulated diffuse reflectance spectroscopy

PubMed Central

Huang, Pin-Yuan; Chien, Chun-Yu; Sheu, Chia-Rong; Chen, Yu-Wen; Tseng, Sheng-Hao

2016-01-01

Typically, a diffuse reflectance spectroscopy (DRS) system employing a continuous wave light source would need to acquire diffuse reflectances measured at multiple source-detector separations for determining the absorption and reduced scattering coefficients of turbid samples. This results in a multi-fiber probe structure and an indefinite probing depth. Here we present a novel DRS method that can utilize a few diffuse reflectances measured at one source-detector separation for recovering the optical properties of samples. The core of innovation is a liquid crystal (LC) cell whose scattering property can be modulated by the bias voltage. By placing the LC cell between the light source and the sample, the spatial distribution of light in the sample can be varied as the scattering property of the LC cell modulated by the bias voltage, and this would induce intensity variation of the collected diffuse reflectance. From a series of Monte Carlo simulations and phantom measurements, we found that this new light distribution modulated DRS (LDM DRS) system was capable of accurately recover the absorption and scattering coefficients of turbid samples and its probing depth only varied by less than 3% over the full bias voltage variation range. Our results suggest that this LDM DRS platform could be developed to various low-cost, efficient, and compact systems for in-vivo superficial tissue investigation. PMID:27375931

Rumor diffusion model with spatio-temporal diffusion and uncertainty of behavior decision in complex social networks

NASA Astrophysics Data System (ADS)

Zhu, Liang; Wang, Youguo

2018-07-01

In this paper, a rumor diffusion model with uncertainty of human behavior under spatio-temporal diffusion framework is established. Take physical significance of spatial diffusion into account, a diffusion threshold is set under which the rumor is not a trend topic and only spreads along determined physical connections. Heterogeneity of degree distribution and distance distribution has also been considered in theoretical model at the same time. The global existence and uniqueness of classical solution are proved with a Lyapunov function and an approximate classical solution in form of infinite series is constructed with a system of eigenfunction. Simulations and numerical solutions both on Watts-Strogatz (WS) network and Barabási-Albert (BA) network display the variation of density of infected connections from spatial and temporal dimensions. Relevant results show that the density of infected connections is dominated by network topology and uncertainty of human behavior at threshold time. With increase of social capability, rumor diffuses to the steady state in a higher speed. And the variation trends of diffusion size with uncertainty are diverse on different artificial networks.

Back-diffusion plasma generator for ionosphere study

NASA Astrophysics Data System (ADS)

Fang, H. K.; Oyama, K.-I.; Chen, A. B.

2017-11-01

To produce ionospheric plasma environments at ground level is essential to get information not only for the development of CubeSat-class spacecraft but also for the design of ionospheric plasma instruments and to confirm their performance. In this paper, we describe the principle of plasma generation and characteristics of the back-diffusion plasma source, which can produce in-lab plasma similar to the Earth’s ionosphere, E and F regions, conditions of electron and ion temperature and density. The ion and electron energy distributions of the plasma generated by a back-diffusion source are measured by means of a cleaned Langmuir probe and gridded particle energy analyzers. The ion motion in front of the source is investigated by a hard-sphere collision model in SIMION software and the simulation results are comparable with the findings of our experiment. Furthermore, plasma densities and ion temperatures at different positions in front of the source are also demonstrated. The back-diffusion source has been accommodated for ionospheric plasma productions in several Asian institutes. The plasma characteristics of the source shown in this paper will benefit space research groups in the development of space plasma instruments.

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.

On the asymptotic behavior of a subcritical convection-diffusion equation with nonlocal diffusion

NASA Astrophysics Data System (ADS)

Cazacu, Cristian M.; Ignat, Liviu I.; Pazoto, Ademir F.

2017-08-01

In this paper we consider a subcritical model that involves nonlocal diffusion and a classical convective term. In spite of the nonlocal diffusion, we obtain an Oleinik type estimate similar to the case when the diffusion is local. First we prove that the entropy solution can be obtained by adding a small viscous term μ uxx and letting μ\\to 0 . Then, by using uniform Oleinik estimates for the viscous approximation we are able to prove the well-posedness of the entropy solutions with L 1-initial data. Using a scaling argument and hyperbolic estimates given by Oleinik’s inequality, we obtain the first term in the asymptotic behavior of the nonnegative solutions. Finally, the large time behavior of changing sign solutions is proved using the classical flux-entropy method and estimates for the nonlocal operator.

Cochlear Implant Microphone Location Affects Speech Recognition in Diffuse Noise

PubMed Central

Kolberg, Elizabeth R.; Sheffield, Sterling W.; Davis, Timothy J.; Sunderhaus, Linsey W.; Gifford, René H.

2015-01-01

Background Despite improvements in cochlear implants (CIs), CI recipients continue to experience significant communicative difficulty in background noise. Many potential solutions have been proposed to help increase signal-to-noise ratio in noisy environments, including signal processing and external accessories. To date, however, the effect of microphone location on speech recognition in noise has focused primarily on hearing aid users. Purpose The purpose of this study was to (1) measure physical output for the T-Mic as compared with the integrated behind-the-ear(BTE) processor mic for various source azimuths, and (2) to investigate the effect of CI processor mic location for speech recognition in semi-diffuse noise with speech originating from various source azimuths as encountered in everyday communicative environments. Research Design A repeated-measures, within-participant design was used to compare performance across listening conditions. Study Sample A total of 11 adults with Advanced Bionics CIs were recruited for this study. Data Collection and Analysis Physical acoustic output was measured on a Knowles Experimental Mannequin for Acoustic Research (KEMAR) for the T-Mic and BTE mic, with broadband noise presented at 0 and 90° (directed toward the implant processor). In addition to physical acoustic measurements, we also assessed recognition of sentences constructed by researchers at Texas Instruments, the Massachusetts Institute of Technology, and the Stanford Research Institute (TIMIT sentences) at 60 dBA for speech source azimuths of 0, 90, and 270°. Sentences were presented in a semi-diffuse restaurant noise originating from the R-SPACE 8-loudspeaker array. Signal-to-noise ratio was determined individually to achieve approximately 50% correct in the unilateral implanted listening condition with speech at 0°. Performance was compared across the T-Mic, 50/50, and the integrated BTE processor mic. Results The integrated BTE mic provided approximately 5

Cochlear implant microphone location affects speech recognition in diffuse noise.

PubMed

Kolberg, Elizabeth R; Sheffield, Sterling W; Davis, Timothy J; Sunderhaus, Linsey W; Gifford, René H

2015-01-01

Despite improvements in cochlear implants (CIs), CI recipients continue to experience significant communicative difficulty in background noise. Many potential solutions have been proposed to help increase signal-to-noise ratio in noisy environments, including signal processing and external accessories. To date, however, the effect of microphone location on speech recognition in noise has focused primarily on hearing aid users. The purpose of this study was to (1) measure physical output for the T-Mic as compared with the integrated behind-the-ear (BTE) processor mic for various source azimuths, and (2) to investigate the effect of CI processor mic location for speech recognition in semi-diffuse noise with speech originating from various source azimuths as encountered in everyday communicative environments. A repeated-measures, within-participant design was used to compare performance across listening conditions. A total of 11 adults with Advanced Bionics CIs were recruited for this study. Physical acoustic output was measured on a Knowles Experimental Mannequin for Acoustic Research (KEMAR) for the T-Mic and BTE mic, with broadband noise presented at 0 and 90° (directed toward the implant processor). In addition to physical acoustic measurements, we also assessed recognition of sentences constructed by researchers at Texas Instruments, the Massachusetts Institute of Technology, and the Stanford Research Institute (TIMIT sentences) at 60 dBA for speech source azimuths of 0, 90, and 270°. Sentences were presented in a semi-diffuse restaurant noise originating from the R-SPACE 8-loudspeaker array. Signal-to-noise ratio was determined individually to achieve approximately 50% correct in the unilateral implanted listening condition with speech at 0°. Performance was compared across the T-Mic, 50/50, and the integrated BTE processor mic. The integrated BTE mic provided approximately 5 dB attenuation from 1500-4500 Hz for signals presented at 0° as compared with 90�

The effect of a realistic thermal diffusivity on numerical model of a subducting slab

NASA Astrophysics Data System (ADS)

Maierova, P.; Steinle-Neumann, G.; Cadek, O.

2010-12-01

A number of numerical studies of subducting slab assume simplified (constant or only depth-dependent) models of thermal conductivity. The available mineral physics data indicate, however, that thermal diffusivity is strongly temperature- and pressure-dependent and may also vary among different mantle materials. In the present study, we examine the influence of realistic thermal properties of mantle materials on the thermal state of the upper mantle and the dynamics of subducting slabs. On the basis of the data published in mineral physics literature we compile analytical relationships that approximate the pressure and temperature dependence of thermal diffusivity for major mineral phases of the mantle (olivine, wadsleyite, ringwoodite, garnet, clinopyroxenes, stishovite and perovskite). We propose a simplified composition of mineral assemblages predominating in the subducting slab and the surrounding mantle (pyrolite, mid-ocean ridge basalt, harzburgite) and we estimate their thermal diffusivity using the Hashin-Shtrikman bounds. The resulting complex formula for the diffusivity of each aggregate is then approximated by a simpler analytical relationship that is used in our numerical model as an input parameter. For the numerical modeling we use the Elmer software (open source finite element software for multiphysical problems, see http://www.csc.fi/english/pages/elmer). We set up a 2D Cartesian thermo-mechanical steady-state model of a subducting slab. The model is partly kinematic as the flow is driven by a boundary condition on velocity that is prescribed on the top of the subducting lithospheric plate. Reology of the material is non-linear and is coupled with the thermal equation. Using the realistic relationship for thermal diffusivity of mantle materials, we compute the thermal and flow fields for different input velocity and age of the subducting plate and we compare the results against the models assuming a constant thermal diffusivity. The importance of the

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.

Objective and Subjective Evaluation of Reflecting and Diffusing Surfaces in Auditoria

NASA Astrophysics Data System (ADS)

Cox, Trevor John

Available from UMI in association with The British Library. Requires signed TDF. The performance of reflectors and diffusers used in auditoria have been evaluated both objectively and subjectively. Two accurate systems have been developed to measure the scattering from surfaces via the cross correlation function. These have been used to measure the scattering from plane panels, curved panels and quadratic residue diffusers (QRDs). The scattering measurements have been used to test theoretical prediction methods based on the Helmholtz-Kirchhoff integral equation. Accurate prediction methods were found for all surfaces tested. The limitations of the more approximate methods have been defined. The assumptions behind Schroeder's design of the QRD have been tested and the local reacting admittance assumption found to be valid over a wide frequency range. It was found that the QRD only produces uniform scattering at low frequencies. For an on-axis source the scattering from a curved panel was as good as from a QRD. For an oblique source the QRD produced much more uniform scattering than the curved panel. The subjective measurements evaluated the smallest perceivable change in the early sound field, the part most influenced by reflectors and diffusers. A natural sounding simulation of a concert hall field within an anechoic chamber was used. Standard objective parameters were reasonable values when compared to values found in real halls and subjective preference measurements. A difference limen was measured for early lateral energy fraction (.048 +/-.005); inter aural cross correlation (.075 +/-.008); clarity index (.67 +/-.13 dB); and centre time (8.6 +/- 1.6 ms). It was found that: (i) when changes are made to diffusers and reflectors, changes in spatial impression will usually be larger than those in clarity; and (ii) acousticians can gain most by paying attention to lateral sound in auditoria. It was also found that: (i) diffuse reflections in the early sound field

Diffusion in random networks

DOE PAGES

Zhang, Duan Z.; Padrino, Juan C.

2017-06-01

The ensemble 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 pockets connected by tortuous channels. Inside a channel, fluid transport is assumed to be governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pocket 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,more » we consider the one-dimensional mass diffusion in a semi-infinite domain. 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. We found this early time similarity can be explained by random walk theory through the network.« less

Radiation hydrodynamics of triggered star formation: the effect of the diffuse radiation field

NASA Astrophysics Data System (ADS)

Haworth, Thomas J.; Harries, Tim J.

2012-02-01

We investigate the effect of including diffuse field radiation when modelling the radiatively driven implosion of a Bonnor-Ebert sphere (BES). Radiation-hydrodynamical calculations are performed by using operator splitting to combine Monte Carlo photoionization with grid-based Eulerian hydrodynamics that includes self-gravity. It is found that the diffuse field has a significant effect on the nature of radiatively driven collapse which is strongly coupled to the strength of the driving shock that is established before impacting the BES. This can result in either slower or more rapid star formation than expected using the on-the-spot approximation depending on the distance of the BES from the source object. As well as directly compressing the BES, stronger shocks increase the thickness and density in the shell of accumulated material, which leads to short, strong, photoevaporative ejections that reinforce the compression whenever it slows. This happens particularly effectively when the diffuse field is included as rocket motion is induced over a larger area of the shell surface. The formation and evolution of 'elephant trunks' via instability is also found to vary significantly when the diffuse field is included. Since the perturbations that seed instabilities are smeared out elephant trunks form less readily and, once formed, are exposed to enhanced thermal compression.

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.

HOW FAR AWAY ARE THE SOURCES OF ICECUBE NEUTRINOS? CONSTRAINTS FROM THE DIFFUSE TERAELECTRONVOLT GAMMA-RAY BACKGROUND

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

Chang, Xiao-Chuan; Liu, Ruo-Yu; Wang, Xiang-Yu, E-mail: xywang@nju.edu.cn

The nearly isotropic distribution of teraelectronvolt to petaelectronvolt neutrinos recently detected by the IceCube Collaboration suggests that they come from sources at a distance beyond our Galaxy, but how far away they are is largely unknown because of a lack of any associations with known sources. In this paper, we propose that the cumulative TeV gamma-ray emission accompanying the production of neutrinos can be used to constrain the distance of these neutrino sources, since the opacity of TeV gamma rays due to absorption by the extragalactic background light depends on the distance these TeV gamma rays have traveled. As themore » diffuse extragalactic TeV background measured by Fermi is much weaker than the expected cumulative flux associated with IceCube neutrinos, the majority of IceCube neutrinos, if their sources are transparent to TeV gamma rays, must come from distances larger than the horizon of TeV gamma rays. We find that above 80% of the IceCube neutrinos should come from sources at redshift z > 0.5. Thus, the chance of finding nearby sources correlated with IceCube neutrinos would be small. We also find that, to explain the flux of neutrinos under the TeV gamma-ray emission constraint, the redshift evolution of neutrino source density must be at least as fast as the cosmic star formation rate.« less

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

Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times.

Field-scale forward and back diffusion through low-permeability zones.

PubMed

Yang, Minjune; Annable, Michael D; Jawitz, James W

2017-07-01

Understanding the effects of back diffusion of groundwater contaminants from low-permeability zones to aquifers is critical to making site management decisions related to remedial actions. Here, we combine aquifer and aquitard data to develop recommended site characterization strategies using a three-stage classification of plume life cycle based on the solute origins: aquifer source zone dissolution, source zone dissolution combined with back diffusion from an aquitard, and only back diffusion. We use measured aquitard concentration profile data from three field sites to identify signature shapes that are characteristic of these three stages. We find good fits to the measured data with analytical solutions that include the effects of advection and forward and back diffusion through low-permeability zones, and linearly and exponentially decreasing flux resulting from source dissolution in the aquifer. Aquifer contaminant time series data at monitoring wells from a mature site were well described using analytical solutions representing the combined case of source zone and back diffusion, while data from a site where the source had been isolated were well described solely by back diffusion. The modeling approach presented in this study is designed to enable site managers to implement appropriate remediation technologies at a proper timing for high- and low-permeability zones, considering estimated plume life cycle. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

Combining Land Use Information and Small Stream Sampling with PCR-Based Methods for Better Characterization of Diffuse Sources of Human Fecal Pollution

EPA Science Inventory

Diffuse sources of human fecal pollution allow for the direct discharge of waste into receiving waters with minimal or no treatment. Traditional culture-based methods are commonly used to characterize fecal pollution in ambient waters, however these methods do not discern between...

Possible effects of free convection on fire behavior - laminar and turbulent line and point sources of heat

Treesearch

S. Scesa; F. M. Sauer

1954-01-01

The transfer theory is applied to the problem of atmospheric diffusion of momentum and heat induced by line and point sources of heat on the surface of the earth. In order that the validity of the approximations of the boundary layer theory be realized, the thickness of the layer in which the temperatures and velocities differ appreciably from the values at...

Multi-Component Diffusion with Application To Computational Aerothermodynamics

NASA Technical Reports Server (NTRS)

Sutton, Kenneth; Gnoffo, Peter A.

1998-01-01

The accuracy and complexity of solving multicomponent gaseous diffusion using the detailed multicomponent equations, the Stefan-Maxwell equations, and two commonly used approximate equations have been examined in a two part study. Part I examined the equations in a basic study with specified inputs in which the results are applicable for many applications. Part II addressed the application of the equations in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) computational code for high-speed entries in Earth's atmosphere. The results showed that the presented iterative scheme for solving the Stefan-Maxwell equations is an accurate and effective method as compared with solutions of the detailed equations. In general, good accuracy with the approximate equations cannot be guaranteed for a species or all species in a multi-component mixture. 'Corrected' forms of the approximate equations that ensured the diffusion mass fluxes sum to zero, as required, were more accurate than the uncorrected forms. Good accuracy, as compared with the Stefan- Maxwell results, were obtained with the 'corrected' approximate equations in defining the heating rates for the three Earth entries considered in Part II.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. PMID:23365552

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...

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.

Inverse Diffusion Curves Using Shape Optimization.

PubMed

Zhao, Shuang; Durand, Fredo; Zheng, Changxi

2018-07-01

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

Electrostatic interactions between diffuse soft multi-layered (bio)particles: beyond Debye-Hückel approximation and Deryagin formulation.

