Complex Geometric Models of Diffusion and Relaxation in Healthy and Damaged White Matter

PubMed Central

Farrell, Jonathan A.D.; Smith, Seth A.; Reich, Daniel S.; Calabresi, Peter A.; van Zijl, Peter C.M.

2010-01-01

Which aspects of tissue microstructure affect diffusion weighted MRI signals? Prior models, many of which use Monte-Carlo simulations, have focused on relatively simple models of the cellular microenvironment and have not considered important anatomic details. With the advent of higher-order analysis models for diffusion imaging, such as high-angular-resolution diffusion imaging (HARDI), more realistic models are necessary. This paper presents and evaluates the reproducibility of simulations of diffusion in complex geometries. Our framework is quantitative, does not require specialized hardware, is easily implemented with little programming experience, and is freely available as open-source software. Models may include compartments with different diffusivities, permeabilities, and T2 time constants using both parametric (e.g., spheres and cylinders) and arbitrary (e.g., mesh-based) geometries. Three-dimensional diffusion displacement-probability functions are mapped with high reproducibility, and thus can be readily used to assess reproducibility of diffusion-derived contrasts. PMID:19739233

The EZ diffusion model provides a powerful test of simple empirical effects.

PubMed

van Ravenzwaaij, Don; Donkin, Chris; Vandekerckhove, Joachim

2017-04-01

Over the last four decades, sequential accumulation models for choice response times have spread through cognitive psychology like wildfire. The most popular style of accumulator model is the diffusion model (Ratcliff Psychological Review, 85, 59-108, 1978), which has been shown to account for data from a wide range of paradigms, including perceptual discrimination, letter identification, lexical decision, recognition memory, and signal detection. Since its original inception, the model has become increasingly complex in order to account for subtle, but reliable, data patterns. The additional complexity of the diffusion model renders it a tool that is only for experts. In response, Wagenmakers et al. (Psychonomic Bulletin & Review, 14, 3-22, 2007) proposed that researchers could use a more basic version of the diffusion model, the EZ diffusion. Here, we simulate experimental effects on data generated from the full diffusion model and compare the power of the full diffusion model and EZ diffusion to detect those effects. We show that the EZ diffusion model, by virtue of its relative simplicity, will be sometimes better able to detect experimental effects than the data-generating full diffusion model.

Modelling Simple Experimental Platform for In Vitro Study of Drug Elution from Drug Eluting Stents (DES)

NASA Astrophysics Data System (ADS)

Kalachev, L. V.

2016-06-01

We present a simple model of experimental setup for in vitro study of drug release from drug eluting stents and drug propagation in artificial tissue samples representing blood vessels. The model is further reduced using the assumption on vastly different characteristic diffusion times in the stent coating and in the artificial tissue. The model is used to derive a relationship between the times at which the measurements have to be taken for two experimental platforms, with corresponding artificial tissue samples made of different materials with different drug diffusion coefficients, to properly compare the drug release characteristics of drug eluting stents.

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

NASA Astrophysics Data System (ADS)

Plimpton, Steven James

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

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

PubMed

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

2008-01-01

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

Identifying mechanisms for superdiffusive dynamics in cell trajectories

NASA Astrophysics Data System (ADS)

Passucci, Giuseppe; Brasch, Megan; Henderson, James; Manning, M. Lisa

Self-propelled particle (SPP) models have been used to explore features of active matter such as motility-induced phase separation, jamming, and flocking, and are often used to model biological cells. However, many cells exhibit super-diffusive trajectories, where displacements scale faster than t 1 / 2 in all directions, and these are not captured by traditional SPP models. We extract cell trajectories from image stacks of mouse fibroblast cells moving on 2D substrates and find super-diffusive mean-squared displacements in all directions across varying densities. Two SPP model modifications have been proposed to capture super-diffusive dynamics: Levy walks and heterogeneous motility parameters. In mouse fibroblast cells displacement probability distributions collapse when time is rescaled by a power greater than 1/2, which is consistent with Levy walks. We show that a simple SPP model with heterogeneous rotational noise can also generate a similar collapse. Furthermore, a close examination of statistics extracted directly from cell trajectories is consistent with a heterogeneous mobility SPP model and inconsistent with a Levy walk model. Our work demonstrates that a simple set of analyses can distinguish between mechanisms for anomalous diffusion in active matter.

Numerical Simulation of the Perrin-Like Experiments

ERIC Educational Resources Information Center

Mazur, Zygmunt; Grech, Dariusz

2008-01-01

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

Fluorescence correlation spectroscopy diffusion laws to probe the submicron cell membrane organization.

PubMed

Wawrezinieck, Laure; Rigneault, Hervé; Marguet, Didier; Lenne, Pierre-François

2005-12-01

To probe the complexity of the cell membrane organization and dynamics, it is important to obtain simple physical observables from experiments on live cells. Here we show that fluorescence correlation spectroscopy (FCS) measurements at different spatial scales enable distinguishing between different submicron confinement models. By plotting the diffusion time versus the transverse area of the confocal volume, we introduce the so-called FCS diffusion law, which is the key concept throughout this article. First, we report experimental FCS diffusion laws for two membrane constituents, which are respectively a putative raft marker and a cytoskeleton-hindered transmembrane protein. We find that these two constituents exhibit very distinct behaviors. To understand these results, we propose different models, which account for the diffusion of molecules either in a membrane comprising isolated microdomains or in a meshwork. By simulating FCS experiments for these two types of organization, we obtain FCS diffusion laws in agreement with our experimental observations. We also demonstrate that simple observables derived from these FCS diffusion laws are strongly related to confinement parameters such as the partition of molecules in microdomains and the average confinement time of molecules in a microdomain or a single mesh of a meshwork.

Suppression of Soot Formation and Shapes of Laminar Jet Diffusion Flames

NASA Technical Reports Server (NTRS)

Xu, F.; Dai, Z.; Faeth, G. M.

2001-01-01

Laminar nonpremixed (diffusion) flames are of interest because they provide model flame systems that are far more tractable for analysis and experiments than practical turbulent flames. In addition, many properties of laminar diffusion flames are directly relevant to turbulent diffusion flames using laminar flamelet concepts. Finally, laminar diffusion flame shapes have been of interest since the classical study of Burke and Schumann because they involve a simple nonintrusive measurement that is convenient for evaluating flame shape predictions. Motivated by these observations, the shapes of round hydrocarbon-fueled laminar jet diffusion flames were considered, emphasizing conditions where effects of buoyancy are small because most practical flames are not buoyant. Earlier studies of shapes of hydrocarbon-fueled nonbuoyant laminar jet diffusion flames considered combustion in still air and have shown that flames at the laminar smoke point are roughly twice as long as corresponding soot-free (blue) flames and have developed simple ways to estimate their shapes. Corresponding studies of hydrocarbon-fueled weakly-buoyant laminar jet diffusion flames in coflowing air have also been reported. These studies were limited to soot-containing flames at laminar smoke point conditions and also developed simple ways to estimate their shapes but the behavior of corresponding soot-free flames has not been addressed. This is unfortunate because ways of selecting flame flow properties to reduce soot concentrations are of great interest; in addition, soot-free flames are fundamentally important because they are much more computationally tractable than corresponding soot-containing flames. Thus, the objectives of the present investigation were to observe the shapes of weakly-buoyant laminar jet diffusion flames at both soot-free and smoke point conditions and to use the results to evaluate simplified flame shape models. The present discussion is brief.

Particle Diffusion in an Inhomogeneous Medium

ERIC Educational Resources Information Center

Bringuier, E.

2011-01-01

This paper is an elementary introduction to particle diffusion in a medium where the coefficient of diffusion varies with position. The introduction is aimed at third-year university courses. We start from a simple model of particles hopping on a discrete lattice, in one or more dimensions, and then take the continuous-space limit so as to obtain…

Chemical and Temperature Effects on Diffusion in a Model Polymer/Nanoparticle Composite

NASA Astrophysics Data System (ADS)

Janes, Dustin; Durning, Christopher

Polymers and inks used in medical devices may be strengthened with nanoparticle fillers, so an understanding of how they may affect the release of residuals and additives via diffusion will help modernize biocompatibility testing. Transport of small molecules in polymers with increasing volume fraction of impermeable nanoparticles is often poorly predicted by the simple Maxwell model for heterogeneous media. In this presentation we will examine two diffusant classes, only one of which possesses hydrogen bonding interactions with the nanoparticle surface. Since similar reductions in mutual diffusion coefficients were observed in both cases we attribute the enhancement of the ''blocking effect'' in nanocomposites to a reduction in polymer mobility in the interfacial volume near the nanoparticle. The temperature and penetrant concentration dependence of the diffusion coefficients were examined in the context of a Vrentas-Duda free volume model that includes a thermally activated prefactor. While data obtained for rubbery poly(methyl acrylate) clearly obeys the expected Arrhenius scaling with EA = 11 kJ/mol, results for films containing d = 14 nm spherical silica nanoparticles do not, providing more evidence that polymer free volume is perturbed in unexpected ways even for conceptually simple systems. National Science Foundation IGERT Program, Pall Corporation.

The Attentional Drift Diffusion Model of Simple Perceptual Decision-Making.

PubMed

Tavares, Gabriela; Perona, Pietro; Rangel, Antonio

2017-01-01

Perceptual decisions requiring the comparison of spatially distributed stimuli that are fixated sequentially might be influenced by fluctuations in visual attention. We used two psychophysical tasks with human subjects to investigate the extent to which visual attention influences simple perceptual choices, and to test the extent to which the attentional Drift Diffusion Model (aDDM) provides a good computational description of how attention affects the underlying decision processes. We find evidence for sizable attentional choice biases and that the aDDM provides a reasonable quantitative description of the relationship between fluctuations in visual attention, choices and reaction times. We also find that exogenous manipulations of attention induce choice biases consistent with the predictions of the model.

Robust estimation of cerebral hemodynamics in neonates using multilayered diffusion model for normal and oblique incidences

NASA Astrophysics Data System (ADS)

Steinberg, Idan; Harbater, Osnat; Gannot, Israel

2014-07-01

The diffusion approximation is useful for many optical diagnostics modalities, such as near-infrared spectroscopy. However, the simple normal incidence, semi-infinite layer model may prove lacking in estimation of deep-tissue optical properties such as required for monitoring cerebral hemodynamics, especially in neonates. To answer this need, we present an analytical multilayered, oblique incidence diffusion model. Initially, the model equations are derived in vector-matrix form to facilitate fast and simple computation. Then, the spatiotemporal reflectance predicted by the model for a complex neonate head is compared with time-resolved Monte Carlo (TRMC) simulations under a wide range of physiologically feasible parameters. The high accuracy of the multilayer model is demonstrated in that the deviation from TRMC simulations is only a few percent even under the toughest conditions. We then turn to solve the inverse problem and estimate the oxygen saturation of deep brain tissues based on the temporal and spatial behaviors of the reflectance. Results indicate that temporal features of the reflectance are more sensitive to deep-layer optical parameters. The accuracy of estimation is shown to be more accurate and robust than the commonly used single-layer diffusion model. Finally, the limitations of such approaches are discussed thoroughly.

Regimes of stability and scaling relations for the removal time in the asteroid belt: a simple kinetic model and numerical tests

NASA Astrophysics Data System (ADS)

Cubrovic, Mihailo

2005-02-01

We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws) between the removal time (the time for an asteroid to experience a qualitative change of dynamical behavior and enter a wide chaotic zone) and the Lyapunov time. The correlations are shown to arise in two different regimes, characterized by exponential and power-law scalings. We also show how is the so-called “stable chaos” (exponential regime) related to anomalous diffusion. Finally, we check our results numerically and discuss their possible applications in analyzing the motion of particular asteroids.

Diffusion of Defaults Among Financial Institutions

NASA Astrophysics Data System (ADS)

Demange, Gabrielle

The paper proposes a simple unified model for the diffusion of defaults across financial institutions and presents some measures for evaluating the risk imposed by a bank on the system. So far the standard contagion processes might not incorporate some important features of financial contagion.

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.

MARMOT simulations of Xe segregation to grain boundaries in UO2

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

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

2012-06-20

Diffusion of Xe and U in UO{sub 2} is controlled by vacancy mechanisms and under irradiation the formation of mobile vacancy clusters is important. We derive continuum thermodynamic and diffusion models for Xe and U in UO{sub 2} based on the vacancy and cluster diffusion mechanisms established from recent density functional theory (DFT) calculations. Segregation of defects to grain boundaries in UO{sub 2} is described by combining the diffusion model with models of the interaction between Xe atoms and vacancies with grain boundaries derived from separate atomistic calculations. The diffusion and segregation models are implemented in the MOOSE/MARMOT (MBM) finitemore » element (FEM) framework and we simulate Xe redistribution for a few simple microstructures. In this report we focus on segregation to grain boundaries. The U or vacancy diffusion model as well as the coupled diffusion of vacancies and Xe have also been implemented, but results are not included in this report.« less

Modeling of hydrogen-air diffusion flame

NASA Technical Reports Server (NTRS)

Isaac, Kakkattukuzhy

1988-01-01

The present research objective is to determine the effects of contaminants on extinction limits of simple, well defined, counterflow Hydrogen 2-air diffusion flames, with combustion at 1 atmosphere. Results of extinction studies and other flame characterizations, with appropriate mechanistic modeling (presently underway), will be used to rationalize the observed effects of contamination over a reasonably wide range of diffusion flame conditions. The knowledge gained should help efforts to anticipate the effects of contaminants on combustion processes in Hydrogen 2-fueled scramjets.

Predicting diffusion paths and interface motion in gamma/gamma + beta, Ni-Cr-Al diffusion couples

NASA Technical Reports Server (NTRS)

Nesbitt, J. A.; Heckel, R. W.

1987-01-01

A simplified model has been developed to predict Beta recession and diffusion paths in ternary gamma/gamma + beta diffusion couples (gamma:fcc, beta: NiAl structure). The model was tested by predicting beta recession and diffusion paths for four gamma/gamma + beta, Ni-Cr-Al couples annealed for 100 hours at 1200 C. The model predicted beta recession within 20 percent of that measured for each of the couples. The model also predicted shifts in the concentration of the gamma phase at the gamma/gamma + beta interface within 2 at. pct Al and 6 at. pct Cr of that measured in each of the couples. A qualitative explanation based on simple kinetic and mass balance arguments has been given which demonstrates the necessity for diffusion in the two-phase region of certain gamma/gamma + beta, Ni-Cr-Al couples.

Simulations of Xe and U diffusion in UO2

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

Andersson, Anders D.; Vyas, Shyam; Tonks, Michael R.

2012-09-10

Diffusion of xenon (Xe) and uranium (U) in UO{sub 2} is controlled by vacancy mechanisms and under irradiation the formation of mobile vacancy clusters is important. Based on the vacancy and cluster diffusion mechanisms established from density functional theory (DFT) calculations, we derive continuum thermodynamic and diffusion models for Xe and U in UO{sub 2}. In order to capture the effects of irradiation, vacancies (Va) are explicitly coupled to the Xe and U dynamics. Segregation of defects to grain boundaries in UO{sub 2} is described by combining the bulk diffusion model with models of the interaction between Xe atoms andmore » vacancies with grain boundaries, which were derived from atomistic calculations. The diffusion and segregation models were implemented in the MOOSE-Bison-Marmot (MBM) finite element (FEM) framework and the Xe/U redistribution was simulated for a few simple microstructures.« less

A scaled-ionic-charge simulation model that reproduces enhanced and suppressed water diffusion in aqueous salt solutions.

PubMed

Kann, Z R; Skinner, J L

2014-09-14

Non-polarizable models for ions and water quantitatively and qualitatively misrepresent the salt concentration dependence of water diffusion in electrolyte solutions. In particular, experiment shows that the water diffusion coefficient increases in the presence of salts of low charge density (e.g., CsI), whereas the results of simulations with non-polarizable models show a decrease of the water diffusion coefficient in all alkali halide solutions. We present a simple charge-scaling method based on the ratio of the solvent dielectric constants from simulation and experiment. Using an ion model that was developed independently of a solvent, i.e., in the crystalline solid, this method improves the water diffusion trends across a range of water models. When used with a good-quality water model, e.g., TIP4P/2005 or E3B, this method recovers the qualitative behaviour of the water diffusion trends. The model and method used were also shown to give good results for other structural and dynamic properties including solution density, radial distribution functions, and ion diffusion coefficients.

Prediction of the blowout of jet diffusion flames in a coflowing stream of air

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

Karbasi, M.; Wierzba, I.

1995-12-31

The blowout limits of a lifted diffusion flame in a coflowing stream of air are estimated using a simple model for extinction, for a range of fuels, jet diameters and co-flowing stream velocities. The proposed model uses a parameter which relates to the ratio of a time associated with the mixing processes in a turbulent jet to a characteristic chemical time. The Kolmogorov microscale of time is used as time scale in this model. It is shown that turbulent diffusion flames are quenched by excessive turbulence for a critical value of this parameter. The predicted blowout velocity of diffusion flamesmore » obtained using this model is in good agreement with the available experimental data.« less

Spatial interactions in a modified Daisyworld model: Heat diffusivity and greenhouse effects

NASA Astrophysics Data System (ADS)

Alberti, T.; Primavera, L.; Vecchio, A.; Lepreti, F.; Carbone, V.

2015-11-01

In this work we investigate a modified version of the Daisyworld model, originally introduced by Lovelock and Watson to describe in a simple way the interactions between an Earth-like planet, its biosphere, and the incoming solar radiation. Here a spatial dependency on latitude is included, and both a variable heat diffusivity along latitudes and a simple greenhouse effect description are introduced in the model. We show that the spatial interactions between the variables of the system can locally stabilize the coexistence of the two vegetation types. The feedback on albedo is able to generate equilibrium solutions which can efficiently self-regulate the planet climate, even for values of the solar luminosity relatively far from the current Earth conditions.

A critical examination of the validity of simplified models for radiant heat transfer analysis.

NASA Technical Reports Server (NTRS)

Toor, J. S.; Viskanta, R.

1972-01-01

Examination of the directional effects of the simplified models by comparing the experimental data with the predictions based on simple and more detailed models for the radiation characteristics of surfaces. Analytical results indicate that the constant property diffuse and specular models do not yield the upper and lower bounds on local radiant heat flux. In general, the constant property specular analysis yields higher values of irradiation than the constant property diffuse analysis. A diffuse surface in the enclosure appears to destroy the effect of specularity of the other surfaces. Semigray and gray analyses predict the irradiation reasonably well provided that the directional properties and the specularity of the surfaces are taken into account. The uniform and nonuniform radiosity diffuse models are in satisfactory agreement with each other.

Interplay between translational diffusion and large-amplitude angular jumps of water molecules

NASA Astrophysics Data System (ADS)

Liu, Chao; Zhang, Yangyang; Zhang, Jian; Wang, Jun; Li, Wenfei; Wang, Wei

2018-05-01

Understanding the microscopic mechanism of water molecular translational diffusion is a challenging topic in both physics and chemistry. Here, we report an investigation on the interplay between the translational diffusion and the large-amplitude angular jumps of water molecules in bulk water using molecular dynamics simulations. We found that large-amplitude angular jumps are tightly coupled to the translational diffusions. Particularly, we revealed that concurrent rotational jumps of spatially neighboring water molecules induce inter-basin translational jumps, which contributes to the fast component of the water translational diffusion. Consequently, the translational diffusion shows positional heterogeneity; i.e., the neighbors of the water molecules with inter-basin translational jumps have larger probability to diffuse by inter-basin translational jumps. Our control simulations showed that a model water molecule with moderate hydrogen bond strength can diffuse much faster than a simple Lennard-Jones particle in bulk water due to the capability of disturbing the hydrogen bond network of the surrounding water molecules. Our results added to the understanding of the microscopic picture of the water translational diffusion and demonstrated the unique features of water diffusion arising from their hydrogen bond network structure compared with those of the simple liquids.

1/f model for long-time memory of the ocean surface temperature

NASA Astrophysics Data System (ADS)

Fraedrich, Klaus; Luksch, Ute; Blender, Richard

2004-09-01

The 1/f spectrum of the ocean surface temperature in the Atlantic and Pacific midlatitudes is explained by a simple vertical diffusion model with a shallow mixed layer on top of a deep ocean. The model is forced at the air-sea interface with the total surface heat flux from a 1000 year climate simulation. The analysis reveals the role of ocean advection and substantiates estimates of internal thermal diffusivities.

Surface diffusion of cyclic hydrocarbons on nickel

NASA Astrophysics Data System (ADS)

Silverwood, I. P.; Armstrong, J.

2018-08-01

Surface diffusion of adsorbates is difficult to measure on realistic systems, yet it is of fundamental interest in catalysis and coating reactions. quasielastic neutron scattering (QENS) was used to investigate the diffusion of cyclohexane and benzene adsorbed on a nickel metal sponge catalyst. Molecular dynamics simulations of benzene on a model (111) nickel surface showed localised motion with diffusion by intermittent jumps. The experimental data was therefore fitted to the Singwi-Sjölander model and activation energies for diffusion of 4.0 kJ mol-1 for benzene and 4.3 kJ mol-1 for cyclohexane were calculated for the two dimensional model. Limited motion out-of plane was seen in the dynamics simulations and is discussed, although the resolution of the scattering experiment is insufficient to quantify this. Good agreement is seen between the use of a perfect crystal as a model for a disordered system over short time scales, suggesting that simple models are adequate to describe diffusion over polycrystalline metal surfaces on the timescale of QENS measurement.

Evaluation of the ability of arsenic species to traverse cell membranes by simple diffusion using octanol-water and liposome-water partition coefficients.

PubMed

Chávez-Capilla, Teresa; Maher, William; Kelly, Tamsin; Foster, Simon

2016-11-01

Arsenic metabolism in living organisms is dependent on the ability of different arsenic species to traverse biological membranes. Simple diffusion provides an alternative influx and efflux route to mediated transport mechanisms that can increase the amount of arsenic available for metabolism in cells. Using octanol-water and liposome-water partition coefficients, the ability of arsenous acid, arsenate, methylarsonate, dimethylarsinate, thio-methylarsonate, thio-dimethylarsinic acid, arsenotriglutathione and monomethylarsonic diglutathione to diffuse through the lipid bilayer of cell membranes was investigated. Molecular modelling of arsenic species was used to explain the results. All arsenic species with the exception of arsenate, methylarsonate and thio-methylarsonate were able to diffuse through the lipid bilayer of liposomes, with liposome-water partition coefficients between 0.04 and 0.13. Trivalent arsenic species and thio-pentavalent arsenic species showed higher partition coefficients, suggesting that they can easily traverse cell membranes by passive simple diffusion. Given the higher toxicity of these species compared to oxo-pentavalent arsenic species, this study provides evidence supporting the risk associated with human exposure to trivalent and thio-arsenic species. Copyright © 2016. Published by Elsevier B.V.

Flame Shapes of Luminous NonBuoyant Laminar Coflowing Jet Diffusion Flames

NASA Technical Reports Server (NTRS)

Lin, K.-C.; Faeth, G. M.

1999-01-01

Laminar diffusion flames are of interest as model flame systems that are more tractable for analysis and experiments than practical turbulent diffusion flames. Certainly understanding laminar flames must precede understanding more complex turbulent flames while man'y laminar diffusion flame properties are directly relevant to turbulent diffusion flames using laminar flamelet concepts. Laminar diffusion flame shapes have been of interest since the classical study of Burke and Schumann because they involve a simple nonintrusive measurement that is convenient for evaluating flame structure predictions. Motivated by these observations, the shapes of laminar flames were considered during the present investigation. The present study was limited to nonbuoyant flames because most practical flames are not buoyant. Effects of buoyancy were minimized by observing flames having large flow velocities at small pressures. Present methods were based on the study of the shapes of nonbu,3yant round laminar jet diffusion flames of Lin et al. where it was found that a simple analysis due to Spalding yielded good predictions of the flame shapes reported by Urban et al. and Sunderland et al.

Regression-based model of skin diffuse reflectance for skin color analysis

NASA Astrophysics Data System (ADS)

Tsumura, Norimichi; Kawazoe, Daisuke; Nakaguchi, Toshiya; Ojima, Nobutoshi; Miyake, Yoichi

2008-11-01

A simple regression-based model of skin diffuse reflectance is developed based on reflectance samples calculated by Monte Carlo simulation of light transport in a two-layered skin model. This reflectance model includes the values of spectral reflectance in the visible spectra for Japanese women. The modified Lambert Beer law holds in the proposed model with a modified mean free path length in non-linear density space. The averaged RMS and maximum errors of the proposed model were 1.1 and 3.1%, respectively, in the above range.

Angular intensity and polarization dependence of diffuse transmission through random media

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

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

1993-03-01

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

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

PubMed

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

2018-03-16

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

On Diffusive Climatological Models.

NASA Astrophysics Data System (ADS)

Griffel, D. H.; Drazin, P. G.

1981-11-01

A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.

The attentional drift-diffusion model extends to simple purchasing decisions.

PubMed

Krajbich, Ian; Lu, Dingchao; Camerer, Colin; Rangel, Antonio

2012-01-01

How do we make simple purchasing decisions (e.g., whether or not to buy a product at a given price)? Previous work has shown that the attentional drift-diffusion model (aDDM) can provide accurate quantitative descriptions of the psychometric data for binary and trinary value-based choices, and of how the choice process is guided by visual attention. Here we extend the aDDM to the case of purchasing decisions, and test it using an eye-tracking experiment. We find that the model also provides a reasonably accurate quantitative description of the relationship between choice, reaction time, and visual fixations using parameters that are very similar to those that best fit the previous data. The only critical difference is that the choice biases induced by the fixations are about half as big in purchasing decisions as in binary choices. This suggests that a similar computational process is used to make binary choices, trinary choices, and simple purchasing decisions.

The Attentional Drift-Diffusion Model Extends to Simple Purchasing Decisions

PubMed Central

Krajbich, Ian; Lu, Dingchao; Camerer, Colin; Rangel, Antonio

2012-01-01

How do we make simple purchasing decisions (e.g., whether or not to buy a product at a given price)? Previous work has shown that the attentional drift-diffusion model (aDDM) can provide accurate quantitative descriptions of the psychometric data for binary and trinary value-based choices, and of how the choice process is guided by visual attention. Here we extend the aDDM to the case of purchasing decisions, and test it using an eye-tracking experiment. We find that the model also provides a reasonably accurate quantitative description of the relationship between choice, reaction time, and visual fixations using parameters that are very similar to those that best fit the previous data. The only critical difference is that the choice biases induced by the fixations are about half as big in purchasing decisions as in binary choices. This suggests that a similar computational process is used to make binary choices, trinary choices, and simple purchasing decisions. PMID:22707945

The Gini coefficient: a methodological pilot study to assess fetal brain development employing postmortem diffusion MRI.

PubMed

Viehweger, Adrian; Riffert, Till; Dhital, Bibek; Knösche, Thomas R; Anwander, Alfred; Stepan, Holger; Sorge, Ina; Hirsch, Wolfgang

2014-10-01

Diffusion-weighted imaging (DWI) is important in the assessment of fetal brain development. However, it is clinically challenging and time-consuming to prepare neuromorphological examinations to assess real brain age and to detect abnormalities. To demonstrate that the Gini coefficient can be a simple, intuitive parameter for modelling fetal brain development. Postmortem fetal specimens(n = 28) were evaluated by diffusion-weighted imaging (DWI) on a 3-T MRI scanner using 60 directions, 0.7-mm isotropic voxels and b-values of 0, 150, 1,600 s/mm(2). Constrained spherical deconvolution (CSD) was used as the local diffusion model. Fractional anisotropy (FA), apparent diffusion coefficient (ADC) and complexity (CX) maps were generated. CX was defined as a novel diffusion metric. On the basis of those three parameters, the Gini coefficient was calculated. Study of fetal brain development in postmortem specimens was feasible using DWI. The Gini coefficient could be calculated for the combination of the three diffusion parameters. This multidimensional Gini coefficient correlated well with age (Adjusted R(2) = 0.59) between the ages of 17 and 26 gestational weeks. We propose a new method that uses an economics concept, the Gini coefficient, to describe the whole brain with one simple and intuitive measure, which can be used to assess the brain's developmental state.

Continuous versus discontinuous albedo representations in a simple diffusive climate model

NASA Astrophysics Data System (ADS)

Simmons, P. A.; Griffel, D. H.

1988-07-01

A one-dimensional annually and zonally averaged energy-balance model, with diffusive meridional heat transport and including icealbedo feedback, is considered. This type of model is found to be very sensitive to the form of albedo used. The solutions for a discontinuous step-function albedo are compared to those for a more realistic smoothly varying albedo. The smooth albedo gives a closer fit to present conditions, but the discontinuous form gives a better representation of climates in earlier epochs.

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

PubMed

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

2010-01-01

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

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.

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.

Interpretation of leaching data for cementitious waste forms using analytical solutions based on mass transport theory and empiricism

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

Spence, R.D.; Godbee, H.W.; Tallent, O.K.

1991-01-01

Despite the demonstrated importance of diffusion control in leaching, other mechanisms have been observed to play a role and leaching from porous solid bodies is not simple diffusion. Only simple diffusion theory has been developed well enough for extrapolation, as yet. The well developed diffusion theory, used in data analysis by ANSI/ANS-16.1 and the NEWBOX program, can help in trying to extrapolate and predict the performance of solidified waste forms over decades and centuries, but the limitations and increased uncertainty must be understood in so doing. Treating leaching as a semi-infinite medium problem, as done in the Cote model, resultsmore » in simpler equations, but limits, application to early leaching behavior when less than 20% of a given component has been leached. 18 refs., 2 tabs.« less

Characteristic power spectrum of diffusive interface dynamics in the two-dimensional Ising model

NASA Astrophysics Data System (ADS)

Masumoto, Yusuke; Takesue, Shinji

2018-05-01

We investigate properties of the diffusive motion of an interface in the two-dimensional Ising model in equilibrium or nonequilibrium situations. We focused on the relation between the power spectrum of a time sequence of spins and diffusive motion of an interface which was already clarified in one-dimensional systems with a nonequilibrium phase transition like the asymmetric simple exclusion process. It is clarified that the interface motion is a diffusion process with a drift force toward the higher-temperature side when the system is in contact with heat reservoirs at different temperatures and heat transfers through the system. Effects of the width of the interface are also discussed.

Diffuse scattering in relaxor ferroelectrics: true three-dimensional mapping, experimental artefacts and modelling.

PubMed

Bosak, A; Chernyshov, D; Vakhrushev, Sergey; Krisch, M

2012-01-01

The available body of experimental data in terms of the relaxor-specific component of diffuse scattering is critically analysed and a collection of related models is reviewed; the sources of experimental artefacts and consequent failures of modelling efforts are enumerated. Furthermore, it is shown that the widely used concept of polar nanoregions as individual static entities is incompatible with the experimental diffuse scattering results. Based on the synchrotron diffuse scattering three-dimensional data set taken for the prototypical ferroelectric relaxor lead magnesium niobate-lead titanate (PMN-PT), a new parameterization of diffuse scattering in relaxors is presented and a simple phenomenological picture is proposed to explain the unusual properties of the relaxor behaviour. The model assumes a specific slowly changing displacement pattern, which is indirectly controlled by the low-energy acoustic phonons of the system. The model provides a qualitative but rather detailed explanation of temperature, pressure and electric-field dependence of diffuse neutron and X-ray scattering, as well as of the existence of a hierarchy in the relaxation times of these materials.

Determination of thermal diffusivities of cylindrical bodies being cooled

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

Dincer, I.

1996-09-01

This paper deals with the development of an analytical model for determining the thermal diffusivities of the individual solid cylindrical bodies subjected to cooling is presented. Applications of this model were made using the experimental center temperature data obtained from the cylindrical products (e.g., cucumber and grape) during air cooling at the flow velocity of 2 m/s. As an experimental result, the thermal diffusivities of products were found to be 1.45{times}10{sup {minus}7} m{sup 2}/s for cucumber and 1.68{times}10{sup {minus}7} m{sup 2}/s for grape. It can be concluded that the present model is capable of determining the thermal diffusivities of cylindricalmore » bodies during cooling in a simple and effective form.« less

A Simple and Accurate Method To Calculate Free Energy Profiles and Reaction Rates from Restrained Molecular Simulations of Diffusive Processes.

PubMed

Ovchinnikov, Victor; Nam, Kwangho; Karplus, Martin

2016-08-25

A method is developed to obtain simultaneously free energy profiles and diffusion constants from restrained molecular simulations in diffusive systems. The method is based on low-order expansions of the free energy and diffusivity as functions of the reaction coordinate. These expansions lead to simple analytical relationships between simulation statistics and model parameters. The method is tested on 1D and 2D model systems; its accuracy is found to be comparable to or better than that of the existing alternatives, which are briefly discussed. An important aspect of the method is that the free energy is constructed by integrating its derivatives, which can be computed without need for overlapping sampling windows. The implementation of the method in any molecular simulation program that supports external umbrella potentials (e.g., CHARMM) requires modification of only a few lines of code. As a demonstration of its applicability to realistic biomolecular systems, the method is applied to model the α-helix ↔ β-sheet transition in a 16-residue peptide in implicit solvent, with the reaction coordinate provided by the string method. Possible modifications of the method are briefly discussed; they include generalization to multidimensional reaction coordinates [in the spirit of the model of Ermak and McCammon (Ermak, D. L.; McCammon, J. A. J. Chem. Phys. 1978, 69, 1352-1360)], a higher-order expansion of the free energy surface, applicability in nonequilibrium systems, and a simple test for Markovianity. In view of the small overhead of the method relative to standard umbrella sampling, we suggest its routine application in the cases where umbrella potential simulations are appropriate.

Scaling laws of passive-scalar diffusion in the interstellar medium

NASA Astrophysics Data System (ADS)

Colbrook, Matthew J.; Ma, Xiangcheng; Hopkins, Philip F.; Squire, Jonathan

2017-05-01

Passive-scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the fundamental scaling laws remain poorly understood in the highly supersonic, magnetized, shearing regime relevant for the ISM. We therefore study the full scaling laws governing passive-scalar transport in idealized simulations of supersonic turbulence. Using simple phenomenological arguments for the variation of diffusivity with scale based on Richardson diffusion, we propose a simple fractional diffusion equation to describe the turbulent advection of an initial passive scalar distribution. These predictions agree well with the measurements from simulations, and vary with turbulent Mach number in the expected manner, remaining valid even in the presence of a large-scale shear flow (e.g. rotation in a galactic disc). The evolution of the scalar distribution is not the same as obtained using simple, constant 'effective diffusivity' as in Smagorinsky models, because the scale dependence of turbulent transport means an initially Gaussian distribution quickly develops highly non-Gaussian tails. We also emphasize that these are mean scalings that apply only to ensemble behaviours (assuming many different, random scalar injection sites): individual Lagrangian 'patches' remain coherent (poorly mixed) and simply advect for a large number of turbulent flow-crossing times.

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

NASA Astrophysics Data System (ADS)

Alejandro Quinones, Angel Luis

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

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

PubMed

Caputo, Michele; Cametti, Cesare

2017-09-01

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

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes.

PubMed

Chatterjee, Abhijit; Vlachos, Dionisios G

2007-07-21

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

Reconciling phase diffusion and Hartree-Fock approximation in condensate systems

NASA Astrophysics Data System (ADS)

Giorgi, Gian Luca; de Pasquale, Ferdinando

2012-01-01

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

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.

Characteristic time scales for diffusion processes through layers and across interfaces

NASA Astrophysics Data System (ADS)

Carr, Elliot J.

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Characteristic time scales for diffusion processes through layers and across interfaces.

PubMed

Carr, Elliot J

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Effects of 3 dimensional crystal geometry and orientation on 1D and 2D time-scale determinations of magmatic processes using olivine and orthopyroxene

NASA Astrophysics Data System (ADS)

Shea, Thomas; Krimer, Daniel; Costa, Fidel; Hammer, Julia

2014-05-01

One of the achievements in recent years in volcanology is the determination of time-scales of magmatic processes via diffusion in minerals and its addition to the petrologists' and volcanologists' toolbox. The method typically requires one-dimensional modeling of randomly cut crystals from two-dimensional thin sections. Here we address the question whether using 1D (traverse) or 2D (surface) datasets exploited from randomly cut 3D crystals introduces a bias or dispersion in the time-scales estimated, and how this error can be improved or eliminated. Computational simulations were performed using a concentration-dependent, finite-difference solution to the diffusion equation in 3D. The starting numerical models involved simple geometries (spheres, parallelepipeds), Mg/Fe zoning patterns (either normal or reverse), and isotropic diffusion coefficients. Subsequent models progressively incorporated more complexity, 3D olivines possessing representative polyhedral morphologies, diffusion anisotropy along the different crystallographic axes, and more intricate core-rim zoning patterns. Sections and profiles used to compare 1, 2 and 3D diffusion models were selected to be (1) parallel to the crystal axes, (2) randomly oriented but passing through the olivine center, or (3) randomly oriented and sectioned. Results show that time-scales estimated on randomly cut traverses (1D) or surfaces (2D) can be widely distributed around the actual durations of 3D diffusion (~0.2 to 10 times the true diffusion time). The magnitude over- or underestimations of duration are a complex combination of the geometry of the crystal, the zoning pattern, the orientation of the cuts with respect to the crystallographic axes, and the degree of diffusion anisotropy. Errors on estimated time-scales retrieved from such models may thus be significant. Drastic reductions in the uncertainty of calculated diffusion times can be obtained by following some simple guidelines during the course of data collection (i.e. selection of crystals and concentration profiles, acquisition of crystallographic orientation data), thus allowing derivation of robust time-scales.