PubMed

Duval, Jérôme F L; Merlin, Jenny; Narayana, Puranam A L

2011-01-21

We report a steady-state theory for the evaluation of electrostatic interactions between identical or dissimilar spherical soft multi-layered (bio)particles, e.g. microgels or microorganisms. These generally consist of a rigid core surrounded by concentric ion-permeable layers that may differ in thickness, soft material density, chemical composition and degree of dissociation for the ionogenic groups. The formalism allows the account of diffuse interphases where distributions of ionogenic groups from one layer to the other are position-dependent. The model is valid for any number of ion-permeable layers around the core of the interacting soft particles and covers all limiting situations in terms of nature of interacting particles, i.e. homo- and hetero-interactions between hard, soft or entirely porous colloids. The theory is based on a rigorous numerical solution of the non-linearized Poisson-Boltzmann equation including radial and angular distortions of the electric field distribution within and outside the interacting soft particles in approach. The Gibbs energy of electrostatic interaction is obtained from a general expression derived following the method by Verwey and Overbeek based on appropriate electric double layer charging mechanisms. Original analytical solutions are provided here for cases where interaction takes place between soft multi-layered particles whose size and charge density are in line with Deryagin treatment and Debye-Hückel approximation. These situations include interactions between hard and soft particles, hard plate and soft particle or soft plate and soft particle. The flexibility of the formalism is highlighted by the discussion of few situations which clearly illustrate that electrostatic interaction between multi-layered particles may be partly or predominantly governed by potential distribution within the most internal layers. A major consequence is that both amplitude and sign of Gibbs electrostatic interaction energy may

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.

Electrochemical Ionization and Analyte Charging in the Array of Micromachined UltraSonic Electrospray (AMUSE) Ion Source

PubMed Central

Forbes, Thomas P.; Degertekin, F. Levent; Fedorov, Andrei G.

2010-01-01

Electrochemistry and ion transport in a planar array of mechanically-driven, droplet-based ion sources are investigated using an approximate time scale analysis and in-depth computational simulations. The ion source is modeled as a controlled-current electrolytic cell, in which the piezoelectric transducer electrode, which mechanically drives the charged droplet generation using ultrasonic atomization, also acts as the oxidizing/corroding anode (positive mode). The interplay between advective and diffusive ion transport of electrochemically generated ions is analyzed as a function of the transducer duty cycle and electrode location. A time scale analysis of the relative importance of advective vs. diffusive ion transport provides valuable insight into optimality, from the ionization prospective, of alternative design and operation modes of the ion source operation. A computational model based on the solution of time-averaged, quasi-steady advection-diffusion equations for electroactive species transport is used to substantiate the conclusions of the time scale analysis. The results show that electrochemical ion generation at the piezoelectric transducer electrodes located at the back-side of the ion source reservoir results in poor ionization efficiency due to insufficient time for the charged analyte to diffuse away from the electrode surface to the ejection location, especially at near 100% duty cycle operation. Reducing the duty cycle of droplet/analyte ejection increases the analyte residence time and, in turn, improves ionization efficiency, but at an expense of the reduced device throughput. For applications where this is undesirable, i.e., multiplexed and disposable device configurations, an alternative electrode location is incorporated. By moving the charging electrode to the nozzle surface, the diffusion length scale is greatly reduced, drastically improving ionization efficiency. The ionization efficiency of all operating conditions considered is

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.

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.

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

Quasiballistic heat removal from small sources studied from first principles

NASA Astrophysics Data System (ADS)

Vermeersch, Bjorn; Mingo, Natalio

2018-01-01

Heat sources whose characteristic dimension R is comparable to phonon mean free paths display thermal resistances that exceed conventional diffusive predictions. This has direct implications to (opto)electronics thermal management and phonon spectroscopy. Theoretical analyses have so far limited themselves to particular experimental configurations. Here, we build upon the multidimensional Boltzmann transport equation (BTE) to derive universal expressions for the apparent conductivity suppression S (R ) =κeff(R ) /κbulk experienced by radially symmetric 2D and 3D sources. In striking analogy to cross-plane heat conduction in thin films, a distinct quasiballistic regime emerges between ballistic (κeff˜R ) and diffusive (κeff≃κbulk ) asymptotes that displays a logarithmic dependence κeff˜ln(R ) in single crystals and fractional power dependence κeff˜R2 -α in alloys (with α the Lévy superdiffusion exponent). Analytical solutions and Monte Carlo simulations for spherical and circular heat sources in Si, GaAs, Si0.99Ge0.01 , and Si0.82Ge0.18 , all carried out from first principles, confirm the predicted generic tendencies. Contrary to the thin film case, common approximations like kinetic theory estimates κeff≃∑Sωgreyκω and modified Fourier temperature curves perform relatively poorly. Up to threefold deviations from the BTE solutions for sub-100 nm sources underline the need for rigorous treatment of multidimensional nondiffusive transport.

Uncertainty Quantification For Physical and Numerical Diffusion Models In Inertial Confinement Fusion Simulations

NASA Astrophysics Data System (ADS)

Rana, Verinder S.

This thesis concerns simulations of Inertial Confinement Fusion. Inertial confinement is carried out in a large scale facility at National Ignition Facility. The experiments have failed to reproduce design calculations, and so uncertainty quantification of calculations is an important asset. Uncertainties can be classified as aleatoric or epistemic. This thesis is concerned with aleatoric uncertainty quantification. Among the many uncertain aspects that affect the simulations, we have narrowed our study of possible uncertainties. The first source of uncertainty we present is the amount of pre-heating of the fuel done by hot electrons. The second source of uncertainty we consider is the effect of the algorithmic and physical transport diffusion and their effect on the hot spot thermodynamics. Physical transport mechanisms play an important role for the entire duration of the ICF capsule, so modeling them correctly becomes extremely vital. In addition, codes that simulate material mixing introduce numerical (algorithmically) generated transport across the material interfaces. This adds another layer of uncertainty in the solution through the artificially added diffusion. The third source of uncertainty we consider is physical model uncertainty. The fourth source of uncertainty we focus on a single localized surface perturbation (a divot) which creates a perturbation to the solution that can potentially enter the hot spot to diminish the thermonuclear environment. Jets of ablator material are hypothesized to enter the hot spot and cool the core, contributing to the observed lower reactions than predicted levels. A plasma transport package, Transport for Inertial Confinement Fusion (TICF) has been implemented into the Radiation Hydrodynamics code FLASH, from the University of Chicago. TICF has thermal, viscous and mass diffusion models that span the entire ICF implosion regime. We introduced a Quantum Molecular Dynamics calibrated thermal conduction model due to Hu for

Proton-driven spin diffusion in rotating solids via reversible and irreversible quantum dynamics

PubMed Central

Veshtort, Mikhail; Griffin, Robert G.

2011-01-01

Proton-driven spin diffusion (PDSD) experiments in rotating solids have received a great deal of attention as a potential source of distance constraints in large biomolecules. However, the quantitative relationship between the molecular structure and observed spin diffusion has remained obscure due to the lack of an accurate theoretical description of the spin dynamics in these experiments. We start with presenting a detailed relaxation theory of PDSD in rotating solids that provides such a description. The theory applies to both conventional and radio-frequency-assisted PDSD experiments and extends to the non-Markovian regime to include such phenomena as rotational resonance (R2). The basic kinetic equation of the theory in the non-Markovian regime has the form of a memory function equation, with the role of the memory function played by the correlation function. The key assumption used in the derivation of this equation expresses the intuitive notion of the irreversible dissipation of coherences in macroscopic systems. Accurate expressions for the correlation functions and for the spin diffusion constants are given. The theory predicts that the spin diffusion constants governing the multi-site PDSD can be approximated by the constants observed in the two-site diffusion. Direct numerical simulations of PDSD dynamics via reversible Liouville-von Neumann equation are presented to support and compliment the theory. Remarkably, an exponential decay of the difference magnetization can be observed in such simulations in systems consisting of only 12 spins. This is a unique example of a real physical system whose typically macroscopic and apparently irreversible behavior can be traced via reversible microscopic dynamics. An accurate value for the spin diffusion constant can be usually obtained through direct simulations of PDSD in systems consisting of two 13C nuclei and about ten 1H nuclei from their nearest environment. Spin diffusion constants computed by this method

Novel Diffusivity Measurement Technique

NASA Technical Reports Server (NTRS)

Rashidnia, Nasser

2001-01-01

A common-path interferometer (CPI) system was developed to measure the diffusivity of liquid pairs. The CPI is an optical technique that can be used to measure changes in the gradient of the refraction index of transparent materials. This system uses a shearing interferometer that shares the same optical path from a laser light source to the final imaging plane. Hence, the molecular diffusion coefficient of liquids can be determined using the physical relations between changes in the optical path length and the liquid phase properties. The data obtained with this interferometer were compared with similar results from other techniques and demonstrated that the instrument is superior in measuring the diffusivity of miscible liquids while keeping the system very compact and robust. CPI can also be used for studies in interface dynamics and other diffusion-dominated-process applications.

Nonequilibrium diffusive gas dynamics: Poiseuille microflow

NASA Astrophysics Data System (ADS)

Abramov, Rafail V.; Otto, Jasmine T.

2018-05-01

We test the recently developed hierarchy of diffusive moment closures for gas dynamics together with the near-wall viscosity scaling on the Poiseuille flow of argon and nitrogen in a one micrometer wide channel, and compare it against the corresponding Direct Simulation Monte Carlo computations. We find that the diffusive regularized Grad equations with viscosity scaling provide the most accurate approximation to the benchmark DSMC results. At the same time, the conventional Navier-Stokes equations without the near-wall viscosity scaling are found to be the least accurate among the tested closures.

Study on gas diffusion emitted from different height of point source.

PubMed

Yassin, Mohamed F

2009-01-01

The flow and dispersion of stack-gas emitted from different elevated point source around flow obstacles in an urban environment have been investigated, using computational fluid dynamics models (CFD). The results were compared with the experimental results obtained from the diffusion wind tunnel under different conditions of thermal stability (stable, neutral or unstable). The flow and dispersion fields in the boundary layer in an urban environment were examined with different flow obstacles. Gaseous pollutant was discharged in the simulated boundary layer over the flat area. The CFD models used for the simulation were based on the steady-state Reynolds-Average Navier-Stoke equations (RANS) with kappa-epsilon turbulence models; standard kappa-epsilon and RNG kappa-epsilon models. The flow and dispersion data measured in the wind tunnel experiments were compared with the results of the CFD models in order to evaluate the prediction accuracy of the pollutant dispersion. The results of the CFD models showed good agreement with the results of the wind tunnel experiments. The results indicate that the turbulent velocity is reduced by the obstacles models. The maximum dispersion appears around the wake region of the obstacles.

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.

Approximation methods in gravitational-radiation theory

NASA Technical Reports Server (NTRS)

Will, C. M.

1986-01-01

The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.

The Use of LiDAR Elevation Data and Satellite Imagery to Locate Critical Source Areas to Diffuse Pollution in Agricultural Watersheds

NASA Astrophysics Data System (ADS)

Drouin, Ariane; Michaud, Aubert; Thériault, Georges; Beaudin, Isabelle; Rodrigue, Jean-François; Denault, Jean-Thomas; Desjardins, Jacques; Côté, Noémi

2013-04-01

In Quebec / Canada, water quality improvement in rural areas greatly depends on the reduction of diffuse pollution. Indeed, point source pollution has been reduced significantly in Canada in recent years by creating circumscribed pits for manure and removing animals from stream. Diffuse pollution differs from point source pollution because it is spread over large areas. In agricultural areas, sediment loss by soil and riverbank erosion along with loss of nutrients (phosphorus, nitrogen, etc.) and pesticides from fields represent the main source of non-point source pollution. The factor mainly responsible for diffuse pollution in agricultural areas is surface runoff occurring in poorly drained areas in fields. The presence of these poorly drained areas is also one of the most limiting factors in crop productivity. Thus, a reconciliation of objectives at the farm (financial concern for farmers) and off-farm concerns (environmental concern) is possible. In short, drainage, runoff, erosion, water quality and crop production are all interconnected issues that need to be tackled together. Two complementary data sources are mainly used in the diagnosis of drainage, surface runoff and erosion : elevation data and multispectral satellite images. In this study of two watersheds located in Québec (Canada), LiDAR elevation data and satellite imagery (QuickBird, Spot and Landsat) were acquired. The studied territories have been partitioned in hydrologic response units (HRUs) according to sub-basins, soils, elevation (topographic index) and land use. These HRUs are afterwards used in a P index software (P-Edit) that calculates the quantities of sediments and phosphorus exported from each HRUs. These exports of sediments and phosphorus are validated with hydrometric and water quality data obtain in two sub-basins and are also compared to soil brightness index derived from multispectral images. This index is sensitive to soil moisture and thus highlights areas where the soil is

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.

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.

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.

Reconstruction of thin fluorophore-filled capillaries in thick scattering medium using fluorescence diffuse optical tomography within the diffusion approximation

NASA Astrophysics Data System (ADS)

Desrochers, Johanne; Vermette, Patrick; Fontaine, Réjean; Bérubé-Lauzière, Yves

2009-02-01

Current efforts in tissue engineering target the growth of 3D volumes of tissue cultures in bioreactor conditions. Fluorescence optical tomography has the potential to monitor cells viability and tissue growth non-destructively directly within the bioreactor via bio-molecular fluorescent labelling strategies. We currently work on developing the imaging instrumentation for tissue cultures in bioreactor conditions. Previously, we localized in 3D thin fluorescent-labelled capillaries in a cylindrically shaped bioreactor phantom containing a diffusive medium with our time-of-flight localization technique. Here, we present our first reconstruction results of the spatial distribution of fluorophore concentrations for labelled capillaries embedded in a bioreactor phantom.

Atomistic models of vacancy-mediated diffusion in silicon

NASA Astrophysics Data System (ADS)

Dunham, Scott T.; Wu, Can Dong

1995-08-01

Vacancy-mediated diffusion of dopants in silicon is investigated using Monte Carlo simulations of hopping diffusion, as well as analytic approximations based on atomistic considerations. Dopant/vacancy interaction potentials are assumed to extend out to third-nearest neighbor distances, as required for pair diffusion theories. Analysis focusing on the third-nearest neighbor sites as bridging configurations for uncorrelated hops leads to an improved analytic model for vacancy-mediated dopant diffusion. The Monte Carlo simulations of vacancy motion on a doped silicon lattice verify the analytic results for moderate doping levels. For very high doping (≳2×1020 cm-3) the simulations show a very rapid increase in pair diffusivity due to interactions of vacancies with more than one dopant atom. This behavior has previously been observed experimentally for group IV and V atoms in silicon [Nylandsted Larsen et al., J. Appl. Phys. 73, 691 (1993)], and the simulations predict both the point of onset and doping dependence of the experimentally observed diffusivity enhancement.

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.

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

Reaction diffusion in the nickel-chromium-aluminum and cobalt-chromium-aluminum systems

NASA Technical Reports Server (NTRS)

Levine, S. R.

1977-01-01

The effects of MCrAl coating-substrate interdiffusion on oxidation life and the general mutliphase, multicomponent diffusion problem were examined. Semi-infinite diffusion couples that had sources representing coatings and sinks representing gas turbine alloys were annealed at 1,000, 1,095, 1,150, or 1,205 C for as long as 500 hours. The source and sink aluminum and chromium contents and the base metal (cobalt or nickel) determined the parabolic diffusion rate constants of the couples and predicted finite coating lives. The beta source strength concept provided a method (1) for correlating beta recession rate constants with composition; (2) for determining reliable average total, diffusion, and constitutional activation energies; and (3) for calculating interdiffusion coefficients.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

PubMed

Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L

2014-03-01

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.

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)…

Open-tube diffusion techniques for InP/LnGaAs heterojunctior bipolar transistors

NASA Astrophysics Data System (ADS)

Schuitemaker, P.; Houston, P. A.

1986-11-01

Open-tube diffusion techniques used between 450 and 600° C are described which involve the supply of diffusant from a vapour source (via a solution) and a solid evaporated metal source. Investigations of Zn into InP and InGaAs(P) have been undertaken using both sources. SIMS profile analyses show that in the case of the vapour source the profiles indicate a concentration-dependent diffusion coefficient while the solid source diffusions can be well described by a Gaussian-type profile. The usefulness of the vapour source method has been demonstrated in the fabrication of bipolar transistors which exhibit good d.c. characteristics. The solid source method is limited by the slow diffusion velocity and more gradual profile. The InGaAs(P)/InP materials system has important applications in optical communications and future high speed microwave and switching devices. Useful technologies allied to the introduction of impurities into Si by diffusion, have gradually been emerging for use in the III-V semiconductor family. Closed tube systems1 have been used in order to contain the volatile group V species and prevent surface erosion. In addition, simpler open tube systems2,3 have been developed that maintain a sufficient overpressure of the group V element. Zn and Cd p-dopants have been studied extensively because of the volatility and relatively large diffusion rates in III-V semiconductors. Opentube diffusion into both InP and InGaAs2-6 has been studied but little detail has appeared concerning InGaAs and InGaAsP. In this paper we describe a comprehensive study of the diffusion of Zn into InP and InGaAs(P) using both open-tube vapour source and a Au/Zn/Au evaporated solid source with SiNx acting both as a mask and also an encapsulant to prevent loss of Zn and decomposition of the substrate material. The techniques have been successfully applied to the fabrication of InP/lnGaAs heterojunction bipolar transistors which show good dc characteristics. Reference to InGaAs in

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

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone

2018-03-01

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas in two dimensions, viz. to the Kob-Andersen model on the square lattice.

Time-domain diffuse optics: towards next generation devices

NASA Astrophysics Data System (ADS)

Contini, Davide; Dalla Mora, Alberto; Arridge, Simon; Martelli, Fabrizio; Tosi, Alberto; Boso, Gianluca; Farina, Andrea; Durduran, Turgut; Martinenghi, Edoardo; Torricelli, Alessandro; Pifferi, Antonio

2015-07-01

Diffuse optics is a powerful tool for clinical applications ranging from oncology to neurology, but also for molecular imaging, and quality assessment of food, wood and pharmaceuticals. We show that ideally time-domain diffuse optics can give higher contrast and a higher penetration depth with respect to standard technology. In order to completely exploit the advantages of a time-domain system a distribution of sources and detectors with fast gating capabilities covering all the sample surface is needed. Here, we present the building block to build up such system. This basic component is made of a miniaturised source-detector pair embedded into the probe based on pulsed Vertical-Cavity Surface-Emitting Lasers (VCSEL) as sources and Single-Photon Avalanche Diodes (SPAD) or Silicon Photomultipliers (SiPM) as detectors. The possibility to miniaturized and dramatically increase the number of source detectors pairs open the way to an advancement of diffuse optics in terms of improvement of performances and exploration of new applications. Furthermore, availability of compact devices with reduction in size and cost can boost the application of this technique.

The Green's functions for peridynamic non-local diffusion.

PubMed

Wang, L J; Xu, J F; Wang, J X

2016-09-01

In this work, we develop the Green's function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green's functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green's functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems.

Feasibility of interstitial diffuse optical tomography using cylindrical diffusing fiber for prostate PDT

PubMed Central

Liang, Xing; Wang, Ken Kang-Hsin; Zhu, Timothy C.

2013-01-01

Interstitial diffuse optical tomography (DOT) has been used to characterize spatial distribution of optical properties for prostate photodynamic therapy (PDT) dosimetry. We have developed an interstitial DOT method using cylindrical diffuse fibers (CDFs) as light sources, so that the same light sources can be used for both DOT measurement and PDT treatment. In this novel interstitial CDF-DOT method, absolute light fluence per source strength (in unit of 1/cm2) is used to separate absorption and scattering coefficients. A mathematical phantom and a solid prostate phantom including anomalies with known optical properties were used, respectively, to test the feasibility of reconstructing optical properties using interstitial CDF-DOT. Three dimension spatial distributions of the optical properties were reconstructed for both scenarios. Our studies show that absorption coefficient can be reliably extrapolated while there are some cross talks between absorption and scattering properties. Even with the suboptimal reduced scattering coefficients, the reconstructed light fluence rate agreed with the measured values to within ±10%, thus the proposed CDF-DOT allows greatly improved light dosimetry calculation for interstitial PDT. PMID:23629149

Evolution Nonlinear Diffusion-Convection PDE Models for Spectrogram Enhancement

NASA Astrophysics Data System (ADS)

Dugnol, B.; Fernández, C.; Galiano, G.; Velasco, J.

2008-09-01

In previous works we studied the application of PDE-based image processing techniques applied to the spectrogram of audio signals in order to improve the readability of the signal. In particular we considered the implementation of the nonlinear diffusive model proposed by Álvarez, Lions and Morel [1](ALM) combined with a convective term inspired by the differential reassignment proposed by Chassandre-Mottin, Daubechies, Auger and Flandrin [2]-[3]. In this work we consider the possibility of replacing the diffusive model of ALM by diffusive terms in divergence form. In particular we implement finite element approximations of nonlinear diffusive terms studied by Chen, Levine, Rao [4] and Antontsev, Shmarev [5]-[8] with a convective term.

HI-bearing Ultra Diffuse Galaxies in the ALFALFA Survey

NASA Astrophysics Data System (ADS)

Leisman, Lukas; Janowiecki, Steven; Jones, Michael G.; ALFALFA Almost Darks Team

2018-01-01

The Arecibo Legacy Fast ALFA (Arecibo L-band Feed Array) extragalactic HI survey, with over 30,000 high significance extragalactic sources, is well positioned to locate gas-bearing, low surface brightness sources missed by optical detection algorithms. We investigate the nature of a population of HI-bearing sources in ALFALFA with properties similar to "ultra-diffuse" galaxies (UDGs): galaxies with stellar masses of dwarf galaxies, but radii of L* galaxies. These "HI-bearing ultra-diffuse" sources (HUDS) constitute a small, but pertinent, fraction of the dwarf-mass galaxies in ALFALFA. They are bluer and have more irregular morphologies than the optically-selected UDGs found in clusters, and they appear to be gas-rich for their stellar mass, indicating low star formation efficiency. To illuminate potential explanations for the extreme properties of these sources we explore their environments and estimate their halo properties. We conclude that environmental mechanism are unlikely the cause of HUDS' properties, as they exist in environments equivalent to that of the other ALFALFA sources of similar HI-masses, however, we do find some suggestion that these HUDS may reside in high spin parameter halos, a potential explanation for their "ultra-diffuse" nature.

Effect of diffusive and nondiffusive surfaces combinations on sound diffusion

NASA Astrophysics Data System (ADS)

Shafieian, Masoume; Kashani, Farokh Hodjat

2010-05-01

One of room acoustic goals, especially in small to medium rooms, is sound diffusion in low frequencies, which have been the subject of lots of researches. Sound diffusion is a very important consideration in acoustics because it minimizes the coherent reflections that cause problems. It also tends to make an enclosed space sound larger than it is. Diffusion is an excellent alternative or complement to sound absorption in acoustic treatment because it doesn’t really remove much energy, which means it can be used to effectively reduce reflections while still leaving an ambient or live sounding space. Distribution of diffusive and nondiffusive surfaces on room walls affect sound diffusion in room, but the amount, combination, and location of these surfaces are still the matter of question. This paper investigates effects of these issues on room acoustic frequency response in different parts of the room with different source-receiver locations. Room acoustic model based on wave method is used (implemented) which is very accurate and convenient for low frequencies in such rooms. Different distributions of acoustic surfaces on room walls have been introduced to the model and room frequency response results are calculated. For the purpose of comparison, some measurements results are presented. Finally for more smooth frequency response in small and medium rooms, some suggestions are made.

A reduction of diffusion in PVA Fricke hydrogels

NASA Astrophysics Data System (ADS)

Smith, S. T.; Masters, K. S.; Hosokawa, K.; Blinco, J.; Crowe, S. B.; Kairn, T.; Trapp, J. V.

2015-01-01

A modification to the PVA-FX hydrogel whereby the chelating agent, xylenol orange, was partially bonded to the gelling agent, poly-vinyl alcohol, resulted in an 8% reduction in the post irradiation Fe3+ diffusion, adding approximately 1 hour to the useful timespan between irradiation and readout. This xylenol orange functionalised poly-vinyl alcohol hydrogel had an OD dose sensitivity of 0.014 Gy-1 and a diffusion rate of 0.133 mm2 h-1. As this partial bond yields only incremental improvement, it is proposed that more efficient methods of bonding xylenol orange to poly-vinyl alcohol be investigated to further reduce the diffusion in Fricke gels.

Discovery of localized TeV gamma-ray sources and diffuse TeV gamma-ray emission from the galactic plane with Milagro using a new background rejection technique

NASA Astrophysics Data System (ADS)

Abdo, Aws Ahmad

2007-08-01

Very high energy gamma-rays can be used to probe some of the most powerful astrophysical objects in the universe, such as active galactic nuclei, supernova remnants and pulsar-powered nebulae. The diffuse gamma radiation arising from the interaction of cosmic-ray particles with matter and radiation in the Galaxy is one of the few probes available to study the origin of cosmic- rays. Milagro is a water Cherenkov detector that continuously views the entire overhead sky. The large field-of-view combined with the long observation time makes Milagro the most sensitive instrument available for the study of large, low surface brightness sources such as the diffuse gamma radiation arising from interactions of cosmic radiation with interstellar matter. In this thesis I present a new background rejection technique for the Milagro detector through the development of a new gamma hadron separation variable. The Abdo variable, A 4 , coupled with the weighting analysis technique significantly improves the sensitivity of the Milagro detector. This new analysis technique resulted in the first discoveries in Milagro. Four localized sources of TeV gamma-ray emission have been discovered, three of which are in the Cygnus region of the Galaxy and one closer to the Galactic center. In addition to these localized sources, a diffuse emission of TeV gamma-rays has been discovered from the Cygnus region of the Galaxy as well. However, the TeV gamma-ray flux as measured at ~12 TeV from the Cygnus region exceeds that predicted from a conventional model of cosmic-ray production and propagation. This observation indicates the existence of either hard-spectrum cosmic-ray sources and/or other sources of TeV gamma rays in the region. Other TeV gamma-ray source candidates with post-trial statistical significances of > 4s have also been observed in the Galactic plane.

Mass-conserving advection-diffusion Lattice Boltzmann model for multi-species reacting flows

NASA Astrophysics Data System (ADS)

Hosseini, S. A.; Darabiha, N.; Thévenin, D.

2018-06-01

Given the complex geometries usually found in practical applications, the Lattice Boltzmann (LB) method is becoming increasingly attractive. In addition to the simple treatment of intricate geometrical configurations, LB solvers can be implemented on very large parallel clusters with excellent scalability. However, reacting flows and especially combustion lead to additional challenges and have seldom been studied by LB methods. Indeed, overall mass conservation is a pressing issue in modeling multi-component flows. The classical advection-diffusion LB model recovers the species transport equations with the generalized Fick approximation under the assumption of an incompressible flow. However, for flows involving multiple species with different diffusion coefficients and density fluctuations - as is the case with weakly compressible solvers like Lattice Boltzmann -, this approximation is known not to conserve overall mass. In classical CFD, as the Fick approximation does not satisfy the overall mass conservation constraint a diffusion correction velocity is usually introduced. In the present work, a local expression is first derived for this correction velocity in a LB framework. In a second step, the error due to the incompressibility assumption is also accounted for through a modified equilibrium distribution function. Theoretical analyses and simulations show that the proposed scheme performs much better than the conventional advection-diffusion Lattice Boltzmann model in terms of overall mass conservation.

Optical processing furnace with quartz muffle and diffuser plate

DOEpatents

Sopori, B.L.

1996-11-19

An optical furnace for annealing a process wafer is disclosed comprising a source of optical energy, a quartz muffle having a door to hold the wafer for processing, and a quartz diffuser plate to diffuse the light impinging on the quartz muffle; a feedback system with a light sensor located in the wall of the muffle is also provided for controlling the source of optical energy. 5 figs.

New design of textile light diffusers for photodynamic therapy.

PubMed

Cochrane, Cédric; Mordon, Serge R; Lesage, Jean Claude; Koncar, Vladan

2013-04-01

A homogeneous and reproducible fluence delivery rate during clinical photodynamic therapy (PDT) plays a determinant role in preventing under- or overtreatment. PDT applied in dermatology has been carried out with a wide variety of light sources delivering a broad range of more or less adapted light doses. Due to the complexities of the human anatomy, these light sources do not in fact deliver a uniform light distribution to the skin. Therefore, the development of flexible light sources would considerably improve the homogeneity of light delivery. The integration of plastic optical fiber (POF) into textile structures could offer an interesting alternative. In this article, a textile light diffuser (TLD) has been developed using POF and Polyester yarns. Predetermined POF macrobending leads to side emission of light when the critical angle is exceeded. Therefore, a specific pattern based on different satin weaves has been developed in order to improve light emission homogeneity and to correct the decrease of side emitted radiation intensity along POF. The prototyped fabrics (approximately 100 cm(2): 5×20 cm) were woven using a hand loom, then both ends of the POF were coupled to a laser diode (5 W, 635 nm). The fluence rate (mW/ cm(2)) and the homogeneity of light delivery by the TLD were evaluated. Temperature evolution, as a function of time, was controlled with an infrared thermographic camera. When using a power source of 5 W, the fluence rate of the TLD was 18±2.5 mw/cm(2). Due to the high efficiency of the TLD, the optical losses were very low. The TLD temperature elevation was 0.6 °C after 10 min of illumination. Our TLD meets the basic requirements for PDT: homogeneous light distribution and flexibility. It also proves that large (500 cm(2)) textile light diffusers adapted to skin, but also to peritoneal or pleural cavity, PDTs can be easily produced by textile manufacturing processes. Copyright © 2012 Elsevier B.V. All rights reserved.

Treatment of boundary conditions in through-diffusion: A case study of (85)Sr(2+) diffusion in compacted illite.

PubMed

Glaus, M A; Aertsens, M; Maes, N; Van Laer, L; Van Loon, L R

2015-01-01

Valuable techniques to measure effective diffusion coefficients in porous media are an indispensable prerequisite for a proper understanding of the migration of chemical-toxic and radioactive micropollutants in the subsurface and geosphere. The present article discusses possible pitfalls and difficulties in the classical through-diffusion technique applied to situations where large diffusive fluxes of cations in compacted clay minerals or clay rocks occur. The results obtained from a benchmark study, in which the diffusion of (85)Sr(2+) tracer in compacted illite has been studied using different experimental techniques, are presented. It is shown that these techniques may yield valuable results provided that an appropriate model is used for numerical simulations. It is further shown that effective diffusion coefficients may be systematically underestimated when the concentration at the downstream boundary is not taken adequately into account in modelling, even for very low concentrations. A criterion is derived for quasi steady-state situations, by which it can be decided whether the simplifying assumption of a zero-concentration at the downstream boundary in through-diffusion is justified or not. The application of the criterion requires, however, knowledge of the effective diffusion coefficient of the clay sample. Such knowledge is often absent or only approximately available during the planning phase of a diffusion experiment. Copyright © 2015 Elsevier B.V. All rights reserved.

Enzyme localization, crowding, and buffers collectively modulate diffusion-influenced signal transduction: Insights from continuum diffusion modeling

PubMed Central

Kekenes-Huskey, Peter M.; Eun, Changsun; McCammon, J. A.

2015-01-01

Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion “barriers” arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to “compartments” of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways. PMID:26342355

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

NASA Technical Reports Server (NTRS)

Menart, J. A.; Lee, Haeok S.; Kim, Tae-Kuk

1993-01-01

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Analytical solution of reaction-diffusion equations for calcium wave propagation in a starburst amacrine cell.

PubMed

Poznanski, R R

2010-09-01

A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 μm from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.

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

NASA Astrophysics Data System (ADS)

Wang, Ken Kang-Hsin; Ye, Zhen

2003-10-01

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

NON-POINT SOURCE POLLUTION

EPA Science Inventory

Non-point source pollution is a diffuse source that is difficult to measure and is highly variable due to different rain patterns and other climatic conditions. In many areas, however, non-point source pollution is the greatest source of water quality degradation. Presently, stat...

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.

Delayed plastic relaxation limit in SiGe islands grown by Ge diffusion from a local source

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

Vanacore, G. M.; Zani, M.; Tagliaferri, A., E-mail: alberto.tagliaferri@polimi.it

2015-03-14

The hetero-epitaxial strain relaxation in nano-scale systems plays a fundamental role in shaping their properties. Here, the elastic and plastic relaxation of self-assembled SiGe islands grown by surface-thermal-diffusion from a local Ge solid source on Si(100) are studied by atomic force and transmission electron microscopies, enabling the simultaneous investigation of the strain relaxation in different dynamical regimes. Islands grown by this technique remain dislocation-free and preserve a structural coherence with the substrate for a base width as large as 350 nm. The results indicate that a delay of the plastic relaxation is promoted by an enhanced Si-Ge intermixing, induced by themore » surface-thermal-diffusion, which takes place already in the SiGe overlayer before the formation of a critical nucleus. The local entropy of mixing dominates, leading the system toward a thermodynamic equilibrium, where non-dislocated, shallow islands with a low residual stress are energetically stable. These findings elucidate the role of the interface dynamics in modulating the lattice distortion at the nano-scale, and highlight the potential use of our growth strategy to create composition and strain-controlled nano-structures for new-generation devices.« less

Approximations to camera sensor noise

NASA Astrophysics Data System (ADS)

Jin, Xiaodan; Hirakawa, Keigo

2013-02-01

Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

Spatially based management of agricultural phosphorus pollution from diffuse sources: the SCIMAP risk based approach

NASA Astrophysics Data System (ADS)

Reaney, S. M.; Heathwaite, L.; Lane, S. N.; Buckley, C.

2007-12-01

Pollution of rivers from agricultural phosphorus is recognised as a significant global problem and is a major management challenge as it involves processes that are small in magnitude, distributed over large areas, operating at fine spatial scales and associated with certain land use types when they are well connected to the receiving waters. Whilst some of these processes have been addressed in terms of water quality forecasting models and field measurements, we lack effective tools to prioritise where action should be taken to remediate the diffuse pollution problem. From a management perspective, the required information is on 'what to do where' rather than absolute values. This change in focus opens up the problem to be considered in a probabilistic / relative framework rather than concentrating on absolute values. The SCIMAP risk management framework is based on the critical source area concept whereby a risk and a connection are required to generate a problem. Treatments of both surface and subsurface hydrological connectivity have been developed. The approach is based on the philosophy that for a point to be considered connected there needs to be a continuous flow path to the receiving water. This information is calculated by simulating the possible flow paths from the source cell to the receiving water and recording the required catchment wetness to allow flow along that route. This algorithm gives information on the ease at which each point in the landscape can export risk along surface and subsurface pathways to the receiving waters. To understand the annual dynamics of the locational diffuse P risk, a temporal risk framework has been developed. This risk framework accounts for land management activies within the agricultural calendar. These events include the application of fertiliser, the P additions from livestock and the offtake of P in crops. Changes to these risks can be made to investigate management options. The SCIMAP risk mapping framework has

Diffusion studies with synchrotron Mössbauer spectroscopy

NASA Astrophysics Data System (ADS)

Jackson, J. M.

2011-12-01

Knowledge of diffusion properties is critical for understanding many physical and chemical processes in planetary interiors. For example, diffusion behavior provides constraints on chemical exchange and viscosity. Nuclear resonances open the window for observing diffusion properties under the extreme conditions that exist deep inside the Earth. Synchrotron Mössbauer spectroscopy (viz. nuclear forward scattering) makes use of synchrotron radiation coherently scattered in the forward direction after nuclear resonant excitation. The decay of the forward-scattered radiation is faster when atoms move on the time scale of the excited-state lifetime because of a loss of coherence. Such diffusion-activated processes lead to accelerated decay and line broadening in the measured signal. In the case of the Mössbauer active isotope 57Fe, the nuclear resonance at 14.4 keV has a natural lifetime of 141 ns. Therefore, one can observe diffusion events ranging from approximately one-sixth to 100 times the natural lifetime of 57Fe, which corresponds to diffusion coefficients of 10-16 and 10-13 m2/s, respectively and a two to three order of magnitude range of suitability. In this contribution, we will describe such measurements that access the microscopic details of the diffusion process for iron-bearing phases.

Crystal surface integrity and diffusion measurements on Earth and planetary materials

NASA Astrophysics Data System (ADS)

Watson, E. B.; Cherniak, D. J.; Thomas, J. B.; Hanchar, J. M.; Wirth, R.

2016-09-01

Characterization of diffusion behavior in minerals is key to providing quantitative constraints on the ages and thermal histories of Earth and planetary materials. Laboratory experiments are a vital source of the needed diffusion measurements, but these can pose challenges because the length scales of diffusion achievable in a laboratory time are commonly less than 1 μm. An effective strategy for dealing with this challenge is to conduct experiments involving inward diffusion of the element of interest from a surface source, followed by quantification of the resulting diffusive-uptake profile using a high-resolution depth-profiling technique such as Rutherford backscattering spectroscopy (RBS), nuclear reaction analysis (NRA), or ion microprobe (SIMS). The value of data from such experiments is crucially dependent on the assumption that diffusion in the near-surface of the sample is representative of diffusion in the bulk material. Historical arguments suggest that the very process of preparing a polished surface for diffusion studies introduces defects-in the form of dislocations and cracks-in the outermost micrometer of the sample that make this region fundamentally different from the bulk crystal in terms of its diffusion properties. Extensive indirect evidence suggests that, in fact, the near-surface region of carefully prepared samples is no different from the bulk crystal in terms of its diffusion properties. A direct confirmation of this conclusion is nevertheless clearly important. Here we use transmission electron microscopy to confirm that the near-surface regions of olivine, quartz and feldspar crystals prepared using careful polishing protocols contain no features that could plausibly affect diffusion. This finding does not preclude damage to the mineral structure from other techniques used in diffusion studies (e.g., ion implantation), but even in this case the role of possible structural damage can be objectively assessed and controlled. While all

Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model.