Simple Analytical Forms of the Perpendicular Diffusion Coefficient for Two-component Turbulence. III. Damping Model of Dynamical Turbulence

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

Gammon, M.; Shalchi, A., E-mail: andreasm4@yahoo.com

2017-10-01

In several astrophysical applications one needs analytical forms of cosmic-ray diffusion parameters. Some examples are studies of diffusive shock acceleration and solar modulation. In the current article we explore perpendicular diffusion based on the unified nonlinear transport theory. While we focused on magnetostatic turbulence in Paper I, we included the effect of dynamical turbulence in Paper II of the series. In the latter paper we assumed that the temporal correlation time does not depend on the wavenumber. More realistic models have been proposed in the past, such as the so-called damping model of dynamical turbulence. In the present paper wemore » derive analytical forms for the perpendicular diffusion coefficient of energetic particles in two-component turbulence for this type of time-dependent turbulence. We present new formulas for the perpendicular diffusion coefficient and we derive a condition for which the magnetostatic result is recovered.« less

Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion.

PubMed

Mak, D O; Webb, W W

1997-03-01

A Green's function approach is developed from first principles to evaluate the power spectral density of conductance fluctuations caused by ion concentration fluctuations via diffusion in an electrolyte system. This is applied to simple geometric models of transmembrane ion channels to obtain an estimate of the magnitude of ion concentration fluctuation noise in the channel current. Pure polypeptide alamethicin forms stable ion channels with multiple conductance states in artificial phospholipid bilayers isolated onto tips of micropipettes with gigaohm seals. In the single-channel current recorded by voltage-clamp techniques, excess noise was found after the background instrumental noise and the intrinsic Johnson and shot noises were removed. The noise que to ion concentration fluctuations via diffusion was isolated by the dependence of the excess current noise on buffer ion concentration. The magnitude of the concentration fluctuation noise derived from experimental data lies within limits estimated using our simple geometric channel models. Variation of the noise magnitude for alamethicin channels in various conductance states agrees with theoretical prediction.

A simple model of the effect of ocean ventilation on ocean heat uptake

NASA Astrophysics Data System (ADS)

Nadiga, Balu; Urban, Nathan

2017-11-01

Transport of water from the surface mixed layer into the ocean interior is achieved, in large part, by the process of ventilation-a process associated with outcropping isopycnals. Starting from such a configuration of outcropping isopycnals, we derive a simple model of the effect of ventilation on ocean uptake of anomalous radiative forcing. This model can be seen as an improvement of the popular anomaly-diffusing class of energy balance models (AD-EBM) that are routinely employed to analyze and emulate the warming response of both observed and simulated Earth system. We demonstrate that neither multi-layer, nor continuous-diffusion AD-EBM variants can properly represent both surface-warming and the vertical distribution of ocean heat uptake. The new model overcomes this deficiency. The simplicity of the models notwithstanding, the analysis presented and the necessity of the modification is indicative of the role played by processes related to the down-welling branch of global ocean circulation in shaping the vertical distribution of ocean heat uptake.

Sustained currents in coupled diffusive systems

NASA Astrophysics Data System (ADS)

Larralde, Hernán; Sanders, David P.

2014-08-01

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

Homogenization of Large-Scale Movement Models in Ecology

USGS Publications Warehouse

Garlick, M.J.; Powell, J.A.; Hooten, M.B.; McFarlane, L.R.

2011-01-01

A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impact of small scale (10-100 m) habitat variability on large scale (10-100 km) movement. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. The simplicity of this homogenization procedure is striking when compared to the multi-dimensional homogenization procedure for Fickian diffusion,and the method will be equally straightforward for more complex models. ?? 2010 Society for Mathematical Biology.

Mathematical model for steady state, simple ampholyte isoelectric focusing: Development, computer simulation and implementation

NASA Technical Reports Server (NTRS)

Palusinski, O. A.; Allgyer, T. T.

1979-01-01

The elimination of Ampholine from the system by establishing the pH gradient with simple ampholytes is proposed. A mathematical model was exercised at the level of the two-component system by using values for mobilities, diffusion coefficients, and dissociation constants representative of glutamic acid and histidine. The constants assumed in the calculations are reported. The predictions of the model and computer simulation of isoelectric focusing experiments are in direct importance to obtain Ampholine-free, stable pH gradients.

Inferring Diffusion Dynamics from FCS in Heterogeneous Nuclear Environments

PubMed Central

Tsekouras, Konstantinos; Siegel, Amanda P.; Day, Richard N.; Pressé, Steve

2015-01-01

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show—first using synthetic data—that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell’s nucleus as well as 2) in the cell’s cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins. PMID:26153697

Chemistry in dynamically evolving clouds

NASA Technical Reports Server (NTRS)

Tarafdar, S. P.; Prasad, S. S.; Huntress, W. T., Jr.; Villere, K. R.; Black, D. C.

1985-01-01

A unified model of chemical and dynamical evolution of isolated, initially diffuse and quiescent interstellar clouds is presented. The model uses a semiempirically derived dependence of the observed cloud temperatures on the visual extinction and density. Even low-mass, low-density, diffuse clouds can collapse in this model, because the inward pressure gradient force assists gravitational contraction. In contrast, previous isothermal collapse models required the low-mass diffuse clouds to be unrealistically cold before gravitational contraction could start. Theoretically predicted dependences of the column densities of various atoms and molecules, such as C and CO, on visual extinction in diffuse clouds are in accord with observations. Similarly, the predicted dependences of the fractional abundances of various chemical species (e.g., CO, H2CO, HCN, HCO(+)) on the total hydrogen density in the core of the dense clouds also agree with observations reported to date in the literature. Compared with previous models of interstellar chemistry, the present model has the potential to explain the wide spectrum of chemical and physical properties of both diffuse and dense clouds with a common formalism employing only a few simple initial conditions.

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

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

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

2014-10-31

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

Coiled to diffuse: Brownian motion of a helical bacterium.

PubMed

Butenko, Alexander V; Mogilko, Emma; Amitai, Lee; Pokroy, Boaz; Sloutskin, Eli

2012-09-11

We employ real-time three-dimensional confocal microscopy to follow the Brownian motion of a fixed helically shaped Leptospira interrogans (LI) bacterium. We extract from our measurements the translational and the rotational diffusion coefficients of this bacterium. A simple theoretical model is suggested, perfectly reproducing the experimental diffusion coefficients, with no tunable parameters. An older theoretical model, where edge effects are neglected, dramatically underestimates the observed rates of translation. Interestingly, the coiling of LI increases its rotational diffusion coefficient by a factor of 5, compared to a (hypothetical) rectified bacterium of the same contour length. Moreover, the translational diffusion coefficients would have decreased by a factor of ~1.5, if LI were rectified. This suggests that the spiral shape of the spirochaete bacteria, in addition to being employed for their active twisting motion, may also increase the ability of these bacteria to explore the surrounding fluid by passive Brownian diffusion.

Room-Temperature Micron-Scale Exciton Migration in a Stabilized Emissive Molecular Aggregate.

PubMed

Caram, Justin R; Doria, Sandra; Eisele, Dörthe M; Freyria, Francesca S; Sinclair, Timothy S; Rebentrost, Patrick; Lloyd, Seth; Bawendi, Moungi G

2016-11-09

We report 1.6 ± 1 μm exciton transport in self-assembled supramolecular light-harvesting nanotubes (LHNs) assembled from amphiphillic cyanine dyes. We stabilize LHNs in a sucrose glass matrix, greatly reducing light and oxidative damage and allowing the observation of exciton-exciton annihilation signatures under weak excitation flux. Fitting to a one-dimensional diffusion model, we find an average exciton diffusion constant of 55 ± 20 cm 2 /s, among the highest measured for an organic system. We develop a simple model that uses cryogenic measurements of static and dynamic energetic disorder to estimate a diffusion constant of 32 cm 2 /s, in agreement with experiment. We ascribe large exciton diffusion lengths to low static and dynamic energetic disorder in LHNs. We argue that matrix-stabilized LHNS represent an excellent model system to study coherent excitonic transport.

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

PubMed

Huang, Kuan-Chun; White, Ryan J

2013-08-28

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

A Simple Classroom Simulation of Heat Energy Diffusing through a Metal Bar

ERIC Educational Resources Information Center

Kinsler, Mark; Kinzel, Evelyn

2007-01-01

We present an iterative procedure that does not rely on calculus to model heat flow through a uniform bar of metal and thus avoids the use of the partial differential equation typically needed to describe heat diffusion. The procedure is based on first principles and can be done with students at the blackboard. It results in a plot that…

Opening the closed box: lattice diffusion in zircon?

NASA Astrophysics Data System (ADS)

Wheeler, J.; MacDonald, J.; Goodenough, K. M.; Crowley, Q.; Harley, S.; Mariani, E.

2015-12-01

In principle, any radiogenic parent or daughter element can diffuse through any crystalline lattice. Given improved analytic techniques and mathematical models, geochronology is beginning to take such diffusion into account in a quantitative fashion. Whilst lattice diffusion compromises simple interpretation of radiometric data, it can, when combined with spatially resolved data, provide more detailed insight into thermal histories. In regions that have experienced particularly high temperatures diffusion may become significant in minerals normally thought to be reliably closed. We have modelled Pb diffusion in zircon, building on earlier work on Ar diffusion in micas - the mathematics being basically the same. We are motivated by some challenging isotope data from zircon in the Lewisian Complex of NW Scotland (a TTG region with a long Archaean and Proterozoic history). For example we have grains with old rims and younger cores. Whilst other explanations are possible, we show how lattice diffusion of Pb is plausible, using experimental diffusion data together with estimates of ultra-high temperatures from the region. We have modified a previous model for Ar diffusion ("Diffarg") to include variations in parent isotope concentration, so we can understand the consequences of U zonation within zircon grains during prolonged thermal histories. This is also relevant to asking why Pb has apparently not diffused in zircon from other UHT regions - or has it?

Simple diffusion can support the pitchfork, the flip bifurcations, and the chaos

NASA Astrophysics Data System (ADS)

Meng, Lili; Li, Xinfu; Zhang, Guang

2017-12-01

In this paper, a discrete rational fration population model with the Dirichlet boundary conditions will be considered. According to the discrete maximum principle and the sub- and supper-solution method, the necessary and sufficient conditions of uniqueness and existence of positive steady state solutions will be obtained. In addition, the dynamical behavior of a special two patch metapopulation model is investigated by using the bifurcation method, the center manifold theory, the bifurcation diagrams and the largest Lyapunov exponent. The results show that there exist the pitchfork, the flip bifurcations, and the chaos. Clearly, these phenomena are caused by the simple diffusion. The theoretical analysis of chaos is very imortant, unfortunately, there is not any results in this hand. However, some open problems are given.

Modelling nematode movement using time-fractional dynamics.

PubMed

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

2007-09-07

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

Self-diffusion in compressively strained Ge

NASA Astrophysics Data System (ADS)

Kawamura, Yoko; Uematsu, Masashi; Hoshi, Yusuke; Sawano, Kentarou; Myronov, Maksym; Shiraki, Yasuhiro; Haller, Eugene E.; Itoh, Kohei M.

2011-08-01

Under a compressive biaxial strain of ˜ 0.71%, Ge self-diffusion has been measured using an isotopically controlled Ge single-crystal layer grown on a relaxed Si0.2Ge0.8 virtual substrate. The self-diffusivity is enhanced by the compressive strain and its behavior is fully consistent with a theoretical prediction of a generalized activation volume model of a simple vacancy mediated diffusion, reported by Aziz et al. [Phys. Rev. B 73, 054101 (2006)]. The activation volume of (-0.65±0.21) times the Ge atomic volume quantitatively describes the observed enhancement due to the compressive biaxial strain very well.

Comparison of ACCENT 2000 Shuttle Plume Data with SIMPLE Model Predictions

NASA Astrophysics Data System (ADS)

Swaminathan, P. K.; Taylor, J. C.; Ross, M. N.; Zittel, P. F.; Lloyd, S. A.

2001-12-01

The JHU/APL Stratospheric IMpact of PLume Effluents (SIMPLE)model was employed to analyze the trace species in situ composition data collected during the ACCENT 2000 intercepts of the space shuttle Space Transportation Launch System (STS) rocket plume as a function of time and radial location within the cold plume. The SIMPLE model is initialized using predictions for species depositions calculated using an afterburning model based on standard TDK/SPP nozzle and SPF plume flowfield codes with an expanded chemical kinetic scheme. The time dependent ambient stratospheric chemistry is fully coupled to the plume species evolution whose transport is based on empirically derived diffusion. Model/data comparisons are encouraging through capturing observed local ozone recovery times as well as overall morphology of chlorine chemistry.

Multiscale simulation of xenon diffusion and grain boundary segregation in UO₂

DOE PAGES

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

2015-07-01

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

Diffusion models of the flanker task: Discrete versus gradual attentional selection

PubMed Central

White, Corey N.; Ratcliff, Roger; Starns, Jeffrey S.

2011-01-01

The present study tested diffusion models of processing in the flanker task, in which participants identify a target that is flanked by items that indicate the same (congruent) or opposite response (incongruent). Single- and dual-process flanker models were implemented in a diffusion-model framework and tested against data from experiments that manipulated response bias, speed/accuracy tradeoffs, attentional focus, and stimulus configuration. There was strong mimcry among the models, and each captured the main trends in the data for the standard conditions. However, when more complex conditions were used, a single-process spotlight model captured qualitative and quantitative patterns that the dual-process models could not. Since the single-process model provided the best balance of fit quality and parsimony, the results indicate that processing in the simple versions of the flanker task is better described by gradual rather than discrete narrowing of attention. PMID:21964663

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

PubMed

Kong, Muwen; Van Houten, Bennett

2017-08-01

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

Laminar flamelet modeling of turbulent diffusion flames

NASA Technical Reports Server (NTRS)

Mell, W. E.; Kosaly, G.; Planche, O.; Poinsot, T.; Ferziger, J. H.

1990-01-01

In modeling turbulent combustion, decoupling the chemistry from the turbulence is of great practical significance. In cases in which the equilibrium chemistry model breaks down, laminar flamelet modeling (LFM) is a promising approach to decoupling. Here, the validity of this approach is investigated using direct numerical simulation of a simple chemical reaction in two-dimensional turbulence.

Out-diffusion of deep donors in nitrogen-doped silicon and the diffusivity of vacancies

NASA Astrophysics Data System (ADS)

Voronkov, V. V.; Falster, R.

2012-07-01

A strong resistivity increase in annealed nitrogen-doped silicon samples was reported long ago—but has remained not fully understood. It is now shown that the complicated evolution of the resistivity depth profiles observed can be reproduced by a simple model based on the out-diffusion of some relevant species. Two versions of such an approach were analyzed: (A) out-diffusion of deep donors treated as VN (off-centre substitutional nitrogen), (B) out-diffusion of vacancies (V) and interstitial trimers (N3) produced by dissociation of VN3. Version B, although more complicated, is attractive due to a coincidence of the deduced vacancy diffusivity DV at 1000 °C with the value extrapolated from low-temperature data by Watkins.

Optical tomography in the presence of void regions

PubMed

Dehghani; Arridge; Schweiger; Delpy

2000-09-01

There is a growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in the use of this technique for obtaining tomographic images of the neonatal head, with the view of determining the levels of oxygenated and deoxygenated blood within the brain. Owing to computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region location; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases in which there exists a nonscattering region. We present reconstructed images of objects that contain a nonscattering region within a diffusive material. Here the forward data is calculated with the radiosity-diffusion model, and the inverse problem is solved with either the radiosity-diffusion model or the diffusion-only model. The reconstructed images show that even in the presence of only a thin nonscattering layer, a diffusion-only reconstruction will fail. When a radiosity-diffusion model is used for image reconstruction, together with a priori information about the position of the nonscattering region, the quality of the reconstructed image is considerably improved. The accuracy of the reconstructed images depends largely on the position of the anomaly with respect to the nonscattering region as well as the thickness of the nonscattering region.

Inferring diffusion dynamics from FCS in heterogeneous nuclear environments.

PubMed

Tsekouras, Konstantinos; Siegel, Amanda P; Day, Richard N; Pressé, Steve

2015-07-07

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show-first using synthetic data-that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell's nucleus as well as 2) in the cell's cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Characterizing acid diffusion lengths in chemically amplified resists from measurements of deprotection kinetics

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

Patil, Abhijit A.; Pandey, Yogendra Narayan; Doxastakis, Manolis

2014-10-01

The acid-catalyzed deprotection of glassy poly(4-hydroxystyrene-co-tertbutyl acrylate) films was studied with infrared absorbance spectroscopy and stochastic simulations. Experimental data were interpreted with a simple description of subdiffusive acid transport coupled to second-order acid loss. This model predicts key attributes of observed deprotection rates, such as fast reaction at short times, slow reaction at long times, and a nonlinear dependence on acid loading. Fickian diffusion is approached by increasing the post-exposure bake temperature or adding plasticizing agents to the polymer resin. These findings demonstrate that acid mobility and overall deprotection kinetics are coupled to glassy matrix dynamics. To complement the analysismore » of bulk kinetics, acid diffusion lengths were calculated from the anomalous transport model and compared with nanopattern line widths. The consistent scaling between experiments and simulations suggests that the anomalous diffusion model could be further developed into a predictive lithography tool.« less

Evidence of complex contagion of information in social media: An experiment using Twitter bots.

PubMed

Mønsted, Bjarke; Sapieżyński, Piotr; Ferrara, Emilio; Lehmann, Sune

2017-01-01

It has recently become possible to study the dynamics of information diffusion in techno-social systems at scale, due to the emergence of online platforms, such as Twitter, with millions of users. One question that systematically recurs is whether information spreads according to simple or complex dynamics: does each exposure to a piece of information have an independent probability of a user adopting it (simple contagion), or does this probability depend instead on the number of sources of exposure, increasing above some threshold (complex contagion)? Most studies to date are observational and, therefore, unable to disentangle the effects of confounding factors such as social reinforcement, homophily, limited attention, or network community structure. Here we describe a novel controlled experiment that we performed on Twitter using 'social bots' deployed to carry out coordinated attempts at spreading information. We propose two Bayesian statistical models describing simple and complex contagion dynamics, and test the competing hypotheses. We provide experimental evidence that the complex contagion model describes the observed information diffusion behavior more accurately than simple contagion. Future applications of our results include more effective defenses against malicious propaganda campaigns on social media, improved marketing and advertisement strategies, and design of effective network intervention techniques.

Modeling diffusion and reaction in soils: 9. The Buckingham-Burdine-Campbell equation for gas diffusivity in undisturbed soil

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

Moldrup, P.; Olesen, T.; Yamaguchi, T.

1999-08-01

Accurate description of gas diffusivity (ratio of gas diffusion coefficients in soil and free air, D{sub s}/D{sub 0}) in undisturbed soils is a prerequisite for predicting in situ transport and fate of volatile organic chemicals and greenhouse gases. Reference point gas diffusivities (R{sub p}) in completely dry soil were estimated for 20 undisturbed soils by assuming a power function relation between gas diffusivity and air-filled porosity ({epsilon}). Among the classical gas diffusivity models, the Buckingham (1904) expression, equal to the soil total porosity squared, best described R{sub p}. Inasmuch, as their previous works implied a soil-type dependency of D{sub s}/D{submore » 0}({epsilon}) in undisturbed soils, the Buckingham R{sub p} expression was inserted in two soil-type-dependent D{sub s}/D{sub 0}({epsilon}) models. One D{sub s}/D{sub 0}({epsilon}) model is a function of pore-size distribution (the Campbell water retention parameter used in a modified Burdine capillary tube model), and the other is a calibrated, empirical function of soil texture (silt + sand fraction). Both the Buckingham-Burdine-Campbell (BBC) and the Buckingham/soil texture-based D{sub s}/D{sub 0}({epsilon}) models described well the observed soil type effects on gas diffusivity and gave improved predictions compared with soil type independent models when tested against an independent data set for six undisturbed surface soils. This study emphasizes that simple but soil-type-dependent power function D{sub s}/D{sub 0}({epsilon}) models can adequately describe and predict gas diffusivity in undisturbed soil. The authors recommend the new BBC model as basis for modeling gas transport and reactions in undisturbed soil systems.« less

Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control.

PubMed

Gan, Qintao; Lv, Tianshi; Fu, Zhenhua

2016-04-01

In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.

Simulation studies of self-organization of microtubules and molecular motors.

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

Jian, Z.; Karpeev, D.; Aranson, I. S.

We perform Monte Carlo type simulation studies of self-organization of microtubules interacting with molecular motors. We model microtubules as stiff polar rods of equal length exhibiting anisotropic diffusion in the plane. The molecular motors are implicitly introduced by specifying certain probabilistic collision rules resulting in realignment of the rods. This approximation of the complicated microtubule-motor interaction by a simple instant collision allows us to bypass the 'computational bottlenecks' associated with the details of the diffusion and the dynamics of motors and the reorientation of microtubules. Consequently, we are able to perform simulations of large ensembles of microtubules and motors onmore » a very large time scale. This simple model reproduces all important phenomenology observed in in vitro experiments: Formation of vortices for low motor density and raylike asters and bundles for higher motor density.« less

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

Effect of measurement on the ballistic-diffusive transition in turbid media.

PubMed

Glasser, Ziv; Yaroshevsky, Andre; Barak, Bavat; Granot, Er'el; Sternklar, Shmuel

2013-10-01

The dependence of the transition between the ballistic and the diffusive regimes of turbid media on the experimental solid angle of the detection system is analyzed theoretically and experimentally. A simple model is developed which shows the significance of experimental conditions on the location of the ballistic-diffusive transition. It is demonstrated that decreasing the solid angle expands the ballistic regime; however, this benefit is bounded by the initial Gaussian beam diffraction. In addition, choosing the appropriate wavelength according to the model's principles provides another means of expanding the ballistic regime. Consequently, by optimizing the experimental conditions, it should be possible to extract the ballistic image of a tissue with a thickness of 1 cm.

Adsorption of basic dyes on granular activated carbon and natural zeolite.

PubMed

Meshko, V; Markovska, L; Mincheva, M; Rodrigues, A E

2001-10-01

The adsorption of basic dyes from aqueous solution onto granular activated carbon and natural zeolite has been studied using an agitated batch adsorber. The influence of agitation, initial dye concentration and adsorbent mass has been studied. The parameters of Langmuir and Freundlich adsorption isotherms have been determined using the adsorption data. Homogeneous diffusion model (solid diffusion) combined with external mass transfer resistance is proposed for the kinetic investigation. The dependence of solid diffusion coefficient on initial concentration and mass adsorbent is represented by the simple empirical equations.

The Diffusion Simulator - Teaching Geomorphic and Geologic Problems Visually.

ERIC Educational Resources Information Center

Gilbert, R.

1979-01-01

Describes a simple hydraulic simulator based on more complex models long used by engineers to develop approximate solutions. It allows students to visualize non-steady transfer, to apply a model to solve a problem, and to compare experimentally simulated information with calculated values. (Author/MA)

Concentration dependence of in vivo biotransformation rates of organic sunscreen agents in rainbow trout following a dietary exposure

EPA Science Inventory

Simple diffusion lipid-partitioning models have historically described the bioaccumulation of hydrophobic chemicals in fish. While these models are sufficient to describe the bioaccumulation of recalcitrant PCBs and other non-metabolized chemicals, they are inadequate for chemica...

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

PubMed

Fronczak, Agata; Fronczak, Piotr

2016-07-01

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

A pore-pressure diffusion model for estimating landslide-inducing rainfall

USGS Publications Warehouse

Reid, M.E.

1994-01-01

Many types of landslide movement are induced by large rainstorms, and empirical rainfall intensity/duration thresholds for initiating movement have been determined for various parts of the world. In this paper, I present a simple pressure diffusion model that provides a physically based hydrologic link between rainfall intensity/duration at the ground surface and destabilizing pore-water pressures at depth. The model approximates rainfall infiltration as a sinusoidally varying flux over time and uses physical parameters that can be determined independently. Using a comprehensive data set from an intensively monitored landslide, I demonstrate that the model is capable of distinguishing movement-inducing rainstorms. -Author

A simple model for closure temperature of a trace element in cooling bi-mineralic systems

NASA Astrophysics Data System (ADS)

Liang, Yan

2015-09-01

Closure temperature is defined as the lower temperature limit at which the element of interest effectively ceases diffusive exchange with its surrounding medium during cooling. Here we generalize the classic equation of Dodson (1973) for cooling mono-mineralic systems to cooling bi-mineralic aggregates by considering diffusive exchange of a trace element between the two minerals in a closed system. We present a simple analytical model that includes key parameters affecting the closure temperature of a trace element in cooling bi-mineralic systems: cooling rate, temperature-dependent diffusion coefficients for the trace element in the two minerals, temperature-dependent partition coefficient of the trace element between the two minerals, effective grain sizes of the two minerals, and volume proportions of the minerals in the system. We show that closure temperatures of a trace element in cooling bi-mineralic systems are bounded by the closure temperatures of the trace element in the two mono-mineralic systems and that our generalized model reduces to Dodson's equation when one of the mineral serves as "an effective infinite" reservoir to the other mineral. Application to closure temperatures of REE in orthopyroxene and clinopyroxene bi-mineralic systems highlights the importance of REE diffusion and partitioning in the pyroxenes as well as clinopyroxene modal abundance and grain size in the systems. Closure temperatures for REE in two-pyroxene bearing equigranular rocks are controlled primarily by diffusion in orthopyroxene unless the modal abundance of clinopyroxene is very small. This has important bearings on the interpretation of temperatures derived from the REE-in-two-pyroxene thermometer.

The nature of the colloidal 'glass' transition.

PubMed

Dawson, Kenneth A; Lawlor, A; DeGregorio, Paolo; McCullagh, Gavin D; Zaccarelli, Emanuela; Foffi, Giuseppe; Tartaglia, Piero

2003-01-01

The dynamically arrested state of matter is discussed in the context of athermal systems, such as the hard sphere colloidal arrest. We believe that the singular dynamical behaviour near arrest expressed, for example, in how the diffusion constant vanishes may be 'universal', in a sense to be discussed in the paper. Based on this we argue the merits of studying the problem with simple lattice models. This, by analogy with the the critical point of the Ising model, should lead us to clarify the questions, and begin the program of establishing the degree of universality to be expected. We deal only with 'ideal' athermal dynamical arrest transitions, such as those found for hard sphere systems. However, it is argued that dynamically available volume (DAV) is the relevant order parameter of the transition, and that universal mechanisms may be well expressed in terms of DAV. For simple lattice models we give examples of simple laws that emerge near the dynamical arrest, emphasising the idea of a near-ideal gas of 'holes', interacting to give the power law diffusion constant scaling near the arrest. We also seek to open the discussion of the possibility of an underlying weak coupling theory of the dynamical arrest transition, based on DAV.

The Role of Diffusion-Weighted Magnetic Resonance Imaging in the Differential Diagnosis of Simple and Hydatid Cysts of the Liver.

PubMed

Aksoy, S; Erdil, I; Hocaoglu, E; Inci, E; Adas, G T; Kemik, O; Turkay, R

2018-02-01

The present study indicates that simple and hydatid cysts in liver are a common health problem in Turkey. The aim of the study is to differentiate different types of hydatid cysts from simple cysts by using diffusion-weighted images. In total, 37 hydatid cysts and 36 simple cysts in the liver were diagnosed. We retrospectively reviewed the medical records of the patients who had both ultrasonography and magnetic resonance imaging. We measured apparent diffusion coefficient (ADC) values of all the cysts and then compared the findings. There was no statistically meaningful difference between the ADC values of simple cysts and type 1 hydatid cysts. However, for the other types of hydatid cysts, it is possible to differentiate hydatid cysts from simple cysts using the ADC values. Although in our study we cannot differentiate between type I hydatid cysts and simple cysts in the liver, diffusion-weighted images are very useful to differentiate different types of hydatid cysts from simple cysts using the ADC values.

Simple model of a photoacoustic system as a CR circuit

NASA Astrophysics Data System (ADS)

Fukuhara, Akiko; Kaneko, Fumitoshi; Ogawa, Naohisa

2012-05-01

We introduce the photoacoustic educational system (PAES), by which we can identify which gas causes the greenhouse effect in a classroom (Kaneko et al 2010 J. Chem. Educ. 87 202-4). PAES is an experimental system in which a pulse of infrared (IR) is absorbed into gas as internal energy, an oscillation of pressure (sound) appears, and then we can measure the absorptance of IR by the strength of sound. In this paper, we construct a simple mathematical model for PAES which is equivalent to the CR circuit. The energy absorption of an IR pulse into gas corresponds to the charge of a condenser and the heat diffusion to the outside corresponds to the energy dissipation by electric resistance. We analyse the experimental results by using this simple model, and check its validity. Although the model is simple, it explains phenomena occurring in PAES and can be a good educational resource.

Front fingering and complex dynamics driven by the interaction of buoyancy and diffusive instabilities.

PubMed

D'Hernoncourt, J; Merkin, J H; De Wit, A

2007-09-01

Traveling fronts can become transversally unstable either because of a diffusive instability arising when the key variables diffuse at sufficiently different rates or because of a buoyancy-driven Rayleigh-Taylor mechanism when the density jump across the front is statically unfavorable. The interaction between such diffusive and buoyancy instabilities of fronts is analyzed theoretically for a simple model system. Linear stability analysis and nonlinear simulations show that their interplay changes considerably the stability properties with regard to the pure Rayleigh-Taylor or diffusive instabilities of fronts. In particular, an instability scenario can arise which triggers convection around statically stable fronts as a result of differential diffusion. Moreover, spatiotemporal chaos can be observed when both buoyancy and diffusive effects cooperate to destabilize the front. Experimental conditions to test our predictions are suggested.

New product forecasting with limited or no data

NASA Astrophysics Data System (ADS)

Ismai, Zuhaimy; Abu, Noratikah; Sufahani, Suliadi

2016-10-01

In the real world, forecasts would always be based on historical data with the assumption that the behaviour be the same for the future. But how do we forecast when there is no such data available? New product or new technologies normally has limited amount of data available. Knowing that forecasting is valuable for decision making, this paper presents forecasting of new product or new technologies using aggregate diffusion models and modified Bass Model. A newly launched Proton car and its penetration was chosen to demonstrate the possibility of forecasting sales demand where there is limited or no data available. The model was developed to forecast diffusion of new vehicle or an innovation in the Malaysian society. It is to represent the level of spread on the new vehicle among a given set of the society in terms of a simple mathematical function that elapsed since the introduction of the new product. This model will forecast the car sales volume. A procedure of the proposed diffusion model was designed and the parameters were estimated. Results obtained by applying the proposed diffusion model and numerical calculation shows that the model is robust and effective for forecasting demand of the new vehicle. The results reveal that newly developed modified Bass diffusion of demand function has significantly contributed for forecasting the diffusion of new Proton car or new product.

Diffuse sorption modeling.

PubMed

Pivovarov, Sergey

2009-04-01

This work presents a simple solution for the diffuse double layer model, applicable to calculation of surface speciation as well as to simulation of ionic adsorption within the diffuse layer of solution in arbitrary salt media. Based on Poisson-Boltzmann equation, the Gaines-Thomas selectivity coefficient for uni-bivalent exchange on clay, K(GT)(Me(2+)/M(+))=(Q(Me)(0.5)/Q(M)){M(+)}/{Me(2+)}(0.5), (Q is the equivalent fraction of cation in the exchange capacity, and {M(+)} and {Me(2+)} are the ionic activities in solution) may be calculated as [surface charge, mueq/m(2)]/0.61. The obtained solution of the Poisson-Boltzmann equation was applied to calculation of ionic exchange on clays and to simulation of the surface charge of ferrihydrite in 0.01-6 M NaCl solutions. In addition, a new model of acid-base properties was developed. This model is based on assumption that the net proton charge is not located on the mathematical surface plane but diffusely distributed within the subsurface layer of the lattice. It is shown that the obtained solution of the Poisson-Boltzmann equation makes such calculations possible, and that this approach is more efficient than the original diffuse double layer model.

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

PubMed

Dehghani, H; Delpy, D T

2002-06-01

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

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

NASA Astrophysics Data System (ADS)

Dehghani, H.; Delpy, D. T.

2002-06-01

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

A First Step towards Variational Methods in Engineering

ERIC Educational Resources Information Center

Periago, Francisco

2003-01-01

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous…

Turbulent shear layers in confining channels

NASA Astrophysics Data System (ADS)

Benham, Graham P.; Castrejon-Pita, Alfonso A.; Hewitt, Ian J.; Please, Colin P.; Style, Rob W.; Bird, Paul A. D.

2018-06-01

We present a simple model for the development of shear layers between parallel flows in confining channels. Such flows are important across a wide range of topics from diffusers, nozzles and ducts to urban air flow and geophysical fluid dynamics. The model approximates the flow in the shear layer as a linear profile separating uniform-velocity streams. Both the channel geometry and wall drag affect the development of the flow. The model shows good agreement with both particle image velocimetry experiments and computational turbulence modelling. The simplicity and low computational cost of the model allows it to be used for benchmark predictions and design purposes, which we demonstrate by investigating optimal pressure recovery in diffusers with non-uniform inflow.

Ultrametric distribution of culture vectors in an extended Axelrod model of cultural dissemination.

PubMed

Stivala, Alex; Robins, Garry; Kashima, Yoshihisa; Kirley, Michael

2014-05-02

The Axelrod model of cultural diffusion is an apparently simple model that is capable of complex behaviour. A recent work used a real-world dataset of opinions as initial conditions, demonstrating the effects of the ultrametric distribution of empirical opinion vectors in promoting cultural diversity in the model. Here we quantify the degree of ultrametricity of the initial culture vectors and investigate the effect of varying degrees of ultrametricity on the absorbing state of both a simple and extended model. Unlike the simple model, ultrametricity alone is not sufficient to sustain long-term diversity in the extended Axelrod model; rather, the initial conditions must also have sufficiently large variance in intervector distances. Further, we find that a scheme for evolving synthetic opinion vectors from cultural "prototypes" shows the same behaviour as real opinion data in maintaining cultural diversity in the extended model; whereas neutral evolution of cultural vectors does not.

Ultrametric distribution of culture vectors in an extended Axelrod model of cultural dissemination

NASA Astrophysics Data System (ADS)

Stivala, Alex; Robins, Garry; Kashima, Yoshihisa; Kirley, Michael

2014-05-01

The Axelrod model of cultural diffusion is an apparently simple model that is capable of complex behaviour. A recent work used a real-world dataset of opinions as initial conditions, demonstrating the effects of the ultrametric distribution of empirical opinion vectors in promoting cultural diversity in the model. Here we quantify the degree of ultrametricity of the initial culture vectors and investigate the effect of varying degrees of ultrametricity on the absorbing state of both a simple and extended model. Unlike the simple model, ultrametricity alone is not sufficient to sustain long-term diversity in the extended Axelrod model; rather, the initial conditions must also have sufficiently large variance in intervector distances. Further, we find that a scheme for evolving synthetic opinion vectors from cultural ``prototypes'' shows the same behaviour as real opinion data in maintaining cultural diversity in the extended model; whereas neutral evolution of cultural vectors does not.

The structure of the solution obtained with Reynolds-stress-transport models at the free-stream edges of turbulent flows

NASA Astrophysics Data System (ADS)

Cazalbou, J.-B.; Chassaing, P.

2002-02-01

The behavior of Reynolds-stress-transport models at the free-stream edges of turbulent flows is investigated. Current turbulent-diffusion models are found to produce propagative (possibly weak) solutions of the same type as those reported earlier by Cazalbou, Spalart, and Bradshaw [Phys. Fluids 6, 1797 (1994)] for two-equation models. As in the latter study, an analysis is presented that provides qualitative information on the flow structure predicted near the edge if a condition on the values of the diffusion constants is satisfied. In this case, the solution appears to be fairly insensitive to the residual free-stream turbulence levels needed with conventional numerical methods. The main specific result is that, depending on the diffusion model, the propagative solution can force turbulence toward definite and rather extreme anisotropy states at the edge (one- or two-component limit). This is not the case with the model of Daly and Harlow [Phys. Fluids 13, 2634 (1970)]; it may be one of the reasons why this "old" scheme is still the most widely used, even in recent Reynolds-stress-transport models. In addition, the analysis helps us to interpret some difficulties encountered in computing even very simple flows with Lumley's pressure-diffusion model [Adv. Appl. Mech. 18, 123 (1978)]. A new realizability condition, according to which the diffusion model should not globally become "anti-diffusive," is introduced, and a recalibration of Lumley's model satisfying this condition is performed using information drawn from the analysis.

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

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

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

PubMed Central

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

2012-01-01

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

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

PubMed

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

2014-07-21

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

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

PubMed

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

2012-10-05

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

A model of oscillatory transport in granular soils, with application to barometric pumping and earth tides.

PubMed

Neeper, D A

2001-04-01

A simple algebraic model is proposed to estimate the transport of a volatile or soluble chemical caused by oscillatory flow of fluid in a porous medium. The model is applied to the barometric pumping of vapors in the vadose zone, and to the transport of dissolved species by earth tides in an aquifer. In the model, the fluid moves sinusoidally with time in the porosity of the soil. The chemical concentration in the mobile fluid is considered to equilibrate with the concentration in the surrounding matrix according to a characteristic time governed by diffusion, sorption, or other rate processes. The model provides a closed form solution, to which barometric pressure data are applied in an example of pore gas motion in the vadose zone. The model predicts that the additional diffusivity due barometric pumping in an unfractured vadose zone would be comparable to the diffusivity in stagnant pore gas if the equilibration time is 1 day or longer. Water motion due to the M2 lunar tide is examined as an example of oscillatory transport in an aquifer. It is shown that the tidal motion of the water in an aquifer might significantly increase the vertical diffusivity of dissolved species when compared to diffusion in an absolutely stagnant aquifer, but the hydrodynamic dispersivity due to tidal motion or gravitational flow would probably exceed the diffusivity due to oscillatory advection.

Computing diffusivities from particle models out of equilibrium

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Scaling behavior in corrosion and growth of a passive film.