PubMed

Bennett, Kevin M; Schmainda, Kathleen M; Bennett, Raoqiong Tong; Rowe, Daniel B; Lu, Hanbing; Hyde, James S

2003-10-01

Experience with diffusion-weighted imaging (DWI) shows that signal attenuation is consistent with a multicompartmental theory of water diffusion in the brain. The source of this so-called nonexponential behavior is a topic of debate, because the cerebral cortex contains considerable microscopic heterogeneity and is therefore difficult to model. To account for this heterogeneity and understand its implications for current models of diffusion, a stretched-exponential function was developed to describe diffusion-related signal decay as a continuous distribution of sources decaying at different rates, with no assumptions made about the number of participating sources. DWI experiments were performed using a spin-echo diffusion-weighted pulse sequence with b-values of 500-6500 s/mm(2) in six rats. Signal attenuation curves were fit to a stretched-exponential function, and 20% of the voxels were better fit to the stretched-exponential model than to a biexponential model, even though the latter model had one more adjustable parameter. Based on the calculated intravoxel heterogeneity measure, the cerebral cortex contains considerable heterogeneity in diffusion. The use of a distributed diffusion coefficient (DDC) is suggested to measure mean intravoxel diffusion rates in the presence of such heterogeneity. Copyright 2003 Wiley-Liss, Inc.

Relation between the neutrino flux from Centaurus A and the associated diffuse neutrino flux

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

Koers, Hylke B. J.; Tinyakov, Peter; Institute for Nuclear Research, 60th October Anniversary Prospect 7a, 117312, Moscow

2008-10-15

Based on recent results obtained by the Pierre Auger Observatory (PAO), it has been hypothesized that Centaurus A (Cen A) is a source of ultrahigh-energy cosmic rays (UHECRs) and associated neutrinos. We point out that the diffuse neutrino flux may be used to constrain the source model if one assumes that the ratio between the UHECR and neutrino fluxes outputted by Cen A is representative for other sources. Under this assumption we investigate the relation between the neutrino flux from Cen A and the diffuse neutrino flux. Assuming furthermore that Cen A is the source of two UHECR events observedmore » by PAO, we estimate the all-sky diffuse neutrino flux to be {approx}200-5000 times larger than the neutrino flux from Cen A. As a result, the diffuse neutrino fluxes associated with some of the recently proposed models of UHECR-related neutrino production in Cen A are above existing limits. Regardless of the underlying source model, our results indicate that the detection of neutrinos from Cen A without the accompanying diffuse flux would mean that Cen A is an exceptionally efficient neutrino source.« less

Radiation Diffusion:. AN Overview of Physical and Numerical Concepts

NASA Astrophysics Data System (ADS)

Graziani, Frank

2005-12-01

An overview of the physical and mathematical foundations of radiation transport is given. Emphasis is placed on how the diffusion approximation and its transport corrections arise. An overview of the numerical handling of radiation diffusion coupled to matter is also given. Discussions center on partial temperature and grey methods with comments concerning fully implicit methods. In addition finite difference, finite element and Pert representations of the div-grad operator is also discussed

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.

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.

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.

The Spectrum of Isotropic Diffuse Gamma-Ray Emission Between 100 Mev and 820 Gev

NASA Technical Reports Server (NTRS)

Ackermann, M.; Ajello, M.; Albert, A.; Atwood, W. B.; Baldini, L.; Ballet, J.; Barbiellini, G.; Bastieri, D.; Brandt, T. J.; Hays, E.;

On the renormalisation of the diffusion asymptotics in the problem of reflection of a narrow optical beam from a biological medium

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

Appanov, A Yu; Barabanenkov, Yu N

2005-12-31

An analytic hybrid method is considered for solving the stationary radiation transfer equation in the problem on reflection of a narrow laser beam from biological media such as the 2% aqueous solution of intralipid and erythrocyte suspension with the volume concentration (hematocrit) H=0.41. The method is based on the reciprocity of the Green function in the radiation transfer theory and on the iteration solution of the integral equation for this function. As a result, the ray intensity is represented as a sum of two terms. The first of them describes the contribution of finite-order scattering to the intensity of amore » beam diffusely reflected from the medium. The second term contains the explicit analytic expression for a spatially distributed effective source of diffuse radiation emerging from the deep layers of the medium to the surface. This approach substantially improves the diffusion approximation for the problem under study and allows one to obtain the uniform asymptotics of the reflection coefficient at the specified interval of distances between the radiation source and detector on the medium surface with the relative error within {+-}6% for the 2% intralipid emulsion and erythrocyte suspension (H=0.41). (radiation scattering)« less

Tension and Approximation in Poetic Translation

ERIC Educational Resources Information Center

Al-Shabab, Omar A. S.; Baka, Farida H.

2015-01-01

Simple observation reveals that each language and each culture enjoys specific linguistic features and rhetorical traditions. In poetry translation difference and the resultant linguistic tension create a gap between Source Language and Target language, a gap that needs to be bridged by creating an approximation processed through the translator's…

Preferential flow, diffuse flow, and perching in an interbedded fractured-rock unsaturated zone

NASA Astrophysics Data System (ADS)

Nimmo, John R.; Creasey, Kaitlyn M.; Perkins, Kim S.; Mirus, Benjamin B.

2017-03-01

Layers of strong geologic contrast within the unsaturated zone can control recharge and contaminant transport to underlying aquifers. Slow diffuse flow in certain geologic layers, and rapid preferential flow in others, complicates the prediction of vertical and lateral fluxes. A simple model is presented, designed to use limited geological site information to predict these critical subsurface processes in response to a sustained infiltration source. The model is developed and tested using site-specific information from the Idaho National Laboratory in the Eastern Snake River Plain (ESRP), USA, where there are natural and anthropogenic sources of high-volume infiltration from floods, spills, leaks, wastewater disposal, retention ponds, and hydrologic field experiments. The thick unsaturated zone overlying the ESRP aquifer is a good example of a sharply stratified unsaturated zone. Sedimentary interbeds are interspersed between massive and fractured basalt units. The combination of surficial sediments, basalts, and interbeds determines the water fluxes through the variably saturated subsurface. Interbeds are generally less conductive, sometimes causing perched water to collect above them. The model successfully predicts the volume and extent of perching and approximates vertical travel times during events that generate high fluxes from the land surface. These developments are applicable to sites having a thick, geologically complex unsaturated zone of substantial thickness in which preferential and diffuse flow, and perching of percolated water, are important to contaminant transport or aquifer recharge.

Preferential flow, diffuse flow, and perching in an interbedded fractured-rock unsaturated zone

USGS Publications Warehouse

Nimmo, John R.; Creasey, Kaitlyn M; Perkins, Kimberlie; Mirus, Benjamin B.

2017-01-01

Layers of strong geologic contrast within the unsaturated zone can control recharge and contaminant transport to underlying aquifers. Slow diffuse flow in certain geologic layers, and rapid preferential flow in others, complicates the prediction of vertical and lateral fluxes. A simple model is presented, designed to use limited geological site information to predict these critical subsurface processes in response to a sustained infiltration source. The model is developed and tested using site-specific information from the Idaho National Laboratory in the Eastern Snake River Plain (ESRP), USA, where there are natural and anthropogenic sources of high-volume infiltration from floods, spills, leaks, wastewater disposal, retention ponds, and hydrologic field experiments. The thick unsaturated zone overlying the ESRP aquifer is a good example of a sharply stratified unsaturated zone. Sedimentary interbeds are interspersed between massive and fractured basalt units. The combination of surficial sediments, basalts, and interbeds determines the water fluxes through the variably saturated subsurface. Interbeds are generally less conductive, sometimes causing perched water to collect above them. The model successfully predicts the volume and extent of perching and approximates vertical travel times during events that generate high fluxes from the land surface. These developments are applicable to sites having a thick, geologically complex unsaturated zone of substantial thickness in which preferential and diffuse flow, and perching of percolated water, are important to contaminant transport or aquifer recharge.

The Green’s functions for peridynamic non-local diffusion

PubMed Central

Wang, L. J.; Xu, J. F.

2016-01-01

In this work, we develop the Green’s function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green’s functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green’s functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems. PMID:27713658

Decoupling of rotational and translational diffusion in supercooled colloidal fluids

PubMed Central

Edmond, Kazem V.; Elsesser, Mark T.; Hunter, Gary L.; Pine, David J.; Weeks, Eric R.

2012-01-01

We use confocal microscopy to directly observe 3D translational and rotational diffusion of tetrahedral clusters, which serve as tracers in colloidal supercooled fluids. We find that as the colloidal glass transition is approached, translational and rotational diffusion decouple from each other: Rotational diffusion remains inversely proportional to the growing viscosity whereas translational diffusion does not, decreasing by a much lesser extent. We quantify the rotational motion with two distinct methods, finding agreement between these methods, in contrast with recent simulation results. The decoupling coincides with the emergence of non-Gaussian displacement distributions for translation whereas rotational displacement distributions remain Gaussian. Ultimately, our work demonstrates that as the glass transition is approached, the sample can no longer be approximated as a continuum fluid when considering diffusion. PMID:23071311

Arrangement, Dopant Source, And Method For Making Solar Cells

DOEpatents

Rohatgi, Ajeet; Krygowski, Thomas W.

1999-10-26

Disclosed is an arrangement, dopant source and method used in the fabrication of photocells that minimize handling of cell wafers and involve a single furnace step. First, dopant sources are created by depositing selected dopants onto both surfaces of source wafers. The concentration of dopant that is placed on the surface is relatively low so that the sources are starved sources. These sources are stacked with photocell wafers in alternating orientation in a furnace. Next, the temperature is raised and thermal diffusion takes place whereby the dopant leaves the source wafers and becomes diffused in a cell wafer creating the junctions necessary for photocells to operate. The concentration of dopant diffused into a single side of the cell wafer is proportional to the concentration placed on the respective dopant source facing the side of the cell wafer. Then, in the same thermal cycle, a layer of oxide is created by introducing oxygen into the furnace environment after sufficient diffusion has taken place. Finally, the cell wafers receive an anti-reflective coating and electrical contacts for the purpose of gathering electrical charge.

Investigation of the abnormal Zn diffusion phenomenon in III-V compound semiconductors induced by the surface self-diffusion of matrix atoms

NASA Astrophysics Data System (ADS)

Tang, Liangliang; Xu, Chang; Liu, Zhuming

2017-01-01

Zn diffusion in III-V compound semiconductorsare commonly processed under group V-atoms rich conditions because the vapor pressure of group V-atoms is relatively high. In this paper, we found that group V-atoms in the diffusion sources would not change the shaped of Zn profiles, while the Zn diffusion would change dramatically undergroup III-atoms rich conditions. The Zn diffusions were investigated in typical III-V semiconductors: GaAs, GaSb and InAs. We found that under group V-atoms rich or pure Zn conditions, the double-hump Zn profiles would be formed in all materials except InAs. While under group III-atoms rich conditions, single-hump Zn profiles would be formed in all materials. Detailed diffusion models were established to explain the Zn diffusion process; the surface self-diffusion of matrix atoms is the origin of the abnormal Zn diffusion phenomenon.

Venus' superrotation, mixing length theory and eddy diffusion - A parametric study

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.; Schatten, K. H.; Stevens-Rayburn, D. R.; Chan, K. L.

1988-01-01

The concept of the Hadley mechanism is adopted to describe the axisymmetric circulation of the Venus atmosphere. It is shown that, for the atmosphere of a slowly rotating planet such as Venus, a form of the nonliner 'closure' (self-consistent solution) of the fluid dynamics system which constrains the magnitude of the eddy diffusion coefficients can be postulated. A nonlinear one-layer spectral model of the zonally symmetric circulation was then used to establish the relationship between the heat source, the meridional circulation, and the eddy diffusion coefficients, yielding large zonal velocities. Computer experiments indicated that proportional changes in the heat source and eddy diffusion coefficients do not significantly change the zonal velocities. It was also found that, for large eddy diffusion coefficients, the meridional velocity is virtually constant; below a threshold in the diffusion rate, the meridional velocity decreases; and, for large eddy diffusion and small heating rates, the zonal velocities decrease with decreasing planetary rotation rates.

Spitzer Photometry of Approximately 1 Million Stars in M31 and 15 Other Galaxies

NASA Technical Reports Server (NTRS)

Khan, Rubab

2017-01-01

We present Spitzer IRAC 3.6-8 micrometer and Multiband Imaging Photometer 24 micrometer point-source catalogs for M31 and 15 other mostly large, star-forming galaxies at distances approximately 3.5-14 Mpc, including M51, M83, M101, and NGC 6946. These catalogs contain approximately 1 million sources including approximately 859,000 in M31 and approximately 116,000 in the other galaxies. They were created following the procedures described in Khan et al. through a combination of pointspread function (PSF) fitting and aperture photometry. These data products constitute a resource to improve our understanding of the IR-bright (3.6-24 micrometer) point-source populations in crowded extragalactic stellar fields and to plan observations with the James Webb Space Telescope.

Diffusion of tricarboxylic acid cycle enzymes in the mitochondrial matrix in vivo. Evidence for restricted mobility of a multienzyme complex.

PubMed

Haggie, Peter M; Verkman, A S

2002-10-25

It has been proposed that enzymes in many metabolic pathways, including the tricarboxylic acid cycle in the mitochondrial matrix, are physically associated to facilitate substrate channeling and overcome diffusive barriers. We have used fluorescence recovery after photobleaching to measure the diffusional mobilities of chimeras consisting of green fluorescent protein (GFP) fused to the C terminus of four tricarboxylic acid cycle enzymes: malate dehydrogenase, citrate synthase, isocitrate dehydrogenase, and succinyl-CoA synthetase. The GFP-enzyme chimeras were localized selectively in the mitochondrial matrix in transfected Chinese hamster ovary (CHO) and COS7 cells. Laser photobleaching using a 0.7-microm diameter spot demonstrated restricted diffusion of the GFP-enzyme chimeras. Interestingly, all four chimeras had similar diffusional characteristics, approximately 45% of each chimera was mobile and had a diffusion coefficient of 4 x 10(-8) cm(2)/s. In contrast, unconjugated GFP in the mitochondrial matrix (targeted using COX8 leader sequence) diffused freely (nearly 100% mobility) with a greater diffusion coefficient of 20 x 10(-8) cm(2)/s. The mobility of the GFP-enzyme chimeras was insensitive to substrate source, ATP depletion, or inhibition of the adenine nucleotide translocase. These results indicate similar mobility characteristics of unrelated tricarboxylic acid cycle enzymes having different sizes and physical properties, providing biophysical evidence for a diffusible multienzyme complex in the mitochondrial matrix.

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.

Self-diffusion in a stochastically heated two-dimensional dusty plasma

NASA Astrophysics Data System (ADS)

Sheridan, T. E.

2016-09-01

Diffusion in a two-dimensional dusty plasma liquid (i.e., a Yukawa liquid) is studied experimentally. The dusty plasma liquid is heated stochastically by a surrounding three-dimensional toroidal dusty plasma gas which acts as a thermal reservoir. The measured dust velocity distribution functions are isotropic Maxwellians, giving a well-defined kinetic temperature. The mean-square displacement for dust particles is found to increase linearly with time, indicating normal diffusion. The measured diffusion coefficients increase approximately linearly with temperature. The effective collision rate is dominated by collective dust-dust interactions rather than neutral gas drag, and is comparable to the dusty-plasma frequency.

Quasi-linear diffusion coefficients for highly oblique whistler mode waves

NASA Astrophysics Data System (ADS)

Albert, J. M.

2017-05-01

Quasi-linear diffusion coefficients are considered for highly oblique whistler mode waves, which exhibit a singular "resonance cone" in cold plasma theory. The refractive index becomes both very large and rapidly varying as a function of wave parameters, making the diffusion coefficients difficult to calculate and to characterize. Since such waves have been repeatedly observed both outside and inside the plasmasphere, this problem has received renewed attention. Here the diffusion equations are analytically treated in the limit of large refractive index μ. It is shown that a common approximation to the refractive index allows the associated "normalization integral" to be evaluated in closed form and that this can be exploited in the numerical evaluation of the exact expression. The overall diffusion coefficient formulas for large μ are then reduced to a very simple form, and the remaining integral and sum over resonances are approximated analytically. These formulas are typically written for a modeled distribution of wave magnetic field intensity, but this may not be appropriate for highly oblique whistlers, which become quasi-electrostatic. Thus, the analysis is also presented in terms of wave electric field intensity. The final results depend strongly on the maximum μ (or μ∥) used to model the wave distribution, so realistic determination of these limiting values becomes paramount.

Modeling diffuse phosphorus emissions to assist in best management practice designing

NASA Astrophysics Data System (ADS)

Kovacs, Adam; Zessner, Matthias; Honti, Mark; Clement, Adrienne

2010-05-01

-bounded P load values at any arbitrary point within the catchment. Finally, a simple design procedure has been built up to plan BMPs in the catchments and simulate their possible impacts on diffuse P fluxes as well as calculate their approximately costs. Both source and transport controlling measures have been involved into the planning procedure. The model also allows examining the impacts of alterations of fertilizer application, point source emissions as well as the climate change on the river loads. Besides this, a simple optimization algorithm has been developed to select the most effective source areas (real hot spots), which should be targeted by the interventions. The fate model performed well in Hungarian pilot catchments. Using the calibrated and validated model, different management scenarios were worked out and their effects and costs evaluated and compared to each other. The results show that the approach is suitable to effectively design BMP measures at local scale. Combinative application of the source and transport controlling BMPs can result in high P reduction efficiency. Optimization of the interventions can remarkably reduce the area demand of the necessary BMPs, consequently the establishment costs can be decreased. The model can be coupled with a larger scale catchment model to form a "screening and planning" modeling system.

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.

Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck approximation.

PubMed

Riegert, Anja; Baba, Nilüfer; Gelfert, Katrin; Just, Wolfram; Kantz, Holger

2005-02-11

The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.