PubMed

Aarão Reis, F D A; Stafiej, Janusz

2007-07-01

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

Diffusion of aqueous solutions of ionic, zwitterionic, and polar solutes

NASA Astrophysics Data System (ADS)

Teng, Xiaojing; Huang, Qi; Dharmawardhana, Chamila Chathuranga; Ichiye, Toshiko

2018-06-01

The properties of aqueous solutions of ionic, zwitterionic, and polar solutes are of interest to many fields. For instance, one of the many anomalous properties of aqueous solutions is the behavior of water diffusion in different monovalent salt solutions. In addition, solutes can affect the stabilities of macromolecules such as proteins in aqueous solution. Here, the diffusivities of aqueous solutions of sodium chloride, potassium chloride, tri-methylamine oxide (TMAO), urea, and TMAO-urea are examined in molecular dynamics simulations. The decrease in the diffusivity of water with the concentration of simple ions and urea can be described by a simple model in which the water molecules hydrogen bonded to the solutes are considered to diffuse at the same rate as the solutes, while the remainder of the water molecules are considered to be bulk and diffuse at almost the same rate as pure water. On the other hand, the decrease in the diffusivity of water with the concentration of TMAO is apparently affected by a decrease in the diffusion rate of the bulk water molecules in addition to the decrease due to the water molecules hydrogen bonded to TMAO. In other words, TMAO enhances the viscosity of water, while urea barely affects it. Overall, this separation of water molecules into those that are hydrogen bonded to solute and those that are bulk can provide a useful means of understanding the short- and long-range effects of solutes on water.

Polarization properties and microfacet-based modelling of white, grey and coloured matte diffuse reflection standards

NASA Astrophysics Data System (ADS)

Quast, T.; Schirmacher, A.; Hauer, K.-O.; Koo, A.

2018-02-01

To elucidate the influence of polarization in diffuse reflectometry, we performed a series of measurements in several bidirectional geometries and determined the Stokes parameters of the diffusely reflected radiation. Different types of matte reflection standards were used, including several common white standards and ceramic colour standards. The dependence of the polarization on the sample type, wavelength and geometry have been studied systematically, the main influence factors have been identified: The effect is largest at large angles of incidence or detection and at wavelengths where the magnitude of the reflectance is small. The results for the colour standards have been modelled using a microfacet-based reflection theory which is derived from the well-known model of Torrance and Sparrow. Although the theory is very simple and only has three free parameters, the agreement with the measured data is very good, all essential features of the data can be reproduced by the model.

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

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

Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp; Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realisticmore » biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.« less

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Transport in Nanoporous Materials Including MOFs: The Applicability of Fick's Laws.

PubMed

Titze, Tobias; Lauerer, Alexander; Heinke, Lars; Chmelik, Christian; Zimmermann, Nils E R; Keil, Frerich J; Ruthven, Douglas M; Kärger, Jörg

2015-11-23

Diffusion in nanoporous host-guest systems is often considered to be too complicated to comply with such "simple" relationships as Fick's first and second law of diffusion. However, it is shown herein that the microscopic techniques of diffusion measurement, notably the pulsed field gradient (PFG) technique of NMR spectroscopy and microimaging by interference microscopy (IFM) and IR microscopy (IRM), provide direct experimental evidence of the applicability of Fick's laws to such systems. This remains true in many situations, even when the detailed mechanism is complex. The limitations of the diffusion model are also discussed with reference to the extensive literature on this subject. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Experimental investigation of the excess charge and time constant of minority carriers in the thin diffused layer of 0.1 ohm-cm silicon solar cells

NASA Technical Reports Server (NTRS)

Godlewski, M. P.; Brandhorst, H. W., Jr.; Lindholm, F. A.; Sah, C. T.

1976-01-01

An experimental method is presented that can be used to interpret the relative roles of bandgap narrowing and recombination processes in the diffused layer. This method involves measuring the device time constant by open-circuit voltage decay and the base region diffusion length by X-ray excitation. A unique illuminated diode method is used to obtain the diode saturation current. These data are interpreted using a simple model to determine individually the minority carrier lifetime and the excess charge. These parameters are then used to infer the relative importance of bandgap narrowing and recombination processes in the diffused layer.

Cosmic Ray Hysteresis as Evidence for Time-dependent Diffusive Processes in the Long Term Solar Modulation

NASA Technical Reports Server (NTRS)

Ogallagher, J. J.

1973-01-01

A simple one-dimensional time-dependent diffusion-convection model for the modulation of cosmic rays is presented. This model predicts that the observed intensity at a given time is approximately equal to the intensity given by the time independent diffusion convection solution under interplanetary conditions which existed a time iota in the past, (U(t sub o) = U sub s(t sub o - tau)) where iota is the average time spent by a particle inside the modulating cavity. Delay times in excess of several hundred days are possible with reasonable modulation parameters. Interpretation of phase lags observed during the 1969 to 1970 solar maximum in terms of this model suggests that the modulating region is probably not less than 10 a.u. and maybe as much as 35 a.u. in extent.

Restoration of rhythmicity in diffusively coupled dynamical networks.

PubMed

Zou, Wei; Senthilkumar, D V; Nagao, Raphael; Kiss, István Z; Tang, Yang; Koseska, Aneta; Duan, Jinqiao; Kurths, Jürgen

2015-07-15

Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.

A radially resolved kinetic model for nonlocal electron ripple diffusion losses in tokamaks

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

Robertson, Scott

A relatively simple radially resolved kinetic model is applied to the ripple diffusion problem for electrons in tokamaks. The distribution function f(r,v) is defined on a two-dimensional grid, where r is the radial coordinate and v is the velocity coordinate. Particle transport in the radial direction is from ripple and banana diffusion and transport in the velocity direction is described by the Fokker-Planck equation. Particles and energy are replaced by source functions that are adjusted to maintain a constant central density and temperature. The relaxed profiles of f(r,v) show that the electron distribution function at the wall contains suprathermal electronsmore » that have diffused from the interior that enhance ripple transport. The transport at the periphery is therefore nonlocal. The energy replacement times from the computational model are near to the experimental replacement times for tokamak discharges in the compilation by Pfeiffer and Waltz [Nucl. Fusion 19, 51 (1979)].« less

Simultaneous measurement for thermal conductivity, diffusivity, and specific heat of methane hydrate bearing sediments recovered from Nankai-Trough wells

NASA Astrophysics Data System (ADS)

Muraoka, M.; Ohtake, M.; Susuki, N.; Yamamoto, Y.; Suzuki, K.; Tsuji, T.

2014-12-01

This study presents the results of the measurements of the thermal constants of natural methane-hydrate-bearing sediments samples recovered from the Tokai-oki test wells (Nankai-Trough, Japan) in 2004. The thermal conductivity, thermal diffusivity, and specific heat of the samples were simultaneously determined using the hot-disk transient method. The thermal conductivity of natural hydrate-bearing sediments decreases slightly with increasing porosity. In addition, the thermal diffusivity of hydrate-bearing sediment decrease as porosity increases. We also used simple models to calculate the thermal conductivity and thermal diffusivity. The results of the distribution model (geometric-mean model) are relatively consistent with the measurement results. In addition, the measurement results are consistent with the thermal diffusivity, which is estimated by dividing the thermal conductivity obtained from the distribution model by the specific heat obtained from the arithmetic mean. In addition, we discuss the relation between the thermal conductivity and mineral composition of core samples in conference. Acknowledgments. This work was financially supported by MH21 Research Consortium for Methane Hydrate Resources in Japan on the National Methane Hydrate Exploitation Program planned by the Ministry of Economy, Trade and Industry.

A Two-Stage Process Model of Sensory Discrimination: An Alternative to Drift-Diffusion

PubMed Central

Landy, Michael S.

2016-01-01

Discrimination of the direction of motion of a noisy stimulus is an example of sensory discrimination under uncertainty. For stimuli that are extended in time, reaction time is quicker for larger signal values (e.g., discrimination of opposite directions of motion compared with neighboring orientations) and larger signal strength (e.g., stimuli with higher contrast or motion coherence, that is, lower noise). The standard model of neural responses (e.g., in lateral intraparietal cortex) and reaction time for discrimination is drift-diffusion. This model makes two clear predictions. (1) The effects of signal strength and value on reaction time should interact multiplicatively because the diffusion process depends on the signal-to-noise ratio. (2) If the diffusion process is interrupted, as in a cued-response task, the time to decision after the cue should be independent of the strength of accumulated sensory evidence. In two experiments with human participants, we show that neither prediction holds. A simple alternative model is developed that is consistent with the results. In this estimate-then-decide model, evidence is accumulated until estimation precision reaches a threshold value. Then, a decision is made with duration that depends on the signal-to-noise ratio achieved by the first stage. SIGNIFICANCE STATEMENT Sensory decision-making under uncertainty is usually modeled as the slow accumulation of noisy sensory evidence until a threshold amount of evidence supporting one of the possible decision outcomes is reached. Furthermore, it has been suggested that this accumulation process is reflected in neural responses, e.g., in lateral intraparietal cortex. We derive two behavioral predictions of this model and show that neither prediction holds. We introduce a simple alternative model in which evidence is accumulated until a sufficiently precise estimate of the stimulus is achieved, and then that estimate is used to guide the discrimination decision. This model is consistent with the behavioral data. PMID:27807167

A Two-Stage Process Model of Sensory Discrimination: An Alternative to Drift-Diffusion.

PubMed

Sun, Peng; Landy, Michael S

2016-11-02

Discrimination of the direction of motion of a noisy stimulus is an example of sensory discrimination under uncertainty. For stimuli that are extended in time, reaction time is quicker for larger signal values (e.g., discrimination of opposite directions of motion compared with neighboring orientations) and larger signal strength (e.g., stimuli with higher contrast or motion coherence, that is, lower noise). The standard model of neural responses (e.g., in lateral intraparietal cortex) and reaction time for discrimination is drift-diffusion. This model makes two clear predictions. (1) The effects of signal strength and value on reaction time should interact multiplicatively because the diffusion process depends on the signal-to-noise ratio. (2) If the diffusion process is interrupted, as in a cued-response task, the time to decision after the cue should be independent of the strength of accumulated sensory evidence. In two experiments with human participants, we show that neither prediction holds. A simple alternative model is developed that is consistent with the results. In this estimate-then-decide model, evidence is accumulated until estimation precision reaches a threshold value. Then, a decision is made with duration that depends on the signal-to-noise ratio achieved by the first stage. Sensory decision-making under uncertainty is usually modeled as the slow accumulation of noisy sensory evidence until a threshold amount of evidence supporting one of the possible decision outcomes is reached. Furthermore, it has been suggested that this accumulation process is reflected in neural responses, e.g., in lateral intraparietal cortex. We derive two behavioral predictions of this model and show that neither prediction holds. We introduce a simple alternative model in which evidence is accumulated until a sufficiently precise estimate of the stimulus is achieved, and then that estimate is used to guide the discrimination decision. This model is consistent with the behavioral data. Copyright © 2016 the authors 0270-6474/16/3611259-16$15.00/0.

Understanding the spectral hardenings and radial distribution of Galactic cosmic rays and Fermi diffuse γ rays with spatially-dependent propagation

NASA Astrophysics Data System (ADS)

Guo, Yi-Qing; Yuan, Qiang

2018-03-01

Recent direct measurements of Galactic cosmic ray spectra by balloon/space-borne detectors reveal spectral hardenings of all major nucleus species at rigidities of a few hundred GV. The all-sky diffuse γ -ray emissions measured by the Fermi Large Area Telescope also show spatial variations of the intensities and spectral indices of cosmic rays. These new observations challenge the traditional simple acceleration and/or propagation scenario of Galactic cosmic rays. In this work, we propose a spatially dependent diffusion scenario to explain all these phenomena. The diffusion coefficient is assumed to be anticorrelated with the source distribution, which is a natural expectation from the charged particle transportation in a turbulent magnetic field. The spatially dependent diffusion model also gives a lower level of anisotropies of cosmic rays, which are consistent with observations by underground muons and air shower experiments. The spectral variations of cosmic rays across the Galaxy can be properly reproduced by this model.

Viscous diffusion of vorticity in unsteady wall layers using the diffusion velocity concept

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

Strickland, J.H.; Kempka, S.N.; Wolfe, W.P.

1995-03-01

The primary purpose of this paper is to provide a careful evaluation of the diffusion velocity concept with regard to its ability to predict the diffusion of vorticity near a moving wall. A computer code BDIF has been written which simulates the evolution of the vorticity field near a wall of infinite length which is moving in an arbitrary fashion. The simulations generated by this code are found to give excellent results when compared to several exact solutions. We also outline a two-dimensional unsteady viscous boundary layer model which utilizes the diffusion velocity concept and is compatible with vortex methods.more » A primary goal of this boundary layer model is to minimize the number of vortices generated on the surface at each time step while achieving good resolution of the vorticity field near the wall. Preliminary results have been obtained for simulating a simple two-dimensional laminar boundary layer.« less

Bioturbation, advection, and diffusion of a conserved tracer in a laboratory flume

NASA Astrophysics Data System (ADS)

Work, P. A.; Moore, P. R.; Reible, D. D.

2002-06-01

Laboratory experiments indicating the relative influences of advection, diffusion, and bioturbation on transport of NaCl tracer between a stream and streambed are described. Data were collected in a recirculating flume housing a box filled with test sediments. Peclet numbers ranged from 0 to 1.5. Sediment components included a medium sand (d50 = 0.31 mm), kaolinite, and topsoil. Lumbriculus variegatus were introduced as bioturbators. Conductivity probes were employed to document the flux of the tracer solution out of the bed. Measurements are compared to one-dimensional effective diffusion models assuming one or two horizontal sediment layers. These simple models provide a good indication of tracer half-life in the bed if a suitable effective diffusion coefficient is chosen but underpredict initial flux and overpredict flux at long times. Organism activity was limited to the upper reaches of the sediment test box but eventually exerts a secondary influence on flux from deeper regions.

Dynamical transition for a particle in a squared Gaussian potential

NASA Astrophysics Data System (ADS)

Touya, C.; Dean, D. S.

2007-02-01

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by ψ = phi2/2 where phi is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.

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

PubMed

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

1997-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

A Simple Educational Method for the Measurement of Liquid Binary Diffusivities

ERIC Educational Resources Information Center

Rice, Nicholas P.; de Beer, Martin P.; Williamson, Mark E.

2014-01-01

A simple low-cost experiment has been developed for the measurement of the binary diffusion coefficients of liquid substances. The experiment is suitable for demonstrating molecular diffusion to small or large undergraduate classes in chemistry or chemical engineering. Students use a cell phone camera in conjunction with open-source image…

A Simple Refraction Experiment for Probing Diffusion in Ternary Mixtures

ERIC Educational Resources Information Center

Coutinho, Cecil A.; Mankidy, Bijith D.; Gupta, Vinay K.

2010-01-01

Diffusion is a fundamental phenomenon that is vital in many chemical processes such as mass transport in living cells, corrosion, and separations. We describe a simple undergraduate-level experiment based on Weiner's Method to probe diffusion in a ternary aqueous mixture of small molecular-weight molecules. As an illustration, the experiment…

Drift diffusion model of reward and punishment learning in schizophrenia: Modeling and experimental data.

PubMed

Moustafa, Ahmed A; Kéri, Szabolcs; Somlai, Zsuzsanna; Balsdon, Tarryn; Frydecka, Dorota; Misiak, Blazej; White, Corey

2015-09-15

In this study, we tested reward- and punishment learning performance using a probabilistic classification learning task in patients with schizophrenia (n=37) and healthy controls (n=48). We also fit subjects' data using a Drift Diffusion Model (DDM) of simple decisions to investigate which components of the decision process differ between patients and controls. Modeling results show between-group differences in multiple components of the decision process. Specifically, patients had slower motor/encoding time, higher response caution (favoring accuracy over speed), and a deficit in classification learning for punishment, but not reward, trials. The results suggest that patients with schizophrenia adopt a compensatory strategy of favoring accuracy over speed to improve performance, yet still show signs of a deficit in learning based on negative feedback. Our data highlights the importance of applying fitting models (particularly drift diffusion models) to behavioral data. The implications of these findings are discussed relative to theories of schizophrenia and cognitive processing. Copyright © 2015 Elsevier B.V. All rights reserved.

Electric-field noise from carbon-adatom diffusion on a Au(110) surface: First-principles calculations and experiments

NASA Astrophysics Data System (ADS)

Kim, E.; Safavi-Naini, A.; Hite, D. A.; McKay, K. S.; Pappas, D. P.; Weck, P. F.; Sadeghpour, H. R.

2017-03-01

The decoherence of trapped-ion quantum gates due to heating of their motional modes is a fundamental science and engineering problem. This heating is attributed to electric-field noise arising from the trap-electrode surfaces. In this work, we investigate the source of this noise by focusing on the diffusion of carbon-containing adsorbates on the surface of Au(110). We show by density functional theory, based on detailed scanning probe microscopy, how the carbon adatom diffusion on the gold surface changes the energy landscape and how the adatom dipole moment varies with the diffusive motion. A simple model for the diffusion noise, which varies quadratically with the variation of the dipole moment, predicts a noise spectrum, in accordance with the measured values.

An electromechanical based deformable model for soft tissue simulation.

PubMed

Zhong, Yongmin; Shirinzadeh, Bijan; Smith, Julian; Gu, Chengfan

2009-11-01

Soft tissue deformation is of great importance to surgery simulation. Although a significant amount of research efforts have been dedicated to simulating the behaviours of soft tissues, modelling of soft tissue deformation is still a challenging problem. This paper presents a new deformable model for simulation of soft tissue deformation from the electromechanical viewpoint of soft tissues. Soft tissue deformation is formulated as a reaction-diffusion process coupled with a mechanical load. The mechanical load applied to a soft tissue to cause a deformation is incorporated into the reaction-diffusion system, and consequently distributed among mass points of the soft tissue. Reaction-diffusion of mechanical load and non-rigid mechanics of motion are combined to govern the simulation dynamics of soft tissue deformation. An improved reaction-diffusion model is developed to describe the distribution of the mechanical load in soft tissues. A three-layer artificial cellular neural network is constructed to solve the reaction-diffusion model for real-time simulation of soft tissue deformation. A gradient based method is established to derive internal forces from the distribution of the mechanical load. Integration with a haptic device has also been achieved to simulate soft tissue deformation with haptic feedback. The proposed methodology does not only predict the typical behaviours of living tissues, but it also accepts both local and large-range deformations. It also accommodates isotropic, anisotropic and inhomogeneous deformations by simple modification of diffusion coefficients.

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

NASA Astrophysics Data System (ADS)

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

2008-12-01

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

Relationships between self-diffusivity, packing fraction, and excess entropy in simple bulk and confined fluids.

PubMed

Mittal, Jeetain; Errington, Jeffrey R; Truskett, Thomas M

2007-08-30

Static measures such as density and entropy, which are intimately connected to structure, have featured prominently in modern thinking about the dynamics of the liquid state. Here, we explore the connections between self-diffusivity, density, and excess entropy for two of the most widely used model "simple" liquids, the equilibrium Lennard-Jones and square-well fluids, in both bulk and confined environments. We find that the self-diffusivity data of the Lennard-Jones fluid can be approximately collapsed onto a single curve (i) versus effective packing fraction and (ii) in appropriately reduced form versus excess entropy, as suggested by two well-known scaling laws. Similar data collapse does not occur for the square-well fluid, a fact that can be understood on the basis of the nontrivial effects that temperature has on its static structure. Nonetheless, we show that the implications of confinement for the self-diffusivity of both of these model fluids, over a broad range of equilibrium conditions, can be predicted on the basis of knowledge of the bulk fluid behavior and either the effective packing fraction or the excess entropy of the confined fluid. Excess entropy is perhaps the most preferable route due to its superior predictive ability and because it is a standard, unambiguous thermodynamic quantity that can be readily predicted via classical density functional theories of inhomogeneous fluids.

A model for the selective amplification of spatially coherent waves in a centrifugal compressor on the verge of rotating stall

NASA Technical Reports Server (NTRS)

Lawless, Patrick B.; Fleeter, Sanford

1993-01-01

A simple model for the stability zones of a low speed centrifugal compressor is developed, with the goal of understanding the driving mechanism for the changes in stalling behavior predicted for, and observed in, the Purdue Low Speed Centrifugal Research Compressor Facility. To this end, earlier analyses of rotating stall suppression in centrifugal compressors are presented in a reduced form that preserves the essential parameters of the model that affect the stalling behavior of the compressor. The model is then used to illuminate the relationship between compressor geometry, expected mode shape, and regions of amplification for weak waves which are indicative of the susceptibility of the system to rotating stall. The results demonstrate that increasing the stagger angle of the diffuser vanes, and consequently the diffusion path length, results in the compressor moving towards a condition where higher-order spatial modes are excited during stall initiation. Similarly, flow acceleration in the diffuser section caused by an increase in the number of diffuser vanes also results in the excitation of higher modes.

A data-led comparison of simple canopy radiative transfer models for the boreal forest

NASA Astrophysics Data System (ADS)

Reid, T.; Essery, R.; Rutter, N.; King, M.

2012-12-01

Given the computational complexity of numerical weather and climate models, it is worthwhile developing very simple parameterizations for processes such as the transmission of radiation through forest canopies. For this reason, the land surface schemes in global models, and most snow hydrological models, tend to use simple one-dimensional approaches based on Beer's Law or two-stream approximations. Such approaches assume a continuous canopy structure that may not be suitable for the varied, heterogeneous forest cover in boreal regions, especially in winter when snow in the canopy and on the ground may either block radiation or produce multiple reflections between the ground and the trees. There is great benefit in comparing models to real transmissivity values calculated from radiation measurements below and above Arctic canopies. In particular, there is a lack of data for leafless boreal deciduous forests, where canopy gaps are prevalent even at low solar elevation angles near the horizon. In this study, models are compared to radiation data collected in an area of boreal birch forest near Abisko, Sweden in March/April 2011 and mixed conifer forest at Sodankylä, Finland in March/April 2012. Arrays comprising ten shortwave pyranometers were deployed for periods of up to 50 days, under forest plots of varying canopy structures and densities. In addition, global and diffuse shortwave irradiances were recorded at nearby open sites representing the top-of-canopy conditions. A model is developed that explicitly accounts for both diffuse radiation and direct beam transmission on a 5-minute timestep, by using upward-looking hemispherical photographs taken from every pyranometer site. This model reproduces measured transmissivity, although with a slight underestimation, especially at low solar elevations - this could be attributed to multiple reflections that are not accounted for in the model. On the other hand, models based on Beer's Law tend to underestimate the canopy transmissivity significantly, especially for leafless birch canopies where the required assumption of a continuous canopy breaks down. These findings are important for the often sparse, heterogeneous forest cover in boreal regions, where forest edges and canopy gaps are plentiful. They could also have an impact on estimations of overall land surface albedo. Moreover, all models are sensitive to the partitioning of top-of-canopy radiation into its direct and diffuse components, which is complicated by the low solar elevations in the Arctic. More research is required to decide the best way of quantifying the diffuse fraction, using data alongside both physical and empirical models.

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

PubMed

Dipierro, Serena; Valdinoci, Enrico

2018-07-01

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

Modeling intragranular diffusion in low-connectivity granular media

NASA Astrophysics Data System (ADS)

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

2012-03-01

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

Biophysical mechanisms of trichloroethene uptake and loss in baldcypress growing in shallow contaminated groundwater

USGS Publications Warehouse

Nietch, C.T.; Morris, J.T.; Vroblesky, D.A.

1999-01-01

Wetland vegetation may be useful in the remediation of shallow contaminated aquifers. Mesocosm experiments were conducted to describe the regulatory mechanisms affecting trichloroethene (TCE) removal rates from groundwater by flood-adapted wetland trees at a contaminated site. TCE flux through baldcypress [Taxodium distichum (L) Rich] seedlings grown in glass- carboys decreased from day to night and from August to December. The diel fluctuation coincided with changes in leaf-level physiology, as the daytime flux was significantly correlated with net photosynthesis but not with respiration at night. A decrease in seedling water use from summer to winter explained the large seasonal difference in TCE flux. A simple model that simulates gas-phase diffusion through aerenchyma tested the importance of diffusion of TCE vapor from roots to the stem. The modeled diffusive flux was within 64% of the observed value during the winter but could only explain 8% of the summer flux. Seedling water use was a good estimator of flux during the summer. Hence, evapotranspiration (ET) in the summer may serve as a good predictor for the potential of TCE removal by baldcypress trees, while diffusive flux may better approximate potential contaminant loss in the winter.Wetland vegetation may be useful in the remediation of shallow contaminated aquifers. Mesocosm experiments were conducted to describe the regulatory mechanisms affecting trichloroethene (TCE) removal rates from groundwater by flood-adapted wetland trees at a contaminated site. TCE flux through baldcypress [Taxodium distichum (L) Rich] seedlings grown in glass-carboys decreased from day to night and from August to December. The diel fluctuation coincided with changes in leaf-level physiology, as the daytime flux was significantly correlated with net photosynthesis but not with respiration at night. A decrease in seedling water use from summer to winter explained the large seasonal difference in TCE flux. A simple model that simulates gas-phase diffusion through aerenchyma tested the importance of diffusion of TCE vapor from roots to the stem. The modeled diffusive flux was within 64% of the observed value during the winter but could only explain 8% of the summer flux. Seedling water use was a good estimator of flux during the summer. Hence, evapotranspiration (ET) in the summer may serve as a good predictor for the potential of TCE removal by baldcypress trees, while diffusive flux may better approximate potential contaminant loss in the winter.

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

Garcia, Andres

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems canmore » be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use Langevin Molecular Dynamics (MD) simulations to assess these parameters.« less

Rocket exhaust ground cloud/atmospheric interactions

NASA Technical Reports Server (NTRS)

Hwang, B.; Gould, R. K.

1978-01-01

An attempt to identify and minimize the uncertainties and potential inaccuracies of the NASA Multilayer Diffusion Model (MDM) is performed using data from selected Titan 3 launches. The study is based on detailed parametric calculations using the MDM code and a comparative study of several other diffusion models, the NASA measurements, and the MDM. The results are discussed and evaluated. In addition, the physical/chemical processes taking place during the rocket cloud rise are analyzed. The exhaust properties and the deluge water effects are evaluated. A time-dependent model for two aerosol coagulations is developed and documented. Calculations using this model for dry deposition during cloud rise are made. A simple model for calculating physical properties such as temperature and air mass entrainment during cloud rise is also developed and incorporated with the aerosol model.

Spatiotemporal pattern in somitogenesis: a non-Turing scenario with wave propagation.

PubMed

Nagahara, Hiroki; Ma, Yue; Takenaka, Yoshiko; Kageyama, Ryoichiro; Yoshikawa, Kenichi

2009-08-01

Living organisms maintain their lives under far-from-equilibrium conditions by creating a rich variety of spatiotemporal structures in a self-organized manner, such as temporal rhythms, switching phenomena, and development of the body. In this paper, we focus on the dynamical process of morphogens in somitogenesis in mice where propagation of the gene expression level plays an essential role in creating the spatially periodic patterns of the vertebral columns. We present a simple discrete reaction-diffusion model which includes neighboring interaction through an activator, but not diffusion of an inhibitor. We can produce stationary periodic patterns by introducing the effect of spatial discreteness to the field. Based on the present model, we discuss the underlying physical principles that are independent of the details of biomolecular reactions. We also discuss the framework of spatial discreteness based on the reaction-diffusion model in relation to a cellular array, by comparison with an actual experimental observation.

Nuclear quadrupole resonance lineshape analysis for different motional models: Stochastic Liouville approach

NASA Astrophysics Data System (ADS)

Kruk, D.; Earle, K. A.; Mielczarek, A.; Kubica, A.; Milewska, A.; Moscicki, J.

2011-12-01

A general theory of lineshapes in nuclear quadrupole resonance (NQR), based on the stochastic Liouville equation, is presented. The description is valid for arbitrary motional conditions (particularly beyond the valid range of perturbation approaches) and interaction strengths. It can be applied to the computation of NQR spectra for any spin quantum number and for any applied magnetic field. The treatment presented here is an adaptation of the "Swedish slow motion theory," [T. Nilsson and J. Kowalewski, J. Magn. Reson. 146, 345 (2000), 10.1006/jmre.2000.2125] originally formulated for paramagnetic systems, to NQR spectral analysis. The description is formulated for simple (Brownian) diffusion, free diffusion, and jump diffusion models. The two latter models account for molecular cooperativity effects in dense systems (such as liquids of high viscosity or molecular glasses). The sensitivity of NQR slow motion spectra to the mechanism of the motional processes modulating the nuclear quadrupole interaction is discussed.

Diffusion of a Concentrated Lattice Gas in a Regular Comb Structure

NASA Astrophysics Data System (ADS)

Garcia, Paul; Wentworth, Christopher

2008-10-01

Understanding diffusion in constrained geometries is of interest in a variety of contexts as varied as mass transport in disordered solids, such as a percolation cluster, or intercellular transport of water molecules in biological tissue. In this investigation we explore diffusion in a very simple constrained geometry: a comb-like structure involving a one-dimensional backbone of lattice sites with regularly spaced teeth of fixed length. The model considered assumes a fixed concentration of diffusing particles can hop to nearest-neighbor sites only, and they do not interact with each other except that double occupancy is not allowed. The system is simulated using a Monte Carlo simulation procedure. The mean-square displacement of a tagged particle is calculated from the simulation as a function of time. The simulation shows normal diffusive behavior after a period of anomalous diffusion that increases as the tooth size increases.

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

PubMed Central

Elcock, Adrian H.

2013-01-01

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

Position-Dependent Diffusion Tensors in Anisotropic Media from Simulation: Oxygen Transport in and through Membranes.

PubMed

Ghysels, An; Venable, Richard M; Pastor, Richard W; Hummer, Gerhard

2017-06-13

A Bayesian-based methodology is developed to estimate diffusion tensors from molecular dynamics simulations of permeants in anisotropic media, and is applied to oxygen in lipid bilayers. By a separation of variables in the Smoluchowski diffusion equation, the multidimensional diffusion is reduced to coupled one-dimensional diffusion problems that are treated by discretization. The resulting diffusivity profiles characterize the membrane transport dynamics as a function of the position across the membrane, discriminating between diffusion normal and parallel to the membrane. The methodology is first validated with neat water, neat hexadecane, and a hexadecane slab surrounded by water, the latter being a simple model for a lipid membrane. Next, a bilayer consisting of pure 1-palmitoyl 2-oleoylphosphatidylcholine (POPC), and a bilayer mimicking the lipid composition of the inner mitochondrial membrane, including cardiolipin, are investigated. We analyze the detailed time evolution of oxygen molecules, in terms of both normal diffusion through and radial diffusion inside the membrane. Diffusion is fast in the more loosely packed interleaflet region, and anisotropic, with oxygen spreading more rapidly in the membrane plane than normal to it. Visualization of the propagator shows that oxygen enters the membrane rapidly, reaching its thermodynamically favored center in about 1 ns, despite the free energy barrier at the headgroup region. Oxygen transport is quantified by computing the oxygen permeability of the membranes and the average radial diffusivity, which confirm the anisotropy of the diffusion. The position-dependent diffusion constants and free energies are used to construct compartmental models and test assumptions used in estimating permeability, including Overton's rule. In particular, a hexadecane slab surrounded by water is found to be a poor model of oxygen transport in membranes because the relevant energy barriers differ substantially.

Role of gravity in preparative electrophoresis

NASA Technical Reports Server (NTRS)

Bier, M.

1975-01-01

The fundamental formulas of electrophoresis are derived microscopically and applied to the problem of isotachophoresis. A simple physical model of the isotachophoresis front is proposed. The front motion and structure are studied in the simplified case without convection, diffusion and non-electric external forces.

Open photoacoustic cell x-ray detection

NASA Astrophysics Data System (ADS)

Bento, A. C.; Aguiar, M. M. F.; Vargas, H.; da Silva, M. D.; Bandeira, I. N.; Miranda, L. C. M.

1989-03-01

A simple open-cell configuration photoacoustic x-ray detector is experimentally demonstrated. The front air chamber of a commercial electret microphone is used as the transducer medium of conventional photoacoustics. The observed signal is well described by the thermal diffusion model for the photoacoustic signal.

Causal electric charge diffusion and balance functions in relativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Kapusta, Joseph I.; Plumberg, Christopher

2018-01-01

We study the propagation and diffusion of electric charge fluctuations in high-energy heavy-ion collisions using the Cattaneo form for the dissipative part of the electric current. As opposed to the ordinary diffusion equation this form limits the speed at which charge can propagate. Including the noise term in the current, which arises uniquely from the fluctuation-dissipation theorem, we calculate the balance functions for charged hadrons in a simple 1+1-dimensional Bjorken hydrodynamical model. Limiting the speed of propagation of charge fluctuations increases the height and reduces the width of these balance functions when plotted versus rapidity. We also estimate the numerical value of the associated diffusion time constant from anti-de Sitter-space/conformal-field theory.

Metabolic compartmentation in rainbow trout cardiomyocytes: coupling of hexokinase but not creatine kinase to mitochondrial respiration.

PubMed

Karro, Niina; Sepp, Mervi; Jugai, Svetlana; Laasmaa, Martin; Vendelin, Marko; Birkedal, Rikke

2017-01-01

Rainbow trout (Oncorhynchus mykiss) cardiomyocytes have a simple morphology with fewer membrane structures such as sarcoplasmic reticulum and t-tubules penetrating the cytosol. Despite this, intracellular ADP diffusion is restricted. Intriguingly, although diffusion is restricted, trout cardiomyocytes seem to lack the coupling between mitochondrial creatine kinase (CK) and respiration. Our aim was to study the distribution of diffusion restrictions in permeabilized trout cardiomyocytes and verify the role of CK. We found a high activity of hexokinase (HK), which led us to reassess the situation in trout cardiomyocytes. We show that diffusion restrictions are more prominent than previously thought. In the presence of a competitive ADP-trapping system, ADP produced by HK, but not CK, was channeled to the mitochondria. In agreement with this, we found no positively charged mitochondrial CK in trout heart homogenate. The results were best fit by a simple mathematical model suggesting that trout cardiomyocytes lack a functional coupling between ATPases and pyruvate kinase. The model simulations show that diffusion is restricted to almost the same extent in the cytosol and by the outer mitochondrial membrane. Furthermore, they confirm that HK, but not CK, is functionally coupled to respiration. In perspective, our results suggest that across a range of species, cardiomyocyte morphology and metabolism go hand in hand with cardiac performance, which is adapted to the circumstances. Mitochondrial CK is coupled to respiration in adult mammalian hearts, which are specialized to high, sustained performance. HK associates with mitochondria in hearts of trout and neonatal mammals, which are more hypoxia-tolerant.

Improved modeling of turbulent forced convection heat transfer in straight ducts

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

Rokni, M.; Sunden, B.

1999-08-01

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in their fully developed state at low Reynolds number. The authors have developed a low Reynolds number version of the nonlinear {kappa}-{epsilon} model combined with the heat flux models of simple eddy diffusivity (SED), low Reynolds number version of generalized gradient diffusion hypothesis (GGDH), and wealth {proportional_to} earning {times} time (WET) in general three-dimensional geometries. The numerical approach is based on the finite volume technique with a nonstaggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with the nonlinear {kappa}-{epsilon} model, combined with themore » Lam-Bremhorst and the Abe-Kondoh-Nagano damping functions for low Reynolds numbers.« less

The coupled effects of chemistry and diffusion on the stratospheric ozone reduction

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Grose, W. L.

1980-01-01

The effect of diffusive-mixing on O3-depletion is estimated using the five-step chemistry model. The coupled treatment uses an equilibrium turbulence field and retains the key features of the kinetics while keeping the chemistry simple. Results indicate that those calculations of Hilst and Donaldson (1973) employing the conservation of NO2/NO will yield erroneous results, and it is found that any significant level of turbulence will reduce the severity of the NOx catalytic cycle for O3 destruction.

Simple models for studying complex spatiotemporal patterns of animal behavior

NASA Astrophysics Data System (ADS)

Tyutyunov, Yuri V.; Titova, Lyudmila I.

2017-06-01

Minimal mathematical models able to explain complex patterns of animal behavior are essential parts of simulation systems describing large-scale spatiotemporal dynamics of trophic communities, particularly those with wide-ranging species, such as occur in pelagic environments. We present results obtained with three different modelling approaches: (i) an individual-based model of animal spatial behavior; (ii) a continuous taxis-diffusion-reaction system of partial-difference equations; (iii) a 'hybrid' approach combining the individual-based algorithm of organism movements with explicit description of decay and diffusion of the movement stimuli. Though the models are based on extremely simple rules, they all allow description of spatial movements of animals in a predator-prey system within a closed habitat, reproducing some typical patterns of the pursuit-evasion behavior observed in natural populations. In all three models, at each spatial position the animal movements are determined by local conditions only, so the pattern of collective behavior emerges due to self-organization. The movement velocities of animals are proportional to the density gradients of specific cues emitted by individuals of the antagonistic species (pheromones, exometabolites or mechanical waves of the media, e.g., sound). These cues play a role of taxis stimuli: prey attract predators, while predators repel prey. Depending on the nature and the properties of the movement stimulus we propose using either a simplified individual-based model, a continuous taxis pursuit-evasion system, or a little more detailed 'hybrid' approach that combines simulation of the individual movements with the continuous model describing diffusion and decay of the stimuli in an explicit way. These can be used to improve movement models for many species, including large marine predators.

Diffusion Dynamics and Creative Destruction in a Simple Classical Model

PubMed Central

2015-01-01

ABSTRACT The article explores the impact of the diffusion of new methods of production on output and employment growth and income distribution within a Classical one‐sector framework. Disequilibrium paths are studied analytically and in terms of simulations. Diffusion by differential growth affects aggregate dynamics through several channels. The analysis reveals the non‐steady nature of economic change and shows that the adaptation pattern depends both on the innovation's factor‐saving bias and on the extent of the bias, which determines the strength of the selection pressure on non‐innovators. The typology of different cases developed shows various aspects of Schumpeter's concept of creative destruction. PMID:27642192

Dependence of surface tension on curvature obtained from a diffuse-interface approach

NASA Astrophysics Data System (ADS)

Badillo, Arnoldo; Lafferty, Nathan; Matar, Omar K.