Color Histogram Diffusion for Image Enhancement

NASA Technical Reports Server (NTRS)

Kim, Taemin

2011-01-01

Various color histogram equalization (CHE) methods have been proposed to extend grayscale histogram equalization (GHE) for color images. In this paper a new method called histogram diffusion that extends the GHE method to arbitrary dimensions is proposed. Ranges in a histogram are specified as overlapping bars of uniform heights and variable widths which are proportional to their frequencies. This diagram is called the vistogram. As an alternative approach to GHE, the squared error of the vistogram from the uniform distribution is minimized. Each bar in the vistogram is approximated by a Gaussian function. Gaussian particles in the vistoram diffuse as a nonlinear autonomous system of ordinary differential equations. CHE results of color images showed that the approach is effective.

EGRET Observations of the Diffuse Gamma-Ray Emission in Orion: Analysis Through Cycle 6

NASA Technical Reports Server (NTRS)

Digel, S. W.; Aprile, E.; Hunter, S. D.; Mukherjee, R.; Xu, F.

1999-01-01

We present a study of the high-energy diffuse emission observed toward Orion by the Energetic Gamma-Ray Experiment Telescope (EGRET) on the Compton Gamma-Ray Observatory. The total exposure by EGRET in this region has increased by more than a factor of two since a previous study. A simple model for the diffuse emission adequately fits the data; no significant point sources are detected in the region studied (1 = 195 deg to 220 deg and b = -25 deg to -10 deg) in either the composite dataset or in two separate groups of EGRET viewing periods considered. The gamma-ray emissivity in Orion is found to be (1.65 +/- 0.11) x 10(exp -26)/s.sr for E > 100 MeV, and the differential emissivity is well-described as a combination of contributions from cosmic-ray electrons and protons with approximately the local density. The molecular mass calibrating ratio is N(H2)/W(sub CO) = (1.35 +/- 0.15) x 10(exp 20)/sq cm.(K.km/s).

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

Self diffusion of interacting membrane proteins.

PubMed Central

Abney, J R; Scalettar, B A; Owicki, J C

1989-01-01

A two-dimensional version of the generalized Smoluchowski equation is used to analyze the time (or distance) dependent self diffusion of interacting membrane proteins in concentrated membrane systems. This equation provides a well established starting point for descriptions of the diffusion of particles that interact through both direct and hydrodynamic forces; in this initial work only the effects of direct interactions are explicitly considered. Data describing diffusion in the presence of hard-core repulsions, soft repulsions, and soft repulsions with weak attractions are presented. The effect that interactions have on the self-diffusion coefficient of a real protein molecule from mouse liver gap junctions is also calculated. The results indicate that self diffusion is always inhibited by direct interactions; this observation is interpreted in terms of the caging that will exist at finite protein concentration. It is also noted that, over small distance scales, the diffusion coefficient is determined entirely by the very strong Brownian forces; therefore, as a function of displacement the self-diffusion coefficient decays (rapidly) from its value at infinite dilution to its steady-state interaction-averaged value. The steady-state self-diffusion coefficient describes motion over distance scales that range from approximately 10 nm to cellular dimensions and is the quantity measured in fluorescence recovery after photobleaching experiments. The short-ranged behavior of the diffusion coefficient is important on the interparticle-distance scale and may therefore influence the rate at which nearest-neighbor collisional processes take place. The hard-disk theoretical results presented here are in excellent agreement with lattice Monte-Carlo results obtained by other workers. The concentration dependence of experimentally measured diffusion coefficients of antibody-hapten complexes bound to the membrane surface is consistent with that predicted by the theory. The

Analytical approximation of the InGaZnO thin-film transistors surface potential

NASA Astrophysics Data System (ADS)

Colalongo, Luigi

2016-10-01

Surface-potential-based mathematical models are among the most accurate and physically based compact models of thin-film transistors, and in turn of indium gallium zinc oxide TFTs, available today. However, the need of iterative computations of the surface potential limits their computational efficiency and diffusion in CAD applications. The existing closed-form approximations of the surface potential are based on regional approximations and empirical smoothing functions that could result not accurate enough in particular to model transconductances and transcapacitances. In this work we present an extremely accurate (in the range of nV) and computationally efficient non-iterative approximation of the surface potential that can serve as a basis for advanced surface-potential-based indium gallium zinc oxide TFTs models.

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Production of ligninolytic enzymes and some diffusible antifungal compounds by white-rot fungi using potato solid wastes as the sole nutrient source.

PubMed

Schalchli, H; Hormazábal, E; Rubilar, O; Briceño, G; Mutis, A; Zocolo, G J; Diez, M C

2017-10-01

The aim of this study was to evaluate the synthesis of ligninolytic enzymes and some diffusible antifungal compounds by white-rot fungi (WRF) using peels or discarded potato as the sole nutrient source. The strain Trametes hirsuta Ru-513 highlighted for its laccase activity (595 ± 33 U l -1 ), which is able to decolourize 87% of an anthraquinone dye using potato peels as the sole nutritional support. A native polyacrylamide gel of laccase proteins showed the presence of two isoenzymes, corresponding to proteins of 56 and 67 kDa, which were detected by SDS-PAGE. The antifungal activity of ethyl acetate extracts was evaluated by the agar diffusion method, where Anthracophyllum discolor Sp4 and Inonotus sp. Sp2 showed the highest inhibition zones of Mucor miehei. The fungal extracts also inhibited Fusarium oxysporum and Botrytis cinerea growth, with inhibition zones of up to 18 mm. The extract with the highest antifungal activity, from A. discolor Sp4 grown in discarded potato medium, was analysed using a gas chromatograph coupled to a mass spectrometer. Among the identified compounds, chlorinated aromatic compounds and veratryl alcohol were the most abundant compounds. The results revealed the relevance of potato waste valorization for the sustainable production of ligninolytic enzymes and antifungal compounds. This study reports the synthesis of ligninolytic enzymes and diffusible antifungal compounds by WRF using potato wastes as the sole nutrient source and suggests a relationship between the enzymatic activity and the synthesis of antifungal compounds. These compounds and the synthesis of halogen compounds by WRF using agro-industrial wastes have been poorly studied before. © 2017 The Society for Applied Microbiology.

Three FORTRAN programs for finite-difference solutions to binary diffusion in one and two phases with composition-and time-dependent diffusion coefficients

USGS Publications Warehouse

Sanford, R.F.

1982-01-01

Geological examples of binary diffusion are numerous. They are potential indicators of the duration and rates of geological processes. Analytical solutions to the diffusion equations generally do not allow for variable diffusion coefficients, changing boundary conditions, and impingement of diffusion fields. The three programs presented here are based on Crank-Nicholson finite-difference approximations, which can take into account these complicating factors. Program 1 describes the diffusion of a component into an initially homogeneous phase that has a constant surface composition. Specifically it is written for Fe-Mg exchange in olivine at oxygen fugacities appropriate for the lunar crust, but other components, phases, or fugacities may be substituted by changing the values of the diffusion coefficient. Program 2 simulates the growth of exsolution lamellae. Program 3 describes the growth of reaction rims. These two programs are written for pseudobinary Ca-(Mg, Fe) exchange in pyroxenes. In all three programs, the diffusion coefficients and boundary conditions can be varied systematically with time. To enable users to employ widely different numerical values for diffusion coefficients and diffusion distance, the grid spacing in the space dimension and the increment by which the grid spacing in the time dimension is increased at each time step are input constants that can be varied each time the programs are run to yield a solution of the desired accuracy. ?? 1982.

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

Functional imaging of the human brain using a modular, fibre-less, high-density diffuse optical tomography system.

PubMed

Chitnis, Danial; Cooper, Robert J; Dempsey, Laura; Powell, Samuel; Quaggia, Simone; Highton, David; Elwell, Clare; Hebden, Jeremy C; Everdell, Nicholas L

2016-10-01

We present the first three-dimensional, functional images of the human brain to be obtained using a fibre-less, high-density diffuse optical tomography system. Our technology consists of independent, miniaturized, silicone-encapsulated DOT modules that can be placed directly on the scalp. Four of these modules were arranged to provide up to 128, dual-wavelength measurement channels over a scalp area of approximately 60 × 65 mm 2 . Using a series of motor-cortex stimulation experiments, we demonstrate that this system can obtain high-quality, continuous-wave measurements at source-detector separations ranging from 14 to 55 mm in adults, in the presence of hair. We identify robust haemodynamic response functions in 5 out of 5 subjects, and present diffuse optical tomography images that depict functional haemodynamic responses that are well-localized in all three dimensions at both the individual and group levels. This prototype modular system paves the way for a new generation of wearable, wireless, high-density optical neuroimaging technologies.

Toward real-time diffuse optical tomography: accelerating light propagation modeling employing parallel computing on GPU and CPU

NASA Astrophysics Data System (ADS)

Doulgerakis, Matthaios; Eggebrecht, Adam; Wojtkiewicz, Stanislaw; Culver, Joseph; Dehghani, Hamid

2017-12-01

Parameter recovery in diffuse optical tomography is a computationally expensive algorithm, especially when used for large and complex volumes, as in the case of human brain functional imaging. The modeling of light propagation, also known as the forward problem, is the computational bottleneck of the recovery algorithm, whereby the lack of a real-time solution is impeding practical and clinical applications. The objective of this work is the acceleration of the forward model, within a diffusion approximation-based finite-element modeling framework, employing parallelization to expedite the calculation of light propagation in realistic adult head models. The proposed methodology is applicable for modeling both continuous wave and frequency-domain systems with the results demonstrating a 10-fold speed increase when GPU architectures are available, while maintaining high accuracy. It is shown that, for a very high-resolution finite-element model of the adult human head with ˜600,000 nodes, consisting of heterogeneous layers, light propagation can be calculated at ˜0.25 s/excitation source.

Using the WSA Model to Test the Parker Spiral Approximation for SEP Event Magnetic Connections

NASA Astrophysics Data System (ADS)

Kahler, S. W.; Arge, C. N.; Smith, D. A.

2016-08-01

In studies of solar energetic (E > 10 MeV) particle (SEP) events the Parker spiral (PS) field approximation, based only on the measured 1 AU solar wind (SW) speed Vsw, is nearly always used to determine the coronal or photospheric source locations of the 1 AU magnetic fields. There is no objective way to validate that approximation, but here we seek guidelines for optimizing its application. We first review recent SEP studies showing the extensive use of the PS approximation with various assumptions about coronal and photospheric source fields. We then run the Wang-Sheeley-Arge (WSA) model over selected Carrington rotations (CRs) to track both the photospheric and 5 R_{⊙} source locations of the forecasted 1 AU SW, allowing us to compare those WSA sources with the PS sources inferred from the WSA Vsw forecast. We compile statistics of the longitude differences (WSA-PS) for all the CRs and discuss the limitations of using the WSA model to validate the PS approximation. Over nearly all of each CR the PS and WSA source longitudes agree to within several degrees. The agreement is poor only in the slow-fast SW interaction regions characterized by high-speed events (HSEs), where the longitude differences can reach several tens of degrees. This result implies that SEP studies should limit use of the PS approximation around HSEs and use magnetic field polarities as an additional check of solar source connections.

Three-Dimensional Tracking of Interfacial Hopping Diffusion

NASA Astrophysics Data System (ADS)

Wang, Dapeng; Wu, Haichao; Schwartz, Daniel K.

2017-12-01

Theoretical predictions have suggested that molecular motion at interfaces—which influences processes including heterogeneous catalysis, (bio)chemical sensing, lubrication and adhesion, and nanomaterial self-assembly—may be dominated by hypothetical "hops" through the adjacent liquid phase, where a diffusing molecule readsorbs after a given hop according to a probabilistic "sticking coefficient." Here, we use three-dimensional (3D) single-molecule tracking to explicitly visualize this process for human serum albumin at solid-liquid interfaces that exert varying electrostatic interactions on the biomacromolecule. Following desorption from the interface, a molecule experiences multiple unproductive surface encounters before readsorption. An average of approximately seven surface collisions is required for the repulsive surfaces, decreasing to approximately two and a half for surfaces that are more attractive. The hops themselves are also influenced by long-range interactions, with increased electrostatic repulsion causing hops of longer duration and distance. These findings explicitly demonstrate that interfacial diffusion is dominated by biased 3D Brownian motion involving bulk-surface coupling and that it can be controlled by influencing short- and long-range adsorbate-surface interactions.

Validation of a mixture-averaged thermal diffusion model for premixed lean hydrogen flames

NASA Astrophysics Data System (ADS)

Schlup, Jason; Blanquart, Guillaume

2018-03-01

The mixture-averaged thermal diffusion model originally proposed by Chapman and Cowling is validated using multiple flame configurations. Simulations using detailed hydrogen chemistry are done on one-, two-, and three-dimensional flames. The analysis spans flat and stretched, steady and unsteady, and laminar and turbulent flames. Quantitative and qualitative results using the thermal diffusion model compare very well with the more complex multicomponent diffusion model. Comparisons are made using flame speeds, surface areas, species profiles, and chemical source terms. Once validated, this model is applied to three-dimensional laminar and turbulent flames. For these cases, thermal diffusion causes an increase in the propagation speed of the flames as well as increased product chemical source terms in regions of high positive curvature. The results illustrate the necessity for including thermal diffusion, and the accuracy and computational efficiency of the mixture-averaged thermal diffusion model.

Theory for source-responsive and free-surface film modeling of unsaturated flow

USGS Publications Warehouse

Nimmo, J.R.

2010-01-01

A new model explicitly incorporates the possibility of rapid response, across significant distance, to substantial water input. It is useful for unsaturated flow processes that are not inherently diffusive, or that do not progress through a series of equilibrium states. The term source-responsive is used to mean that flow responds sensitively to changing conditions at the source of water input (e.g., rainfall, irrigation, or ponded infiltration). The domain of preferential flow can be conceptualized as laminar flow in free-surface films along the walls of pores. These films may be considered to have uniform thickness, as suggested by field evidence that preferential flow moves at an approximately uniform rate when generated by a continuous and ample water supply. An effective facial area per unit volume quantitatively characterizes the medium with respect to source-responsive flow. A flow-intensity factor dependent on conditions within the medium represents the amount of source-responsive flow at a given time and position. Laminar flow theory provides relations for the velocity and thickness of flowing source-responsive films. Combination with the Darcy-Buckingham law and the continuity equation leads to expressions for both fluxes and dynamic water contents. Where preferential flow is sometimes or always significant, the interactive combination of source-responsive and diffuse flow has the potential to improve prediction of unsaturated-zone fluxes in response to hydraulic inputs and the evolving distribution of soil moisture. Examples for which this approach is efficient and physically plausible include (i) rainstorm-generated rapid fluctuations of a deep water table and (ii) space- and time-dependent soil water content response to infiltration in a macroporous soil. ?? Soil Science Society of America.

VOXES: a high precision X-ray spectrometer for diffused sources with HAPG crystals in the 2–20 keV range

NASA Astrophysics Data System (ADS)

Scordo, A.; Curceanu, C.; Miliucci, M.; Shi, H.; Sirghi, F.; Zmeskal, J.

2018-04-01

Bragg spectroscopy is one of the best established experimental methods for high energy resolution X-ray measurements and has been widely used in several fields, going from fundamental physics to quantum mechanics tests, synchrotron radiation and X-FEL applications, astronomy, medicine and industry. However, this technique is limited to the measurement of photons produced from well collimated or point-like sources and becomes quite inefficient for photons coming from extended and diffused sources like those, for example, emitted in the exotic atoms radiative transitions. The VOXES project's goal is to realise a prototype of a high resolution and high precision X-ray spectrometer, using Highly Annealed Pyrolitic Graphite (HAPG) crystals in the Von Hamos configuration, working also for extended sources. The aim is to deliver a cost effective system having an energy resolution at the level of eV for X-ray energies from about 2 keV up to tens of keV, able to perform sub-eV precision measurements with non point-like sources. In this paper, the working principle of VOXES, together with first results, are presented.

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.

Diffusion of protein through the human cornea.

PubMed

Charalel, Resmi A; Engberg, Kristin; Noolandi, Jaan; Cochran, Jennifer R; Frank, Curtis; Ta, Christopher N

2012-01-01

To determine the rate of diffusion of myoglobin and bovine serum albumin (BSA) through the human cornea. These small proteins have hydrodynamic diameters of approximately 4.4 and 7.2 nm, and molecular weights of 16.7 and 66 kDa, for myoglobin and BSA, respectively. Diffusion coefficients were measured using a diffusion chamber where the protein of interest and balanced salt solution were in different chambers separated by an ex vivo human cornea. Protein concentrations in the balanced salt solution chamber were measured over time. Diffusion coefficients were calculated using equations derived from Fick's law and conservation of mass in a closed system. Our experiments demonstrate that the diffusion coefficient of myoglobin is 5.5 ± 0.9 × 10(-8) cm(2)/s (n = 8; SD = 1.3 × 10(-8) cm(2)/s; 95% CI: 4.6 × 10(-8) to 6.4 × 10(-8) cm(2)/s) and the diffusion coefficient of BSA is 3.1 ± 1.0 × 10(-8) cm(2)/s (n = 8; SD = 1.4 × 10(-8) cm(2)/s; 95% CI: 2.1 × 10(-8) to 4.1 × 10(-8) cm(2)/s). Our study suggests that molecules as large as 7.2 nm may be able to passively diffuse through the human cornea. With applications in pharmacotherapy and the development of an artificial cornea, further experiments are warranted to fully understand the limits of human corneal diffusion and its clinical relevance. Copyright © 2012 S. Karger AG, Basel.

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.

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Rosen, I. G.

1988-01-01

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Diffusive Fractionation of Lithium Isotopes in Olivine Grain Boundaries

NASA Astrophysics Data System (ADS)

Homolova, V.; Watson, E. B.

2012-12-01

Diffusive fractionation of isotopes has been documented in silicate melts, aqueous fluids, and single crystals. In polycrystalline rocks, the meeting place of two grains, or grain boundaries, may also be a site of diffusive fractionation of isotopes. We have undertaken an experimental and modeling approach to investigate diffusive fractionation of lithium (Li) isotopes by grain boundary diffusion. The experimental procedure consists of packing a Ni metal capsule with predominantly ground San Carlos olivine and subjecting the capsule to 1100C and 1GPa for two days in a piston cylinder apparatus to create a nominally dry, 'dunite rock'. After this synthesis step, the capsule is sectioned and polished. One of the polished faces of the 'dunite rock' is then juxtaposed to a source material of spodumene and this diffusion couple is subject to the same experimental conditions as the synthesis step. Li abundances and isotopic profiles (ratios of count rates) were analyzed using LA-ICP-MS. Li concentrations linearly decrease away from the source from 550ppm to the average concentration of the starting olivine (2.5ppm). As a function of distance from the source, the 7Li/6Li ratio decreases to a minimum before increasing to the background ratio of the 'dunite rock'. The 7Li/6Li ratio minimum coincides with the lowest Li concentrations above average 'dunite rock' abundances. The initial decrease in the 7Li/6Li ratio is similar to that seen in other studies of diffusive fractionation of isotopes and is thought to be caused by the higher diffusivity (D) of the lighter isotope relative to the heavier isotope. The relationship between D and mass (m) is given by (D1/D2) =(m2/m1)^β, where β is an empirical fractionation factor; 1 and 2 denote the lighter and heavier isotope, respectively. A fit to the Li isotopic data reveals an effective DLi of ~1.2x10^-12 m/s^2 and a β of 0.1. Numerical modelling was utilized to elucidate the relationship between diffusive fractionation

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.