2017-11-01

From a sharp-interface viewpoint, the surface tension force is f = σκδ (x -xi) n , where σ is the surface tension, κ the local interface curvature, δ the delta function, and n the unit normal vector. The numerical implementation of this force on discrete domains poses challenges that arise from the calculation of the curvature. The continuous surface tension force model, proposed by Brackbill et al. (1992), is an alternative, used commonly in two-phase computational models. In this model, δ is replaced by the gradient of a phase indicator field, whose integral across a diffuse-interface equals unity. An alternative to the Brackbill model are Phase-Field models, which do not require an explicit calculation of the curvature. However, and just as in Brackbill's approach, there are numerical errors that depend on the thickness of the diffuse interface, the grid spacing, and the curvature. We use differential geometry to calculate the leading errors in this force when obtained from a diffuse-interface approach, and outline possible routes to eliminate them. Our results also provide a simple geometrical explanation to the dependence of surface tension on curvature, and to the problem of line tension.

A new paradigm for predicting zonal-mean climate and climate change

NASA Astrophysics Data System (ADS)

Armour, K.; Roe, G.; Donohoe, A.; Siler, N.; Markle, B. R.; Liu, X.; Feldl, N.; Battisti, D. S.; Frierson, D. M.

2016-12-01

How will the pole-to-equator temperature gradient, or large-scale patterns of precipitation, change under global warming? Answering such questions typically involves numerical simulations with comprehensive general circulation models (GCMs) that represent the complexities of climate forcing, radiative feedbacks, and atmosphere and ocean dynamics. Yet, our understanding of these predictions hinges on our ability to explain them through the lens of simple models and physical theories. Here we present evidence that zonal-mean climate, and its changes, can be understood in terms of a moist energy balance model that represents atmospheric heat transport as a simple diffusion of latent and sensible heat (as a down-gradient transport of moist static energy, with a diffusivity coefficient that is nearly constant with latitude). We show that the theoretical underpinnings of this model derive from the principle of maximum entropy production; that its predictions are empirically supported by atmospheric reanalyses; and that it successfully predicts the behavior of a hierarchy of climate models - from a gray radiation aquaplanet moist GCM, to comprehensive GCMs participating in CMIP5. As an example of the power of this paradigm, we show that, given only patterns of local radiative feedbacks and climate forcing, the moist energy balance model accurately predicts the evolution of zonal-mean temperature and atmospheric heat transport as simulated by the CMIP5 ensemble. These results suggest that, despite all of its dynamical complexity, the atmosphere essentially responds to energy imbalances by simply diffusing latent and sensible heat down-gradient; this principle appears to explain zonal-mean climate and its changes under global warming.

Effects of Anomalous Cosmic Rays on the Structure of the Outer Heliosphere

NASA Astrophysics Data System (ADS)

Guo, Xiaocheng; Florinski, Vladimir; Wang, Chi

2018-06-01

Based on Voyager 1 observations, some anomalous cosmic rays (ACRs) may have crossed the heliopause and escaped into the interstellar medium, providing a mechanism of energy transfer between the inner and outer heliosheaths that is not included in conventional magnetohydrodynamics (MHD) models. In this paper, we study the effect of energetic particles’ escape through the heliopause on the size and shape of the heliosphere using a simple model that includes diffusive transport of cosmic rays. We show that the presence of ACRs significantly changes the heliosphere structure, including the location of the heliopause and termination shock. It was found that the heliopause would contract for certain values of the ACR diffusion coefficients when the diffusive particles’ pressure is comparable to the pressure of the plasma background. The difference in Voyager 1 and 2 observations of energetic particles during their respective termination shock crossings is interpreted here as due to the differences in diffusion environments during the different phases of the solar cycle. The shorter period of enhanced ACR intensities upstream of the shock measured by Voyager 2 may have been caused by weaker radial diffusive transport compared with the time of Voyager 1 crossing. We conclude that ACR diffusive effects could be prominent and should be included in MHD models of the heliosphere.

Interpreting high time resolution galactic cosmic ray observations in a diffusive context

NASA Astrophysics Data System (ADS)

Jordan, A.; Spence, H. E.; Blake, J. B.; Shaul, D. A.

2009-12-01

We interpret galactic cosmic ray (GCR) variations near Earth within a diffusive context. The variations occur on time-/size-scales ranging from Forbush decreases (Fds), to substructure embedded within Fds, to smaller amplitude and shorter duration variations during relatively benign interplanetary conditions. We use high time resolution GCR observations from the High Sensitivity Telescope (HIST) on Polar and from the Spectrometer for INTEGRAL (SPI) and also use solar wind plasma and magnetic field observations from ACE and/or Wind. To calculate the coefficient of diffusion, we combine these datasets with a simple convection-diffusion model for relativistic charged particles in a magnetic field. We find reasonable agreement between our and previous estimates of the coefficient. We also show whether changes in the coefficient of diffusion are sufficient to explain the above GCR variations.

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

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2008-12-01

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

Time-dependent diffusion MRI in cancer: tissue modeling and applications

NASA Astrophysics Data System (ADS)

Reynaud, Olivier

2017-11-01

In diffusion weighted imaging (DWI), the apparent diffusion coefficient has been recognized as a useful and sensitive surrogate for cell density, paving the way for non-invasive tumor staging, and characterization of treatment efficacy in cancer. However, microstructural parameters, such as cell size, density and/or compartmental diffusivities affect diffusion in various fashions, making of conventional DWI a sensitive but non-specific probe into changes happening at cellular level. Alternatively, tissue complexity can be probed and quantified using the time dependence of diffusion metrics, sometimes also referred to as temporal diffusion spectroscopy when only using oscillating diffusion gradients. Time-dependent diffusion (TDD) is emerging as a strong candidate for specific and non-invasive tumor characterization. Despite the lack of a general analytical solution for all diffusion times / frequencies, TDD can be probed in various regimes where systems simplify in order to extract relevant information about tissue microstructure. The fundamentals of TDD are first reviewed (a) in the short time regime, disentangling structural and diffusive tissue properties, and (b) near the tortuosity limit, assuming weakly heterogeneous media near infinitely long diffusion times. Focusing on cell bodies (as opposed to neuronal tracts), a simple but realistic model for intracellular diffusion can offer precious insight on diffusion inside biological systems, at all times. Based on this approach, the main three geometrical models implemented so far (IMPULSED, POMACE, VERDICT) are reviewed. Their suitability to quantify cell size, intra- and extracellular spaces (ICS and ECS) and diffusivities are assessed. The proper modeling of tissue membrane permeability – hardly a newcomer in the field, but lacking applications - and its impact on microstructural estimates are also considered. After discussing general issues with tissue modeling and microstructural parameter estimation (i.e. fitting), potential solutions are detailed. The in vivo applications of this new, non-invasive, specific approach in cancer are reviewed, ranging from the characterization of gliomas in rodent brains and observation of time-dependence in breast tissue lesions and prostate cancer, to the recent preclinical evaluation of new treatments efficacy. It is expected that clinical applications of TDD will strongly benefit the community in terms of non-invasive cancer screening.

Solar energy distribution over Egypt using cloudiness from Meteosat photos

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

Mosalam Shaltout, M.A.; Hassen, A.H.

1990-01-01

In Egypt, there are 10 ground stations for measuring the global solar radiation, and five stations for measuring the diffuse solar radiation. Every day at noon, the Meteorological Authority in Cairo receives three photographs of cloudiness over Egypt from the Meteosat satellite, one in the visible, and two in the infra-red bands (10.5-12.5 {mu}m) and (5.7-7.1 {mu}m). The monthly average cloudiness for 24 sites over Egypt are measured and calculated from Meteosat observations during the period 1985-1986. Correlation analysis between the cloudiness observed by Meteosat and global solar radiation measured from the ground stations is carried out. It is foundmore » that, the correlation coefficients are about 0.90 for the simple linear regression, and increase for the second and third degree regressions. Also, the correlation coefficients for the cloudiness with the diffuse solar radiation are about 0.80 for the simple linear regression, and increase for the second and third degree regression. Models and empirical relations for estimating the global and diffuse solar radiation from Meteosat cloudiness data over Egypt are deduced and tested. Seasonal maps for the global and diffuse radiation over Egypt are carried out.« less

A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

PubMed

Song, Yun S; Steinrücken, Matthias

2012-03-01

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.

A Simple Method for Finding Explicit Analytic Transition Densities of Diffusion Processes with General Diploid Selection

PubMed Central

Song, Yun S.; Steinrücken, Matthias

2012-01-01

The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899

Compartment models of the diffusion MR signal in brain white matter: a taxonomy and comparison.

PubMed

Panagiotaki, Eleftheria; Schneider, Torben; Siow, Bernard; Hall, Matt G; Lythgoe, Mark F; Alexander, Daniel C

2012-02-01

This paper aims to identify the minimum requirements for an accurate model of the diffusion MR signal in white matter of the brain. We construct a taxonomy of multi-compartment models of white matter from combinations of simple models for the intra- and the extra-axonal spaces. We devise a new diffusion MRI protocol that provides measurements with a wide range of imaging parameters for diffusion sensitization both parallel and perpendicular to white matter fibres. We use the protocol to acquire data from two fixed rat brains, which allows us to fit, study and compare the different models. The study examines a total of 47 analytic models, including several well-used models from the literature, which we place within the taxonomy. The results show that models that incorporate intra-axonal restriction, such as ball and stick or CHARMED, generally explain the data better than those that do not, such as the DT or the biexponential models. However, three-compartment models which account for restriction parallel to the axons and incorporate pore size explain the measurements most accurately. The best fit comes from combining a full diffusion tensor (DT) model of the extra-axonal space with a cylindrical intra-axonal component of single radius and a third spherical compartment of non-zero radius. We also measure the stability of the non-zero radius intra-axonal models and find that single radius intra-axonal models are more stable than gamma distributed radii models with similar fitting performance. Copyright © 2011 Elsevier Inc. All rights reserved.

When push comes to shove: Exclusion processes with nonlocal consequences

NASA Astrophysics Data System (ADS)

Almet, Axel A.; Pan, Michael; Hughes, Barry D.; Landman, Kerry A.

2015-11-01

Stochastic agent-based models are useful for modelling collective movement of biological cells. Lattice-based random walk models of interacting agents where each site can be occupied by at most one agent are called simple exclusion processes. An alternative motility mechanism to simple exclusion is formulated, in which agents are granted more freedom to move under the compromise that interactions are no longer necessarily local. This mechanism is termed shoving. A nonlinear diffusion equation is derived for a single population of shoving agents using mean-field continuum approximations. A continuum model is also derived for a multispecies problem with interacting subpopulations, which either obey the shoving rules or the simple exclusion rules. Numerical solutions of the derived partial differential equations compare well with averaged simulation results for both the single species and multispecies processes in two dimensions, while some issues arise in one dimension for the multispecies case.

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

PubMed Central

2015-01-01

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

Simulating Donnan equilibria based on the Nernst-Planck equation

NASA Astrophysics Data System (ADS)

Gimmi, Thomas; Alt-Epping, Peter

2018-07-01

Understanding ion transport through clays and clay membranes is important for many geochemical and environmental applications. Ion transport is affected by electrostatic forces exerted by charged clay surfaces. Anions are partly excluded from pore water near these surfaces, whereas cations are enriched. Such effects can be modeled by the Donnan approach. Here we introduce a new, comparatively simple way to represent Donnan equilibria in transport simulations. We include charged surfaces as immobile ions in the balance equation and calculate coupled transport of all components, including the immobile charges, with the Nernst-Planck equation. This results in an additional diffusion potential that influences ion transport, leading to Donnan ion distributions while maintaining local charge balance. The validity of our new approach was demonstrated by comparing Nernst-Planck simulations using the reactive transport code Flotran with analytical solutions available for simple Donnan systems. Attention has to be paid to the numerical evaluation of the electrochemical migration term in the Nernst-Planck equation to obtain correct results for asymmetric electrolytes. Sensitivity simulations demonstrate the influence of various Donnan model parameters on simulated anion accessible porosities. It is furthermore shown that the salt diffusion coefficient in a Donnan pore depends on local concentrations, in contrast to the aqueous salt diffusion coefficient. Our approach can be easily implemented into other transport codes. It is versatile and facilitates, for instance, assessing the implications of different activity models for the Donnan porosity.

Model-based analysis of multi-shell diffusion MR data for tractography: How to get over fitting problems

PubMed Central

Jbabdi, Saad; Sotiropoulos, Stamatios N; Savio, Alexander M; Graña, Manuel; Behrens, Timothy EJ

2012-01-01

In this article, we highlight an issue that arises when using multiple b-values in a model-based analysis of diffusion MR data for tractography. The non-mono-exponential decay, commonly observed in experimental data, is shown to induce over-fitting in the distribution of fibre orientations when not considered in the model. Extra fibre orientations perpendicular to the main orientation arise to compensate for the slower apparent signal decay at higher b-values. We propose a simple extension to the ball and stick model based on a continuous Gamma distribution of diffusivities, which significantly improves the fitting and reduces the over-fitting. Using in-vivo experimental data, we show that this model outperforms a simpler, noise floor model, especially at the interfaces between brain tissues, suggesting that partial volume effects are a major cause of the observed non-mono-exponential decay. This model may be helpful for future data acquisition strategies that may attempt to combine multiple shells to improve estimates of fibre orientations in white matter and near the cortex. PMID:22334356

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.

Evidence of diffusive fractal aggregation of TiO2 nanoparticles by femtosecond laser ablation at ambient conditions

NASA Astrophysics Data System (ADS)

Celardo, G. L.; Archetti, D.; Ferrini, G.; Gavioli, L.; Pingue, P.; Cavaliere, E.

2017-01-01

The specific mechanisms which lead to the formation of fractal nanostructures by pulsed laser deposition remain elusive despite intense research efforts, motivated mainly by the technological interest in obtaining tailored nanostructures with simple and scalable production methods. Here we focus on fractal nanostructures of titanium dioxide, TiO2, a strategic material for many applications, obtained by femtosecond laser ablation at ambient conditions. We compare a theoretical model of fractal formation with experimental data. The comparison of theory and experiment confirms that fractal aggregates are formed after landing of the ablated material on the substrate surface by a simple diffusive mechanism. We model the fractal formation through extensive Monte Carlo simulations based on a set of minimal assumptions: TiO2 nanoparticles arrive already formed on the substrate, then they diffuse in a size/mass independent way and stick irreversibly upon touching, thus forming fractal clusters. Despite its simplicity, our model explains the main features of the fractal structures arising from the complex interaction of large TiO2 nanoparticles with different substrates. Indeed our model is able to reproduce both the fractal dimensions and the area distributions of the nanostructures for different densities of the ablated material. Finally we discuss the role of the thermal conductivity of the substrate and the laser fluence on the properties of the fractal nanostructures. Our results represent an advancement towards controlling the production of fractal nanostructures by pulsed laser deposition.

Time scale of random sequential adsorption.

PubMed

Erban, Radek; Chapman, S Jonathan

2007-04-01

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

Anomalous diffusion and scaling in coupled stochastic processes

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

Bel, Golan; Nemenman, Ilya

2009-01-01

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the Pocker-Planck the friction coefficient of the first depends on the state of the second. Integrating out the latter, we derive the Focker-Planck equation for the probability distribution of the former. This has the fonn of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well. Themore » diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standandard, diffusive Langevin descritpion.« less

Reaction-diffusion systems and external morphogen gradients: the two-dimensional case, with an application to skeletal pattern formation.

PubMed

Glimm, Tilmann; Zhang, Jianying; Shen, Yun-Qiu; Newman, Stuart A

2012-03-01

We investigate a reaction-diffusion system consisting of an activator and an inhibitor in a two-dimensional domain. There is a morphogen gradient in the domain. The production of the activator depends on the concentration of the morphogen. Mathematically, this leads to reaction-diffusion equations with explicitly space-dependent terms. It is well known that in the absence of an external morphogen, the system can produce either spots or stripes via the Turing bifurcation. We derive first-order expansions for the possible patterns in the presence of an external morphogen and show how both stripes and spots are affected. This work generalizes previous one-dimensional results to two dimensions. Specifically, we consider the quasi-one-dimensional case of a thin rectangular domain and the case of a square domain. We apply the results to a model of skeletal pattern formation in vertebrate limbs. In the framework of reaction-diffusion models, our results suggest a simple explanation for some recent experimental findings in the mouse limb which are much harder to explain in positional-information-type models.

NMR signals within the generalized Langevin model for fractional Brownian motion

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-03-01

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

Modeling packed bed sorbent systems with the Pore Surface Diffusion Model: Evidence of facilitated surface diffusion of arsenate in nano-metal (hydr)oxide hybrid ion exchange media.

PubMed

Dale, Sachie; Markovski, Jasmina; Hristovski, Kiril D

2016-09-01

This study explores the possibility of employing the Pore Surface Diffusion Model (PSDM) to predict the arsenic breakthrough curve of a packed bed system operated under continuous flow conditions with realistic groundwater, and consequently minimize the need to conduct pilot scale tests. To provide the nano-metal (hydr)oxide hybrid ion exchange media's performance in realistic water matrices without engaging in taxing pilot scale testing, the multi-point equilibrium batch sorption tests under pseudo-equilibrium conditions were performed; arsenate breakthrough curve of short bed column (SBC) was predicted by the PSDM in the continuous flow experiments; SBC tests were conducted under the same conditions to validate the model. The overlapping Freundlich isotherms suggested that the water matrix and competing ions did not have any denoting effect on sorption capacity of the media when the matrix was changed from arsenic-only model water to real groundwater. As expected, the PSDM provided a relatively good prediction of the breakthrough profile for arsenic-only model water limited by intraparticle mass transports. In contrast, the groundwater breakthrough curve demonstrated significantly faster intraparticle mass transport suggesting to a surface diffusion process, which occurs in parallel to the pore diffusion. A simple selection of DS=1/2 DP appears to be sufficient when describing the facilitated surface diffusion of arsenate inside metal (hydr)oxide nano-enabled hybrid ion-exchange media in presence of sulfate, however, quantification of the factors determining the surface diffusion coefficient's magnitude under different treatment scenarios remained unexplored. Copyright © 2015 Elsevier B.V. All rights reserved.

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

PubMed

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

2009-12-01

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

Determination of charge-carrier diffusion length in the photosensing layer of HgCdTe n-on-p photovoltaic infrared focal plane array detectors

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

Vishnyakov, A. V.; Stuchinsky, V. A., E-mail: stuchin@isp.nsc.ru; Brunev, D. V.

2014-03-03

In the present paper, we propose a method for evaluating the bulk diffusion length of minority charge carriers in the photosensing layer of photovoltaic focal plane array (FPA) photodetectors. The method is based on scanning a strip-shaped illumination spot with one of the detector diodes at a low level of photocurrents j{sub ph} being registered; such scanning provides data for subsequent analysis of measured spot-scan profiles within a simple diffusion model. The asymptotic behavior of the effective (at j{sub ph} ≠ 0) charge-carrier diffusion length l{sub d} {sub eff} as a function of j{sub ph} for j{sub ph} → 0 inferred frommore » our experimental data proved to be consistent with the behavior of l{sub d} {sub eff} vs j{sub ph} as predicted by the model, while the obtained values of the bulk diffusion length of minority carriers (electrons) in the p-HgCdTe film of investigated HgCdTe n-on-p FPA photodetectors were found to be in a good agreement with the previously reported carrier diffusion-length values for HgCdTe.« less

Passive Membrane Permeability: Beyond the Standard Solubility-Diffusion Model.

PubMed

Parisio, Giulia; Stocchero, Matteo; Ferrarini, Alberta

2013-12-10

The spontaneous diffusion of solutes through lipid bilayers is still a challenge for theoretical predictions. Since permeation processes remain beyond the capabilities of unbiased molecular dynamics simulations, an alternative strategy is currently adopted to gain insight into their mechanism and time scale. This is based on a monodimensional description of the translocation process only in terms of the position of the solute along the normal to the lipid bilayer, which is formally expressed in the solubility-diffusion model. Actually, a role of orientational and conformational motions has been pointed out, and the use of advanced simulation techniques has been proposed to take into account their effect. Here, we discuss the limitations of the standard solubility-diffusion approach and propose a more general description of membrane translocation as a diffusion process on a free energy surface, which is a function of the translational and rotational degrees of freedom of the molecule. Simple expressions for the permeability coefficient are obtained under suitable conditions. For fast solute reorientation, the classical solubility-diffusion equation is recovered. Under the assumption that well-defined minima can be identified on the free energy landscape, a mechanistic interpretation of the permeability coefficient in terms of all possible permeation paths is given.

Increased Accuracy of Ligand Sensing by Receptor Internalization and Lateral Receptor Diffusion

NASA Astrophysics Data System (ADS)

Aquino, Gerardo; Endres, Robert

2010-03-01

Many types of cells can sense external ligand concentrations with cell-surface receptors at extremely high accuracy. Interestingly, ligand-bound receptors are often internalized, a process also known as receptor-mediated endocytosis. While internalization is involved in a vast number of important functions for the life of a cell, it was recently also suggested to increase the accuracy of sensing ligand as overcounting of the same ligand molecules is reduced. A similar role may be played by receptor diffusion om the cell membrane. Fast, lateral receptor diffusion is known to be relevant in neurotransmission initiated by release of neurotransmitter glutamate in the synaptic cleft between neurons. By binding ligand and removal by diffusion from the region of release of the neurotransmitter, diffusing receptors can be reasonably expected to reduce the local overcounting of the same ligand molecules in the region of signaling. By extending simple ligand-receptor models to out-of-equilibrium thermodynamics, we show that both receptor internalization and lateral diffusion increase the accuracy with which cells can measure ligand concentrations in the external environment. We confirm this with our model and give quantitative predictions for experimental parameters values. We give quantitative predictions, which compare favorably to experimental data of real receptors.

The Long and Viscous Road: Uncovering Nuclear Diffusion Barriers in Closed Mitosis

PubMed Central

Zavala, Eder; Marquez-Lago, Tatiana T.

2014-01-01

Diffusion barriers are effective means for constraining protein lateral exchange in cellular membranes. In Saccharomyces cerevisiae, they have been shown to sustain parental identity through asymmetric segregation of ageing factors during closed mitosis. Even though barriers have been extensively studied in the plasma membrane, their identity and organization within the nucleus remains poorly understood. Based on different lines of experimental evidence, we present a model of the composition and structural organization of a nuclear diffusion barrier during anaphase. By means of spatial stochastic simulations, we propose how specialised lipid domains, protein rings, and morphological changes of the nucleus may coordinate to restrict protein exchange between mother and daughter nuclear lobes. We explore distinct, plausible configurations of these diffusion barriers and offer testable predictions regarding their protein exclusion properties and the diffusion regimes they generate. Our model predicts that, while a specialised lipid domain and an immobile protein ring at the bud neck can compartmentalize the nucleus during early anaphase; a specialised lipid domain spanning the elongated bridge between lobes would be entirely sufficient during late anaphase. Our work shows how complex nuclear diffusion barriers in closed mitosis may arise from simple nanoscale biophysical interactions. PMID:25032937

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

A diffuse emission modeling tool has been developed, which is appropriate to support decision-making in watershed management. The PhosFate (Phosphorus Fate) tool allows planning best management practices (BMPs) in catchments and simulating their possible impacts on the phosphorus (P) loads. PhosFate is a simple fate model to calculate diffuse P emissions and their transport within a catchment. The model is a semi-empirical, catchment scale, distributed parameter and long-term (annual) average model. It has two main parts: (a) the emission and (b) the transport model. The main input data of the model are digital maps (elevation, soil types and landuse categories), statistical data (crop yields, animal numbers, fertilizer amounts and precipitation distribution) and point information (precipitation, meteorology, soil humus content, point source emissions and reservoir data). The emission model calculates the diffuse P emissions at their source. It computes the basic elements of the hydrology as well as the soil loss. The model determines the accumulated P surplus of the topsoil and distinguishes the dissolved and the particulate P forms. Emissions are calculated according to the different pathways (surface runoff, erosion and leaching). The main outputs are the spatial distribution (cell values) of the runoff components, the soil loss and the P emissions within the catchment. The transport model joins the independent cells based on the flow tree and it follows the further fate of emitted P from each cell to the catchment outlets. Surface runoff and P fluxes are accumulated along the tree and the field and in-stream retention of the particulate forms are computed. In case of base flow and subsurface P loads only the channel transport is taken into account due to the less known hydrogeological conditions. During the channel transport, point sources and reservoirs are also considered. Main results of the transport algorithm are the discharge, dissolved and sediment-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.

Monte Carlo simulations of coupled diffusion and surface reactions during the aqueous corrosion of borosilicate glasses

DOE PAGES

Kerisit, Sebastien; Pierce, Eric M.; Ryan, Joseph V.

2014-09-19

Borosilicate nuclear waste glasses develop complex altered layers as a result of coupled processes such as hydrolysis of network species, condensation of Si species, and diffusion. However, diffusion has often been overlooked in Monte Carlo models of the aqueous corrosion of borosilicate glasses. Therefore, in this paper three different models for dissolved Si diffusion in the altered layer were implemented in a Monte Carlo model and evaluated for glasses in the compositional range (75 - x) mol% SiO 2 (12.5 + x/2) mol% B 2O 3 and (12.5 + x/2) mol% Na 2O, where 0 ≤ x ≤ 20%, andmore » corroded in static conditions at a surface-area-to-volume ratio of 1000 m -1. The three models considered instantaneous homogenization (M1), linear concentration gradients (M2), and concentration profiles determined by solving Fick's 2nd law using a finite difference method (M3). Model M3 revealed that concentration profiles in the altered layer are not linear and show changes in shape and magnitude as corrosion progresses, unlike those assumed in model M2. Furthermore, model M3 showed that, for borosilicate glasses with a high forward dissolution rate compared to the diffusion rate, the gradual polymerization and densification of the altered layer is significantly delayed compared to models M1 and M2. Finally, models M1 and M2 were found to be appropriate models only for glasses with high release rates such as simple borosilicate glasses with low ZrO 2 content.« less

On the Mass Distribution of Animal Species

NASA Astrophysics Data System (ADS)

Redner, Sidney; Clauset, Aaron; Schwab, David

2009-03-01

We develop a simple diffusion-reaction model to account for the broad and asymmetric distribution of adult body masses for species within related taxonomic groups. The model assumes three basic evolutionary features that control body mass: (i) a fixed lower limit that is set by metabolic constraints, (ii) a species extinction risk that is a weakly increasing function of body mass, and (iii) cladogenetic diffusion, in which daughter species have a slight tendency toward larger mass. The steady-state solution for the distribution of species masses in this model can be expressed in terms of the Airy function. This solution gives mass distributions that are in good agreement with data on 4002 terrestrial mammal species from the late Quaternary and 8617 extant bird species.

Discriminating the effects of collapse models from environmental diffusion with levitated nanospheres

NASA Astrophysics Data System (ADS)

Li, Jie; Zippilli, Stefano; Zhang, Jing; Vitali, David

2016-05-01

Collapse models postulate the existence of intrinsic noise which modifies quantum mechanics and is responsible for the emergence of macroscopic classicality. Assessing the validity of these models is extremely challenging because it is nontrivial to discriminate unambiguously their presence in experiments where other hardly controllable sources of noise compete to the overall decoherence. Here we provide a simple procedure that is able to probe the hypothetical presence of the collapse noise with a levitated nanosphere in a Fabry-Pérot cavity. We show that the stationary state of the system is particularly sensitive, under specific experimental conditions, to the interplay between the trapping frequency, the cavity size, and the momentum diffusion induced by the collapse models, allowing one to detect them even in the presence of standard environmental noises.

Electric-field noise from carbon-adatom diffusion on a Au(110) surface: First-principles calculations and experiments

DOE PAGES

Kim, E.; Safavi-Naini, A.; Hite, D. A.; ...

2017-03-01

The decoherence of trapped-ion quantum bits due to heating of their motional modes is a fundamental science and engineering problem. This heating is attributed to electric-field noise arising from processes on the trap-electrode surfaces. In this work, we address the source of this noise by focusing on the diffusion of carbon-containing adsorbates on the surface of Au(110). We show by detailed scanned probe microscopy and density functional theory how the carbon adatom diffusion on the gold surface changes the energy landscape, and how the adatom dipole moment varies with the diffusive motion. Lastly, a simple model for the diffusion noise,more » which varies quadratically with the variation of the dipole moment, qualitatively reproduces the measured noise spectrum, and the estimate of the noise spectral density is in accord with measured values.« less

Electric-field noise from carbon-adatom diffusion on a Au(110) surface: First-principles calculations and experiments

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

Kim, E.; Safavi-Naini, A.; Hite, D. A.

The decoherence of trapped-ion quantum bits due to heating of their motional modes is a fundamental science and engineering problem. This heating is attributed to electric-field noise arising from processes on the trap-electrode surfaces. In this work, we address the source of this noise by focusing on the diffusion of carbon-containing adsorbates on the surface of Au(110). We show by detailed scanned probe microscopy and density functional theory how the carbon adatom diffusion on the gold surface changes the energy landscape, and how the adatom dipole moment varies with the diffusive motion. Lastly, a simple model for the diffusion noise,more » which varies quadratically with the variation of the dipole moment, qualitatively reproduces the measured noise spectrum, and the estimate of the noise spectral density is in accord with measured values.« less

λ-Repressor Oligomerization Kinetics at High Concentrations Using Fluorescence Correlation Spectroscopy in Zero-Mode Waveguides

PubMed Central

Samiee, K. T.; Foquet, M.; Guo, L.; Cox, E. C.; Craighead, H. G.

2005-01-01

Fluorescence correlation spectroscopy (FCS) has demonstrated its utility for measuring transport properties and kinetics at low fluorophore concentrations. In this article, we demonstrate that simple optical nanostructures, known as zero-mode waveguides, can be used to significantly reduce the FCS observation volume. This, in turn, allows FCS to be applied to solutions with significantly higher fluorophore concentrations. We derive an empirical FCS model accounting for one-dimensional diffusion in a finite tube with a simple exponential observation profile. This technique is used to measure the oligomerization of the bacteriophage λ repressor protein at micromolar concentrations. The results agree with previous studies utilizing conventional techniques. Additionally, we demonstrate that the zero-mode waveguides can be used to assay biological activity by measuring changes in diffusion constant as a result of ligand binding. PMID:15613638

TURBULENT TRANSPORT IN A STRONGLY STRATIFIED FORCED SHEAR LAYER WITH THERMAL DIFFUSION

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

Garaud, Pascale

2016-04-10

This work presents numerical results on the transport of heat and chemical species by shear-induced turbulence in strongly stratified, thermally diffusive environments. The shear instabilities driven in this regime are sometimes called “secular” shear instabilities, and can take place when the Richardson number of the flow is large, provided the Péclet number is small. We have identified a set of simple criteria to determine whether these instabilities can take place or not. Generally speaking, we find that they may be relevant whenever the thermal diffusivity of the fluid is very large (typically larger than 10{sup 14} cm{sup 2} s{sup −1}),more » which is the case in the outer layers of high-mass stars (M ≥ 10 M{sub ⊙}), for instance. Using a simple model setup in which the shear is forced by a spatially sinusoidal, constant-amplitude body-force, we have identified several regimes ranging from effectively unstratified to very strongly stratified, each with its own set of dynamical properties. Unless the system is in one of the two extreme regimes (effectively unstratified or completely stable), however, we find that (1) only about 10% of the input power is used toward heat transport, while the remaining 90% is viscously dissipated; (2) that the effective compositional mixing coefficient is well-approximated by the model of Zahn, with D ≃ 0.02κ{sub T}/J where κ{sub T} is the thermal diffusivity and J is the Richardson number. These results need to be confirmed, however, with simulations in different model setups and at higher effective Reynolds number.« less

An entropic barriers diffusion theory of decision-making in multiple alternative tasks

PubMed Central

Sigman, Mariano; Cecchi, Guillermo A.

2018-01-01

We present a theory of decision-making in the presence of multiple choices that departs from traditional approaches by explicitly incorporating entropic barriers in a stochastic search process. We analyze response time data from an on-line repository of 15 million blitz chess games, and show that our model fits not just the mean and variance, but the entire response time distribution (over several response-time orders of magnitude) at every stage of the game. We apply the model to show that (a) higher cognitive expertise corresponds to the exploration of more complex solution spaces, and (b) reaction times of users at an on-line buying website can be similarly explained. Our model can be seen as a synergy between diffusion models used to model simple two-choice decision-making and planning agents in complex problem solving. PMID:29499036

Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

NASA Technical Reports Server (NTRS)

Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.

2009-01-01

Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

Massively Parallel Simulations of Diffusion in Dense Polymeric Structures

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

Faulon, Jean-Loup, Wilcox, R.T.

1997-11-01

An original computational technique to generate close-to-equilibrium dense polymeric structures is proposed. Diffusion of small gases are studied on the equilibrated structures using massively parallel molecular dynamics simulations running on the Intel Teraflops (9216 Pentium Pro processors) and Intel Paragon(1840 processors). Compared to the current state-of-the-art equilibration methods this new technique appears to be faster by some orders of magnitude.The main advantage of the technique is that one can circumvent the bottlenecks in configuration space that inhibit relaxation in molecular dynamics simulations. The technique is based on the fact that tetravalent atoms (such as carbon and silicon) fit in themore » center of a regular tetrahedron and that regular tetrahedrons can be used to mesh the three-dimensional space. Thus, the problem of polymer equilibration described by continuous equations in molecular dynamics is reduced to a discrete problem where solutions are approximated by simple algorithms. Practical modeling applications include the constructing of butyl rubber and ethylene-propylene-dimer-monomer (EPDM) models for oxygen and water diffusion calculations. Butyl and EPDM are used in O-ring systems and serve as sealing joints in many manufactured objects. Diffusion coefficients of small gases have been measured experimentally on both polymeric systems, and in general the diffusion coefficients in EPDM are an order of magnitude larger than in butyl. In order to better understand the diffusion phenomena, 10, 000 atoms models were generated and equilibrated for butyl and EPDM. The models were submitted to a massively parallel molecular dynamics simulation to monitor the trajectories of the diffusing species.« less

Messages Do Diffuse Faster than Messengers: Reconciling Disparate Estimates of the Morphogen Bicoid Diffusion Coefficient

PubMed Central

Sigaut, Lorena; Pearson, John E.; Colman-Lerner, Alejandro; Ponce Dawson, Silvina

2014-01-01

The gradient of Bicoid (Bcd) is key for the establishment of the anterior-posterior axis in Drosophila embryos. The gradient properties are compatible with the SDD model in which Bcd is synthesized at the anterior pole and then diffuses into the embryo and is degraded with a characteristic time. Within this model, the Bcd diffusion coefficient is critical to set the timescale of gradient formation. This coefficient has been measured using two optical techniques, Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Correlation Spectroscopy (FCS), obtaining estimates in which the FCS value is an order of magnitude larger than the FRAP one. This discrepancy raises the following questions: which estimate is "correct''; what is the reason for the disparity; and can the SDD model explain Bcd gradient formation within the experimentally observed times? In this paper, we use a simple biophysical model in which Bcd diffuses and interacts with binding sites to show that both the FRAP and the FCS estimates may be correct and compatible with the observed timescale of gradient formation. The discrepancy arises from the fact that FCS and FRAP report on different effective (concentration dependent) diffusion coefficients, one of which describes the spreading rate of the individual Bcd molecules (the messengers) and the other one that of their concentration (the message). The latter is the one that is more relevant for the gradient establishment and is compatible with its formation within the experimentally observed times. PMID:24901638

Messages do diffuse faster than messengers: reconciling disparate estimates of the morphogen bicoid diffusion coefficient.

PubMed

Sigaut, Lorena; Pearson, John E; Colman-Lerner, Alejandro; Ponce Dawson, Silvina

2014-06-01

The gradient of Bicoid (Bcd) is key for the establishment of the anterior-posterior axis in Drosophila embryos. The gradient properties are compatible with the SDD model in which Bcd is synthesized at the anterior pole and then diffuses into the embryo and is degraded with a characteristic time. Within this model, the Bcd diffusion coefficient is critical to set the timescale of gradient formation. This coefficient has been measured using two optical techniques, Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Correlation Spectroscopy (FCS), obtaining estimates in which the FCS value is an order of magnitude larger than the FRAP one. This discrepancy raises the following questions: which estimate is "correct''; what is the reason for the disparity; and can the SDD model explain Bcd gradient formation within the experimentally observed times? In this paper, we use a simple biophysical model in which Bcd diffuses and interacts with binding sites to show that both the FRAP and the FCS estimates may be correct and compatible with the observed timescale of gradient formation. The discrepancy arises from the fact that FCS and FRAP report on different effective (concentration dependent) diffusion coefficients, one of which describes the spreading rate of the individual Bcd molecules (the messengers) and the other one that of their concentration (the message). The latter is the one that is more relevant for the gradient establishment and is compatible with its formation within the experimentally observed times.

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

NASA Astrophysics Data System (ADS)

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

1999-12-01

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

Diffusion and chaos from near AdS 2 horizons

DOE PAGES

Blake, Mike; Donos, Aristomenis

2017-02-03

We calculate the thermal diffusivity D =more » $$\\kappa/c_\\rho$$ and butterfy velocity $$\\upsilon_\\beta$$ in holographic models that flow to $$AdS_2$$ x $R^d$ fixed points in the infra-red. We show that both these quantities are governed by the same irrelevant deformation of $$AdS_2$$ and hence establish a simple relationship between them. When this deformation corresponds to a universal dilaton mode of dimension $$\\Delta$$ = 2 then this relationship is always given by D = $$\\upsilon_B^2$$/(2$$\\pi$$T).« less

Laser Interferometry Method as a Novel Tool in Endotoxins Research.

PubMed

Arabski, Michał; Wąsik, Sławomir

2017-01-01

Optical properties of chemical substances are widely used at present for assays thereof in a variety of scientific disciplines. One of the measurement techniques applied in physical sciences, with a potential for novel applications in biology, is laser interferometry. This method enables to record the diffusion properties of chemical substances. Here we describe the novel application of laser interferometry in chitosan interactions with lipopolysaccharide by detection of colistin diffusion. The proposed model could be used in simple measurements of polymer interactions with endotoxins and/or biological active compounds, like antibiotics.

Fragmentation, rings and coarsening: structure and transformations of nanocrystal aggregate networks on a liquid surface

NASA Astrophysics Data System (ADS)

Yang, Bo; Scheidtmann, Jens; Mayer, Joachim; Wuttig, Matthias; Michely, Thomas

2002-01-01

Deposition of Ag on a silicon oil surface leads to the formation of nm-sized Ag crystals floating on the oil surface. These nanocrystals mutually attract each other, forming strongly branched nanocrystal aggregates and continuous aggregate networks. Transformation processes of such nanocrystal aggregate networks are imaged in situ by optical microscopy. The observations are explained on the basis of a simple model involving diffusion of nanocrystals along aggregate edges and the rupture of branches resulting from branch width fluctuations due to edge diffusion.

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 wastewater treatment plants. Only a small number of problematic substances are expected from grassland. Landfills and roadways are insignificant within the entire Swiss river network, but may locally lead to considerable water pollution. Considering all substance groups, pesticides and some heavy metals are the main polluters. Many pesticides are expected to exceed AA-EQS and in a substantial percentage of the river network. Modeling a large number of substances from many sources and a huge quantity of stream sections is only possible with a simple model. Nevertheless conclusions are robust and may indicate where and for what kind of substance groups additional efforts for water quality improvements should be undertaken.

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

Spatial dilemmas of diffusible public goods

PubMed Central

Allen, Benjamin; Gore, Jeff; Nowak, Martin A

2013-01-01

The emergence of cooperation is a central question in evolutionary biology. Microorganisms often cooperate by producing a chemical resource (a public good) that benefits other cells. The sharing of public goods depends on their diffusion through space. Previous theory suggests that spatial structure can promote evolution of cooperation, but the diffusion of public goods introduces new phenomena that must be modeled explicitly. We develop an approach where colony geometry and public good diffusion are described by graphs. We find that the success of cooperation depends on a simple relation between the benefits and costs of the public good, the amount retained by a producer, and the average amount retained by each of the producer’s neighbors. These quantities are derived as analytic functions of the graph topology and diffusion rate. In general, cooperation is favored for small diffusion rates, low colony dimensionality, and small rates of decay of the public good. DOI: http://dx.doi.org/10.7554/eLife.01169.001 PMID:24347543

Improved Cook-off Modeling of Multi-component Cast Explosives

NASA Astrophysics Data System (ADS)

Nichols, Albert

2017-06-01

In order to understand the hazards associated with energetic materials, it is important to understand their behavior in adverse thermal environments. These processes have been relatively well understood for solid explosives, however, the same cannot be said for multi-component melt-cast explosives. Here we describe the continued development of ALE3D, a coupled thermal/chemical/mechanical code, to improve its description of fluid explosives. The improved physics models include: 1) Chemical potential driven species segregation. This model allows us to model the complex flow fields associated with the melting and decomposing Comp-B, where the denser RDX tends to settle and the decomposing gasses rise, 2) Automatically scaled stream-wise diffusion model for thermal, species, and momentum diffusion. These models add sufficient numerical diffusion in the direction of flow to maintain numerical stability when the system is under resolved, as occurs for large systems. And 3) a slurry viscosity model, required to properly define the flow characteristics of the multi-component fluidized system. These models will be demonstrated on a simple Comp-B system. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.

Forward and back diffusion through argillaceous formations

NASA Astrophysics Data System (ADS)

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

2017-05-01

The exchange of solutes between aquifers and lower-permeability argillaceous formations is of considerable interest for solute and contaminant fate and transport. We present a synthesis of analytical solutions for solute diffusion between aquifers and single aquitard systems, validated in well-controlled experiments, and applied to several data sets from laboratory and field-scale problems with diffusion time and length scales ranging from 10-2 to 108 years and 10-2 to 102 m. One-dimensional diffusion models were applied using the method of images to consider the general cases of a finite aquitard bounded by two aquifers at the top and bottom, or a semiinfinite aquitard bounded by an aquifer. The simpler semiinfinite equations are appropriate for all domains with dimensionless relative diffusion length, ZD < 0.7. At dimensionless length scales above this threshold, application of semiinfinite equations to aquitards of finite thickness leads to increasing errors and solutions based on the method of images are required. Measured resident solute concentration profiles in aquitards and flux-averaged solute concentrations in surrounding aquifers were accurately modeled by appropriately accounting for generalized dynamic aquifer-aquitard boundary conditions, including concentration gradient reversals. Dimensionless diffusion length scales were used to illustrate the transferability of these relatively simple models to physical systems with dimensions that spanned 10 orders of magnitude. The results of this study offer guidance on the application of a simplified analytical approach to environmentally important layered problems with one or two diffusion interfaces.

Self-Consistent Drift-Diffusion Transport in Thermoelectrics and Implications for Measuring the Scattering Parameter

NASA Astrophysics Data System (ADS)

Santhanam, Parthiban; Ram, Rajeev J.

2010-09-01

We present a microscopic model of the Seebeck effect based on a generalized drift-diffusion equation and use it to predict a simple relationship between the electric field within an operating thermoelectric and the scattering parameter. Our model replicates existing theoretical results and permits an intuitive spatial picture of the Seebeck effect. A similar formalism was independently developed by Cai and Mahan, but this work includes numerical results for high dopant concentrations where the thermoelectric power factor is maximized. Based on these results, we propose that measurement of the bulk electric field should constitute a measurement of the scattering parameter, the improvement of which could lead to greater thermoelectric efficiency.

A diffusion model of protected population on bilocal habitat with generalized resource

NASA Astrophysics Data System (ADS)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

An attentional drift diffusion model over binary-attribute choice.

PubMed

Fisher, Geoffrey

2017-11-01

In order to make good decisions, individuals need to identify and properly integrate information about various attributes associated with a choice. Since choices are often complex and made rapidly, they are typically affected by contextual variables that are thought to influence how much attention is paid to different attributes. I propose a modification of the attentional drift-diffusion model, the binary-attribute attentional drift diffusion model (baDDM), which describes the choice process over simple binary-attribute choices and how it is affected by fluctuations in visual attention. Using an eye-tracking experiment, I find the baDDM makes accurate quantitative predictions about several key variables including choices, reaction times, and how these variables are correlated with attention to two attributes in an accept-reject decision. Furthermore, I estimate an attribute-based fixation bias that suggests attention to an attribute increases its subjective weight by 5%, while the unattended attribute's weight is decreased by 10%. Copyright © 2017 Elsevier B.V. All rights reserved.

On a nonlocal reaction-diffusion-advection system modelling the growth of phytoplankton with cell quota structure

NASA Astrophysics Data System (ADS)

Hsu, Sze-Bi; Mei, Linfeng; Wang, Feng-Bin

2015-11-01

Phytoplankton species in a water column compete for mineral nutrients and light, and the existing models usually neglect differences in the nutrient content and the amount of light absorbed of individuals. In this current paper, we examine a size-structured and nonlocal reaction-diffusion-advection system which describes the dynamics of a single phytoplankton species in a water column where the species depends simply on light for its growth. Our model is under the assumption that the amount of light absorbed by individuals is proportional to cell size, which varies for populations that reproduce by simple division into two equally-sized daughters. We first establish the existence of a critical death rate and our analysis indicates that the phytoplankton survives if and only if its death rate is less than the critical death rate. The critical death rate depends on a general reproductive rate, the characteristics of the water column (e.g., turbulent diffusion rate, sinking, depth), cell growth, cell division, and cell size.

Crawling and turning in a minimal reaction-diffusion cell motility model: Coupling cell shape and biochemistry

NASA Astrophysics Data System (ADS)

Camley, Brian A.; Zhao, Yanxiang; Li, Bo; Levine, Herbert; Rappel, Wouter-Jan

2017-01-01

We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.

Double-Diffusive Convection at Low Prandtl Number

NASA Astrophysics Data System (ADS)

Garaud, Pascale

2018-01-01

This work reviews present knowledge of double-diffusive convection at low Prandtl number obtained using direct numerical simulations, in both the fingering regime and the oscillatory regime. Particular emphasis is given to modeling the induced turbulent mixing and its impact in various astrophysical applications. The nonlinear saturation of fingering convection at low Prandtl number usually drives small-scale turbulent motions whose transport properties can be predicted reasonably accurately using a simple semi-analytical model. In some instances, large-scale internal gravity waves can be excited by a collective instability and eventually cause layering. The nonlinear saturation of oscillatory double-diffusive convection exhibits much more complex behavior. Weakly stratified systems always spontaneously transition into layered convection associated with very efficient mixing. More strongly stratified systems remain dominated by weak wave turbulence unless they are initialized into a layered state. The effects of rotation, shear, lateral gradients, and magnetic fields are briefly discussed.

Solute segregation kinetics and dislocation depinning in a binary alloy

NASA Astrophysics Data System (ADS)

Dontsova, E.; Rottler, J.; Sinclair, C. W.

2015-06-01

Static strain aging, a phenomenon caused by diffusion of solute atoms to dislocations, is an important contributor to the strength of substitutional alloys. Accurate modeling of this complex process requires both atomic spatial resolution and diffusional time scales, which is very challenging to achieve with commonly used atomistic computational methods. In this paper, we use the recently developed "diffusive molecular dynamics" (DMD) method that is capable of describing the kinetics of the solute segregation process at the atomic level while operating on diffusive time scales in a computationally efficient way. We study static strain aging in the Al-Mg system and calculate the depinning shear stress between edge and screw dislocations and their solute atmospheres formed for various waiting times with different solute content and for a range of temperatures. A simple phenomenological model is also proposed that describes the observed behavior of the critical shear stress as a function of segregation level.

Diffusion in silicate melts: III. Empirical models for multicomponent diffusion

NASA Astrophysics Data System (ADS)

Yan, Liang; Richter, Frank M.; Chamberlin, Laurinda

1997-12-01

Empirical models for multicomponent diffusion in an isotropic fluid were derived by splitting the component's dispersion velocity into two parts: (a) an intrinsic velocity which is proportional to each component's electrochemical potential gradient and independent of reference frame and (b) a net interaction velocity which is both model and reference frame dependent. Simple molecules (e.g., M pO q) were chosen as endmember components. The interaction velocity is assumed to be either the same for each component (leading to a common relaxation velocity U) or proportional to a common interaction force ( F). U or F is constrained by requiring no local buildup in either volume or charge. The most general form of the model-derived diffusion matrix [ D] can be written as a product of a model-dependent kinetic matrix [ L] and a model independent thermodynamic matrix [ G], [ D] = [ L] · [ G]. The elements of [ G] are functions of derivatives of chemical potential with respect to concentration. The elements of [ L] are functions of concentration and partial molar volume of the endmember components, Cio and Vio, and self diffusivity Di, and charge number zi of individual diffusing species. When component n is taken as the dependent variable they can be written in a common form L ij = D jδ ij + C io[V noD n - V joD j)A i + (p nz nD n - p jz jD j)B i] where the functional forms of the scaling factors Ai and Bi depend on the model considered. The off-diagonal element Lij ( i ≠ j) is directly proportional to the concentration of component i, and thus negligible when i is a dilute component. The salient feature of kinetic interaction or relaxation is to slow down larger (volume or charge) and faster diffusing components and to speed up smaller (volume or charge) and slower moving species, in order to prevent local volume or charge buildup. Empirical models for multicomponent diffusion were tested in the ternary system CaOAl 2O 3SiO 2 at 1500°C and 1 GPa over a large range of melt compositions. Model-derived diffusion matrices calculated using measured self diffusivities (Ca, Al, Si, and O), partial molar volumes, and activities were compared with experimentally derived diffusion matrices at two melt compositions. Chemical diffusion profiles computed using the model-derived diffusion matrices, accounting for the compositional dependency of self diffusivities and activity coefficients, were also compared with the experimentally measured ones. Good agreement was found between the ionic common-force model derived diffusion profiles and the experimentally measured ones. Secondary misfits could result from either inadequacies of the model or inaccuracies in activity-composition relationship. The results show that both kinetic interactions and thermodynamic nonideality contribute significantly to the observed diffusive coupling in the molten CaOAl 2O 3SiO 2.

What lies beneath? Diffusion EAP-based study of brain tissue microstructure.

PubMed

Zucchelli, Mauro; Brusini, Lorenza; Andrés Méndez, C; Daducci, Alessandro; Granziera, Cristina; Menegaz, Gloria

2016-08-01

Diffusion weighted magnetic resonance signals convey information about tissue microstructure and cytoarchitecture. In the last years, many models have been proposed for recovering the diffusion signal and extracting information to constitute new families of numerical indices. Two main categories of reconstruction models can be identified in diffusion magnetic resonance imaging (DMRI): ensemble average propagator (EAP) models and compartmental models. From both, descriptors can be derived for elucidating the underlying microstructural architecture. While compartmental models indices directly quantify the fraction of different cell compartments in each voxel, EAP-derived indices are only a derivative measure and the effect of the different microstructural configurations on the indices is still unclear. In this paper, we analyze three EAP indices calculated using the 3D Simple Harmonic Oscillator based Reconstruction and Estimation (3D-SHORE) model and estimate their changes with respect to the principal microstructural configurations. We take advantage of the state of the art simulations to quantify the variations of the indices with the simulation parameters. Analysis of in-vivo data correlates the EAP indices with the microstructural parameters obtained from the Neurite Orientation Dispersion and Density Imaging (NODDI) model as a pseudo ground truth for brain data. Results show that the EAP derived indices convey information on the tissue microstructure and that their combined values directly reflect the configuration of the different compartments in each voxel. Copyright © 2016 Elsevier B.V. All rights reserved.

Dynamical patterns and regime shifts in the nonlinear model of soil microorganisms growth

NASA Astrophysics Data System (ADS)

Zaitseva, Maria; Vladimirov, Artem; Winter, Anna-Marie; Vasilyeva, Nadezda

2017-04-01

Dynamical model of soil microorganisms growth and turnover is formulated as a system of nonlinear partial differential equations of reaction-diffusion type. We consider spatial distributions of concentrations of several substrates and microorganisms. Biochemical reactions are modelled by chemical kinetic equations. Transport is modelled by simple linear diffusion for all chemical substances, while for microorganisms we use different transport functions, e.g. some of them can actively move along gradient of substrate concentration, while others cannot move. We solve our model in two dimensions, starting from uniform state with small initial perturbations for various parameters and find parameter range, where small initial perturbations grow and evolve. We search for bifurcation points and critical regime shifts in our model and analyze time-space profile and phase portraits of these solutions approaching critical regime shifts in the system, exploring possibility to detect such shifts in advance. This work is supported by NordForsk, project #81513.

Pattern formation in three-dimensional reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Callahan, T. K.; Knobloch, E.

1999-08-01

Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.

Magnetization of Cloud Cores and Envelopes and Other Observational Consequences of Reconnection Diffusion

NASA Astrophysics Data System (ADS)

Lazarian, A.; Esquivel, A.; Crutcher, R.

2012-10-01

Recent observational results for magnetic fields in molecular clouds reviewed by Crutcher seem to be inconsistent with the predictions of the ambipolar diffusion theory of star formation. These include the measured decrease in mass to flux ratio between envelopes and cores, the failure to detect any self-gravitating magnetically subcritical clouds, the determination of the flat probability distribution function (PDF) of the total magnetic field strengths implying that there are many clouds with very weak magnetic fields, and the observed scaling Bvpropρ2/3 that implies gravitational contraction with weak magnetic fields. We consider the problem of magnetic field evolution in turbulent molecular clouds and discuss the process of magnetic field diffusion mediated by magnetic reconnection. For this process that we termed "reconnection diffusion," we provide a simple physical model and explain that this process is inevitable in view of the present-day understanding of MHD turbulence. We address the issue of the expected magnetization of cores and envelopes in the process of star formation and show that reconnection diffusion provides an efficient removal of magnetic flux that depends only on the properties of MHD turbulence in the core and the envelope. We show that as the amplitude of turbulence as well as the scale of turbulent motions decrease from the envelope to the core of the cloud, the diffusion of the magnetic field is faster in the envelope. As a result, the magnetic flux trapped during the collapse in the envelope is being released faster than the flux trapped in the core, resulting in much weaker fields in envelopes than in cores, as observed. We provide simple semi-analytical model calculations which support this conclusion and qualitatively agree with the observational results. Magnetic reconnection is also consistent with the lack of subcritical self-gravitating clouds, with the observed flat PDF of field strengths, and with the scaling of field strength with density. In addition, we demonstrate that the reconnection diffusion process can account for the empirical Larson relations and list a few other implications of the reconnection diffusion concept. We argue that magnetic reconnection provides a solution to the magnetic flux problem of star formation that agrees better with observations than the long-standing ambipolar diffusion paradigm. Due to the illustrative nature of our simplified model we do not seek quantitative agreement, but discuss the complementary nature of our approach to the three-dimensional MHD numerical simulations.

The diffusivity and solubility of deuterium in a high chromium martensitic steel

NASA Astrophysics Data System (ADS)

Forcey, K. S.; Iordanova, I.; Yaneva, M.

1997-01-01

The permeability, diffusivity and solubility of deuterium in the martensitic stainless steel MANET II have been studied in the temperature range 194-465°C by applying a time dependent gas-phase permeation technique. It was found that the temperature dependence of diffusivity and solubility could not be described by a simple Arrhenius expression over the entire temperature range investigated. At lower temperatures (below about 330°C) the diffusivity was found to be greatly reduced by the effects of trapping. Oriani's model has been applied to obtain the trapping energy and number density of the traps as well as the relative amounts of deuterium dissolved at lattice and trap sites. It is suggested that the most likely sites for trapping are at interfaces between the martensitic laths and between second phase particles and the surrounding metal matrix.

The contribution of the diffuse light component to the topographic effect on remotely sensed data

NASA Technical Reports Server (NTRS)

Justice, C.; Holben, B.

1980-01-01

The topographic effect is measured by the difference between the global radiance from inclined surfaces as a function of their orientation relative to the sensor position and light source. The short wave radiant energy incident on a surface is composed of direct sunlight, scattered skylight, and light reflected from surrounding terrain. The latter two components are commonly known as the diffuse component. The contribution of the diffuse light component to the topographic effect was examined and the significance of this diffuse component with respect to two direct radiance models was assessed. Diffuse and global spectral radiances were measured for a series of slopes and aspects of a uniform and surface in the red and photographic infrared parts of the spectrum, using a nadir pointing two channel handheld radiometer. The diffuse light was found to produce a topographic effect which varied from the topographic effect for direct light. The topographic effect caused by diffuse light was found to increase slightly with solar elevation and wavelength for the channels examined. The correlations between data derived from two simple direct radiance simulation models and the field data were not significantly affected when the diffuse component was removed from the radiances. Radiances from a 60 percent reflective surface, assuming no atmospheric path radiance, the diffuse light topographic effect contributed a maximum range of 3 pixel values in simulated LANDSAT data from all aspects with slopes up to 30 degrees.

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells.

PubMed

Longeville, Stéphane; Stingaciu, Laura-Roxana

2017-09-05

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement by neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells ([Formula: see text]330 g.L -1 ) corresponds to an optimum for oxygen transport for individuals under strong activity.

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells

DOE PAGES

Longeville, Stéphane; Stingaciu, Laura-Roxana

2017-09-05

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement bymore » neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells (≃330 g.L -1) corresponds to an optimum for oxygen transport for individuals under strong activity.« less

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells

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

Longeville, Stéphane; Stingaciu, Laura-Roxana

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement bymore » neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells (≃330 g.L -1) corresponds to an optimum for oxygen transport for individuals under strong activity.« less

Time-independent models of asset returns revisited

NASA Astrophysics Data System (ADS)

Gillemot, L.; Töyli, J.; Kertesz, J.; Kaski, K.

2000-07-01

In this study we investigate various well-known time-independent models of asset returns being simple normal distribution, Student t-distribution, Lévy, truncated Lévy, general stable distribution, mixed diffusion jump, and compound normal distribution. For this we use Standard and Poor's 500 index data of the New York Stock Exchange, Helsinki Stock Exchange index data describing a small volatile market, and artificial data. The results indicate that all models, excluding the simple normal distribution, are, at least, quite reasonable descriptions of the data. Furthermore, the use of differences instead of logarithmic returns tends to make the data looking visually more Lévy-type distributed than it is. This phenomenon is especially evident in the artificial data that has been generated by an inflated random walk process.

Periodic Viscous Shear Heating Instability in Fine-Grained Shear Zones: Possible Mechanism for Intermediate Depth Earthquakes and Slow Earthquakes?

NASA Astrophysics Data System (ADS)

Kelemen, P. B.; Hirth, G.

2004-12-01

Localized ductile shear zones with widths of cm to m are observed in exposures of Earth's shallow mantle (e.g., Kelemen & Dick JGR 95; Vissers et al. Tectonophys 95) and dredged from oceanic fracture zones (e.g., Jaroslow et al. Tectonophys 96). These are mylonitic (grain size 10 to 100 microns) and record mineral cooling temperatures from 1100 to 600 C. Pseudotachylites in a mantle shear zone show that shear heating temperatures can exceed the mantle solidus (e.g., Obata & Karato Tectonophys 95). Simple shear, recrystallization, and grain boundary sliding all decrease the spacing between pyroxenes, so olivine grain growth at lower stress is inhibited; thus, once formed, these shear zones do not "heal" on geological time scales. Reasoning that grain-size sensitive creep will be localized within these shear zones, rather than host rocks (grain size 1 to 10 mm), and inspired by the work of Whitehead & Gans (GJRAS 74), we thought these might undergo repeated shear heating instabilities. In this view, as elastic stress increases, the shear zone weakens via shear heating; rapid deformation of the weak shear zone releases most stored elastic stress; lower stress and strain rate coupled with diffusion of heat into host rocks leads to cooling and strengthening, after which the cycle repeats. We constructed a simple numerical model incorporating olivine flow laws for dislocation creep, diffusion creep, grain boundary sliding, and low T plasticity. We assumed that viscous deformation remains localized in shear zones, surrounded by host rocks undergoing elastic deformation. We fixed the velocity along one side of an elastic half space, and calculated stress due to elastic strain. This stress drives viscous deformation in a shear zone of specified width. Shear heating and thermal diffusion control temperature evolution in the shear zone and host rocks. A maximum of 1400 C (where substantial melting of peridotite would occur) is imposed. Grain size evolves during dislocation creep and grain boundary sliding as a function of stress and strain, and undergoes diffusive growth during diffusion creep. For strain rates ca E-13 per second and initial temperatures ca 600 to 850 C, this model produces periodic viscous shear heating events with periods of 100's of years. Strain rates during these events approach 1 per second as temperatures reach 1400 C, so future models will incorporate inertial terms in the stress. Cooling between events returns the shear zone almost to its initial temperature, but ultimately shear zone temperature between events exceeds 850 C resulting in stable viscous creep. Back of the envelope calculations based on model results support the view that viscous deformation in both shear zone and host will be mainly via grain-size sensitive creep, and thus deformation will remain localized in shear zones. Similarly, we infer that inertial terms will remain small. Future models will test and quantify these inferences. The simple model described above provides an attractive explanation for intermediate-depth earthquakes, especially those in subduction zones that occur in a narrow thermal window (e.g., Hacker et al JGR 2003). We think that a "smoother"periodic instability might be produced via the same mechanism in weaker materials, which could provide a viscous mechanism for some slow earthquakes. By AGU, we will construct a second, simple model using quartz rheology to investigate this. Finally, coupling of viscous shear heating instabilities in the shallow mantle with brittle stick-slip deformation in the weaker, overlying crust may influence earthquake frequency.

An (almost) solvable model for bacterial pattern formation

NASA Astrophysics Data System (ADS)

Grammaticos, B.; Badoual, M.; Aubert, M.

2007-10-01

We present a simple model for the description of ring-like concentric structures in bacterial colonies. We model the differences between Bacillus subtilis and Proteus mirabilis colonies by using a different dependence of the duration of the consolidation phase on the concentration of agar. We compare our results to experimental data from these two bacterial species colonies and obtain a good agreement. Based on this analysis, we formulate a hypothesis on the connection of the diffusion constant that appears in the model to the experimental agar concentration.

Centimetre-scale electron diffusion in photoactive organic heterostructures

NASA Astrophysics Data System (ADS)

Burlingame, Quinn; Coburn, Caleb; Che, Xiaozhou; Panda, Anurag; Qu, Yue; Forrest, Stephen R.

2018-02-01

The unique properties of organic semiconductors, such as flexibility and lightness, are increasingly important for information displays, lighting and energy generation. But organics suffer from both static and dynamic disorder, and this can lead to variable-range carrier hopping, which results in notoriously poor electrical properties, with low electron and hole mobilities and correspondingly short charge-diffusion lengths of less than a micrometre. Here we demonstrate a photoactive (light-responsive) organic heterostructure comprising a thin fullerene channel sandwiched between an electron-blocking layer and a blended donor:C70 fullerene heterojunction that generates charges by dissociating excitons. Centimetre-scale diffusion of electrons is observed in the fullerene channel, and this can be fitted with a simple electron diffusion model. Our experiments enable the direct measurement of charge diffusivity in organic semiconductors, which is as high as 0.83 ± 0.07 square centimetres per second in a C60 channel at room temperature. The high diffusivity of the fullerene combined with the extraordinarily long charge-recombination time yields diffusion lengths of more than 3.5 centimetres, orders of magnitude larger than expected for an organic system.

Connecting the molecular scale to the continuum scale for diffusion processes in smectite-rich porous media.

PubMed

Bourg, Ian C; Sposito, Garrison

2010-03-15

In this paper, we address the manner in which the continuum-scale diffusive properties of smectite-rich porous media arise from their molecular- and pore-scale features. Our starting point is a successful model of the continuum-scale apparent diffusion coefficient for water tracers and cations, which decomposes it as a sum of pore-scale terms describing diffusion in macropore and interlayer "compartments." We then apply molecular dynamics (MD) simulations to determine molecular-scale diffusion coefficients D(interlayer) of water tracers and representative cations (Na(+), Cs(+), Sr(2+)) in Na-smectite interlayers. We find that a remarkably simple expression relates D(interlayer) to the pore-scale parameter δ(nanopore) ≤ 1, a constrictivity factor that accounts for the lower mobility in interlayers as compared to macropores: δ(nanopore) = D(interlayer)/D(0), where D(0) is the diffusion coefficient in bulk liquid water. Using this scaling expression, we can accurately predict the apparent diffusion coefficients of tracers H(2)0, Na(+), Sr(2+), and Cs(+) in compacted Na-smectite-rich materials.

Growth of semimetallic ErAs films epitaxially embedded in GaAs

NASA Astrophysics Data System (ADS)

Crook, Adam M.; Nair, Hari P.; Lee, Jong H.; Ferrer, Domingo A.; Akinwande, Deji; Bank, Seth R.

2011-10-01

We present models for the growth and electrical conductivity of ErAs films grown with the nanoparticle-seeded film growth technique. This growth mode overcomes the mismatch in rotational symmetry between the rocksalt ErAs crystal structure and the zincblende GaAs crystal structure. This results in films of ErAs grown through a thin film of GaAs that preserves the symmetry of the substrate. The conductivity of the films, as a function of film thickness, are investigated and a surface roughness model is used to explain observed trends. Transmission electron micrographs confirm the suppression of anti-phase domains. A simple diffusion model is developed to describe the diffusion and incorporation of surface erbium into subsurface ErAs layers and predict potential failure mechanisms of the growth method.

Kin Selection in the RNA World.

PubMed

Levin, Samuel R; West, Stuart A

2017-12-05

Various steps in the RNA world required cooperation. Why did life's first inhabitants, from polymerases to synthetases, cooperate? We develop kin selection models of the RNA world to answer these questions. We develop a very simple model of RNA cooperation and then elaborate it to model three relevant issues in RNA biology: (1) whether cooperative RNAs receive the benefits of cooperation; (2) the scale of competition in RNA populations; and (3) explicit replicator diffusion and survival. We show: (1) that RNAs are likely to express partial cooperation; (2) that RNAs will need mechanisms for overcoming local competition; and (3) in a specific example of RNA cooperation, persistence after replication and offspring diffusion allow for cooperation to overcome competition. More generally, we show how kin selection can unify previously disparate answers to the question of RNA world cooperation.

Simulations of induced-charge electro-osmosis in microfluidic devices

NASA Astrophysics Data System (ADS)

Ben, Yuxing

2005-03-01

Theories of nonlinear electrokinetic phenomena generally assume a uniform, neutral bulk electroylte in contact with a polarizable thin double layer near a metal or dielectric surface, which acts as a "capacitor skin". Induced-charge electro-osmosis (ICEO) is the general effect of nonlinear electro-osmotic slip, when an applied electric field acts on its own induced (diffuse) double-layer charge. In most theoretical and experimental work, ICEO has been studied in very simple geometries, such as colloidal spheres and planar, periodic micro-electrode arrays. Here we use finite-element simulations to predict how more complicated geometries of polarizable surfaces and/or electrodes yield flow profiles with subtle dependence on the amplitude and frequency of the applied voltage. We also consider how the simple model equations break down, due to surface conduction, bulk diffusion, and concentration polarization, for large applied voltages (as in most experiments).

A high-resolution conceptual model for diffuse organic micropollutant loads in streams

NASA Astrophysics Data System (ADS)

Stamm, Christian; Honti, Mark; Ghielmetti, Nico

2013-04-01

The ecological state of surface waters has become the dominant aspect in water quality assessments. Toxicity is a key determinant of the ecological state, but organic micropollutants (OMP) are seldom monitored with the same spatial and temporal frequency as for example nutrients, mainly due the demanding analytical methods and costs. However, diffuse transport pathways are at least equally complex for OMPs as for nutrients and there are still significant knowledge gaps. Moreover, concentrations of the different compounds would need to be known with fairly high temporal resolution because acute toxicity can be as important as the chronic one. Fully detailed mechanistic models of diffuse OMP loads require an immense set of site-specific knowledge and are rarely applicable for catchments lacking an exceptional monitoring coverage. Simple empirical methods are less demanding but usually work with more temporal aggregation and that's why they have limited possibilities to support the estimation of the ecological state. This study presents a simple conceptual model that aims to simulate the concentrations of selected organic micropollutants with daily resolution at 11 locations in the stream network of a small catchment (46 km2). The prerequisite is a known hydrological and meteorological background (daily discharge, precipitation and air temperature time series), a land use map and some historic measurements of the desired compounds. The model is conceptual in the sense that all important diffuse transport pathways are simulated separately, but each with a simple empirical process rate. Consequently, some site-specific observations are required to calibrate the model, but afterwards the model can be used for forecasting and scenario analysis as the calibrated process rates typically describe invariant properties of the catchment. We simulated 6 different OMPs from the categories of agricultural and urban pesticides and urban biocides. The application of agricultural pesticides was also simulated with the model using a heat-sum approach. Calibration was carried out with weekly aggregated samples covering the growing season in 2 years. The model could reproduce the observed OMP concentrations with varying success. Compounds that are less persistent in the environment and thus have a dominant temporal dynamics (pesticides with a short half-life) could be simulated in general better than the persistent ones. For the latter group the relatively stable available stock meant that there were no clear seasonal dynamics, which revealed that transport processes are quite uncertain even when daily rainfall is used as the main driver. Nevertheless the daily concentration distribution could still be simulated with higher accuracy than the individual peaks. Thus we can model the concentration-duration relationship for daily resolution in an acceptable way for each compound.

Coherent pulses in the diffusive transport of charged particles`

NASA Technical Reports Server (NTRS)

Kota, J.

1994-01-01

We present exact solutions to the diffusive transport of charged particles following impulsive injection for a simple model of scattering. A modified, two-parameter relaxation-time model is considered that simulates the low rate of scattering through perpendicular pitch-angle. Scattering is taken to be isotropic within each of the foward- and backward-pointing hemispheres, respectively, but, at the same time, a reduced rate of sccattering is assumed from one hemisphere to the other one. By applying a technique of Fourier- and Laplace-transform, the inverse transformation can be performed and exact solutions can be reached. By contrast with the first, and so far only exact solutions of Federov and Shakov, this wider class of solutions gives rise to coherent pulses to appear. The present work addresses omnidirectional densities for isotropic injection from an instantaneous and localized source. The dispersion relations are briefly discussed. We find, for this particular model, two diffusive models to exist up to a certain limiting wavenumber. The corresponding eigenvalues are real at the lowest wavenumbers. Complex eigenvalues, which are responsible for coherent pulses, appear at higher wavenumbers.

A Semi-Analytical Model for Dispersion Modelling Studies in the Atmospheric Boundary Layer

NASA Astrophysics Data System (ADS)

Gupta, A.; Sharan, M.

2017-12-01

The severe impact of harmful air pollutants has always been a cause of concern for a wide variety of air quality analysis. The analytical models based on the solution of the advection-diffusion equation have been the first and remain the convenient way for modeling air pollutant dispersion as it is easy to handle the dispersion parameters and related physics in it. A mathematical model describing the crosswind integrated concentration is presented. The analytical solution to the resulting advection-diffusion equation is limited to a constant and simple profiles of eddy diffusivity and wind speed. In practice, the wind speed depends on the vertical height above the ground and eddy diffusivity profiles on the downwind distance from the source as well as the vertical height. In the present model, a method of eigen-function expansion is used to solve the resulting partial differential equation with the appropriate boundary conditions. This leads to a system of first order ordinary differential equations with a coefficient matrix depending on the downwind distance. The solution of this system, in general, can be expressed in terms of Peano-baker series which is not easy to compute, particularly when the coefficient matrix becomes non-commutative (Martin et al., 1967). An approach based on Taylor's series expansion is introduced to find the numerical solution of first order system. The method is applied to various profiles of wind speed and eddy diffusivities. The solution computed from the proposed methodology is found to be efficient and accurate in comparison to those available in the literature. The performance of the model is evaluated with the diffusion datasets from Copenhagen (Gryning et al., 1987) and Hanford (Doran et al., 1985). In addition, the proposed method is used to deduce three dimensional concentrations by considering the Gaussian distribution in crosswind direction, which is also evaluated with diffusion data corresponding to a continuous point source.

Estimating the Diffusion Coefficients of Sugars Using Diffusion Experiments in Agar-Gel and Computer Simulations.

PubMed

Miyamoto, Shuichi; Atsuyama, Kenji; Ekino, Keisuke; Shin, Takashi

2018-01-01

The isolation of useful microbes is one of the traditional approaches for the lead generation in drug discovery. As an effective technique for microbe isolation, we recently developed a multidimensional diffusion-based gradient culture system of microbes. In order to enhance the utility of the system, it is favorable to have diffusion coefficients of nutrients such as sugars in the culture medium beforehand. We have, therefore, built a simple and convenient experimental system that uses agar-gel to observe diffusion. Next, we performed computer simulations-based on random-walk concepts-of the experimental diffusion system and derived correlation formulas that relate observable diffusion data to diffusion coefficients. Finally, we applied these correlation formulas to our experimentally-determined diffusion data to estimate the diffusion coefficients of sugars. Our values for these coefficients agree reasonably well with values published in the literature. The effectiveness of our simple technique, which has elucidated the diffusion coefficients of some molecules which are rarely reported (e.g., galactose, trehalose, and glycerol) is demonstrated by the strong correspondence between the literature values and those obtained in our experiments.

Dexamethasone diffusion across contact lenses is inhibited by Staphylococcus epidermidis biofilms in vitro.

PubMed

Brothers, Kimberly M; Nau, Amy C; Romanowski, Eric G; Shanks, Robert M Q

2014-10-01

This study was designed to measure the impact of bacterial biofilms on diffusion of an ocular therapeutic through silicone hydrogel bandage lenses in vitro. An assay was designed to study the passage of a commonly used steroid, dexamethasone, through silicone hydrogel soft contact lenses. Diffused dexamethasone was measured using a spectrophotometer over a period of 18 hours and quantified using a standard curve. This assay was performed with control and Staphylococcus epidermidis biofilm-coated contact lenses comprised of lotrafilcon A and methafilcon. Biofilms were formed in brain heart infusion broth supplemented with D-glucose. The presented data validate a simple in vitro model that can be used to measure the penetration of a topical therapeutic through silicone hydrogel soft contact lenses. Using this model, we measured a reduction in dexamethasone diffusion up to 88% through S. epidermidis biofilm-coated silicone hydrogel lenses compared with control lenses. The results of this in vitro study demonstrate that bacterial biofilms impede dexamethasone diffusion through silicone hydrogel contact lenses and warrant future studies regarding the clinical benefit of using ocular therapeutics in the setting of bandage contact lens use for corneal epithelial defects.

Dexamethasone diffusion across contact lenses is inhibited by Staphylococcus epidermidis biofilms in vitro

PubMed Central

Brothers, Kimberly M.; Nau, Amy C.; Romanowski, Eric G.; Shanks, Robert M. Q.

2014-01-01

Purpose This study was designed to measure the impact of bacterial biofilms on diffusion of an ocular therapeutic through silicone hydrogel bandage lenses in vitro. Methods An assay was designed to study the passage of a commonly used steroid dexamethasone through the silicone hydrogel soft contact lenses. Diffused dexamethasone was measured using a spectrophotometer over a period of 18 hours and quantified using a standard curve. This assay was performed with control and Staphylococcus epidermidis biofilm-coated contact lenses composed of lotrafilcon A and methafilcon. Biofilms were formed in brain heart infusion broth supplemented with D-glucose. Results The presented data validate a simple in vitro model that can be used to measure penetration of a topical therapeutic through silicone hydrogel soft contact lenses. Using this model we measured a reduction of dexamethasone diffusion by up to 88% through S. epidermidis biofilm-coated silicon hydrogel lenses compared to control lenses. Conclusions The results of this in vitro study demonstrate that bacterial biofilms impede dexamethasone diffusion through silicon hydrogel contact lenses, and warrant future studies regarding the clinical benefit of using ocular therapeutics in the setting of bandage contact lens use for corneal epithelial defects. PMID:25090165

Designing for diffusion: how can we increase uptake of cancer communication innovations?