Evaluation of diffusion models in breast cancer.

PubMed

Panek, Rafal; Borri, Marco; Orton, Matthew; O'Flynn, Elizabeth; Morgan, Veronica; Giles, Sharon L; deSouza, Nandita; Leach, Martin O; Schmidt, Maria A

2015-08-01

The purpose of this study is to investigate whether the microvascular pseudodiffusion effects resulting with non-monoexponential behavior are present in breast cancer, taking into account tumor spatial heterogeneity. Additionally, methodological factors affecting the signal in low and high diffusion-sensitizing gradient ranges were explored in phantom studies. The effect of eddy currents and accuracy of b-value determination using a multiple b-value diffusion-weighted MR imaging sequence were investigated in test objects. Diffusion model selection and noise were then investigated in volunteers (n = 5) and breast tumor patients (n = 21) using the Bayesian information criterion. 54.3% of lesion voxels were best fitted by a monoexponential, 26.2% by a stretched-exponential, and 19.5% by a biexponential intravoxel incoherent motion (IVIM) model. High correlation (0.92) was observed between diffusion coefficients calculated using mono- and stretched-exponential models and moderate (0.59) between monoexponential and IVIM (medians: 0.96/0.84/0.72 × 10(-3) mm(2)/s, respectively). Distortion due to eddy currents depended on the direction of the diffusion gradient and displacement varied between 1 and 6 mm for high b-value images. Shift in the apparent diffusion coefficient due to intrinsic field gradients was compensated for by averaging diffusion data obtained from opposite directions. Pseudodiffusion and intravoxel heterogeneity effects were not observed in approximately half of breast cancer and normal tissue voxels. This result indicates that stretched and IVIM models should be utilized in regional analysis rather than global tumor assessment. Cross terms between diffusion-sensitization gradients and other imaging or susceptibility-related gradients are relevant in clinical protocols, supporting the use of geometric averaging of diffusion-weighted images acquired with diffusion-sensitization gradients in opposite directions.

Plasma Radiation Sources. Quasi-Adiabatic Theory and Numerical Modeling in the Electro-Diffusive Approximation.

DTIC Science & Technology

1984-07-16

can use the model ing - in gpk - B[in(T/T pk)]2 [III.29] (with fit parameter B) to do the resulting integral. Car- rying out this procedure, we have e...A0- B0 2g(’) i -B02 m do- d - t- - F-, gpk e pkf CIII.303 f 0 g B f+b-aT,(e0-1) with = Zn(T/T,), A = C-’ + 2B0p, £ = gCrO, and pk# el + be - aT,(e - 1...4’ ..4’ --%" . .𔃾 - % ."-: --- 7 ’.-., - -’j. "-"-.’." ’... - 0 Modeling g by gpk exp(-Bx2 ) as before and neglecting b com- pared with aT one

FRETBursts: An Open Source Toolkit for Analysis of Freely-Diffusing Single-Molecule FRET

PubMed Central

Lerner, Eitan; Chung, SangYoon; Weiss, Shimon; Michalet, Xavier

2016-01-01

Single-molecule Förster Resonance Energy Transfer (smFRET) allows probing intermolecular interactions and conformational changes in biomacromolecules, and represents an invaluable tool for studying cellular processes at the molecular scale. smFRET experiments can detect the distance between two fluorescent labels (donor and acceptor) in the 3-10 nm range. In the commonly employed confocal geometry, molecules are free to diffuse in solution. When a molecule traverses the excitation volume, it emits a burst of photons, which can be detected by single-photon avalanche diode (SPAD) detectors. The intensities of donor and acceptor fluorescence can then be related to the distance between the two fluorophores. While recent years have seen a growing number of contributions proposing improvements or new techniques in smFRET data analysis, rarely have those publications been accompanied by software implementation. In particular, despite the widespread application of smFRET, no complete software package for smFRET burst analysis is freely available to date. In this paper, we introduce FRETBursts, an open source software for analysis of freely-diffusing smFRET data. FRETBursts allows executing all the fundamental steps of smFRET bursts analysis using state-of-the-art as well as novel techniques, while providing an open, robust and well-documented implementation. Therefore, FRETBursts represents an ideal platform for comparison and development of new methods in burst analysis. We employ modern software engineering principles in order to minimize bugs and facilitate long-term maintainability. Furthermore, we place a strong focus on reproducibility by relying on Jupyter notebooks for FRETBursts execution. Notebooks are executable documents capturing all the steps of the analysis (including data files, input parameters, and results) and can be easily shared to replicate complete smFRET analyzes. Notebooks allow beginners to execute complex workflows and advanced users to

Improved bioluminescence and fluorescence reconstruction algorithms using diffuse optical tomography, normalized data, and optimized selection of the permissible source region

PubMed Central

Naser, Mohamed A.; Patterson, Michael S.

2011-01-01

Reconstruction algorithms are presented for two-step solutions of the bioluminescence tomography (BLT) and the fluorescence tomography (FT) problems. In the first step, a continuous wave (cw) diffuse optical tomography (DOT) algorithm is used to reconstruct the tissue optical properties assuming known anatomical information provided by x-ray computed tomography or other methods. Minimization problems are formed based on L1 norm objective functions, where normalized values for the light fluence rates and the corresponding Green’s functions are used. Then an iterative minimization solution shrinks the permissible regions where the sources are allowed by selecting points with higher probability to contribute to the source distribution. Throughout this process the permissible region shrinks from the entire object to just a few points. The optimum reconstructed bioluminescence and fluorescence distributions are chosen to be the results of the iteration corresponding to the permissible region where the objective function has its global minimum This provides efficient BLT and FT reconstruction algorithms without the need for a priori information about the bioluminescence sources or the fluorophore concentration. Multiple small sources and large distributed sources can be reconstructed with good accuracy for the location and the total source power for BLT and the total number of fluorophore molecules for the FT. For non-uniform distributed sources, the size and magnitude become degenerate due to the degrees of freedom available for possible solutions. However, increasing the number of data points by increasing the number of excitation sources can improve the accuracy of reconstruction for non-uniform fluorophore distributions. PMID:21326647

Utilizing Diffusion Theory to predict carbon dioxide concentration in an indoor environment

NASA Astrophysics Data System (ADS)

Kramer, Andrew R.

This research details a new method of relating sources of carbon dioxide to carbon dioxide concentration in a room operating in a reduced ventilation mode by utilizing Diffusion Theory. The theoretical basis of this research involved solving Fick's Second Law of Diffusion in spherical coordinates for a source of carbon dioxide flowing at a constant rate and located in the center of an impermeable spherical boundary. The solution was developed using a Laplace Transformation. A spherical diffusion test chamber was constructed and used to validate and benchmark the developed theory. The method was benchmarked by using Dispersion Coefficients for large carbon dioxide flow rates due to diffusion induced convection. The theoretical model was adapted to model a room operating with restricted ventilation in the presence of a known, constant source of carbon dioxide. The room was modeled as a sphere of volume equal to the room and utilized a Dispersion Coefficient that is consistent with published values. The developed Diffusion Model successfully predicted the spatial concentration of carbon dioxide in a room operating in a reduced ventilation mode in the presence of a source of carbon dioxide. The flow rates of carbon dioxide that were used in the room are comparable to the average flow rate of carbon dioxide from a person during quiet breathing, also known as the Tidal Breathing. This indicates the Diffusion Model developed from this research has the potential to correlate carbon dioxide concentration with static occupancy levels which can lead to energy savings through a reduction in air exchange rates when low occupancy is detected.

X-ray Diffuse Scattering from Ultrafast Laser Excited Solids

NASA Astrophysics Data System (ADS)

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

2009-03-01

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

Zr diffusion in titanite

NASA Astrophysics Data System (ADS)

Cherniak, D. J.

2006-11-01

Chemical diffusion of Zr under anhydrous, pO2-buffered conditions has been measured in natural titanite. The source of diffusant was either zircon powder or a ZrO2-Al2O3-titanite mixture. Experiments were run in sealed silica glass capsules with solid buffers (to buffer at NNO or QFM). Rutherford Backscattering Spectrometry (RBS) was used to measure diffusion profiles. The following Arrhenius parameters were obtained for Zr diffusion parallel to c over the temperature range 753-1,100°C under NNO-buffered conditions: D Zr = 5.33 × 10-7 exp(-325 ± 30 kJ mol-1/RT) m2 s-1 Diffusivities are similar for experiments buffered at QFM. These data suggest that titanite should be moderately retentive of Zr chemical signatures, with diffusivities slower than those for O and Pb in titanite, but faster than those for Sr and the REE. When applied in evaluation of the relative robustness of the recently developed Zr-in-titanite geothermometer (Hayden and Watson, Abstract, 16th V.M. Goldschmidt Conference 2006), these findings suggest that Zr concentrations in titanite will be less likely to be affected by later thermal disturbance than the geothermometer based on Zr concentrations in rutile (Zack et al. in Contrib Mineral Petrol 148:471-488, 2004; Watson et al. in Contrib Mineral. Petrol, 2006), but much less resistant to diffusional alteration subsequent to crystallization than the Ti-in-Zircon geothermometer (Watson and Harrison in Science 308:841-844, 2005).

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.

Diffusion across the modified polyethylene separator GX in the heat-sterilizable AgO-Zn battery

NASA Technical Reports Server (NTRS)

Lutwack, R.

1973-01-01

Models of diffusion across an inert membrane have been studied using the computer program CINDA. The models were constructed to simulate various conditions obtained in the consideration of the diffusion of Ag (OH)2 ions in the AgO-Zn battery. The effects on concentrations across the membrane at the steady state and on the fluxout as a function of time were used to examine the consequences of stepwise reducing the number of sources of ions, of stepwise blocking the source and sink surfaces, of varying the magnitude of the diffusion coefficient for a uniform membrane, of varying the diffusion coefficient across the membrane, and of excluding volumes to diffusion.

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.

Diffusivity anomaly in modified Stillinger-Weber liquids

NASA Astrophysics Data System (ADS)

Sengupta, Shiladitya; Vasisht, Vishwas V.; Sastry, Srikanth

2014-01-01

By modifying the tetrahedrality (the strength of the three body interactions) in the well-known Stillinger-Weber model for silicon, we study the diffusivity of a series of model liquids as a function of tetrahedrality and temperature at fixed pressure. Previous work has shown that at constant temperature, the diffusivity exhibits a maximum as a function of tetrahedrality, which we refer to as the diffusivity anomaly, in analogy with the well-known anomaly in water upon variation of pressure at constant temperature. We explore to what extent the structural and thermodynamic changes accompanying changes in the interaction potential can help rationalize the diffusivity anomaly, by employing the Rosenfeld relation between diffusivity and the excess entropy (over the ideal gas reference value), and the pair correlation entropy, which provides an approximation to the excess entropy in terms of the pair correlation function. We find that in the modified Stillinger-Weber liquids, the Rosenfeld relation works well above the melting temperatures but exhibits deviations below, with the deviations becoming smaller for smaller tetrahedrality. Further we find that both the excess entropy and the pair correlation entropy at constant temperature go through maxima as a function of the tetrahedrality, thus demonstrating the close relationship between structural, thermodynamic, and dynamical anomalies in the modified Stillinger-Weber liquids.

Unsteady behavior of leading-edge vortex and diffuser stall in a centrifugal compressor with vaned diffuser

NASA Astrophysics Data System (ADS)

Fujisawa, Nobumichi; Hara, Shotaro; Ohta, Yutaka

2016-02-01

The characteristics of a rotating stall of an impeller and diffuser and the evolution of a vortex generated at the diffuser leading-edge (i.e., the leading-edge vortex (LEV)) in a centrifugal compressor were investigated by experiments and numerical analysis. The results of the experiments revealed that both the impeller and diffuser rotating stalls occurred at 55 and 25 Hz during off-design flow operation. For both, stall cells existed only on the shroud side of the flow passages, which is very close to the source location of the LEV. According to the CFD results, the LEV is made up of multiple vortices. The LEV is a combination of a separated vortex near the leading- edge and a longitudinal vortex generated by the extended tip-leakage flow from the impeller. Therefore, the LEV is generated by the accumulation of vorticity caused by the velocity gradient of the impeller discharge flow. In partial-flow operation, the spanwise extent and the position of the LEV origin are temporarily transmuted. The LEV develops with a drop in the velocity in the diffuser passage and forms a significant blockage within the diffuser passage. Therefore, the LEV may be regarded as being one of the causes of a diffuser stall in a centrifugal compressor.

Distribution and sources of polyfluoroalkyl substances (PFAS) in the River Rhine watershed.

PubMed

Möller, Axel; Ahrens, Lutz; Surm, Renate; Westerveld, Joke; van der Wielen, Frans; Ebinghaus, Ralf; de Voogt, Pim

2010-10-01

The concentration profile of 40 polyfluoroalkyl substances (PFAS) in surface water along the River Rhine watershed from the Lake Constance to the North Sea was investigated. The aim of the study was to investigate the influence of point as well as diffuse sources, to estimate fluxes of PFAS into the North Sea and to identify replacement compounds of perfluorooctane sulfonate (PFOS) and perfluorooctanoic acid (PFOA). In addition, an interlaboratory comparison of the method performance was conducted. The PFAS pattern was dominated by perfluorobutane sulfonate (PFBS) and perfluorobutanoic acid (PFBA) with concentrations up to 181 ng/L and 335 ng/L, respectively, which originated from industrial point sources. Fluxes of SigmaPFAS were estimated to be approximately 6 tonnes/year which is much higher than previous estimations. Both, the River Rhine and the River Scheldt, seem to act as important sources of PFAS into the North Sea. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Use of cylindrical diffusing fibers as detectors for interstitial tissue spectroscopy

NASA Astrophysics Data System (ADS)

Baran, Timothy M.; Foster, Thomas H.

2015-03-01

Interstitial photodynamic therapy (iPDT) describes the use of implanted optical fibers for delivery of treatment light to activate photosensitizer in regions that can be located deep within the body. Since sensitive healthy structures are often located nearby, this requires careful treatment planning that is dependent on tissue optical properties. Determination of these values usually involves the insertion of additional fibers into the volume, or the use of flat-cleaved optical fibers as both treatment sources and detectors. The insertion of additional fibers is undesirable, and cylindrical diffusers have been shown to offer superior treatment characteristics compared to flat-cleaved fibers. Using cylindrical diffusers as detectors for spectroscopic measurement is therefore attractive. We describe the determination of the detection profile for a particular cylindrical diffuser design and derive the scatterer concentration gradient within the diffuser core. This detection profile is compared to previously characterized diffusers, and is shown to be dependent on the diffuser design. For diffusers with a constant scatterer concentration and distal mirror, the detection profile is localized to the proximal end of the diffusing region. For diffusers with variable scattering concentration along their length and no distal mirror, the detection profile is shown to be more uniform along the diffusing region. We also present preliminary results showing the recovery of optical properties using arrays of cylindrical diffusing fibers as sources and detectors, with a mean error of 4.4% in the determination of μeff. The accuracy of these results is comparable to those obtained with other methods of optical property recovery.

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.

Comparison of Boron diffused emitters from BN, BSoD and H3BO3 dopants

NASA Astrophysics Data System (ADS)

Singha, Bandana; Singh Solanki, Chetan

2016-12-01

In this work, we are comparing different limited boron dopant sources for the emitter formation in n-type c-Si solar cells. High purity boric acid solution, commercially available boron spin on dopant and boron nitride solid source are used for comparison of emitter doping profiles for the same time and temperature conditions of diffusion. The characterizations done for the similar sheet resistance values for all the dopant sources show different surface morphologies and different device parameters. The measured emitter saturation current densities (Joe) are more than 20 fA cm-2 for all the dopant sources. The bulk carrier lifetimes measured for different diffusion conditions and different solar cell parameters for the similar sheet resistance values show the best result for boric acid diffusion and the least for BN solid source. So, different dopant sources result in different emitter and cell performances.

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.;

The contaminant legacy from historic coastal landfills and their potential as sources of diffuse pollution.

PubMed

O'Shea, Francis T; Cundy, Andrew B; Spencer, Kate L

2018-03-01

Prior to modern environmental regulation landfills in low-lying coastal environments were frequently constructed without leachate control, relying on natural attenuation within inter-tidal sediments to dilute and disperse contaminants reducing environmental impact. With sea level rise and coastal erosion these sites may now pose a pollution risk, yet have received little investigation. This work examines the extent of metal contamination in saltmarsh sediments surrounding a historic landfill in the UK. Patterns of sediment metal data suggest typical anthropogenic pollution chronologies for saltmarsh sediments in industrialised nations. However, many metals were also enriched at depth in close proximity to the landfill boundary and are indicative of a historical leachate plume. Though this total metal load is low, e.g., c. 1200 and 1650kg Pb and Zn respectively, with >1000 historic landfills on flood risk or eroding coastlines in the UK this could represent a significant, yet under-investigated, source of diffuse pollution. Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.

The faint galaxy contribution to the diffuse extragalactic background light

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

OpinionFlow: Visual Analysis of Opinion Diffusion on Social Media.

PubMed

Wu, Yingcai; Liu, Shixia; Yan, Kai; Liu, Mengchen; Wu, Fangzhao

2014-12-01

It is important for many different applications such as government and business intelligence to analyze and explore the diffusion of public opinions on social media. However, the rapid propagation and great diversity of public opinions on social media pose great challenges to effective analysis of opinion diffusion. In this paper, we introduce a visual analysis system called OpinionFlow to empower analysts to detect opinion propagation patterns and glean insights. Inspired by the information diffusion model and the theory of selective exposure, we develop an opinion diffusion model to approximate opinion propagation among Twitter users. Accordingly, we design an opinion flow visualization that combines a Sankey graph with a tailored density map in one view to visually convey diffusion of opinions among many users. A stacked tree is used to allow analysts to select topics of interest at different levels. The stacked tree is synchronized with the opinion flow visualization to help users examine and compare diffusion patterns across topics. Experiments and case studies on Twitter data demonstrate the effectiveness and usability of OpinionFlow.