PubMed

Dearing, James W; Kreuter, Matthew W

2010-12-01

The best innovations in cancer communication do not necessarily achieve uptake by researchers, public health and clinical practitioners, and policy makers. This paper describes design activities that can be applied and combined for the purpose of spreading effective cancer communication innovations. A previously developed Push-Pull-Infrastructure Model is used to organize and highlight the types of activities that can be deployed during the design phase of innovations. Scientific literature about the diffusion of innovations, knowledge utilization, marketing, public health, and our experiences in working to spread effective practices, programs, and policies are used for this purpose. Attempts to broaden the reach, quicken the uptake, and facilitate the use of cancer communication innovations can apply design activities to increase the likelihood of diffusion. Some simple design activities hold considerable promise for improving dissemination and subsequent diffusion. Augmenting current dissemination practices with evidence-based concepts from diffusion science, marketing science, and knowledge utilization hold promise for improving results by eliciting greater market pull. Inventors and change agencies seeking to spread cancer communication innovations can experience more success by explicit consideration of design activities that reflect an expanded version of the Push-Pull-Infrastructure Model. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

Designing for Diffusion: How Can We Increase Uptake of Cancer Communication Innovations?

PubMed Central

Dearing, James W.; Kreuter, Matthew W.

2010-01-01

Objective The best innovations in cancer communication do not necessarily achieve uptake by researchers, public health and clinical practitioners, and policy makers. This paper describes design activities that can be applied and combined for the purpose of spreading effective cancer communication innovations. Methods A previously developed Push-Pull-Infrastructure Model is used to organize and highlight the types of activities that can be deployed during the design phase of innovations. Scientific literature about the diffusion of innovations, knowledge utilization, marketing, public health, and our experiences in working to spread effective practices, programs, and policies are used for this purpose. Results Attempts to broaden the reach, quicken the uptake, and facilitate the use of cancer communication innovations can apply design activities to increase the likelihood of diffusion. Some simple design activities hold considerable promise for improving dissemination and subsequent diffusion. Conclusion Augmenting current dissemination practices with evidence-based concepts from diffusion science, marketing science, and knowledge utilization hold promise for improving results by eliciting greater market pull. Practice Implications Inventors and change agencies seeking to spread cancer communication innovations can experience more success by explicit consideration of design activities that reflect an expanded version of the Push-Pull-Infrastructure Model. PMID:21067884

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

PubMed

Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng

2018-06-01

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

Effects of Material Degradation on the Structural Integrity of Composite Materials: Experimental Investigation and Modeling of High Temperature Degradation Mechanisms

NASA Technical Reports Server (NTRS)

Cunningham, Ronan A.; McManus, Hugh L.

1996-01-01

It has previously been demonstrated that simple coupled reaction-diffusion models can approximate the aging behavior of PMR-15 resin subjected to different oxidative environments. Based on empirically observed phenomena, a model coupling chemical reactions, both thermal and oxidative, with diffusion of oxygen into the material bulk should allow simulation of the aging process. Through preliminary modeling techniques such as this it has become apparent that accurate analytical models cannot be created until the phenomena which cause the aging of these materials are quantified. An experimental program is currently underway to quantify all of the reaction/diffusion related mechanisms involved. The following contains a summary of the experimental data which has been collected through thermogravimetric analyses of neat PMR-15 resin, along with analytical predictions from models based on the empirical data. Thermogravimetric analyses were carried out in a number of different environments - nitrogen, air and oxygen. The nitrogen provides data for the purely thermal degradation mechanisms while those in air provide data for the coupled oxidative-thermal process. The intent here is to effectively subtract the nitrogen atmosphere data (assumed to represent only thermal reactions) from the air and oxygen atmosphere data to back-figure the purely oxidative reactions. Once purely oxidative (concentration dependent) reactions have been quantified it should then be possible to quantify the diffusion of oxygen into the material bulk.

Coupled Protein Diffusion and Folding in the Cell

PubMed Central

Guo, Minghao; Gelman, Hannah; Gruebele, Martin

2014-01-01

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control's diffusion coefficient, PGK's diffusion coefficient is a non-monotonic function of temperature, signaling ‘sticking’ of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates. PMID:25436502

Coupled protein diffusion and folding in the cell.

PubMed

Guo, Minghao; Gelman, Hannah; Gruebele, Martin

2014-01-01

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control's diffusion coefficient, PGK's diffusion coefficient is a non-monotonic function of temperature, signaling 'sticking' of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates.

Understanding quantum tunneling using diffusion Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Inack, E. M.; Giudici, G.; Parolini, T.; Santoro, G.; Pilati, S.

2018-03-01

In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as 1 /Δ2 , where Δ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests that there is no quantum advantage in using QAs with respect to quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model (Andriyash and Amin, arXiv:1703.09277), where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving open the possibility for potential quantum speedup, even for stoquastic models. In this work we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as 1 /Δ , i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However, a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain indicates an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.

The twin cell model and its excellence in determining the glass transition temperature of thin film metallic glass

NASA Astrophysics Data System (ADS)

Kanjilal, Baishali; Iram, Samreen; Das, Atreyee; Chakrabarti, Haimanti

2018-05-01

This work reports a novel two dimensional approach to the theoretical computation of the glass transition temperature in simple hypothetical icosahedral packed structures based on Thin Film metallic glasses using liquid state theories in the realm of transport properties. The model starts from Navier-Stokes equation and evaluates the statistical average velocity of each different species of atom under the condition of ensemble equality to compute diffusion lengths and the diffusion coefficients as a function of temperature. The additional correction brought in is that of the limited states due to tethering of one nodule vis -a-vis the others. The movement of the molecules use our Twin Cell Model a typical model pertinent for modeling chain motions. A temperature viscosity correction by Cohen and Grest is included through the temperature dependence of the relaxation times for glass formers.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Effects of Inter- and Intra-aggregate Pore Space on the Soil-Gas Diffusivity Behavior in Unsaturated, Undisturbed Volcanic Ash Soils

NASA Astrophysics Data System (ADS)

Resurreccion, A. C.; Kawamoto, K.; Komatsu, T.; Moldrup, P.

2006-12-01

Volcanic ash soils (Andisols) have a unique dual porosity structure that results in good drainage and high soil- water retention. Despite of the complicated and highly developed soil structure, recent studies have reported a simple, highly linear relation between the soil-gas diffusion coefficient, Dp, and the soil-air content, ɛ, for several Japanese Andisols. In this study, we explain the linear Dp(ɛ) behavior from the effects of the inter- and intra-aggregate pore-size distributions. We couple the bimodal van Genuchten soil-water retention model with a general Dp(ɛ) model, ɛ^{X}, allowing the tortuosity- connectivity factor X to vary with pF (= log(-ψ; the soil-water matric potential in cm H2O)). Measured data suggest that the tortuosity-connectivity parameter X is at the minimum at pF 3 (where X ~ 2, following Buckingham, 1904), equal to the water retention point where a separation of inter- and intra-aggregate effects on Dp is observed. At pF < 3, the X values increased as pF decreased because of inactive/remote air-filled pore space entrapped by the inter-connected water films between inter-aggregate pore spaces. At pF > 3, X increased to a high value at very dry conditions due to remote air-filled space inside the intra-aggregate pores. By combining the complex dual porosity soil-water retention model with the power- law gas diffusivity model using a parabolic X(pF) function, the surprisingly simple linear behavior of Dp with ɛ was captured while the variation of Dp with pF followed a dual s-shaped curve similar to the water retention curve. A simple linear model to predict Dp(ɛ) is suggested, with slope C and threshold soil-air content, ɛth, calculated from the power-law model ɛ^{X} at pF 2 (near field capacity) and at pF 4.1 (near wilting point) using the same X value (= 2.3) at both pF in agreement with measured data. This linear Dp(ɛ) model performed better, especially at dry conditions, compared to the traditionally-used predictive models when tested against several independent Andisol datasets from literature.

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.

The Effect of Pickling on Blue Borscht Gelatin and Other Interesting Diffusive Phenomena.

ERIC Educational Resources Information Center

Davis, Lawrence C.; Chou, Nancy C.

1998-01-01

Presents some simple demonstrations that students can construct for themselves in class to learn the difference between diffusion and convection rates. Uses cabbage leaves and gelatin and focuses on diffusion in ungelified media, a quantitative diffusion estimate with hydroxyl ions, and a quantitative diffusion estimate with photons. (DDR)

Effect of sharp maximum in ion diffusivity for liquid xenon

NASA Astrophysics Data System (ADS)

Lankin, A. V.; Orekhov, M. A.

2016-11-01

Ion diffusion in a liquid usually could be treated as a movement of an ion cluster in a viscous media. For small ions this leads to a special feature: diffusion coefficient is either independent of the ion size or increases with it. We find a different behavior for small ions in liquid xenon. Calculation of the dependence of an ion diffusion coefficient in liquid xenon on the ion size is carried out. Classical molecular dynamics method is applied. Calculated dependence of the ion diffusion coefficient on its radius has sharp maximums at the ion radiuses 1.75 and 2 Å. Every maximum is placed between two regions with different stable ion cluster configurations. This leads to the instability of these configurations in a small region between them. Consequently ion with radius near 1.75 or 2 Å could jump from one configuration to another. This increases the speed of the diffusion. A simple qualitative model for this effect is suggested. The decomposition of the ion movement into continuous and jump diffusion shows that continuous part of the diffusion is the same as for the ion cluster in the stable region.

Use of Inert Gases to Study the Interaction of Blood Flow and Diffusion during Passive Absorption from the Gastrointestinal Tract of the Rat

PubMed Central

Levitt, Michael D.; Levitt, David G.

1973-01-01

Measurement of the relative absorption rates of inert gases (H2, He, CH4, SF6, and 133Xe) was used to investigate the interaction between diffusion and blood flow during passive absorption from the stomach, small bowel, and colon of the rat. If uptake is blood flow limited, the gases should be absorbed in proportion to their solubilities in blood, but if diffusion limited, uptake should be proportional to the diffusion rate of the gases in mucosal tissues. The observed absorption data were fitted to a series of models of interaction between perfusion and diffusion. A simple model accurately predicted the absorption rates of the gases from all segments of bowel. In this model, gas is absorbed into two distinct blood flows: one which flows in proximity to the lumen and completely equilibrates with the lumen, and a second which is sufficiently rapid and distant from the lumen that its gas uptake is entirely diffusion limited. The fraction of the total absorption attributable to the equilibrating flow can be readily calculated and equalled 93%, 77%, and 33% for the small bowel, colon, and stomach, respectively. Thus the rate of passive absorption of gases from the small bowel is limited almost entirely by the blood flow to the mucosa, and absorption from the stomach is largely limited by the diffusion rate of the gases. The flow which equilibrates with the lumen can be quantitated, and this flow may provide a useful measure of “effective” mucosal blood flow. Images PMID:4719667

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes.

PubMed

Horno, J; González-Caballero, F; González-Fernández, C F

1990-01-01

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

Nutrient chemotaxis suppression of a diffusive instability in bacterial colony dynamics

NASA Astrophysics Data System (ADS)

Arouh, Scott; Levine, Herbert

2000-07-01

Bacteria grown on a semisolid agar surface have been observed to form branching patterns as the colony envelope propagates outward. The fundamental cause of this instability relates to the need for limited nutrient to diffuse towards the colony. Here, we investigate the effect on this instability of allowing the bacteria to move chemotactically in response to the nutrient gradient. Our results show that this additional effect has a tendency to suppress the instability. Our calculations are done within the context of a simple ``cutoff'' model of colony dynamics, but presumably remain valid for more complex and hence more realistic approaches.

A simple biosphere model (SiB) for use within general circulation models

NASA Technical Reports Server (NTRS)

Sellers, P. J.; Mintz, Y.; Sud, Y. C.; Dalcher, A.

1986-01-01

A simple realistic biosphere model for calculating the transfer of energy, mass and momentum between the atmosphere and the vegetated surface of the earth has been developed for use in atmospheric general circulation models. The vegetation in each terrestrial model grid is represented by an upper level, representing the perennial canopy of trees and shrubs, and a lower level, representing the annual cover of grasses and other heraceous species. The vegetation morphology and the physical and physiological properties of the vegetation layers determine such properties as: the reflection, transmission, absorption and emission of direct and diffuse radiation; the infiltration, drainage, and storage of the residual rainfall in the soil; and the control over the stomatal functioning. The model, with prescribed vegetation parameters and soil interactive soil moisture, can be used for prediction of the atmospheric circulation and precipitaion fields for short periods of up to a few weeks.

Two-dimensional atmospheric transport and chemistry model - Numerical experiments with a new advection algorithm

NASA Technical Reports Server (NTRS)

Shia, Run-Lie; Ha, Yuk Lung; Wen, Jun-Shan; Yung, Yuk L.

1990-01-01

Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.

Selection of intracellular calcium patterns in a model with clustered Ca2+ release channels

NASA Astrophysics Data System (ADS)

Shuai, J. W.; Jung, P.

2003-03-01

A two-dimensional model is proposed for intracellular Ca2+ waves, which incorporates both the discrete nature of Ca2+ release sites in the endoplasmic reticulum membrane and the stochastic dynamics of the clustered inositol 1,4,5-triphosphate (IP3) receptors. Depending on the Ca2+ diffusion coefficient and concentration of IP3, various spontaneous Ca2+ patterns, such as calcium puffs, local waves, abortive waves, global oscillation, and tide waves, can be observed. We further investigate the speed of the global waves as a function of the IP3 concentration and the Ca2+ diffusion coefficient and under what conditions the spatially averaged Ca2+ response can be described by a simple set of ordinary differential equations.

A new mathematical solution for predicting char activation reactions

USGS Publications Warehouse

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

2002-01-01

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

Brownian Dynamics of Colloidal Particles in Lyotropic Chromonic Liquid Crystals

NASA Astrophysics Data System (ADS)

Martinez, Angel; Collings, Peter J.; Yodh, Arjun G.

We employ video microscopy to study the Brownian dynamics of colloidal particles in the nematic phase of lyotropic chromonic liquid crystals (LCLCs). These LCLCs (in this case, DSCG) are water soluble, and their nematic phases are characterized by an unusually large elastic anisotropy. Our preliminary measurements of particle mean-square displacement for polystyrene colloidal particles (~5 micron-diameter) show diffusive and sub-diffusive behaviors moving parallel and perpendicular to the nematic director, respectively. In order to understand these motions, we are developing models that incorporate the relaxation of elastic distortions of the surrounding nematic field. Further experiments to confirm these preliminary results and to determine the origin of these deviations compared to simple diffusion theory are ongoing; our results will also be compared to previous diffusion experiments in nematic liquid crystals. We gratefully acknowledge financial support through NSF DMR12-05463, MRSEC DMR11-20901, and NASA NNX08AO0G.

Diffusion processes in tumors: A nuclear medicine approach

NASA Astrophysics Data System (ADS)

Amaya, Helman

2016-07-01

The number of counts used in nuclear medicine imaging techniques, only provides physical information about the desintegration of the nucleus present in the the radiotracer molecules that were uptaken in a particular anatomical region, but that information is not a real metabolic information. For this reason a mathematical method was used to find a correlation between number of counts and 18F-FDG mass concentration. This correlation allows a better interpretation of the results obtained in the study of diffusive processes in an agar phantom, and based on it, an image from the PETCETIX DICOM sample image set from OsiriX-viewer software was processed. PET-CT gradient magnitude and Laplacian images could show direct information on diffusive processes for radiopharmaceuticals that enter into the cells by simple diffusion. In the case of the radiopharmaceutical 18F-FDG is necessary to include pharmacokinetic models, to make a correct interpretation of the gradient magnitude and Laplacian of counts images.

A method for the estimate of the wall diffusion for non-axisymmetric fields using rotating external fields

NASA Astrophysics Data System (ADS)

Frassinetti, L.; Olofsson, K. E. J.; Fridström, R.; Setiadi, A. C.; Brunsell, P. R.; Volpe, F. A.; Drake, J.

2013-08-01

A new method for the estimate of the wall diffusion time of non-axisymmetric fields is developed. The method based on rotating external fields and on the measurement of the wall frequency response is developed and tested in EXTRAP T2R. The method allows the experimental estimate of the wall diffusion time for each Fourier harmonic and the estimate of the wall diffusion toroidal asymmetries. The method intrinsically considers the effects of three-dimensional structures and of the shell gaps. Far from the gaps, experimental results are in good agreement with the diffusion time estimated with a simple cylindrical model that assumes a homogeneous wall. The method is also applied with non-standard configurations of the coil array, in order to mimic tokamak-relevant settings with a partial wall coverage and active coils of large toroidal extent. The comparison with the full coverage results shows good agreement if the effects of the relevant sidebands are considered.

A novel multiple headspace extraction gas chromatographic method for measuring the diffusion coefficient of methanol in water and in olive oil.

PubMed

Zhang, Chun-Yun; Chai, Xin-Sheng

2015-03-13

A novel method for the determination of the diffusion coefficient (D) of methanol in water and olive oil has been developed. Based on multiple headspace extraction gas chromatography (MHE-GC), the methanol released from the liquid sample of interest in a closed sample vial was determined in a stepwise fashion. A theoretical model was derived to establish the relationship between the diffusion coefficient and the GC signals from MHE-GC measurements. The results showed that the present method has an excellent precision (RSD<1%) in the linear fitting procedure and good accuracy for the diffusion coefficients of methanol in both water and olive oil, when compared with data reported in the literature. The present method is simple and practical and can be a valuable tool for the determination of the diffusion coefficient of volatile analyte(s) into food simulants from food and beverage packaging material, both in research studies and in actual applications. Copyright © 2015 Elsevier B.V. All rights reserved.

Experimental detection of long-distance interactions between biomolecules through their diffusion behavior: numerical study.

PubMed

Nardecchia, Ilaria; Spinelli, Lionel; Preto, Jordane; Gori, Matteo; Floriani, Elena; Jaeger, Sebastien; Ferrier, Pierre; Pettini, Marco

2014-08-01

The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is shown that when the particles are uniformly distributed throughout the accessible space, the self-diffusion coefficient is always lowered by the considered interparticle interactions, irrespective of their attractive or repulsive character. This fact is also confirmed by a simple model to compute the correction to the Brownian diffusion coefficient due to the interactions among the particles. These interactions are also responsible for the onset of dynamical chaos and an associated chaotic diffusion which still follows an Einstein-Fick-like law for the mean-square displacement as a function of time. Transitional phenomena are observed for Coulomb-electrostatic (repulsive) and dipole-electrodynamic (attractive) interactions considered both separately and in competition. The outcomes reported in this paper clearly indicate a feasible experimental method to probe the activation of resonant electrodynamic interactions among biomolecules.

Surface diffusion of a carbon-adatom on Au(110) surfaces

NASA Astrophysics Data System (ADS)

Kim, E.; Safavi-Naini, A.; Hite, D. A.; McKay, K. S.; Pappas, D. P.; Weck, P. F.; Sadeghpour, H. R.

We have investigated the surface diffusion of carbon-adatom on gold surfaces using density functional theory and detailed scanning probe microscopy. The decoherence of trapped-ion quantum gates due to heating of their motional modes is a fundamental science and engineering problem. In an effort to understand heating at the trap-electrode surfaces, we investigate the possible source of noise by focusing on the diffusion of carbon-containing adsorbates onto the Au(110) surface. In this study, we show how the diffusive motion of carbon adatom on gold surface significantly affects the energy landscape and adatom dipole moment variation. A simple model for the diffusion noise, which varies quadratically with the variation of the dipole moment, qualitatively reproduces the measured noise spectrum, and the estimate of the noise spectral density is in accord with measured values. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Company, for the United States Department of Energy's NNSA under Contract DE-AC04-94AL85000.

Comparative study between simple and optimized liposomal dispersion of quetiapine fumarate for diffusion through nasal route.

PubMed

Upadhyay, Pratik; Trivedi, Jatin; Pundarikakshudu, Kilambi; Sheth, Navin

2016-05-01

Nasal route of drug administration is preferred more and more for the targeted delivery to the brain in current drug development scenario due to its ease of use, reliability, quick action, and lesser side effects. Those CNS drugs which have limited oral bioavailability due to pharmacokinetic consequences and brain barrier repulsion are getting onto this direction. Quetiapine fumarate, an analogous to above and an antischizophrenic agent, is tested for its diffusion property with and without lipophilic carrier through sheep nasal membrane. Being a BCS class II' and high permeable candidate, it tends to crossover easily, so made up in a simple dispersion. To improve its diffusion rate, it was embedded into liposomal dispersion, which has proven that it has advanced efficiency for diffusion. For this, both the formulations were checked and compared for their diffusion profile, as it is an essential property for bioavailability through nasal route. Comparison was made on the basis of % drug diffusion within 6 h, rate, mechanism, profile, and coefficient. Liposomal dispersion has been proved superior with greater percentage diffusion of 32.61 ± 1.70 and very high permeability with a coefficient value of 4.1334 ± 0.7321 (× 10 (-) (5 )cm/s). Diffusion profile comparison bearing dissimilarity of 18 and similarity of 74 indicated that the diffusion profiles of liposomal dispersions and simple dispersion were similar but not identical. Liposomal diffusion supremacy was further sustained by in vivo, ciliotoxicity, and gamma scintigraphy studies.

Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Oleschko, K.; Khrennikov, A.

2017-10-01

This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.

Nonlinear Porous Diffusion Modeling of Hydrophilic Ionic Agrochemicals in Astomatous Plant Cuticle Aqueous Pores: A Mechanistic Approach.

PubMed

Tredenick, Eloise C; Farrell, Troy W; Forster, W Alison; Psaltis, Steven T P

2017-01-01

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects.

Nonlinear Porous Diffusion Modeling of Hydrophilic Ionic Agrochemicals in Astomatous Plant Cuticle Aqueous Pores: A Mechanistic Approach

PubMed Central

Tredenick, Eloise C.; Farrell, Troy W.; Forster, W. Alison; Psaltis, Steven T. P.

2017-01-01

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects. PMID:28539930

Comparison of liquid-state anomalies in Stillinger-Weber models of water, silicon, and germanium

NASA Astrophysics Data System (ADS)

Dhabal, Debdas; Chakravarty, Charusita; Molinero, Valeria; Kashyap, Hemant K.

2016-12-01

We use molecular dynamics simulations to compare and contrast the liquid-state anomalies in the Stillinger-Weber models of monatomic water (mW), silicon (Si), and germanium (Ge) over a fairly wide range of temperatures and densities. The relationships between structure, entropy, and mobility, as well as the extent of the regions of anomalous behavior, are discussed as a function of the degree of tetrahedrality. We map out the cascade of density, structural, pair entropy, excess entropy, viscosity, and diffusivity anomalies for these three liquids. Among the three liquids studied here, only mW displays anomalies in the thermal conductivity, and this anomaly is evident only at very low temperatures. Diffusivity and viscosity, on the other hand, show pronounced anomalous regions for the three liquids. The temperature of maximum density of the three liquids shows re-entrant behavior consistent with either singularity-free or liquid-liquid critical point scenarios proposed to explain thermodynamic anomalies. The order-map, which shows the evolution of translational versus tetrahedral order in liquids, is different for Ge than for Si and mW. We find that although the monatomic water reproduces several thermodynamic and dynamic properties of rigid-body water models (e.g., SPC/E, TIP4P/2005), its sequence of anomalies follows, the same as Si and Ge, the silica-like hierarchy: the region of dynamic (diffusivity and viscosity) anomalies encloses the region of structural anomalies, which in turn encloses the region of density anomaly. The hierarchy of the anomalies based on excess entropy and Rosenfeld scaling, on the other hand, reverses the order of the structural and dynamic anomalies, i.e., predicts that the three Stillinger-Weber liquids follow a water-like hierarchy of anomalies. We investigate the scaling of diffusivity, viscosity, and thermal conductivity with the excess entropy of the liquid and find that for dynamical properties that present anomalies there is no universal scaling of the reduced property with excess entropy for the whole range of temperatures and densities. Instead, Rosenfeld's scaling holds for all the three liquids at high densities and high temperatures, although deviations from simple exponential dependence are observed for diffusivity and viscosity at lower temperatures and intermediate densities. The slope of the scaling of transport properties obtained for Ge is comparable to that obtained for simple liquids, suggesting that this low tetrahedrality liquid, although it stabilizes a diamond crystal, is already close to simple liquid behavior for certain properties.

Comparison of liquid-state anomalies in Stillinger-Weber models of water, silicon, and germanium.

PubMed

Dhabal, Debdas; Chakravarty, Charusita; Molinero, Valeria; Kashyap, Hemant K

2016-12-07

We use molecular dynamics simulations to compare and contrast the liquid-state anomalies in the Stillinger-Weber models of monatomic water (mW), silicon (Si), and germanium (Ge) over a fairly wide range of temperatures and densities. The relationships between structure, entropy, and mobility, as well as the extent of the regions of anomalous behavior, are discussed as a function of the degree of tetrahedrality. We map out the cascade of density, structural, pair entropy, excess entropy, viscosity, and diffusivity anomalies for these three liquids. Among the three liquids studied here, only mW displays anomalies in the thermal conductivity, and this anomaly is evident only at very low temperatures. Diffusivity and viscosity, on the other hand, show pronounced anomalous regions for the three liquids. The temperature of maximum density of the three liquids shows re-entrant behavior consistent with either singularity-free or liquid-liquid critical point scenarios proposed to explain thermodynamic anomalies. The order-map, which shows the evolution of translational versus tetrahedral order in liquids, is different for Ge than for Si and mW. We find that although the monatomic water reproduces several thermodynamic and dynamic properties of rigid-body water models (e.g., SPC/E, TIP4P/2005), its sequence of anomalies follows, the same as Si and Ge, the silica-like hierarchy: the region of dynamic (diffusivity and viscosity) anomalies encloses the region of structural anomalies, which in turn encloses the region of density anomaly. The hierarchy of the anomalies based on excess entropy and Rosenfeld scaling, on the other hand, reverses the order of the structural and dynamic anomalies, i.e., predicts that the three Stillinger-Weber liquids follow a water-like hierarchy of anomalies. We investigate the scaling of diffusivity, viscosity, and thermal conductivity with the excess entropy of the liquid and find that for dynamical properties that present anomalies there is no universal scaling of the reduced property with excess entropy for the whole range of temperatures and densities. Instead, Rosenfeld's scaling holds for all the three liquids at high densities and high temperatures, although deviations from simple exponential dependence are observed for diffusivity and viscosity at lower temperatures and intermediate densities. The slope of the scaling of transport properties obtained for Ge is comparable to that obtained for simple liquids, suggesting that this low tetrahedrality liquid, although it stabilizes a diamond crystal, is already close to simple liquid behavior for certain properties.

Structure and Dynamics of Solvent Landscapes in Charge-Transfer Reactions

NASA Astrophysics Data System (ADS)

Leite, Vitor B. Pereira

The dynamics of solvent polarization plays a major role in the control of charge transfer reactions. The success of Marcus theory describing the solvent influence via a single collective quadratic polarization coordinate has been remarkable. Onuchic and Wolynes have recently proposed (J. Chem Phys 98 (3) 2218, 1993) a simple model demonstrating how a many-dimensional-complex model composed by several dipole moments (representing solvent molecules or polar groups in proteins) can be reduced under the appropriate limits into the Marcus Model. This work presents a dynamical study of the same model, which is characterized by two parameters, an average dipole-dipole interaction as a term associated with the potential energy landscape roughness. It is shown why the effective potential, obtained using a thermodynamic approach, is appropriate for the dynamics of the system. At high temperatures, the system exhibits effective diffusive one-dimensional dynamics, where the Born-Marcus limit is recovered. At low temperatures, a glassy phase appears with a slow non-self-averaging dynamics. At intermediate temperatures, the concept of equivalent diffusion paths and polarization dependence effects are discussed. This approach is extended to treat more realistic solvent models. Real solvents are discussed in terms of simple parameters described above, and an analysis of how different regimes affect the rate of charge transfer is presented. Finally, these ideas are correlated to analogous problems in other areas.

Mathematical Model for the Mineralization of Bone

NASA Technical Reports Server (NTRS)

Martin, Bruce

1994-01-01

A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.

Comparison of Alcator C data with the Rebut-Lallia-Watkins critical gradient scaling

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

Hutchinson, I.H.

The critical temperature gradient model of Rebut, Lallia and Watkins is compared with data from Alcator C. The predicted central electron temperature is derived from the model, and a simple analytic formula is given. It is found to be in quite good agreement with the observed temperatures on Alcator C under ohmic heating conditions. However, the thermal diffusivity postulated in the model for gradients that exceed the critical is not consistent with the observed electron heating by Lower Hybrid waves.

Compact modeling of nanoscale triple-gate junctionless transistors covering drift-diffusion to quasi-ballistic carrier transport

NASA Astrophysics Data System (ADS)

Oproglidis, T. A.; Karatsori, T. A.; Barraud, S.; Ghibaudo, G.; Dimitriadis, C. A.

2018-04-01

In this work, we extend our analytical compact model for nanoscale junctionless triple-gate (JL TG) MOSFETs, capturing carrier transport from drift-diffusion to quasi-ballistic regime. This is based on a simple formulation of the low-field mobility extracted from experimental data using the Y-function method, taking into account the ballistic carrier motion and an increased carrier scattering in process-induced defects near the source/drain regions. The case of a Schottky junction in non-ideal ohmic contact at the drain side was also taken into account by modifying the threshold voltage and ideality factor of the JL transistor. The model is validated with experimental data for n-channel JL TG MOSFETs with channel length varying from 95 down to 25 nm. It can be easily implemented as a compact model for use in Spice circuit simulators.

Translucent Radiosity: Efficiently Combining Diffuse Inter-Reflection and Subsurface Scattering.

PubMed

Sheng, Yu; Shi, Yulong; Wang, Lili; Narasimhan, Srinivasa G

2014-07-01

It is hard to efficiently model the light transport in scenes with translucent objects for interactive applications. The inter-reflection between objects and their environments and the subsurface scattering through the materials intertwine to produce visual effects like color bleeding, light glows, and soft shading. Monte-Carlo based approaches have demonstrated impressive results but are computationally expensive, and faster approaches model either only inter-reflection or only subsurface scattering. In this paper, we present a simple analytic model that combines diffuse inter-reflection and isotropic subsurface scattering. Our approach extends the classical work in radiosity by including a subsurface scattering matrix that operates in conjunction with the traditional form factor matrix. This subsurface scattering matrix can be constructed using analytic, measurement-based or simulation-based models and can capture both homogeneous and heterogeneous translucencies. Using a fast iterative solution to radiosity, we demonstrate scene relighting and dynamically varying object translucencies at near interactive rates.

Use of a parallel artificial membrane system to evaluate passive absorption and elimination in small fish.

PubMed

Kwon, Jung-Hwan; Katz, Lynn E; Liljestrand, Howard M

2006-12-01

A parallel artificial lipid membrane system was developed to mimic passive mass transfer of hydrophobic organic chemicals in fish. In this physical model system, a membrane filter-supported lipid bilayer separates two aqueous phases that represent the external and internal aqueous environments of fish. To predict bioconcentration kinetics in small fish with this system, literature absorption and elimination rates were analyzed with an allometric diffusion model to quantify the mass transfer resistances in the aqueous and lipid phases of fish. The effect of the aqueous phase mass transfer resistance was controlled by adjusting stirring intensity to mimic bioconcentration rates in small fish. Twenty-three simple aromatic hydrocarbons were chosen as model compounds for purposes of evaluation. For most of the selected chemicals, literature absorption/elimination rates fall into the range predicted from measured membrane permeabilities and elimination rates of the selected chemicals determined by the diffusion model system.

Field validation of a free-agent cellular automata model of fire spread with fire–atmosphere coupling

Treesearch

Gary Achtemeier

2012-01-01

A cellular automata fire model represents ‘elements’ of fire by autonomous agents. A few simple algebraic expressions substituted for complex physical and meteorological processes and solved iteratively yield simulations for ‘super-diffusive’ fire spread and coupled surface-layer (2-m) fire–atmosphere processes. Pressure anomalies, which are integrals of the thermal...

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

PubMed

Sheppard, C W.

1969-03-01

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

Charge Transfer Inefficiency in Pinned Photodiode CMOS image sensors: Simple Montecarlo modeling and experimental measurement based on a pulsed storage-gate method

NASA Astrophysics Data System (ADS)

Pelamatti, Alice; Goiffon, Vincent; Chabane, Aziouz; Magnan, Pierre; Virmontois, Cédric; Saint-Pé, Olivier; de Boisanger, Michel Breart

2016-11-01

The charge transfer time represents the bottleneck in terms of temporal resolution in Pinned Photodiode (PPD) CMOS image sensors. This work focuses on the modeling and estimation of this key parameter. A simple numerical model of charge transfer in PPDs is presented. The model is based on a Montecarlo simulation and takes into account both charge diffusion in the PPD and the effect of potential obstacles along the charge transfer path. This work also presents a new experimental approach for the estimation of the charge transfer time, called pulsed Storage Gate (SG) method. This method, which allows reproduction of a ;worst-case; transfer condition, is based on dedicated SG pixel structures and is particularly suitable to compare transfer efficiency performances for different pixel geometries.

Absorption Kinetics of Phage Lambda on Its Host Under Shear Flow

NASA Astrophysics Data System (ADS)

Yip, C. W.; Wu, X. L.

2000-03-01

Classical blender experiment by Hershey and Chase played a seminal role in illustrating the infectious process of bacteriophage to its host, and showed unequivocally that DNA is responsible for the transmission of heredity. Subsequent works by others have established that interaction between phage particles and bacterial cells is a diffusion-limited process in that, statistically speaking, each collision results in an irreversible infection. However, such a result is hard to reconcile with the fact that the infection appears to be independent of the density of phage receptors on the bacterial cell membrane. Thus, quantitative experiments showing how a phage finds its receptor and how long does it take would be valuable to this paradoxical view. Simple calculations based on Brownian motion of the phage particles show that the interaction time between the receptor and the phage is given by tau=b^2/(5D), where b is the length of the phage and D is its diffusion coefficient. Using a shear flow apparatus we study absorption kinetics of lambda phage on E. Coli (strain YMEL) under different flow conditions, and the results are compared with a simple diffusion model taking into account the hydrodynamic convection and the interaction time tau.

Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

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

Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong

2014-05-30

The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closedmore » solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.« less

Conceptual models governing leaching behavior and their long-term predictive capability

USGS Publications Warehouse

Claassen, Hans C.

1981-01-01

Six models that may be used to describe the interaction of radioactive waste solids with aqueous solutions are as follows:Simple linear mass transfer;Simple parabolic mass transfer;Parabolic mass transfer with the formation of a diffusion-limiting surface layer at an arbitrary time;Initial parabolic mass transfer followed by linear mass transfer at an arbitrary time;Parabolic (or linear) mass transfer and concomitant surface sorption; andParabolic (or linear) mass transfer and concomitant chemical precipitation.Some of these models lead to either illogical or unrealistic predictions when published data are extrapolated to long times. These predictions result because most data result from short-term experimentation. Probably for longer times, processes will occur that have not been observed in the shorter experiments. This hypothesis has been verified by mass-transfer data from laboratory experiments using natural volcanic glass to predict the composition of groundwater. That such rate-limiting mechanisms do occur is reassuring, although now it is not possible to deduce a single mass-transfer limiting mechanism that could control the solution concentration of all components of all waste forms being investigated. Probably the most reasonable mechanisms are surface sorption and chemical precipitation of the species of interest. Another is limiting of mass transfer by chemical precipitation on the waste form surface of a substance not containing the species of interest, that is, presence of a diffusion-limiting layer. The presence of sorption and chemical precipitation as factors limiting mass transfer has been verified in natural groundwater systems, whereas the diffusion-limiting mechanism has not been verified yet.

Kin Selection in the RNA World

PubMed Central

West, Stuart A.

2017-01-01

Various steps in the RNA world required cooperation. Why did life’s first inhabitants, from polymerases to synthetases, cooperate? We develop kin selection models of the RNA world to answer these questions. We develop a very simple model of RNA cooperation and then elaborate it to model three relevant issues in RNA biology: (1) whether cooperative RNAs receive the benefits of cooperation; (2) the scale of competition in RNA populations; and (3) explicit replicator diffusion and survival. We show: (1) that RNAs are likely to express partial cooperation; (2) that RNAs will need mechanisms for overcoming local competition; and (3) in a specific example of RNA cooperation, persistence after replication and offspring diffusion allow for cooperation to overcome competition. More generally, we show how kin selection can unify previously disparate answers to the question of RNA world cooperation. PMID:29206171

A cooperation and competition based simple cell receptive field model and study of feed-forward linear and nonlinear contributions to orientation selectivity.

PubMed

Bhaumik, Basabi; Mathur, Mona

2003-01-01

We present a model for development of orientation selectivity in layer IV simple cells. Receptive field (RF) development in the model, is determined by diffusive cooperation and resource limited competition guided axonal growth and retraction in geniculocortical pathway. The simulated cortical RFs resemble experimental RFs. The receptive field model is incorporated in a three-layer visual pathway model consisting of retina, LGN and cortex. We have studied the effect of activity dependent synaptic scaling on orientation tuning of cortical cells. The mean value of hwhh (half width at half the height of maximum response) in simulated cortical cells is 58 degrees when we consider only the linear excitatory contribution from LGN. We observe a mean improvement of 22.8 degrees in tuning response due to the non-linear spiking mechanisms that include effects of threshold voltage and synaptic scaling factor.

Atomic-scale Modeling of the Structure and Dynamics of Dislocations in Complex Alloys at High Temperatures

NASA Technical Reports Server (NTRS)

Daw, Murray S.; Mills, Michael J.

2003-01-01

We report on the progress made during the first year of the project. Most of the progress at this point has been on the theoretical and computational side. Here are the highlights: (1) A new code, tailored for high-end desktop computing, now combines modern Accelerated Dynamics (AD) with the well-tested Embedded Atom Method (EAM); (2) The new Accelerated Dynamics allows the study of relatively slow, thermally-activated processes, such as diffusion, which are much too slow for traditional Molecular Dynamics; (3) We have benchmarked the new AD code on a rather simple and well-known process: vacancy diffusion in copper; and (4) We have begun application of the AD code to the diffusion of vacancies in ordered intermetallics.

Porous medium acoustics of wave-induced vorticity diffusion

NASA Astrophysics Data System (ADS)

Müller, T. M.; Sahay, P. N.