Diffusion of radon through concrete block walls: A significant source of indoor radon

USGS Publications Warehouse

Lively, R.S.; Goldberg, L.F.

1999-01-01

Basement modules located in southern Minnesota have been the site of continuous radon and environmental measurements during heating seasons since 1993. Concentrations of radon within the basement modules ranged from 70 Bq.m-3 to over 4000 Bq.m-3 between November to April during the three measurement periods. In the soil gas for the same times, concentrations of radon ranged between 25,000 and 70,000 Bq.m-3. Levels of radon within the basement modules changed by factors of five or more within 24 h, in concert with pressure gradients of 4 to 20 Pa that developed between the basement modules and their surroundings. Diffusion is identified as the principal method by which radon is transferred into and out of the basement modules, and appears to be relatively independent of insulating materials and vapour retarders. The variability of radon and correlations with differential pressure gradients may be related to air currents in the block walls and soil that interrupt radon diffusing inward. This yields a net decrease of radon in the basement modules by decay and outward diffusion. Levels of radon within the basement modules increase when the pressure differential is zero and air flow ceases, allowing diffusion gradients to be re-established. Radon levels in both the soil and the basement modules then increase until an equilibrium is achieved.

STARBLADE: STar and Artefact Removal with a Bayesian Lightweight Algorithm from Diffuse Emission

NASA Astrophysics Data System (ADS)

Knollmüller, Jakob; Frank, Philipp; Ensslin, Torsten A.

2018-05-01

STARBLADE (STar and Artefact Removal with a Bayesian Lightweight Algorithm from Diffuse Emission) separates superimposed point-like sources from a diffuse background by imposing physically motivated models as prior knowledge. The algorithm can also be used on noisy and convolved data, though performing a proper reconstruction including a deconvolution prior to the application of the algorithm is advised; the algorithm could also be used within a denoising imaging method. STARBLADE learns the correlation structure of the diffuse emission and takes it into account to determine the occurrence and strength of a superimposed point source.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

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

Planetary Ices and the Linear Mixing Approximation

DOE PAGES

Bethkenhagen, M.; Meyer, Edmund Richard; Hamel, S.; ...

2017-10-10

Here, the validity of the widely used linear mixing approximation (LMA) for the equations of state (EOSs) of planetary ices is investigated at pressure–temperature conditions typical for the interiors of Uranus and Neptune. The basis of this study is ab initio data ranging up to 1000 GPa and 20,000 K, calculated via density functional theory molecular dynamics simulations. In particular, we determine a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the LMA from the results of the real mixture are generally small; for the thermal EOSs they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior (more » $${T}_{\\mathrm{core}}\\sim 4000$$ K).« less

Approximation of super-ions for single-file diffusion of multiple ions through narrow pores.

PubMed

Kharkyanen, Valery N; Yesylevskyy, Semen O; Berezetskaya, Natalia M

2010-11-01

The general theory of the single-file multiparticle diffusion in the narrow pores could be greatly simplified in the case of inverted bell-like shape of the single-particle energy profile, which is often observed in biological ion channels. There is a narrow and deep groove in the energy landscape of multiple interacting ions in such profiles, which corresponds to the pre-defined optimal conduction pathway in the configurational space. If such groove exists, the motion of multiple ions can be reduced to the motion of single quasiparticle, called the superion, which moves in one-dimensional effective potential. The concept of the superions dramatically reduces the computational complexity of the problem and provides very clear physical interpretation of conduction phenomena in the narrow pores.

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.

PubMed

Vorobev, Anatoliy

2010-11-01

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

ICP-MS measurement of iodine diffusion in IG-110 graphite for HTGR/VHTR

NASA Astrophysics Data System (ADS)

Carter, L. M.; Brockman, J. D.; Robertson, J. D.; Loyalka, S. K.

2016-05-01

Graphite functions as a structural material and as a barrier to fission product release in HTGR/VHTR designs, and elucidation of transport parameters for fission products in reactor-grade graphite is thus required for reactor source terms calculations. We measured iodine diffusion in spheres of IG-110 graphite using a release method based on Fickain diffusion kinetics. Two sources of iodine were loaded into the graphite spheres; molecular iodine (I2) and cesium iodide (CsI). Measurements of the diffusion coefficient were made over a temperature range of 873-1293 K. We have obtained the following Arrhenius expressions for iodine diffusion:DI , CsI infused =(6 ×10-12 2/s) exp(30,000 J/mol RT) And,DI , I2 infused =(4 ×10-10 m2/s) exp(-11,000 J/mol RT ) The results indicate that iodine diffusion in IG-110 graphite is not well-described by Fickan diffusion kinetics. To our knowledge, these are the first measurements of iodine diffusion in IG-110 graphite.

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.

Transport and fluctuation-dissipation relations in asymptotic and preasymptotic diffusion across channels with variable section.

PubMed

Forte, Giuseppe; Cecconi, Fabio; Vulpiani, Angelo

2014-12-01

We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient D(eff) is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.

Estimation of diffuse and point source microbial pollution in the ribble catchment discharging to bathing waters in the north west of England.

PubMed

Wither, A; Greaves, J; Dunhill, I; Wyer, M; Stapleton, C; Kay, D; Humphrey, N; Watkins, J; Francis, C; McDonald, A; Crowther, J

2005-01-01

Achieving compliance with the mandatory standards of the 1976 Bathing Water Directive (76/160/EEC) is required at all U.K. identified bathing waters. In recent years, the Fylde coast has been an area of significant investments in 'point source' control, which have not proven, in isolation, to satisfactorily achieve compliance with the mandatory, let alone the guide, levels of water quality in the Directive. The potential impact of riverine sources of pollution was first confirmed after a study in 1997. The completion of sewerage system enhancements offered the potential for the study of faecal indicator delivery from upstream sources comprising both point sources and diffuse agricultural sources. A research project to define these elements commenced in 2001. Initially, a desk study reported here, estimated the principal infrastructure contributions within the Ribble catchment. A second phase of this investigation has involved acquisition of empirical water quality and hydrological data from the catchment during the 2002 bathing season. These data have been used further to calibrate the 'budgets' and 'delivery' modelling and these data are still being analysed. This paper reports the initial desk study approach to faecal indicator budget estimation using available data from the sewerage infrastructure and catchment sources of faecal indicators.

Understanding Coupling of Global and Diffuse Solar Radiation with Climatic Variability

NASA Astrophysics Data System (ADS)

Hamdan, Lubna

Global solar radiation data is very important for wide variety of applications and scientific studies. However, this data is not readily available because of the cost of measuring equipment and the tedious maintenance and calibration requirements. Wide variety of models have been introduced by researchers to estimate and/or predict the global solar radiations and its components (direct and diffuse radiation) using other readily obtainable atmospheric parameters. The goal of this research is to understand the coupling of global and diffuse solar radiation with climatic variability, by investigating the relationships between these radiations and atmospheric parameters. For this purpose, we applied multilinear regression analysis on the data of National Solar Radiation Database 1991--2010 Update. The analysis showed that the main atmospheric parameters that affect the amount of global radiation received on earth's surface are cloud cover and relative humidity. Global radiation correlates negatively with both variables. Linear models are excellent approximations for the relationship between atmospheric parameters and global radiation. A linear model with the predictors total cloud cover, relative humidity, and extraterrestrial radiation is able to explain around 98% of the variability in global radiation. For diffuse radiation, the analysis showed that the main atmospheric parameters that affect the amount received on earth's surface are cloud cover and aerosol optical depth. Diffuse radiation correlates positively with both variables. Linear models are very good approximations for the relationship between atmospheric parameters and diffuse radiation. A linear model with the predictors total cloud cover, aerosol optical depth, and extraterrestrial radiation is able to explain around 91% of the variability in diffuse radiation. Prediction analysis showed that the linear models we fitted were able to predict diffuse radiation with efficiency of test adjusted R2 values

Leading non-Gaussian corrections for diffusion orientation distribution function.

PubMed

Jensen, Jens H; Helpern, Joseph A; Tabesh, Ali

2014-02-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. 2013 John Wiley & Sons, Ltd.

Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function

PubMed Central

Jensen, Jens H.; Helpern, Joseph A.; Tabesh, Ali

2014-01-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed out of the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves upon the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. PMID:24738143

An Experimental and Computational Evaluation of the Importance of Molecular Diffusion in Gas Gravity Currents

NASA Astrophysics Data System (ADS)

Herman, Jeremy J.

The accidental release of hazardous, denser-than-air gases during their transport or manufacture is a vital area of study for process safety researchers. This project examines the importance of molecular diffusion on the developing concentration field of a gas gravity current released into a calm environment. Questions which arose from the unexpectedly severe explosion in 2005 at Buncefield, England were of particular interest. The accidental overfilling of a large tank with gasoline on a completely calm morning led to a massive open air explosion. Forensic evidence showed that at the time of ignition, a vapor cloud, most of which now appears to have been within the flammability limits, covered approximately 120,000 m2. Neither the severity of the explosion, nor the size of the vapor cloud would have been anticipated. Experiments were conducted in which carbon dioxide was released from a sunken source into a one meter wide channel devoid of any wind. These experiments were designed in such a way as to mitigate the formation of a raised head at the front of the gravity current which would have resulted in turbulent entrainment of air. This was done to create a flow in which molecular diffusion was the controlling form of mixing between the carbon dioxide and air. Concentration measurements were taken using flame ionization detection at varying depths and down channel locations. A model of the experiments was developed using COMSOL Multiphysics. The only form of mixing allowed between carbon dioxide and air in the model was molecular diffusion. In this manner the accuracy of the assertion that molecular diffusion was controlling in our experiments was checked and verified. Experimental measurements showed a large variation of gas concentration with depth of the gravity current at the very beginning of the channel where the gas emerged up from the sunken source and began flowing down channel. Due to this variation, molecular diffusion caused the vertical concentration

The gamma ray continuum spectrum from the galactic center disk and point sources

NASA Technical Reports Server (NTRS)

Gehrels, Neil; Tueller, Jack

1992-01-01

A light curve of gamma-ray continuum emission from point sources in the galactic center region is generated from balloon and satellite observations made over the past 25 years. The emphasis is on the wide field-of-view instruments which measure the combined flux from all sources within approximately 20 degrees of the center. These data have not been previously used for point-source analyses because of the unknown contribution from diffuse disk emission. In this study, the galactic disk component is estimated from observations made by the Gamma Ray Imaging Spectrometer (GRIS) instrument in Oct. 1988. Surprisingly, there are several times during the past 25 years when all gamma-ray sources (at 100 keV) within about 20 degrees of the galactic center are turned off or are in low emission states. This implies that the sources are all variable and few in number. The continuum gamma-ray emission below approximately 150 keV from the black hole candidate 1E1740.7-2942 is seen to turn off in May 1989 on a time scale of less than two weeks, significantly shorter than ever seen before. With the continuum below 150 keV turned off, the spectral shape derived from the HEXAGONE observation on 22 May 1989 is very peculiar with a peak near 200 keV. This source was probably in its normal state for more than half of all observations since the mid-1960's. There are only two observations (in 1977 and 1979) for which the sum flux from the point sources in the region significantly exceeds that from 1E1740.7-2942 in its normal state.

Exact Magnetic Diffusion Solutions for Magnetohydrodynamic Code Verification

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

Miller, D S

In this paper, the authors present several new exact analytic space and time dependent solutions to the problem of magnetic diffusion in R-Z geometry. These problems serve to verify several different elements of an MHD implementation: magnetic diffusion, external circuit time integration, current and voltage energy sources, spatially dependent conductivities, and ohmic heating. The exact solutions are shown in comparison with 2D simulation results from the Ares code.

X-Ray Investigation of the Diffuse Emission around Plausible γ-Ray Emitting Pulsar Wind Nebulae in Kookaburra Region

NASA Astrophysics Data System (ADS)

Kishishita, Tetsuichi; Bamba, Aya; Uchiyama, Yasunobu; Tanaka, Yasuyuki; Takahashi, Tadayuki

2012-05-01

We report on the results from Suzaku X-ray observations of the radio complex region called Kookaburra, which includes two adjacent TeV γ-ray sources HESS J1418-609 and HESS J1420-607. The Suzaku observation revealed X-ray diffuse emission around a middle-aged pulsar PSR J1420-6048 and a plausible pulsar wind nebula (PWN) Rabbit with elongated sizes of σX = 1farcm66 and σX = 1farcm49, respectively. The peaks of the diffuse X-ray emission are located within the γ-ray excess maps obtained by H.E.S.S. and the offsets from the γ-ray peaks are 2farcm8 for PSR J1420-6048 and 4farcm5 for Rabbit. The X-ray spectra of the two sources were well reproduced by absorbed power-law models with Γ = 1.7-2.3. The spectral shapes tend to become softer according to the distance from the X-ray peaks. Assuming the one-zone electron emission model as the first-order approximation, the ambient magnetic field strengths of HESS J1420-607 and HESS J1418-609 can be estimated as 3 μG and 2.5 μG, respectively. The X-ray spectral and spatial properties strongly support that both TeV sources are PWNe, in which electrons and positrons accelerated at termination shocks of the pulsar winds are losing their energies via the synchrotron radiation and inverse Compton scattering as they are transported outward.

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.

Can the Lyman Continuum Leaked Out of H II Regions Explain Diffuse Ionized Gas?

NASA Astrophysics Data System (ADS)

Seon, Kwang-Il

2009-09-01

We present an attempt to explain the diffuse Hα emission of a face-on galaxy M 51 with the "standard" photoionization model, in which the Lyman continuum (Lyc) escaping from H II regions propagates large distances into the diffuse interstellar medium (ISM). The diffuse Hα emission of M 51 is analyzed using thin slab models and exponential disk models in the context of the "on-the-spot" approximation. The scale height of the ionized gas needed to explain the diffuse Hα emission with the scenario is found to be of the order of ~1-2 kpc, consistent with those of our Galaxy and edge-on galaxies. The model also provides a vertical profile, when the galaxy is viewed edge-on, consisting of two-exponential components. However, it is found that an incredibly low absorption coefficient of κ0 ≈ 0.4-0.8 kpc-1 at the galactic plane, or, equivalently, an effective cross section as low as σeff ~ 10-5 of the photoionization cross section at 912 Å is required to allow the stellar Lyc photons to travel through the H I disk. Such a low absorption coefficient is out of accord with the properties of the ISM. Furthermore, we found that even the model that has the diffuse ionized gas (DIG) phase only and no H I gas phase shows highly concentrated Hα emissions around H II regions, and can account for only lsim26% of the Hα luminosity of the DIG. This result places a strong constraint on the ionizing source of the DIG. We also report that the Hα intensity distribution functions not only of the DIG, but also of H II regions in M 51, appear to be lognormal.

Apparent diffusive motion of centrin foci in living cells: implications for diffusion-based motion in centriole duplication

NASA Astrophysics Data System (ADS)

Rafelski, Susanne M.; Keller, Lani C.; Alberts, Jonathan B.; Marshall, Wallace F.

2011-04-01

The degree to which diffusion contributes to positioning cellular structures is an open question. Here we investigate the question of whether diffusive motion of centrin granules would allow them to interact with the mother centriole. The role of centrin granules in centriole duplication remains unclear, but some proposed functions of these granules, for example, in providing pre-assembled centriole subunits, or by acting as unstable 'pre-centrioles' that need to be captured by the mother centriole (La Terra et al 2005 J. Cell Biol. 168 713-22), require the centrin foci to reach the mother. To test whether diffusive motion could permit such interactions in the necessary time scale, we measured the motion of centrin-containing foci in living human U2OS cells. We found that these centrin foci display apparently diffusive undirected motion. Using the apparent diffusion constant obtained from these measurements, we calculated the time scale required for diffusion to capture by the mother centrioles and found that it would greatly exceed the time available in the cell cycle. We conclude that mechanisms invoking centrin foci capture by the mother, whether as a pre-centriole or as a source of components to support later assembly, would require a form of directed motility of centrin foci that has not yet been observed.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into

Atoms in carbon cages as a source of interstellar diffuse lines

NASA Technical Reports Server (NTRS)

Ballester, J. L.; Antoniewicz, P. R.; Smoluchowski, R.

1990-01-01

A model to describe the resonance absorption lines of various atoms trapped in closed carbon cages is presented. These systems may be responsible for some of the as yet unexplained diffuse interstellar bands. Model potentials for possible atom-C60 systems are obtained and used to calculate the resonance lines. The trapped atoms considered are O, N, Si, Mg, Al, Na, and S, and in all cases the resonance lines are shifted toward the red as compared to the isolated atoms. The calculated wavelengths are compared to the range of wavelengths observed for the diffuse interstellar bands, and good agreement is found for Mg and Si resonance lines. Other lines may be caused by other than resonance transitions or by trapped molecules. The oscillator strengths and the abundances are evaluated and compared with observation. Mechanisms to explain the observed band width of the lines and the existence of certain correlated pairs of lines are discussed.

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.

Diffusion in coronas around clinopyroxene: modelling with local equilibrium and steady state, and a non-steady-state modification to account for zoned actinolite-hornblende

NASA Astrophysics Data System (ADS)

Ashworth, J. R.; Birdi, J. J.; Emmett, T. F.

1992-01-01

Retrograde coronas of Caledonian age, between clinopyroxene and plagioclase in the Jotun Nappe Complex, Norway, illustrate the effects of diffusion kinetics on mineral distributions among layers and on the compositions of hornblende-actinolite. One corona type comprises a symplectite of epidote + quartz adjacent to plagioclase, and a less well-organized intergrowth of amphibole + quartz replacing clinopyroxene. The observed mineral proportions imply an open-system reaction, but the similarity of Al/Si ratios in reactant plagioclase and product symplectite indicates approximate conservation of Al2O3 and SiO2. The largest inferred open-system flux is a loss of CaO, mostly derived from consumption of clinopyroxene. The approximate layer structure, Pl|Ep + Qtz|Hbl + Qtz|Act±Hbl + Qtz|Cpx, is modelled using the theory of steady-state diffusion-controlled growth with local equilibrium. To obtain a solution, it is necessary to use a reactant plagioclase composition which takes into account aluminous (epidote) inclusions. The results indicate that, in terms of Onsager diffusion coefficients L ii , Ca is more mobile than AL ( L CaCa/ L AlAl≳3.) (where ≳ means greater than or approximately equal to). This behaviour of Ca is comparable with that of Mg in previously studied coronas around olivine. Si is non-diffusing in the present modelling, because of silica saturation. Oxidation of some Fe2+ to Fe3+ occurs within the corona. Mg diffuses towards its source (clinopyroxene) to maintain local equilibrium. Other coronas consist of two layers, hornblende adjacent to plagioclase and zoned amphibole + quartz adjacent to clinopyroxene. In the zoned layer, actinolitic hornblende forms relict patches, separated from quartz blebs by more aluminous hornblende. A preliminary steady-state, local-equilibrium model of grain-boundary diffusion explains the formation of low-Al and high-Al layers as due to Al immobility. Zoning and replacement are qualitatively explained in terms of

Exploratory laboratory study of lateral turbulent diffusion at the surface of an alluvial channel

USGS Publications Warehouse

Sayre, William W.; Chamberlain, A.R.