2011-02-01

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

An Eddy-Diffusivity Mass-flux (EDMF) closure for the unified representation of cloud and convective processes

NASA Astrophysics Data System (ADS)

Tan, Z.; Schneider, T.; Teixeira, J.; Lam, R.; Pressel, K. G.

2014-12-01

Sub-grid scale (SGS) closures in current climate models are usually decomposed into several largely independent parameterization schemes for different cloud and convective processes, such as boundary layer turbulence, shallow convection, and deep convection. These separate parameterizations usually do not converge as the resolution is increased or as physical limits are taken. This makes it difficult to represent the interactions and smooth transition among different cloud and convective regimes. Here we present an eddy-diffusivity mass-flux (EDMF) closure that represents all sub-grid scale turbulent, convective, and cloud processes in a unified parameterization scheme. The buoyant updrafts and precipitative downdrafts are parameterized with a prognostic multiple-plume mass-flux (MF) scheme. The prognostic term for the mass flux is kept so that the life cycles of convective plumes are better represented. The interaction between updrafts and downdrafts are parameterized with the buoyancy-sorting model. The turbulent mixing outside plumes is represented by eddy diffusion, in which eddy diffusivity (ED) is determined from a turbulent kinetic energy (TKE) calculated from a TKE balance that couples the environment with updrafts and downdrafts. Similarly, tracer variances are decomposed consistently between updrafts, downdrafts and the environment. The closure is internally coupled with a probabilistic cloud scheme and a simple precipitation scheme. We have also developed a relatively simple two-stream radiative scheme that includes the longwave (LW) and shortwave (SW) effects of clouds, and the LW effect of water vapor. We have tested this closure in a single-column model for various regimes spanning stratocumulus, shallow cumulus, and deep convection. The model is also run towards statistical equilibrium with climatologically relevant large-scale forcings. These model tests are validated against large-eddy simulation (LES) with the same forcings. The comparison of results verifies the capacity of this closure to realistically represent different cloud and convective processes. Implementation of the closure in an idealized GCM allows us to study cloud feedbacks to climate change and to study the interactions between clouds, convections, and the large-scale circulation.

Diffusion models for corona formation in metagabbros from the Western Grenville Province, Canada

NASA Astrophysics Data System (ADS)

Grant, Shona M.

1988-01-01

Metagabbro bodies in SW Grenville Province display a variety of disequilibrium corona textures between spinel-clouded plagioclase and primary olivine or opaque oxide. Textural evidence favours a single-stage, subsolidus origin for the olivine coronas and diffusive mass transfer is believed to have been the rate-controlling process. Irreversible thermodynamics have been used to model two different garnet symplectite-bearing corona sequences in terms of steady state diffusion. In the models the flux of each component is related to the chemical potential gradients of all diffusing species by the Onsager or L-coefficients for diffusion. These coefficients are analogous to experimentally determined diffusion coefficients ( d), but relate the flux of components to chemical potential rather than concentration gradients. The major constraint on the relative values of Onsager coefficients comes from the observed mole fraction, X, of garnet in the symplectites; in (amph-gt) symplectites X {Gt/Sym}˜0.80, compared with ˜0.75 in (cpx-gt) symplectites. Several models using simple oxide components, and two different modifications of the reactant plagioclase composition, give the following qualitative results: the very low mobility of aluminium appears to control the rate of corona formation. Mg and Fe have similar mobility, and Mg can be up to 6 8 times more mobile than sodium. Determination of calcium mobility is problematical because of a proposed interaction with cross-coefficient terms reflecting “uphill” Ca-diffusion, i.e., calcium diffusing up its own chemical potential gradient. If these terms are not introduced, it is difficult to generate the required proportions of garnet in the symplectite. However, at moderate values of the cross-coefficient ratios, Mg can be up to 4 6 times more mobile than calcium ( L MgMg/LCaCa<4 6) and calcium must be 3 4 times more mobile than aluminium ( L CaCa/LAlAl>3).

A Simple Experiment for Visualizing Diffusion

ERIC Educational Resources Information Center

Helseth, L. E.

2011-01-01

We propose a simple and fascinating experiment for studying diffusion in gels using a pH-sensitive dye. By doping agar with methyl red, we obtain a gel which rapidly reacts to changes in pH by changing its absorption spectrum. The pH gradients can be followed using a digital camera, and we demonstrate here that the pH-sensitive colour changes can…

Insight from simulations of single-well injection-withdrawal tracer tests on simple and complex fractures

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

Tsang, C.-F.; Doughty, C.

2009-08-06

The single-well injection withdrawal (SWIW) test, a tracer test utilizing only one well, is proposed as a useful contribution to site characterization of fractured rock, as well as providing parameters relevant to tracer diffusion and sorption. The usual conceptual model of flow and solute transport through fractured rock with low matrix permeability involves solute advection and dispersion through a fracture network coupled with diffusion and sorption into the surrounding rock matrix. Unlike two-well tracer tests, results of SWIW tests are ideally independent of advective heterogeneity, channeling and flow dimension, and, instead, focus on diffusive and sorptive characteristics of tracer (solute)more » transport. Thus, they can be used specifically to study such characteristics and evaluate the diffusive parameters associated with tracer transport through fractured media. We conduct simulations of SWIW tests on simple and complex fracture models, the latter being defined as having two subfractures with altered rock blocks in between and gouge material in their apertures. Using parameters from the Aspo site in Sweden, we calculate and study SWIW tracer breakthrough curves (BTCs) from a test involving four days of injection and then withdrawal. By examining the peak concentration C{sub pk} of the SWIW BTCs for a variety of parameters, we confirm that C{sub pk} is largely insensitive to the fracture advective flow properties, in particular to permeability heterogeneity over the fracture plane or to subdividing the flow into two subfractures in the third dimension orthogonal to the fracture plane. The peak arrival time t{sub pk} is not a function of fracture or rock properties, but is controlled by the time schedule of the SWIW test. The study shows that the SWIW test is useful for the study of tracer diffusion-sorption processes, including the effect of the so-called flow-wetted surface (FWS) of the fracture. Calculations with schematic models with different FWS values are conducted and the possibility of direct in situ measurement of FWS with SWIW tests is demonstrated.« less

Role of spatial inhomogenity in GPCR dimerisation predicted by receptor association-diffusion models

NASA Astrophysics Data System (ADS)

Deshpande, Sneha A.; Pawar, Aiswarya B.; Dighe, Anish; Athale, Chaitanya A.; Sengupta, Durba

2017-06-01

G protein-coupled receptor (GPCR) association is an emerging paradigm with far reaching implications in the regulation of signalling pathways and therapeutic interventions. Recent super resolution microscopy studies have revealed that receptor dimer steady state exhibits sub-second dynamics. In particular the GPCRs, muscarinic acetylcholine receptor M1 (M1MR) and formyl peptide receptor (FPR), have been demonstrated to exhibit a fast association/dissociation kinetics, independent of ligand binding. In this work, we have developed a spatial kinetic Monte Carlo model to investigate receptor homo-dimerisation at a single receptor resolution. Experimentally measured association/dissociation kinetic parameters and diffusion coefficients were used as inputs to the model. To test the effect of membrane spatial heterogeneity on the simulated steady state, simulations were compared to experimental statistics of dimerisation. In the simplest case the receptors are assumed to be diffusing in a spatially homogeneous environment, while spatial heterogeneity is modelled to result from crowding, membrane micro-domains and cytoskeletal compartmentalisation or ‘corrals’. We show that a simple association-diffusion model is sufficient to reproduce M1MR association statistics, but fails to reproduce FPR statistics despite comparable kinetic constants. A parameter sensitivity analysis is required to reproduce the association statistics of FPR. The model reveals the complex interplay between cytoskeletal components and their influence on receptor association kinetics within the features of the membrane landscape. These results constitute an important step towards understanding the factors modulating GPCR organisation.

Diffusion of Salt in Tap Water

ERIC Educational Resources Information Center

Booth, C.; And Others

1978-01-01

A simple experiment is described to measure the diffusion coefficient of a solute in a fluid. Laboratory-made floats are used to monitor the density changes associated with diffusion behavior. The experiment is ideally suited for undergraduate project work. (BB)

Precombination Cloud Collapse and Baryonic Dark Matter

NASA Technical Reports Server (NTRS)

Hogan, Craig J.

1993-01-01

A simple spherical model of dense baryon clouds in the hot big bang 'strongly nonlinear primordial isocurvature baryon fluctuations' is reviewed and used to describe the dependence of cloud behavior on the model parameters, baryon mass, and initial over-density. Gravitational collapse of clouds before and during recombination is considered including radiation diffusion and trapping, remnant type and mass, and effects on linear large-scale fluctuation modes. Sufficiently dense clouds collapse early into black holes with a minimum mass of approx. 1 solar mass, which behave dynamically like collisionless cold dark matter. Clouds below a critical over-density, however, delay collapse until recombination, remaining until then dynamically coupled to the radiation like ordinary diffuse baryons, and possibly producing remnants of other kinds and lower mass. The mean density in either type of baryonic remnant is unconstrained by observed element abundances. However, mixed or unmixed spatial variations in abundance may survive in the diffuse baryon and produce observable departures from standard predictions.

Influence investigation of a void region on modeling light propagation in a heterogeneous medium.

PubMed

Yang, Defu; Chen, Xueli; Ren, Shenghan; Qu, Xiaochao; Tian, Jie; Liang, Jimin

2013-01-20

A void region exists in some biological tissues, and previous studies have shown that inaccurate images would be obtained if it were not processed. A hybrid radiosity-diffusion method (HRDM) that couples the radiosity theory and the diffusion equation has been proposed to deal with the void problem and has been well demonstrated in two-dimensional and three-dimensional (3D) simple models. However, the extent of the impact of the void region on the accuracy of modeling light propagation has not been investigated. In this paper, we first implemented and verified the HRDM in 3D models, including both the regular geometries and a digital mouse model, and then investigated the influences of the void region on modeling light propagation in a heterogeneous medium. Our investigation results show that the influence of the region can be neglected when the size of the void is less than a certain range, and other cases must be taken into account.

Diffusion-controlled reactions: hydrodynamic interaction between charged, uniformly reactive spherical reactants.

PubMed

Allison, Stuart

2006-12-28

In this work, different models of hydrodynamic interaction (HI) are examined in the diffusion-controlled reaction between uniformly reactive charged spherical particles. In addition to Oseen "stick" and "slip" models of HI, one is considered that accounts for the disturbance of fluid flow by the ions around one reactive partner as they interact with a neighboring reactive species. This interaction is closely related to the "electrophoretic effect" in electrokinetics and can be described by a fairly simple electrophoretic, or E-tensor. These models are applied to the electron-transfer quenching reaction of Ru(bpy)3(2+) and methyl viologen (MV2+) over a wide range of NaCl concentrations (Chiorboli, C. et al., J. Phys. Chem. 1988, 92, 156). The back reaction is also considered. From a comparison of the salt dependence of the model and experimental rates, it is concluded that the "E-tensor" model works best and ignoring HI altogether works worst. The Oseen "stick" and "slip" models fall between these.

Dynamics of non-Markovian exclusion processes

NASA Astrophysics Data System (ADS)

Khoromskaia, Diana; Harris, Rosemary J.; Grosskinsky, Stefan

2014-12-01

Driven diffusive systems are often used as simple discrete models of collective transport phenomena in physics, biology or social sciences. Restricting attention to one-dimensional geometries, the asymmetric simple exclusion process (ASEP) plays a paradigmatic role to describe noise-activated driven motion of entities subject to an excluded volume interaction and many variants have been studied in recent years. While in the standard ASEP the noise is Poissonian and the process is therefore Markovian, in many applications the statistics of the activating noise has a non-standard distribution with possible memory effects resulting from internal degrees of freedom or external sources. This leads to temporal correlations and can significantly affect the shape of the current-density relation as has been studied recently for a number of scenarios. In this paper we report a general framework to derive the fundamental diagram of ASEPs driven by non-Poissonian noise by using effectively only two simple quantities, viz., the mean residual lifetime of the jump distribution and a suitably defined temporal correlation length. We corroborate our results by detailed numerical studies for various noise statistics under periodic boundary conditions and discuss how our approach can be applied to more general driven diffusive systems.

A Numerical Method for the Simulation of Skew Brownian Motion and its Application to Diffusive Shock Acceleration of Charged Particles

NASA Astrophysics Data System (ADS)

McEvoy, Erica L.

Stochastic differential equations are becoming a popular tool for modeling the transport and acceleration of cosmic rays in the heliosphere. In diffusive shock acceleration, cosmic rays diffuse across a region of discontinuity where the up- stream diffusion coefficient abruptly changes to the downstream value. Because the method of stochastic integration has not yet been developed to handle these types of discontinuities, I utilize methods and ideas from probability theory to develop a conceptual framework for the treatment of such discontinuities. Using this framework, I then produce some simple numerical algorithms that allow one to incorporate and simulate a variety of discontinuities (or boundary conditions) using stochastic integration. These algorithms were then modified to create a new algorithm which incorporates the discontinuous change in diffusion coefficient found in shock acceleration (known as Skew Brownian Motion). The originality of this algorithm lies in the fact that it is the first of its kind to be statistically exact, so that one obtains accuracy without the use of approximations (other than the machine precision error). I then apply this algorithm to model the problem of diffusive shock acceleration, modifying it to incorporate the additional effect of the discontinuous flow speed profile found at the shock. A steady-state solution is obtained that accurately simulates this phenomenon. This result represents a significant improvement over previous approximation algorithms, and will be useful for the simulation of discontinuous diffusion processes in other fields, such as biology and finance.

Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection

NASA Astrophysics Data System (ADS)

Chen, Xueli; Yang, Defu; Qu, Xiaochao; Hu, Hao; Liang, Jimin; Gao, Xinbo; Tian, Jie

2012-06-01

Bioluminescence tomography (BLT) has been successfully applied to the detection and therapeutic evaluation of solid cancers. However, the existing BLT reconstruction algorithms are not accurate enough for cavity cancer detection because of neglecting the void problem. Motivated by the ability of the hybrid radiosity-diffusion model (HRDM) in describing the light propagation in cavity organs, an HRDM-based BLT reconstruction algorithm was provided for the specific problem of cavity cancer detection. HRDM has been applied to optical tomography but is limited to simple and regular geometries because of the complexity in coupling the boundary between the scattering and void region. In the provided algorithm, HRDM was first applied to three-dimensional complicated and irregular geometries and then employed as the forward light transport model to describe the bioluminescent light propagation in tissues. Combining HRDM with the sparse reconstruction strategy, the cavity cancer cells labeled with bioluminescent probes can be more accurately reconstructed. Compared with the diffusion equation based reconstruction algorithm, the essentiality and superiority of the HRDM-based algorithm were demonstrated with simulation, phantom and animal studies. An in vivo gastric cancer-bearing nude mouse experiment was conducted, whose results revealed the ability and feasibility of the HRDM-based algorithm in the biomedical application of gastric cancer detection.

Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection.

PubMed

Chen, Xueli; Yang, Defu; Qu, Xiaochao; Hu, Hao; Liang, Jimin; Gao, Xinbo; Tian, Jie

2012-06-01

Bioluminescence tomography (BLT) has been successfully applied to the detection and therapeutic evaluation of solid cancers. However, the existing BLT reconstruction algorithms are not accurate enough for cavity cancer detection because of neglecting the void problem. Motivated by the ability of the hybrid radiosity-diffusion model (HRDM) in describing the light propagation in cavity organs, an HRDM-based BLT reconstruction algorithm was provided for the specific problem of cavity cancer detection. HRDM has been applied to optical tomography but is limited to simple and regular geometries because of the complexity in coupling the boundary between the scattering and void region. In the provided algorithm, HRDM was first applied to three-dimensional complicated and irregular geometries and then employed as the forward light transport model to describe the bioluminescent light propagation in tissues. Combining HRDM with the sparse reconstruction strategy, the cavity cancer cells labeled with bioluminescent probes can be more accurately reconstructed. Compared with the diffusion equation based reconstruction algorithm, the essentiality and superiority of the HRDM-based algorithm were demonstrated with simulation, phantom and animal studies. An in vivo gastric cancer-bearing nude mouse experiment was conducted, whose results revealed the ability and feasibility of the HRDM-based algorithm in the biomedical application of gastric cancer detection.

Particle transport through hydrogels is charge asymmetric.

PubMed

Zhang, Xiaolu; Hansing, Johann; Netz, Roland R; DeRouchey, Jason E

2015-02-03

Transport processes within biological polymer networks, including mucus and the extracellular matrix, play an important role in the human body, where they serve as a filter for the exchange of molecules and nanoparticles. Such polymer networks are complex and heterogeneous hydrogel environments that regulate diffusive processes through finely tuned particle-network interactions. In this work, we present experimental and theoretical studies to examine the role of electrostatics on the basic mechanisms governing the diffusion of charged probe molecules inside model polymer networks. Translational diffusion coefficients are determined by fluorescence correlation spectroscopy measurements for probe molecules in uncharged as well as cationic and anionic polymer solutions. We show that particle transport in the charged hydrogels is highly asymmetric, with diffusion slowed down much more by electrostatic attraction than by repulsion, and that the filtering capability of the gel is sensitive to the solution ionic strength. Brownian dynamics simulations of a simple model are used to examine key parameters, including interaction strength and interaction range within the model networks. Simulations, which are in quantitative agreement with our experiments, reveal the charge asymmetry to be due to the sticking of particles at the vertices of the oppositely charged polymer networks. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers

PubMed Central

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation. PMID:28239346

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers.

PubMed

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation.

A Diffuse Interface Model with Immiscibility Preservation

PubMed Central

Tiwari, Arpit; Freund, Jonathan B.; Pantano, Carlos

2013-01-01

A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results. PMID:24058207

Promoting protein crystallization using a plate with simple geometry.

PubMed

Chen, Rui-Qing; Yin, Da-Chuan; Liu, Yong-Ming; Lu, Qin-Qin; He, Jin; Liu, Yue

2014-03-01

Increasing the probability of obtaining protein crystals in crystallization screening is always an important goal for protein crystallography. In this paper, a new method called the cross-diffusion microbatch (CDM) method is presented, which aims to efficiently promote protein crystallization and increase the chance of obtaining protein crystals. In this method, a very simple crystallization plate was designed in which all crystallization droplets are in one sealed space, so that a variety of volatile components from one droplet can diffuse into any other droplet via vapour diffusion. Crystallization screening and reproducibility tests indicate that this method could be a potentially powerful technique in practical protein crystallization screening. It can help to obtain crystals with higher probability and at a lower cost, while using a simple and easy procedure.

A simulation of water pollution model parameter estimation

NASA Technical Reports Server (NTRS)

Kibler, J. F.

1976-01-01

A parameter estimation procedure for a water pollution transport model is elaborated. A two-dimensional instantaneous-release shear-diffusion model serves as representative of a simple transport process. Pollution concentration levels are arrived at via modeling of a remote-sensing system. The remote-sensed data are simulated by adding Gaussian noise to the concentration level values generated via the transport model. Model parameters are estimated from the simulated data using a least-squares batch processor. Resolution, sensor array size, and number and location of sensor readings can be found from the accuracies of the parameter estimates.

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.

The Formation and Physical Origin of Highly Ionized Cooling Gas

NASA Astrophysics Data System (ADS)

Bordoloi, Rongmon; Wagner, Alexander Y.; Heckman, Timothy M.; Norman, Colin A.

2017-10-01

We present a simple model that explains the origin of warm, diffuse gas seen primarily as highly ionized absorption-line systems in the spectra of background sources. We predict the observed column densities of several highly ionized transitions such as O VI, O vii, Ne viii, N v, and Mg x, and we present a unified comparison of the model predictions with absorption lines seen in the Milky Way disk, Milky Way halo, starburst galaxies, the circumgalactic medium, and the intergalactic medium at low and high redshifts. We show that diffuse gas seen in such diverse environments can be simultaneously explained by a simple model of radiatively cooling gas. We show that most such absorption-line systems are consistent with being collisionally ionized, and we estimate the maximum-likelihood temperature of the gas in each observation. This model satisfactorily explains why O VI is regularly observed around star-forming low-z L* galaxies, and why N v is rarely seen around the same galaxies. We further present some consequences of this model in quantifying the dynamics of the cooling gas around galaxies and predict the shock velocities associated with such flows. A unique strength of this model is that while it has only one free (but physically well-constrained) parameter, it nevertheless successfully reproduces the available data on O VI absorbers in the interstellar, circumgalactic, intragroup, and intergalactic media, as well as the available data on other absorption lines from highly ionized species.

The Formation and Physical Origin of Highly Ionized Cooling Gas

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

Bordoloi, Rongmon; Wagner, Alexander Y.; Heckman, Timothy M.

We present a simple model that explains the origin of warm, diffuse gas seen primarily as highly ionized absorption-line systems in the spectra of background sources. We predict the observed column densities of several highly ionized transitions such as O vi, O vii, Ne viii, N v, and Mg x, and we present a unified comparison of the model predictions with absorption lines seen in the Milky Way disk, Milky Way halo, starburst galaxies, the circumgalactic medium, and the intergalactic medium at low and high redshifts. We show that diffuse gas seen in such diverse environments can be simultaneously explainedmore » by a simple model of radiatively cooling gas. We show that most such absorption-line systems are consistent with being collisionally ionized, and we estimate the maximum-likelihood temperature of the gas in each observation. This model satisfactorily explains why O vi is regularly observed around star-forming low- z L* galaxies, and why N v is rarely seen around the same galaxies. We further present some consequences of this model in quantifying the dynamics of the cooling gas around galaxies and predict the shock velocities associated with such flows. A unique strength of this model is that while it has only one free (but physically well-constrained) parameter, it nevertheless successfully reproduces the available data on O vi absorbers in the interstellar, circumgalactic, intragroup, and intergalactic media, as well as the available data on other absorption lines from highly ionized species.« less

Webcam camera as a detector for a simple lab-on-chip time based approach.

PubMed

Wongwilai, Wasin; Lapanantnoppakhun, Somchai; Grudpan, Supara; Grudpan, Kate

2010-05-15

A modification of a webcam camera for use as a small and low cost detector was demonstrated with a simple lab-on-chip reactor. Real time continuous monitoring of the reaction zone could be done. Acid-base neutralization with phenolphthalein indicator was used as a model reaction. The fading of pink color of the indicator when the acidic solution diffused into the basic solution zone was recorded as the change of red, blue and green colors (%RBG.) The change was related to acid concentration. A low cost portable semi-automation analysis system was achieved.

EIT Noise Resonance Power Broadening: a probe for coherence dynamics

NASA Astrophysics Data System (ADS)

Crescimanno, Michael; O'Leary, Shannon; Snider, Charles

2012-06-01

EIT noise correlation spectroscopy holds promise as a simple, robust method for performing high resolution spectroscopy used in devices as diverse as magnetometers and clocks. One useful feature of these noise correlation resonances is that they do not power broaden with the EIT window. We report on measurements of the eventual power broadening (at higher optical powers) of these resonances and a simple, quantitative theoretical model that relates the observed power broadening slope with processes such as two-photon detuning gradients and coherence diffusion. These processes reduce the ground state coherence relative to that of a homogeneous system, and thus the power broadening slope of the EIT noise correlation resonance may be a simple, useful probe for coherence dynamics.

Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process.

PubMed

Jahn, Patrick; Berg, Rune W; Hounsgaard, Jørn; Ditlevsen, Susanne

2011-11-01

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein-Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein-Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential.

Self-Organized Percolation and Critical Sales Fluctuations

NASA Astrophysics Data System (ADS)

Weisbuch, Gérard; Solomon, Sorin

There is a discrepancy between the standard view of equilibrium through price adjustment in economics and the observation of large fluctuations in stock markets. We study here a simple model where agents decisions not only depend upon their individual preferences but also upon information obtained from their neighbors in a social network. The model shows that information diffusion coupled to the adjustment process drives the system to criticality with large fluctuations rather than converging smoothly to equilibrium.

Epidemic modeling in complex realities.

PubMed

Colizza, Vittoria; Barthélemy, Marc; Barrat, Alain; Vespignani, Alessandro

2007-04-01

In our global world, the increasing complexity of social relations and transport infrastructures are key factors in the spread of epidemics. In recent years, the increasing availability of computer power has enabled both to obtain reliable data allowing one to quantify the complexity of the networks on which epidemics may propagate and to envision computational tools able to tackle the analysis of such propagation phenomena. These advances have put in evidence the limits of homogeneous assumptions and simple spatial diffusion approaches, and stimulated the inclusion of complex features and heterogeneities relevant in the description of epidemic diffusion. In this paper, we review recent progresses that integrate complex systems and networks analysis with epidemic modelling and focus on the impact of the various complex features of real systems on the dynamics of epidemic spreading.

Effective Dynamics of Microorganisms That Interact with Their Own Trail

NASA Astrophysics Data System (ADS)

Kranz, W. Till; Gelimson, Anatolij; Zhao, Kun; Wong, Gerard C. L.; Golestanian, Ramin

2016-07-01

Like ants, some microorganisms are known to leave trails on surfaces to communicate. We explore how trail-mediated self-interaction could affect the behavior of individual microorganisms when diffusive spreading of the trail is negligible on the time scale of the microorganism using a simple phenomenological model for an actively moving particle and a finite-width trail. The effective dynamics of each microorganism takes on the form of a stochastic integral equation with the trail interaction appearing in the form of short-term memory. For a moderate coupling strength below an emergent critical value, the dynamics exhibits effective diffusion in both orientation and position after a phase of superdiffusive reorientation. We report experimental verification of a seemingly counterintuitive perpendicular alignment mechanism that emerges from the model.

Simple stochastic model for El Niño with westerly wind bursts

PubMed Central

Thual, Sulian; Majda, Andrew J.; Chen, Nan; Stechmann, Samuel N.

2016-01-01

Atmospheric wind bursts in the tropics play a key role in the dynamics of the El Niño Southern Oscillation (ENSO). A simple modeling framework is proposed that summarizes this relationship and captures major features of the observational record while remaining physically consistent and amenable to detailed analysis. Within this simple framework, wind burst activity evolves according to a stochastic two-state Markov switching–diffusion process that depends on the strength of the western Pacific warm pool, and is coupled to simple ocean–atmosphere processes that are otherwise deterministic, stable, and linear. A simple model with this parameterization and no additional nonlinearities reproduces a realistic ENSO cycle with intermittent El Niño and La Niña events of varying intensity and strength as well as realistic buildup and shutdown of wind burst activity in the western Pacific. The wind burst activity has a direct causal effect on the ENSO variability: in particular, it intermittently triggers regular El Niño or La Niña events, super El Niño events, or no events at all, which enables the model to capture observed ENSO statistics such as the probability density function and power spectrum of eastern Pacific sea surface temperatures. The present framework provides further theoretical and practical insight on the relationship between wind burst activity and the ENSO. PMID:27573821

Action video games do not improve the speed of information processing in simple perceptual tasks.

PubMed

van Ravenzwaaij, Don; Boekel, Wouter; Forstmann, Birte U; Ratcliff, Roger; Wagenmakers, Eric-Jan

2014-10-01

Previous research suggests that playing action video games improves performance on sensory, perceptual, and attentional tasks. For instance, Green, Pouget, and Bavelier (2010) used the diffusion model to decompose data from a motion detection task and estimate the contribution of several underlying psychological processes. Their analysis indicated that playing action video games leads to faster information processing, reduced response caution, and no difference in motor responding. Because perceptual learning is generally thought to be highly context-specific, this transfer from gaming is surprising and warrants corroborative evidence from a large-scale training study. We conducted 2 experiments in which participants practiced either an action video game or a cognitive game in 5 separate, supervised sessions. Prior to each session and following the last session, participants performed a perceptual discrimination task. In the second experiment, we included a third condition in which no video games were played at all. Behavioral data and diffusion model parameters showed similar practice effects for the action gamers, the cognitive gamers, and the nongamers and suggest that, in contrast to earlier reports, playing action video games does not improve the speed of information processing in simple perceptual tasks.

Action Video Games Do Not Improve the Speed of Information Processing in Simple Perceptual Tasks

PubMed Central

van Ravenzwaaij, Don; Boekel, Wouter; Forstmann, Birte U.; Ratcliff, Roger; Wagenmakers, Eric-Jan

2015-01-01

Previous research suggests that playing action video games improves performance on sensory, perceptual, and attentional tasks. For instance, Green, Pouget, and Bavelier (2010) used the diffusion model to decompose data from a motion detection task and estimate the contribution of several underlying psychological processes. Their analysis indicated that playing action video games leads to faster information processing, reduced response caution, and no difference in motor responding. Because perceptual learning is generally thought to be highly context-specific, this transfer from gaming is surprising and warrants corroborative evidence from a large-scale training study. We conducted 2 experiments in which participants practiced either an action video game or a cognitive game in 5 separate, supervised sessions. Prior to each session and following the last session, participants performed a perceptual discrimination task. In the second experiment, we included a third condition in which no video games were played at all. Behavioral data and diffusion model parameters showed similar practice effects for the action gamers, the cognitive gamers, and the nongamers and suggest that, in contrast to earlier reports, playing action video games does not improve the speed of information processing in simple perceptual tasks. PMID:24933517

New Results from Fermi-LAT and Their Implications for the Nature of Dark Matter and the Origin of Cosmic Rays

NASA Technical Reports Server (NTRS)

Moiseev, Alexander

2009-01-01

The measured spectrum is compatible with a power law within our current systematic errors. The spectral index (-3.04) is harder than expected from previous experiments and simple theoretical considerations. "Pre-Fermi" diffusive model requires a harder electron injection spectrum (by 0.12) to fit the Fermi data, but inconsistent with positron excess reported by Pamela if it extends to higher energy. Additional component of electron flux from local source(s) may solve the problem; its origin, astrophysical or exotic, is still unclear. Valuable contribution to the calculation of IC component of diffuse gamma radiation.

Ballistic and diffusive dynamics in a two-dimensional ideal gas of macroscopic chaotic Faraday waves.

PubMed

Welch, Kyle J; Hastings-Hauss, Isaac; Parthasarathy, Raghuveer; Corwin, Eric I

2014-04-01

We have constructed a macroscopic driven system of chaotic Faraday waves whose statistical mechanics, we find, are surprisingly simple, mimicking those of a thermal gas. We use real-time tracking of a single floating probe, energy equipartition, and the Stokes-Einstein relation to define and measure a pseudotemperature and diffusion constant and then self-consistently determine a coefficient of viscous friction for a test particle in this pseudothermal gas. Because of its simplicity, this system can serve as a model for direct experimental investigation of nonequilibrium statistical mechanics, much as the ideal gas epitomizes equilibrium statistical mechanics.

Tracking Water Diffusion Fronts in a Highly Viscous Aerosol Particle

NASA Astrophysics Data System (ADS)

Bastelberger, Sandra; Krieger, Ulrich; Peter, Thomas

2016-04-01

Field measurements indicate that atmospheric secondary aerosol particles can be present in a highly viscous, glassy state [1]. In contrast to liquid state particles, the gas phase equilibration is kinetically limited and governed by condensed phase diffusion. In recent water diffusion experiments on highly viscous single aerosol particles levitated in an electrodynamic balance (EDB) we observed a characteristic shift behavior of the Mie whispering gallery modes (WGM) indicative of the changing radial structure of the particle, thus providing us with an experimental method to track the diffusion process inside the particle. When a highly viscous, homogeneous particle is exposed to an abrupt increase in relative humidity, the rapid gas phase diffusion and strong concentration dependence of the diffusion coefficient in the condensed phase lead to extremely steep water concentration gradients inside the particle, reminiscent of diffusion fronts. The resulting quasi step-like concentration profile motivates the introduction of a simple core-shell model describing the morphology of the non-equilibrium particle during humidification. The subsequent particle growth and reduction of the shell refractive index can be observed as red and blueshift behavior of the WGM, respectively. The shift pattern can be attributed to a core-shell radius ratio and particle radius derived from model calculations [2]. If supplemented with growth information obtained from the WGM redshift and thermodynamic equilibrium data, we can infer a comprehensive picture of the time evolution of the diffusion fronts in the framework of our core-shell model. The measured time dependent concentration profile is then compared with simulations solving the non-linear diffusion equation [3] [1] Virtanen, A., et al., Nature, 467, 824-827, 2010 [2] Kaiser, T., Schweiger, G., Computers in Physics, Vol. 7, No. 6, 682-686, Nov/Dec 1993 [3] Zobrist, B., Soonsin, V., Luo, B.P., Peter, T. et al., Phys. Chem. Chem. Phys., 13,3514-3526, 2011

Use of the temporal median and trimmed mean mitigates effects of respiratory motion in multiple-acquisition abdominal diffusion imaging

NASA Astrophysics Data System (ADS)

Jerome, N. P.; Orton, M. R.; d'Arcy, J. A.; Feiweier, T.; Tunariu, N.; Koh, D.-M.; Leach, M. O.; Collins, D. J.

2015-01-01

Respiratory motion commonly confounds abdominal diffusion-weighted magnetic resonance imaging, where averaging of successive samples at different parts of the respiratory cycle, performed in the scanner, manifests the motion as blurring of tissue boundaries and structural features and can introduce bias into calculated diffusion metrics. Storing multiple averages separately allows processing using metrics other than the mean; in this prospective volunteer study, median and trimmed mean values of signal intensity for each voxel over repeated averages and diffusion-weighting directions are shown to give images with sharper tissue boundaries and structural features for moving tissues, while not compromising non-moving structures. Expert visual scoring of derived diffusion maps is significantly higher for the median than for the mean, with modest improvement from the trimmed mean. Diffusion metrics derived from mono- and bi-exponential diffusion models are comparable for non-moving structures, demonstrating a lack of introduced bias from using the median. The use of the median is a simple and computationally inexpensive alternative to complex and expensive registration algorithms, requiring only additional data storage (and no additional scanning time) while returning visually superior images that will facilitate the appropriate placement of regions-of-interest when analysing abdominal diffusion-weighted magnetic resonance images, for assessment of disease characteristics and treatment response.

Use of the temporal median and trimmed mean mitigates effects of respiratory motion in multiple-acquisition abdominal diffusion imaging.

PubMed

Jerome, N P; Orton, M R; d'Arcy, J A; Feiweier, T; Tunariu, N; Koh, D-M; Leach, M O; Collins, D J

2015-01-21

Respiratory motion commonly confounds abdominal diffusion-weighted magnetic resonance imaging, where averaging of successive samples at different parts of the respiratory cycle, performed in the scanner, manifests the motion as blurring of tissue boundaries and structural features and can introduce bias into calculated diffusion metrics. Storing multiple averages separately allows processing using metrics other than the mean; in this prospective volunteer study, median and trimmed mean values of signal intensity for each voxel over repeated averages and diffusion-weighting directions are shown to give images with sharper tissue boundaries and structural features for moving tissues, while not compromising non-moving structures. Expert visual scoring of derived diffusion maps is significantly higher for the median than for the mean, with modest improvement from the trimmed mean. Diffusion metrics derived from mono- and bi-exponential diffusion models are comparable for non-moving structures, demonstrating a lack of introduced bias from using the median. The use of the median is a simple and computationally inexpensive alternative to complex and expensive registration algorithms, requiring only additional data storage (and no additional scanning time) while returning visually superior images that will facilitate the appropriate placement of regions-of-interest when analysing abdominal diffusion-weighted magnetic resonance images, for assessment of disease characteristics and treatment response.

Modeling and Measuring the Effects of Radiation Damage Annealing on Helium Diffusion Kinetics in Apatite

NASA Astrophysics Data System (ADS)

Willett, C. D.; Fox, M.; Shuster, D. L.

2016-12-01

Understanding helium diffusion kinetics in apatite is critical for the accurate interpretation of (U-Th)/He thermochronometric data. This problem is complicated by the observation that helium diffusivity is not a simple function of temperature, but may evolve as a function of damage to the apatite crystal lattice resulting from alpha recoil. This `radiation damage' increases as a function of the amount of radiometric parent products, or effective uranium concentration, and time, but decreases due to thermal annealing of damage, necessitating a detailed understanding of radiation damage production and annealing in cases of burial heating over geologic timescales. Published observations [1,2] suggest that annealing rates of damage caused by alpha recoil and fission tracks in apatite differ. Existing models, however, assume the diffusion kinetics resulting from the two sources of damage are identical [3], demonstrating the need for further investigation of these damage sources. We present modeling and experimental work designed to interrogate the effects of radiation damage and its annealing on helium diffusion kinetics in apatite. Using previously published results [4] that investigated the effects of annealing temperature and duration on measured helium diffusivity, we fit a set of functions that are then integrated into a numerical model that tracks the evolution of radiation damage and apparent (U-Th)/He age. We compare the results of this model calibration to existing models [3]. In addition, we present data from two suites of diffusion experiments. The first suite, intended to test the published methodology and results, uses Durango apatite, while the second uses Sierran (CA) granite as a first test to determine if apatite of varying chemistry and age responds differently to the thermal annealing of radiation damage. Ultimately, the updated model and experimental results will benefit the interpretation of the effects of radiation damage accumulation and annealing in apatite and expand the range of geologic settings that can be studied using low-temperature thermochronology. References: [1] Fox, M., Shuster, D. (2014), EPSL 397, 174-183; [2] Gautheron, C. et al. (2013), Chem. Geol. 351, 257-267; [3] Flowers, R. et al. (2009), GCA 73, 2347-2365; [4] Shuster, D., Farley, K. (2009), GCA 73, 6183-6196.

Discrete effect on the halfway bounce-back boundary condition of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations.