1964-01-01

In natural streams turbulent diffusion is one of the principal mechanisms by which liquid and suspended-particulate contaminants are dispersed in the flow. A knowledge of turbulence characteristics is therefore essential in predicting the dispersal rates of contaminants in streams. In this study the theory of diffusion by continuous movements for homogeneous turbulence is applied to lateral diffusion at the surface of an open channel in which there is uniform flow. An exploratory-laboratory investigation was conducted in which the lateral dispersion at the water surface of a sand-Led flume was studied by measuring the lateral spread from a point source of small floating polyethylene articles. The experiment was restricted to a single set of low and channel geometry conditions. The results of the study indicate that with certain restrictions lateral dispersion in alluvial channels may be successfully described by the theory of diffusion by continuous movements. The experiment demonstrates a means for evaluating the lateral diffusion coefficient and also methods for quantitatively estimating fundamental turbulence properties, such as the intensity and the Lagrangian integral scale of turbulence in an alluvial channel. The experimental results show that with increasing distance from the source the coefficient of lateral turbulent diffusion increases initially but tends toward a constant limiting value. This result is in accordance with turbulent diffusion theory. Indications are that the distance downstream from the source required for the diffusion coefficient to reach its limiting value is actually very small when compared to the length scale of most diffusion phenomena in natural streams which are of practical interest.

Performance of active feedforward control systems in non-ideal, synthesized diffuse sound fields.

PubMed

Misol, Malte; Bloch, Christian; Monner, Hans Peter; Sinapius, Michael

2014-04-01

The acoustic performance of passive or active panel structures is usually tested in sound transmission loss facilities. A reverberant sending room, equipped with one or a number of independent sound sources, is used to generate a diffuse sound field excitation which acts as a disturbance source on the structure under investigation. The spatial correlation and coherence of such a synthesized non-ideal diffuse-sound-field excitation, however, might deviate significantly from the ideal case. This has consequences for the operation of an active feedforward control system which heavily relies on the acquisition of coherent disturbance source information. This work, therefore, evaluates the spatial correlation and coherence of ideal and non-ideal diffuse sound fields and considers the implications on the performance of a feedforward control system. The system under consideration is an aircraft-typical double panel system, equipped with an active sidewall panel (lining), which is realized in a transmission loss facility. Experimental results for different numbers of sound sources in the reverberation room are compared to simulation results of a comparable generic double panel system excited by an ideal diffuse sound field. It is shown that the number of statistically independent noise sources acting on the primary structure of the double panel system depends not only on the type of diffuse sound field but also on the sample lengths of the processed signals. The experimental results show that the number of reference sensors required for a defined control performance exhibits an inverse relationship to control filter length.

Diffusion MRI and its role in neuropsychology

PubMed Central

Mueller, Bryon A; Lim, Kelvin O; Hemmy, Laura; Camchong, Jazmin

2015-01-01

Diffusion Magnetic Resonance Imaging (dMRI) is a popular method used by neuroscientists to uncover unique information about the structural connections within the brain. dMRI is a non-invasive imaging methodology in which image contrast is based on the diffusion of water molecules in tissue. While applicable to many tissues in the body, this review focuses exclusively on the use of dMRI to examine white matter in the brain. In this review, we begin with a definition of diffusion and how diffusion is measured with MRI. Next we introduce the diffusion tensor model, the predominant model used in dMRI. We then describe acquisition issues related to acquisition parameters and scanner hardware and software. Sources of artifacts are then discussed, followed by a brief review of analysis approaches. We provide an overview of the limitations of the traditional diffusion tensor model, and highlight several more sophisticated non-tensor models that better describe the complex architecture of the brain’s white matter. We then touch on reliability and validity issues of diffusion measurements. Finally, we describe examples of ways in which dMRI has been applied to studies of brain disorders and how identified alterations relate to symptomatology and cognition. PMID:26255305

Classical electromagnetic fields from quantum sources in heavy-ion collisions

NASA Astrophysics Data System (ADS)

Holliday, Robert; McCarty, Ryan; Peroutka, Balthazar; Tuchin, Kirill

2017-01-01

Electromagnetic fields are generated in high energy nuclear collisions by spectator valence protons. These fields are traditionally computed by integrating the Maxwell equations with point sources. One might expect that such an approach is valid at distances much larger than the proton size and thus such a classical approach should work well for almost the entire interaction region in the case of heavy nuclei. We argue that, in fact, the contrary is true: due to the quantum diffusion of the proton wave function, the classical approximation breaks down at distances of the order of the system size. We compute the electromagnetic field created by a charged particle described initially as a Gaussian wave packet of width 1 fm and evolving in vacuum according to the Klein-Gordon equation. We completely neglect the medium effects. We show that the dynamics, magnitude and even sign of the electromagnetic field created by classical and quantum sources are different.

RADIATION SOURCES

DOEpatents

Brucer, M.H.

1958-04-15

A novel long-lived source of gamma radiation especially suitable for calibration purposes is described. The source of gamma radiation is denoted mock iodine131, which comprises a naixture of barium-133 and cesium-137. The barium and cesium are present in a barium-cesium ratio of approximately 5.7/1 to 14/1, uniformly dispersed in an ion exchange resin and a filter surrounding the resin comprised of a material of atomic number below approximately 51, and substantially 0.7 to 0.9 millimeter thick.

Dopant diffusion and segregation in semiconductor heterostructures: Part III, diffusion of Si into GaAs

NASA Astrophysics Data System (ADS)

Chen, C.-H.; Gösele, U. M.; Tan, T. Y.

We have mentioned previously that in the third part of the present series of papers, a variety of n-doping associated phenomena will be treated. Instead, we have decided that this paper, in which the subject treated is diffusion of Si into GaAs, shall be the third paper of the series. This choice is arrived at because this subject is a most relevent heterostructure problem, and also because of space and timing considerations. The main n-type dopant Si in GaAs is amphoteric which may be incorporated as shallow donor species SiGa+ and as shallow acceptor species SiAs-. The solubility of SiAs- is much lower than that of SiGa+ except at very high Si concentration levels. Hence, a severe electrical self-compensation occurs at very high Si concentrations. In this study we have modeled the Si distribution process in GaAs by assuming that the diffusing species is SiGa+ which will convert into SiAs- in accordance with their solubilities and that the point defect species governing the diffusion of SiGa+ are triply-negatively-charged Ga vacancies VGa3-. The outstanding features of the Si indiffusion profiles near the Si/GaAs interface have been quantitatively explained for the first time. Deposited on the GaAs crystal surface, the Si source material is a polycrystalline Si layer which may be undoped or n+-doped using As or P. Without the use of an As vapor phase in the ambient, the As- and P-doped source materials effectively render the GaAs crystals into an As-rich composition, which leads to a much more efficient Si indiffusion process than for the case of using undoped source materials which maintains the GaAs crystals in a relatively As-poor condition. The source material and the GaAs crystal together form a heterostructure with its junction influencing the electron distribution in the region, which, in turn, affects the Si indiffusion process prominently.

Soils as sinks or sources for diffuse pollution of the water cycle

NASA Astrophysics Data System (ADS)

Grathwohl, Peter

2010-05-01

Numerous chemical compounds have been released into the environment by human activities and can nowadays be found everywhere, i.e. in the compartments water, soil, and air, at the poles and in high mountains. Examples for a global distribution of toxic compounds are the persistent organic pollutants (PCB, dioxins, PAH, fluorinated surfactants and flame retardants, etc.: "the Stockholm dirty dozen") but also mercury and other metals. Many of these compounds reached a global distribution via the atmo¬sphere; others have been and are still directly applied to top soils at the large scale by agriculture or are released into groundwater at landfill sites or by discharge of treated or untreated waste waters. Sooner or later such compounds end up in the water cycle - often via an intermediate storage in soils. Pollutants in soils are leached by seepage waters, transferred to ground¬water, and transported to rivers via groundwater flow. Adsorbed compounds may be transported from soils into surface waters by erosion processes and will end up in the sediments. Diffuse pollution of the subsurface environment not only reflects the history of the economic development of the modern society but it is still ongoing - e.g. the number of organic pollutants released into the environment is increasing even though the con¬centrations may decrease compared to the past. Evidence shows that many compounds are persistent in the subsurface environment at large time scales (up to centuries). Thus polluted soils already are or may become a future source for pollution of adjacent compartments such as the atmosphere and groundwater. A profound understanding on how diffuse pollutants are stored and processed in the subsurface environment is crucial to assess their long term fate and transport at large scales. Thus integrated studies e.g. at the catchment scale and models are needed which couple not only the relevant compartments (soil - atmosphere - groundwater/surface waters) but also flow

An analytic model of axisymmetric mantle plume due to thermal and chemical diffusion

NASA Technical Reports Server (NTRS)

Liu, Mian; Chase, Clement G.

1990-01-01

An analytic model of axisymmetric mantle plumes driven by either thermal diffusion or combined diffusion of both heat and chemical species from a point source is presented. The governing equations are solved numerically in cylindrical coordinates for a Newtonian fluid with constant viscosity. Instead of starting from an assumed plume source, constraints on the source parameters, such as the depth of the source regions and the total heat input from the plume sources, are deduced using the geophysical characteristics of mantle plumes inferred from modelling of hotspot swells. The Hawaiian hotspot and the Bermuda hotspot are used as examples. Narrow mantle plumes are expected for likely mantle viscosities. The temperature anomaly and the size of thermal plumes underneath the lithosphere can be sensitive indicators of plume depth. The Hawaiian plume is likely to originate at a much greater depth than the Bermuda plume. One suggestive result puts the Hawaiian plume source at a depth near the core-mantle boundary and the source of the Bermuda plume in the upper mantle, close to the 700 km discontinuity. The total thermal energy input by the source region to the Hawaiian plume is about 5 x 10(10) watts. The corresponding diameter of the source region is about 100 to 150 km. Chemical diffusion from the same source does not affect the thermal structure of the plume.

Determination of Diffusion Parameters of Mean Moderation by Means of a Pulsed Neutron Source. I. Dowtherm A at 20 C; DETERMINAZIONE DEI PARAMETRI DI DIFFUSIONE DEI MEZZI MODERANTI CONIL METODO DELLA SORGENTE DI NEUTRONI PULSATA. I.DOWTHERM A (TEMPERATURE 20 C)

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

Demanins, F.; Rado, V.; Vinci, F.

1963-04-01

The macroscopic absorption cross section, diffusion constant, diffusion cooling constant, transport mean free patu, extrapolated distance, diffusion length, and mean life for thermal neutrons were determined for Dowtherm A at 20 deg C, using a pulsed neutron source. The experimental assembly and data analysis method are described, and the results are compared with other determinations. (auth)

Marangoni convection in Casson liquid flow due to an infinite disk with exponential space dependent heat source and cross-diffusion effects

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.; Shashikumar, N. S.; Hayat, T.; Alsaedi, A.

2018-06-01

Present work aims to investigate the features of the exponential space dependent heat source (ESHS) and cross-diffusion effects in Marangoni convective heat mass transfer flow due to an infinite disk. Flow analysis is comprised with magnetohydrodynamics (MHD). The effects of Joule heating, viscous dissipation and solar radiation are also utilized. The thermal and solute field on the disk surface varies in a quadratic manner. The ordinary differential equations have been obtained by utilizing Von Kármán transformations. The resulting problem under consideration is solved numerically via Runge-Kutta-Fehlberg based shooting scheme. The effects of involved pertinent flow parameters are explored by graphical illustrations. Results point out that the ESHS effect dominates thermal dependent heat source effect on thermal boundary layer growth. The concentration and temperature distributions and their associated layer thicknesses are enhanced by Marangoni effect.

Intergenerational Associations in Numerical Approximation and Mathematical Abilities

ERIC Educational Resources Information Center

Braham, Emily J.; Libertus, Melissa E.

2017-01-01

Although growing evidence suggests a link between children's math skills and their ability to estimate numerical quantities using the approximate number system (ANS), little is known about the sources underlying individual differences in ANS acuity and their relation with specific mathematical skills. To examine the role of intergenerational…

The spectrum of isotropic diffuse gamma-ray emission between 100 MeV and 820 GeV

DOE PAGES

Ackermann, M.; Ajello, M.; Albert, A.; ...

2015-01-19

We present that the γ-ray sky can be decomposed into individually detected sources, diffuse emission attributed to the interactions of Galactic cosmic rays with gas and radiation fields, and a residual all-sky emission component commonly called the isotropic diffuse γ-ray background (IGRB). The IGRB comprises all extragalactic emissions too faint or too diffuse to be resolved in a given survey, as well as any residual Galactic foregrounds that are approximately isotropic. The first IGRB measurement with the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope (Fermi) used 10 months of sky-survey data and considered an energy rangemore » between 200 MeV and 100 GeV. Improvements in event selection and characterization of cosmic-ray backgrounds, better understanding of the diffuse Galactic emission (DGE), and a longer data accumulation of 50 months allow for a refinement and extension of the IGRB measurement with the LAT, now covering the energy range from 100 MeV to 820 GeV. The IGRB spectrum shows a significant high-energy cutoff feature and can be well described over nearly four decades in energy by a power law with exponential cutoff having a spectral index of 2.32 ± 0.02 and a break energy of (279 ± 52) GeV using our baseline DGE model. In conclusion, the total intensity attributed to the IGRB is (7.2 ± 0.6) × 10 –6 cm –2 s –1 sr –1 above 100 MeV, with an additional +15%/–30% systematic uncertainty due to the Galactic diffuse foregrounds.« less

Non-kinematic Flux-transport Dynamos Including the Effects of Diffusivity Quenching

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

Ichimura, Chiaki; Yokoyama, Takaaki

2017-04-10

Turbulent magnetic diffusivity is quenched when strong magnetic fields suppress turbulent motion in a phenomenon known as diffusivity quenching. Diffusivity quenching can provide a mechanism for amplifying magnetic field and influencing global velocity fields through Lorentz force feedback. To investigate this effect, we conducted mean field flux-transport dynamo simulations that included the effects of diffusivity quenching in a non-kinematic regime. We found that toroidal magnetic field strength is amplified by up to approximately 1.5 times in the convection zone as a result of diffusivity quenching. This amplification is much weaker than that in kinematic cases as a result of Lorentzmore » force feedback on the system’s differential rotation. While amplified toroidal fields lead to the suppression of equatorward meridional flow locally near the base of the convection zone, large-scale equatorward transport of magnetic flux via meridional flow, which is the essential process of the flux-transport dynamo, is sustainable in our calculations.« less

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

Multi-mode Li diffusion in natural zircons: Evidence for diffusion in the presence of step-function concentration boundaries

NASA Astrophysics Data System (ADS)

Tang, Ming; Rudnick, Roberta L.; McDonough, William F.; Bose, Maitrayee; Goreva, Yulia

2017-09-01

Micron- to submicron-scale observations of Li distribution and Li isotope composition profiles can be used to infer the mechanisms of Li diffusion in natural zircon. Extreme fractionation (20-30‰) within each single crystal studied here confirms that Li diffusion commonly occurs in zircon. Sharp Li concentration gradients frequently seen in zircons suggest that the effective diffusivity of Li is significantly slower than experimentally determined (Cherniak and Watson, 2010; Trail et al., 2016), otherwise the crystallization/metamorphic heating of these zircons would have to be unrealistically fast (years to tens of years). Charge coupling with REE and Y has been suggested as a mechanism that may considerably reduce Li diffusivity in zircon (Ushikubo et al., 2008; Bouvier et al., 2012). We show that Li diffused in the direction of decreasing Li/Y ratio and increasing Li concentration (uphill diffusion) in one of the zircons, demonstrating charge coupling with REE and Y. Quantitative modeling reveals that Li may diffuse in at least two modes in natural zircons: one being slow and possibly coupled with REE+Y, and the other one being fast and not coupled with REE+Y. The partitioning of Li between these two modes during its diffusion may depend on the pre-diffusion substitution mechanism of REE and Y in the zircon lattice. Based on our results, sharp Li concentration gradients are not indicative of limited diffusion, and can be preserved at temperatures >700 °C on geologic timescales. Finally, large δ7 Li variations observed in the Hadean Jack Hills zircons may record kinetic fractionation, rather than a record of ancient intense weathering in the granite source materials.

Toward real-time diffuse optical tomography: accelerating light propagation modeling employing parallel computing on GPU and CPU.

PubMed

Doulgerakis, Matthaios; Eggebrecht, Adam; Wojtkiewicz, Stanislaw; Culver, Joseph; Dehghani, Hamid

2017-12-01

Parameter recovery in diffuse optical tomography is a computationally expensive algorithm, especially when used for large and complex volumes, as in the case of human brain functional imaging. The modeling of light propagation, also known as the forward problem, is the computational bottleneck of the recovery algorithm, whereby the lack of a real-time solution is impeding practical and clinical applications. The objective of this work is the acceleration of the forward model, within a diffusion approximation-based finite-element modeling framework, employing parallelization to expedite the calculation of light propagation in realistic adult head models. The proposed methodology is applicable for modeling both continuous wave and frequency-domain systems with the results demonstrating a 10-fold speed increase when GPU architectures are available, while maintaining high accuracy. It is shown that, for a very high-resolution finite-element model of the adult human head with ∼600,000 nodes, consisting of heterogeneous layers, light propagation can be calculated at ∼0.25  s/excitation source. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Vapor Transport Within the Thermal Diffusion Cloud Chamber

NASA Technical Reports Server (NTRS)

Ferguson, Frank T.; Heist, Richard H.; Nuth, Joseph A., III

2000-01-01

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

Anomalous Diffusion of Water in Lamellar Membranes Formed by Pluronic Polymers

NASA Astrophysics Data System (ADS)

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

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