PubMed

Cui, Shuqi; Hong, Ning; Shi, Baochang; Chai, Zhenhua

2016-04-01

In this paper, we will focus on the multiple-relaxation-time (MRT) lattice Boltzmann model for two-dimensional convection-diffusion equations (CDEs), and analyze the discrete effect on the halfway bounce-back (HBB) boundary condition (or sometimes called bounce-back boundary condition) of the MRT model where three different discrete velocity models are considered. We first present a theoretical analysis on the discrete effect of the HBB boundary condition for the simple problems with a parabolic distribution in the x or y direction, and a numerical slip proportional to the second-order of lattice spacing is observed at the boundary, which means that the MRT model has a second-order convergence rate in space. The theoretical analysis also shows that the numerical slip can be eliminated in the MRT model through tuning the free relaxation parameter corresponding to the second-order moment, while it cannot be removed in the single-relaxation-time model or the Bhatnagar-Gross-Krook model unless the relaxation parameter related to the diffusion coefficient is set to be a special value. We then perform some simulations to confirm our theoretical results, and find that the numerical results are consistent with our theoretical analysis. Finally, we would also like to point out the present analysis can be extended to other boundary conditions of lattice Boltzmann models for CDEs.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Word of Mouth : An Agent-based Approach to Predictability of Stock Prices

NASA Astrophysics Data System (ADS)

Shimokawa, Tetsuya; Misawa, Tadanobu; Watanabe, Kyoko

This paper addresses how communication processes among investors affect stock prices formation, especially emerging predictability of stock prices, in financial markets. An agent based model, called the word of mouth model, is introduced for analyzing the problem. This model provides a simple, but sufficiently versatile, description of informational diffusion process and is successful in making lucidly explanation for the predictability of small sized stocks, which is a stylized fact in financial markets but difficult to resolve by traditional models. Our model also provides a rigorous examination of the under reaction hypothesis to informational shocks.

Numerical calculation on a two-step subdiffusion behavior of lateral protein movement in plasma membranes

NASA Astrophysics Data System (ADS)

Sumi, Tomonari; Okumoto, Atsushi; Goto, Hitoshi; Sekino, Hideo

2017-10-01

A two-step subdiffusion behavior of lateral movement of transmembrane proteins in plasma membranes has been observed by using single-molecule experiments. A nested double-compartment model where large compartments are divided into several smaller ones has been proposed in order to explain this observation. These compartments are considered to be delimited by membrane-skeleton "fences" and membrane-protein "pickets" bound to the fences. We perform numerical simulations of a master equation using a simple two-dimensional lattice model to investigate the heterogeneous diffusion dynamics behavior of transmembrane proteins within plasma membranes. We show that the experimentally observed two-step subdiffusion process can be described using fence and picket models combined with decreased local diffusivity of transmembrane proteins in the vicinity of the pickets. This allows us to explain the two-step subdiffusion behavior without explicitly introducing nested double compartments.

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

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

NASA Astrophysics Data System (ADS)

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

2008-08-01

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

Fluorescence Diffusion in the Presence of Optically Clear Tissues in a Mouse Head Model.

PubMed

Ancora, Daniele; Zacharopoulos, Athanasios; Ripoll, Jorge; Zacharakis, Giannis

2017-05-01

Diffuse Optical Tomography commonly neglects or assumes as insignificant the presence of optically clear regions in biological tissues, estimating their contribution as a small perturbation to light transport. The inaccuracy introduced by this practice is examined in detail in the context of a complete, based on realistic geometry, virtual fluorescence Diffuse Optical Tomography experiment where a mouse head is imaged in the presence of cerebral spinal fluid. Despite the small thickness of such layer, we point out that an error is introduced when neglecting it from the model with possibly reduction in the accuracy of the reconstruction and localization of the fluorescence distribution within the brain. The results obtained in the extensive study presented here suggest that fluorescence diffuse neuroimaging studies can be improved in terms of quantitative and qualitative reconstruction by accurately taking into account optically transparent regions especially in the cases where the reconstruction is aided by the prior knowledge of the structural geometry of the specimen. Thus, this has only recently become an affordable choice, thanks to novel computation paradigms that allow to run Monte Carlo photon propagation on a simple graphic card, hence speeding up the process a thousand folds compared to CPU-based solutions.

Modeling Bimolecular Reactive Transport With Mixing-Limitation: Theory and Application to Column Experiments

NASA Astrophysics Data System (ADS)

Ginn, T. R.

2018-01-01

The challenge of determining mixing extent of solutions undergoing advective-dispersive-diffusive transport is well known. In particular, reaction extent between displacing and displaced solutes depends on mixing at the pore scale, that is, generally smaller than continuum scale quantification that relies on dispersive fluxes. Here a novel mobile-mobile mass transfer approach is developed to distinguish diffusive mixing from dispersive spreading in one-dimensional transport involving small-scale velocity variations with some correlation, such as occurs in hydrodynamic dispersion, in which short-range ballistic transports give rise to dispersed but not mixed segregation zones, termed here ballisticules. When considering transport of a single solution, this approach distinguishes self-diffusive mixing from spreading, and in the case of displacement of one solution by another, each containing a participant reactant of an irreversible bimolecular reaction, this results in time-delayed diffusive mixing of reactants. The approach generates models for both kinetically controlled and equilibrium irreversible reaction cases, while honoring independently measured reaction rates and dispersivities. The mathematical solution for the equilibrium case is a simple analytical expression. The approach is applied to published experimental data on bimolecular reactions for homogeneous porous media under postasymptotic dispersive conditions with good results.

On high b diffusion imaging in the human brain: ruminations and experimental insights.

PubMed

Mulkern, Robert V; Haker, Steven J; Maier, Stephan E

2009-10-01

Interest in the manner in which brain tissue signal decays with b factor in diffusion imaging schemes has grown in recent years following the observation that the decay curves depart from purely monoexponential decay behavior. Regardless of the model or fitting function proposed for characterizing sufficiently sampled decay curves (vide infra), the departure from monoexponentiality spells increased tissue characterization potential. The degree to which this potential can be harnessed to improve specificity, sensitivity and spatial localization of diseases in brain, and other tissues, largely remains to be explored. Furthermore, the degree to which currently popular diffusion tensor imaging methods, including visually impressive white matter fiber "tractography" results, have almost completely ignored the nonmonoexponential nature of the basic signal decay with b factor is worthy of communal introspection. Here we limit our attention to a review of the basic experimental features associated with brain water signal diffusion decay curves as measured over extended b-factor ranges, the simple few parameter fitting functions that have been proposed to characterize these decays and the more involved models, e.g.,"ruminations," which have been proposed to account for the nonmonoexponentiality to date.

On high b diffusion imaging in the human brain: ruminations and experimental insights✩

PubMed Central

Mulkern, Robert V.; Haker, Steven J.; Maier, Stephan E.

2010-01-01

Interest in the manner in which brain tissue signal decays with b factor in diffusion imaging schemes has grown in recent years following the observation that the decay curves depart from purely monoexponential decay behavior. Regardless of the model or fitting function proposed for characterizing sufficiently sampled decay curves (vide infra), the departure from monoexponentiality spells increased tissue characterization potential. The degree to which this potential can be harnessed to improve specificity, sensitivity and spatial localization of diseases in brain, and other tissues, largely remains to be explored. Furthermore, the degree to which currently popular diffusion tensor imaging methods, including visually impressive white matter fiber “tractography” results, have almost completely ignored the nonmonoexponential nature of the basic signal decay with b factor is worthy of communal introspection. Here we limit our attention to a review of the basic experimental features associated with brain water signal diffusion decay curves as measured over extended b-factor ranges, the simple few parameter fitting functions that have been proposed to characterize these decays and the more involved models, e.g.,“ruminations,” which have been proposed to account for the nonmonoexponentiality to date. PMID:19520535

Quantitative confirmation of diffusion-limited oxidation theories

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

Gillen, K.T.; Clough, R.L.

1990-01-01

Diffusion-limited (heterogeneous) oxidation effects are often important for studies of polymer degradation. Such effects are common in polymers subjected to ionizing radiation at relatively high dose rate. To better understand the underlying oxidation processes and to aid in the planning of accelerated aging studies, it would be desirable to be able to monitor and quantitatively understand these effects. In this paper, we briefly review a theoretical diffusion approach which derives model profiles for oxygen surrounded sheets of material by combining oxygen permeation rates with kinetically based oxygen consumption expressions. The theory leads to a simple governing expression involving the oxygenmore » consumption and permeation rates together with two model parameters {alpha} and {beta}. To test the theory, gamma-initiated oxidation of a sheet of commercially formulated EPDM rubber was performed under conditions which led to diffusion-limited oxidation. Profile shapes from the theoretical treatments are shown to accurately fit experimentally derived oxidation profiles. In addition, direct measurements on the same EPDM material of the oxygen consumption and permeation rates, together with values of {alpha} and {beta} derived from the fitting procedure, allow us to quantitatively confirm for the first time the governing theoretical relationship. 17 refs., 3 figs.« less

Sensitivity studies and a simple ozone perturbation experiment with a truncated two-dimensional model of the stratosphere

NASA Technical Reports Server (NTRS)

Stordal, Frode; Garcia, Rolando R.

1987-01-01

The 1-1/2-D model of Holton (1986), which is actually a highly truncated two-dimensional model, describes latitudinal variations of tracer mixing ratios in terms of their projections onto second-order Legendre polynomials. The present study extends the work of Holton by including tracers with photochemical production in the stratosphere (O3 and NOy). It also includes latitudinal variations in the photochemical sources and sinks, improving slightly the calculated global mean profiles for the long-lived tracers studied by Holton and improving substantially the latitudinal behavior of ozone. Sensitivity tests of the dynamical parameters in the model are performed, showing that the response of the model to changes in vertical residual meridional winds and horizontal diffusion coefficients is similar to that of a full two-dimensional model. A simple ozone perturbation experiment shows the model's ability to reproduce large-scale latitudinal variations in total ozone column depletions as well as ozone changes in the chemically controlled upper stratosphere.

Epithelial cancers and photon migration: Monte Carlo simulations and diffuse reflectance measurements

NASA Astrophysics Data System (ADS)

Tubiana, Jerome; Kass, Alex J.; Newman, Maya Y.; Levitz, David

2015-07-01

Detecting pre-cancer in epithelial tissues such as the cervix is a challenging task in low-resources settings. In an effort to achieve low cost cervical cancer screening and diagnostic method for use in low resource settings, mobile colposcopes that use a smartphone as their engine have been developed. Designing image analysis software suited for this task requires proper modeling of light propagation from the abnormalities inside tissues to the camera of the smartphones. Different simulation methods have been developed in the past, by solving light diffusion equations, or running Monte Carlo simulations. Several algorithms exist for the latter, including MCML and the recently developed MCX. For imaging purpose, the observable parameter of interest is the reflectance profile of a tissue under some specific pattern of illumination and optical setup. Extensions of the MCX algorithm to simulate this observable under these conditions were developed. These extensions were validated against MCML and diffusion theory for the simple case of contact measurements, and reflectance profiles under colposcopy imaging geometry were also simulated. To validate this model, the diffuse reflectance profiles of tissue phantoms were measured with a spectrometer under several illumination and optical settings for various homogeneous tissues phantoms. The measured reflectance profiles showed a non-trivial deviation across the spectrum. Measurements of an added absorber experiment on a series of phantoms showed that absorption of dye scales linearly when fit to both MCX and diffusion models. More work is needed to integrate a pupil into the experiment.

Diffusion coefficients of water in biobased hydrogel polymer matrices by nuclear magnetic resonance imaging

USDA-ARS?s Scientific Manuscript database

The diffusion coefficient of water in biobased hydrogels were measured utilizing a simple NMR method. This method tracks the migration of deuterium oxide through imaging data that is fit to a diffusion equation. The results show that a 5 wt% soybean oil based hydrogel gives aqueous diffusion of 1.37...

Preparation of char from lotus seed biomass and the exploration of its dye removal capacity through batch and column adsorption studies.

PubMed

Nethaji, S; Sivasamy, A; Kumar, R Vimal; Mandal, A B

2013-06-01

Char was obtained from lotus seed biomass by a simple single-step acid treatment process. It was used as an adsorbent for the removal of malachite green dye (MG) from simulated dye bath effluent. The adsorbent was characterized for its surface morphology, surface functionalities, and zero point charge. Batch studies were carried out by varying the parameters such as initial aqueous pH, adsorbent dosage, adsorbent particle size, and initial adsorbate concentration. Langmuir and Freundlich isotherms were used to test the isotherm data and the Freundlich isotherm best fitted the data. Thermodynamic studies were carried out and the thermodynamic parameters such as ∆G, ∆H, and ∆S were evaluated. Adsorption kinetics was carried out and the data were tested with pseudofirst-order model, pseudosecond-order model, and intraparticle diffusion model. Adsorption of MG was not solely by intraparticle diffusion but film diffusion also played a major role. Continuous column experiments were also conducted using microcolumn and the spent adsorbent was regenerated using ethanol and was repeatedly used for three cycles in the column to determine the reusability of the regenerated adsorbent. The column data were modeled with the modeling equations such as Adam-Bohart model, Bed Depth Service Time (BDST) model, and Yoon-Nelson model for all the three cycles.

Modeling the drug transport in the anterior segment of the eye.

PubMed

Avtar, Ram; Tandon, Deepti

2008-10-02

The aim of the present work is the development of a simple mathematical model for the time course concentration profile of topically administered drugs in the anterior chamber aqueous humor and investigation of the effects of various model parameters on the aqueous humor concentration of lipophilic and hydrophilic drugs. A simple pharmacokinetic model for the transient drug transport in the anterior segment has been developed by using the conservation of mass in the precorneal tear film, Fick's law of diffusion and Michaelis-Menten kinetics of drug metabolism in cornea, and the conservation of mass in the anterior chamber. An analytical solution describing the drug concentration in the anterior chamber has been obtained. The model predicts that an increase in the drug metabolic (consumption) rate in the corneal epithelium reduces the drug concentration in the anterior chamber for both lipophilic and hydrophilic molecules. A decrease in the clearance rate and distribution volume of the drug in the anterior chamber raises the aqueous humor concentration significantly. It is also observed that decay rate of drug concentration in the anterior chamber is higher for lipophilic molecules than that for hydrophilic molecules. The bioavailability of drugs applied topically to the eye may be improved by a rise in the precorneal tear volume, diffusion coefficient in corneal epithelium and distribution coefficient across the endothelium anterior chamber interface, and by reducing the drug metabolism, drug clearance rate and distribution volume in anterior chamber.

The Controversial Role of Inter-diffusion in Glass Alteration

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

Gin, Stephane; Neill, Lindsay; Fournier, M.

2016-11-15

Current kinetic models for nuclear waste glasses (e.g. GM2001, GRAAL) are based on a set of mechanisms that have been generally agreed upon within the international waste glass community. These mechanisms are: hydration of the glass, ion exchange reactions (the two processes are referred as inter-diffusion), hydrolysis of the silicate network, and condensation/precipitation of partly or completely hydrolyzed species that produces a porous and amorphous layer and crystalline phases on surface of the altered glass. Recently, a new idea with origins in the mineral dissolution community has been proposed that excludes inter-diffusion process as a potential rate-limiting mechanism. To understandmore » how the so-called interfacial dissolution/precipitation model can change the current understanding of glass behavior, a key experiment used to account for this model was replicated to further revisit the interpretation. This experiment was performed at 50°C, with SON68 glass, in static mode, deionized water and S/V ratio of 10 m-1 for 6 months. It turn out that glass alters in an intermediate kinetic regime between the forward and the residual rate. According to previous and new solid characterizations, it is concluded that neither a simple inter-diffusion model nor the interfacial dissolution precipitation model can account for the observed elemental profiles within the alteration layer. More generally, far and close-to-saturation conditions must be distinguished and literature provides evidences that inter-diffusion takes place in slightly acidic conditions and far from saturation. However, closer to saturation, when a sufficiently dense layer is formed, a new approach is proposed requiring a full description of chemical reactions taking place within the alteration layer and involving water molecules as it is thought that water accessibility to the pristine glass is the rate-limiting process.« less

On the Chemical Mixing Induced by Internal Gravity Waves

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

Rogers, T. M.; McElwaine, J. N.

Detailed modeling of stellar evolution requires a better understanding of the (magneto)hydrodynamic processes that mix chemical elements and transport angular momentum. Understanding these processes is crucial if we are to accurately interpret observations of chemical abundance anomalies, surface rotation measurements, and asteroseismic data. Here, we use two-dimensional hydrodynamic simulations of the generation and propagation of internal gravity waves in an intermediate-mass star to measure the chemical mixing induced by these waves. We show that such mixing can generally be treated as a diffusive process. We then show that the local diffusion coefficient does not depend on the local fluid velocity,more » but rather on the wave amplitude. We then use these findings to provide a simple parameterization for this diffusion, which can be incorporated into stellar evolution codes and tested against observations.« less

Interfacial layers in high-temperature-oxidized NiCrAl

NASA Technical Reports Server (NTRS)

Larson, L. A.; Browning, R.; Poppa, H.; Smialek, J.

1983-01-01

The utility of Auger electron spectroscopy combined with ball cratering for depth analysis of oxide and diffusion layers produced in a Ni-14Cr-24Al alloy by oxidation in air at 1180 C for 25 hr is demonstrated. During postoxidation cooling, the oxide layers formed by this alloy spalled profusely. The remaining very thin oxide was primarily Cr2O3 with a trace of Ni. The underlying metal substrate exhibited gamma/gamma-prime and beta phases with a metallic interfacial layer which was similar to the bulk gamma/gamma-prime phase but slightly enriched in Cr and Al. These data are compared to electron microprobe results from a nominally identical alloy. The diffusion layer thickness is modelled with a simple mass balance equation and compared to recent results on the diffusion process in NiCrAl alloys.

Plasma transport in the Io torus - The importance of microscopic diffusion

NASA Technical Reports Server (NTRS)

Mei, YI; Thorne, Richard M.

1991-01-01

This paper considers the question of whether the distribution of mass in the Io plasma torus is consistent with the concept of interchange eddy transport. Specifically, the flux tube content exhibits a gradual decrease with increasing radial distance from the source near Io without any evidence for substantial density irregularity associated with the plasma source or loss. Using a simple one-dimensional numerical model to simulate macroscopic interchange eddy transport, it is demonstrated that this smooth equilibrium distribution of mass can occur but only with the inclusion of a minimal level of small scale microscopic mixing at a rate approaching Bohm diffusion. Otherwise, the system exhibits a chaotic appearance which never approaches an equilibrium distribution. Various physical mechanisms for the microscopic diffusion process which is required to provide a sufficiently rapid mixing of material between the macroscopic eddies are discussed.

Modeling of electron behaviors under microwave electric field in methane and air pre-mixture gas plasma assisted combustion

NASA Astrophysics Data System (ADS)

Akashi, Haruaki; Sasaki, K.; Yoshinaga, T.

2011-10-01

Recently, plasma-assisted combustion has been focused on for achieving more efficient combustion way of fossil fuels, reducing pollutants and so on. Shinohara et al has reported that the flame length of methane and air premixed burner shortened by irradiating microwave power without increase of gas temperature. This suggests that electrons heated by microwave electric field assist the combustion. They also measured emission from 2nd Positive Band System (2nd PBS) of nitrogen during the irradiation. To clarify this mechanism, electron behavior under microwave power should be examined. To obtain electron transport parameters, electron Monte Carlo simulations in methane and air mixture gas have been done. A simple model has been developed to simulate inside the flame. To make this model simple, some assumptions are made. The electrons diffuse from the combustion plasma region. And the electrons quickly reach their equilibrium state. And it is found that the simulated emission from 2nd PBS agrees with the experimental result. Recently, plasma-assisted combustion has been focused on for achieving more efficient combustion way of fossil fuels, reducing pollutants and so on. Shinohara et al has reported that the flame length of methane and air premixed burner shortened by irradiating microwave power without increase of gas temperature. This suggests that electrons heated by microwave electric field assist the combustion. They also measured emission from 2nd Positive Band System (2nd PBS) of nitrogen during the irradiation. To clarify this mechanism, electron behavior under microwave power should be examined. To obtain electron transport parameters, electron Monte Carlo simulations in methane and air mixture gas have been done. A simple model has been developed to simulate inside the flame. To make this model simple, some assumptions are made. The electrons diffuse from the combustion plasma region. And the electrons quickly reach their equilibrium state. And it is found that the simulated emission from 2nd PBS agrees with the experimental result. This work was supported by KAKENHI (22340170).

18O-tracer diffusion along nanoscaled Sc2O3/yttria stabilized zirconia (YSZ) multilayers: on the influence of strain.

PubMed

Aydin, Halit; Korte, Carsten; Janek, Jürgen

2013-06-01

The oxygen tracer diffusion coefficient describing transport along nano-/microscaled YSZ/Sc 2 O 3 multilayers as a function of the thick-ness of the ion-conducting YSZ layers has been measured by isotope exchange depth profiling (IEDP), using secondary ion mass spec-trometry (SIMS). The multilayer samples were prepared by pulsed laser deposition (PLD) on (0001) Al 2 O 3 single crystalline substrates. The values for the oxygen tracer diffusion coefficient were analyzed as a combination of contributions from bulk and interface contributions and compared with results from YSZ/Y 2 O 3 -multilayers with similar microstructure. Using the Nernst-Einstein equation as the relation between diffusivity and electrical conductivity we find very good agreement between conductivity and diffusion data, and we exclude substantial electronic conductivity in the multilayers. The effect of hetero-interface transport can be well explained by a simple interface strain model. As the multilayer samples consist of columnar film crystallites with a defined inter-face structure and texture, we also discuss the influence of this particular microstructure on the interfacial strain.

Communication: Diverse nanoscale cluster dynamics: Diffusion of 2D epitaxial clusters

NASA Astrophysics Data System (ADS)

Lai, King C.; Evans, James W.; Liu, Da-Jiang

2017-11-01

The dynamics of nanoscale clusters can be distinct from macroscale behavior described by continuum formalisms. For diffusion of 2D clusters of N atoms in homoepitaxial systems mediated by edge atom hopping, macroscale theory predicts simple monotonic size scaling of the diffusion coefficient, DN ˜ N-β, with β = 3/2. However, modeling for nanoclusters on metal(100) surfaces reveals that slow nucleation-mediated diffusion displaying weak size scaling β < 1 occurs for "perfect" sizes Np = L2 and L(L+1) for integer L = 3,4,… (with unique square or near-square ground state shapes), and also for Np+3, Np+4,…. In contrast, fast facile nucleation-free diffusion displaying strong size scaling β ≈ 2.5 occurs for sizes Np+1 and Np+2. DN versus N oscillates strongly between the slowest branch (for Np+3) and the fastest branch (for Np+1). All branches merge for N = O(102), but macroscale behavior is only achieved for much larger N = O(103). This analysis reveals the unprecedented diversity of behavior on the nanoscale.

Three-compartment model for contaminant accumulation by semipermeable membrane devices

USGS Publications Warehouse

Gale, Robert W.

1998-01-01

Passive sampling of dissolved hydrophobic contaminants with lipid (triolein)-containing semipermeable membrane devices (SPMDs) has been gaining acceptance for environmental monitoring. Understanding of the accumulation process has employed a simple polymer film-control model of uptake by the polymer-enclosed lipid, while aqueous film control has been only briefly discussed. A more complete three-compartment model incorporating both aqueous film (turbulent-diffusive) and polymer film (diffusive) mass transfer is developed here and is fit to data from accumulation studies conducted in constant-concentration, flow-through dilutors. This model predicts aqueous film control of the whole device for moderate to high Kow compounds, rather than polymer film control. Uptake rates for phenanthrene and 2,2‘,5,5‘-tetrachlorobiphenyl were about 4.8 and 4.2 L/day/standard SPMD, respectively. Maximum 28 day SPMD concentration factors of 30 000 are predicted for solutes with log Kow values of >5.5. Effects of varying aqueous and polymer film thicknesses and solute diffusivities in the polymer film are modeled, and overall accumulation by the whole device is predicted to remain under aqueous film control, although accumulation in the triolein may be subject to polymer film control. The predicted half-life and integrative response of SPMDs to pulsed concentration events is proportional to log KSPMD.

A predictive parameter estimation approach for the thermodynamically constrained averaging theory applied to diffusion in porous media

NASA Astrophysics Data System (ADS)

Valdes-Parada, F. J.; Ostvar, S.; Wood, B. D.; Miller, C. T.

2017-12-01

Modeling of hierarchical systems such as porous media can be performed by different approaches that bridge microscale physics to the macroscale. Among the several alternatives available in the literature, the thermodynamically constrained averaging theory (TCAT) has emerged as a robust modeling approach that provides macroscale models that are consistent across scales. For specific closure relation forms, TCAT models are expressed in terms of parameters that depend upon the physical system under study. These parameters are usually obtained from inverse modeling based upon either experimental data or direct numerical simulation at the pore scale. Other upscaling approaches, such as the method of volume averaging, involve an a priori scheme for parameter estimation for certain microscale and transport conditions. In this work, we show how such a predictive scheme can be implemented in TCAT by studying the simple problem of single-phase passive diffusion in rigid and homogeneous porous media. The components of the effective diffusivity tensor are predicted for several porous media by solving ancillary boundary-value problems in periodic unit cells. The results are validated through a comparison with data from direct numerical simulation. This extension of TCAT constitutes a useful advance for certain classes of problems amenable to this estimation approach.

On extreme points of the diffusion polytope

DOE PAGES

Hay, M. J.; Schiff, J.; Fisch, N. J.

2017-01-04

Here, we consider a class of diffusion problems defined on simple graphs in which the populations at any two vertices may be averaged if they are connected by an edge. The diffusion polytope is the convex hull of the set of population vectors attainable using finite sequences of these operations. A number of physical problems have linear programming solutions taking the diffusion polytope as the feasible region, e.g. the free energy that can be removed from plasma using waves, so there is a need to describe and enumerate its extreme points. We also review known results for the case ofmore » the complete graph Kn, and study a variety of problems for the path graph Pn and the cyclic graph Cn. Finall, we describe the different kinds of extreme points that arise, and identify the diffusion polytope in a number of simple cases. In the case of increasing initial populations on Pn the diffusion polytope is topologically an n-dimensional hypercube.« less

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

Optical response of photopolymer materials for holographic data storage applications.

PubMed

Sheridan, J T; Gleeson, M R; Close, C E; Kelly, J V

2007-01-01

We briefly review the application of photopolymer recording materials in the area of holographic data storage. In particular we discuss the recent development of the Non-local Polymerisation Driven Diffusion model. Applying this model we develop simple first-order analytic expressions describing the spatial frequency response of photopolymer materials. The assumptions made in the derivation of these formulae are described and their ranges of validity are examined. The effects of particular physical parameters of a photopolymer on the material response are discussed.

The effect of shear flow on the rotational diffusivity of a single axisymmetric particle

NASA Astrophysics Data System (ADS)

Leahy, Brian; Koch, Donald; Cohen, Itai

2014-11-01

Colloidal suspensions of nonspherical particles abound in the world around us, from red blood cells in arteries to kaolinite discs in clay. Understanding the orientation dynamics of these particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in simple shear flow, the orientation dynamics of Brownian nonspherical particles are poorly understood at large shear rates. Here, we analytically calculate the time-dependent orientation distributions of particles confined to the flow-gradient plane when the rotary diffusion is small but nonzero. For both startup and oscillatory shear flows, we find a coordinate change that maps the convection-diffusion equation to a simple diffusion equation with an enhanced diffusion constant, simplifying the orientation dynamics. For oscillatory shear, this enhanced diffusion drastically alters the quasi-steady orientation distributions. Our theory of the unsteady orientation dynamics provides an understanding of a nonspherical particle suspension's rheology for a large class of unsteady flows. For particles with aspect ratio 10 under oscillatory shear, the rotary diffusion and intrinsic viscosity vary with amplitude by a factor of ~ 40 and ~ 2 , respectively.

In vivo burn diagnosis by camera-phone diffuse reflectance laser speckle detection.

PubMed

Ragol, S; Remer, I; Shoham, Y; Hazan, S; Willenz, U; Sinelnikov, I; Dronov, V; Rosenberg, L; Bilenca, A

2016-01-01

Burn diagnosis using laser speckle light typically employs widefield illumination of the burn region to produce two-dimensional speckle patterns from light backscattered from the entire irradiated tissue volume. Analysis of speckle contrast in these time-integrated patterns can then provide information on burn severity. Here, by contrast, we use point illumination to generate diffuse reflectance laser speckle patterns of the burn. By examining spatiotemporal fluctuations in these time-integrated patterns along the radial direction from the incident point beam, we show the ability to distinguish partial-thickness burns in a porcine model in vivo within the first 24 hours post-burn. Furthermore, our findings suggest that time-integrated diffuse reflectance laser speckle can be useful for monitoring burn healing over time post-burn. Unlike conventional diffuse reflectance laser speckle detection systems that utilize scientific or industrial-grade cameras, our system is designed with a camera-phone, demonstrating the potential for burn diagnosis with a simple imager.

Microscopic origin and macroscopic implications of lane formation in mixtures of oppositely-driven particles

NASA Astrophysics Data System (ADS)

Whitelam, Stephen

Colloidal particles of two types, driven in opposite directions, can segregate into lanes. I will describe some results on this phenomenon obtained by simple physical arguments and computer simulations. Laning results from rectification of diffusion on the scale of a particle diameter: oppositely-driven particles must, in the time taken to encounter each other in the direction of the drive, diffuse in the perpendicular direction by about one particle diameter. This geometric constraint implies that the diffusion constant of a particle, in the presence of those of the opposite type, grows approximately linearly with Peclet number, a prediction confirmed by our numerics. Such environment-dependent diffusion is statistically similar to an effective interparticle attraction; consistent with this observation, we find that oppositely-driven colloids display features characteristic of the simplest model system possessing both interparticle attractions and persistent motion, the driven Ising lattice gas. Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

In vivo burn diagnosis by camera-phone diffuse reflectance laser speckle detection

PubMed Central

Ragol, S.; Remer, I.; Shoham, Y.; Hazan, S.; Willenz, U.; Sinelnikov, I.; Dronov, V.; Rosenberg, L.; Bilenca, A.

2015-01-01

Burn diagnosis using laser speckle light typically employs widefield illumination of the burn region to produce two-dimensional speckle patterns from light backscattered from the entire irradiated tissue volume. Analysis of speckle contrast in these time-integrated patterns can then provide information on burn severity. Here, by contrast, we use point illumination to generate diffuse reflectance laser speckle patterns of the burn. By examining spatiotemporal fluctuations in these time-integrated patterns along the radial direction from the incident point beam, we show the ability to distinguish partial-thickness burns in a porcine model in vivo within the first 24 hours post-burn. Furthermore, our findings suggest that time-integrated diffuse reflectance laser speckle can be useful for monitoring burn healing over time post-burn. Unlike conventional diffuse reflectance laser speckle detection systems that utilize scientific or industrial-grade cameras, our system is designed with a camera-phone, demonstrating the potential for burn diagnosis with a simple imager. PMID:26819831

Diffusion processes in tumors: A nuclear medicine approach

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

Amaya, Helman, E-mail: haamayae@unal.edu.co

The number of counts used in nuclear medicine imaging techniques, only provides physical information about the desintegration of the nucleus present in the the radiotracer molecules that were uptaken in a particular anatomical region, but that information is not a real metabolic information. For this reason a mathematical method was used to find a correlation between number of counts and {sup 18}F-FDG mass concentration. This correlation allows a better interpretation of the results obtained in the study of diffusive processes in an agar phantom, and based on it, an image from the PETCETIX DICOM sample image set from OsiriX-viewer softwaremore » was processed. PET-CT gradient magnitude and Laplacian images could show direct information on diffusive processes for radiopharmaceuticals that enter into the cells by simple diffusion. In the case of the radiopharmaceutical {sup 18}F-FDG is necessary to include pharmacokinetic models, to make a correct interpretation of the gradient magnitude and Laplacian of counts images.« less

The effects of heterogeneities on memory-dependent diffusion

NASA Astrophysics Data System (ADS)

Adib, Farhad; Neogi, P.

1993-07-01

Case II diffusion is often seen in glassy polymers, where the mass uptake in sorption is proportional to time t instead of sqrt{t}. A memory dependent diffusion is needed to explain such effects, where the relaxation function used to describe the memory effect has a characteristic time. The ratio of this time to the overall diffusion times is the diffusional Deborah number. Simple models show that case II results when the Deborah number is around one, that is, when the two time scales are comparable. Under investigation are the possible effects of the fact that the glassy polymers are heterogeneous over molecular scales. The averaging form given by DiMarzio and Sanchez has been used to obtain the averaged response. The calculated dynamics of sorption show that whereas case II is still observed, the long term tails change dramatically from the oscillatory to torpid, to chaotic, which are all observed in the experiments. The Deborah number defined here in a self-consistent manner collapses in those cases, but causes no other ill-effects.

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

A Simple Noise Correction Scheme for Diffusional Kurtosis Imaging

PubMed Central

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

2014-01-01

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

Study of kinetic desorption rate constant in fish muscle and agarose gel model using solid phase microextraction coupled with liquid chromatography with tandem mass spectrometry.

PubMed

Togunde, Oluranti Paul; Oakes, Ken; Servos, Mark; Pawliszyn, Janusz

2012-09-12

This study aims to use solid phase microextraction (SPME), a simple tool to investigate diffusion rate (time) constant of selected pharmaceuticals in gel and fish muscle by comparing desorption rate of diffusion of the drugs in both agarose gel prepared with phosphate-buffered saline (PBS; pH 7.4) and fish muscle. The gel concentration (agarose gel model) that could be used to simulate tissue matrix (fish muscle) for free diffusion of drugs under in vitro and in vivo conditions was determined to model mass transfer phenomena between fibre polymer coating and environmental matrix such that partition coefficients and desorption time constant (diffusion coefficient) can be determined. SPME procedure involves preloading the extraction phase (fibre) with the standards from spiked PBS for 1h via direct extraction. Subsequently, the preloaded fibre is introduced to the sample such fish or agarose gel for specified time ranging from 0.5 to 60 h. Then, fibre is removed at specified time and desorbed in 100 μL of desorption solution (acetonitrile: water 1:1) for 90 min under agitation speed of 1000 rpm. The samples extract were immediately injected to the instrument and analysed using liquid chromatography coupled with tandem mass spectrometry (LC/MS/MS). The limit of detection of the method in gel and fish muscle was 0.01-0.07 ng mL(-1) and 0.07-0.34 ng g(-1), respectively, while the limit quantification was 0.10-0.20 ng mL(-1) in gel samples and 0.40-0.97 ng g(-1) in fish sample. The reproducibility of the method was good (5-15% RSD). The results suggest that kinetics of desorption of the compounds in fish tissue and different viscosity of gel can be determined using desorption time constant. In this study, desorption time constant which is directly related to desorption rate (diffusion kinetics) of selected drugs from the fibre to the gel matrix is faster as the viscosity of the gel matrix reduces from 2% (w/v) to 0.8% (w/v). As the concentration of gel reduces, viscosity of the gel will be reduced therefore allowing faster diffusion which invariably affect desorption time constant. Also, desorption time constant of model drugs in the fish muscle and 0.8-0.9% (w/v) gel model are similar based on free diffusion of studied compounds. In addition, in vitro and in vivo desorption time constant comparison shows that desorption time constant in an in vivo system (live fish muscle) is generally higher than an in vitro system (dead fish muscle) except for sertraline and nordiazepam. This study demonstrates SPME as a simple investigative tool to understand kinetics of desorption in an in vivo system with a goal to measure desorption rate of pharmaceuticals in fish. Copyright © 2011 Elsevier B.V. All rights reserved.

The Melting of Aqueous Foams

NASA Technical Reports Server (NTRS)

Durian, Douglas J.; Gopal, Anthony D.; Vera, Moin U.; Langer, Stephen A.

1996-01-01

Diffusing-wave spectroscopy measurements show that ordinarily solid aqueous foams flow by a series of stick-slip avalanche-like rearrangements of neighboring bubbles from one tight packing configuration to another. Contrary to a recent prediction, the distribution of avalanche sizes do not obey a power-law distribution characteristic of self-organized criticality. This can be understood from a simple model of foam mechanics based on bubble-bubble interactions.

Steady-state solution of the semi-empirical diffusion equation for area sources. [air pollution studies

NASA Technical Reports Server (NTRS)

Lebedeff, S. A.; Hameed, S.

1975-01-01

The problem investigated can be solved exactly in a simple manner if the equations are written in terms of a similarity variable. The exact solution is used to explore two questions of interest in the modelling of urban air pollution, taking into account the distribution of surface concentration downwind of an area source and the distribution of concentration with height.

Confinement regulates complex biochemical networks: initiation of blood clotting by "diffusion acting".

PubMed

Shen, Feng; Pompano, Rebecca R; Kastrup, Christian J; Ismagilov, Rustem F

2009-10-21

This study shows that environmental confinement strongly affects the activation of nonlinear reaction networks, such as blood coagulation (clotting), by small quantities of activators. Blood coagulation is sensitive to the local concentration of soluble activators, initiating only when the activators surpass a threshold concentration, and therefore is regulated by mass transport phenomena such as flow and diffusion. Here, diffusion was limited by decreasing the size of microfluidic chambers, and it was found that microparticles carrying either the classical stimulus, tissue factor, or a bacterial stimulus, Bacillus cereus, initiated coagulation of human platelet-poor plasma only when confined. A simple analytical argument and numerical model were used to describe the mechanism for this phenomenon: confinement causes diffusible activators to accumulate locally and surpass the threshold concentration. To interpret the results, a dimensionless confinement number, Cn, was used to describe whether a stimulus was confined, and a Damköhler number, Da(2), was used to describe whether a subthreshold stimulus could initiate coagulation. In the context of initiation of coagulation by bacteria, this mechanism can be thought of as "diffusion acting", which is distinct from "diffusion sensing". The ability of confinement and diffusion acting to change the outcome of coagulation suggests that confinement should also regulate other biological "on" and "off" processes that are controlled by thresholds.

A Physical Mechanism for the Asymmetry in Top-Down and Bottom-Up Diffusion.

NASA Astrophysics Data System (ADS)

Wyngaard, J. C.

1987-04-01

Recent large-eddy simulations of the vertical diffusion of a passive, conservative scalar through the convective boundary layer (CBL) show strikingly different eddy diffusivity profiles in the `top-down' and `bottom-up' cases. These results indicate that for a given turbulent velocity field and associated scalar flux, the mean change in scalar mixing ratio across the CBL is several times larger if the flux originates at the top of the boundary layer (i.e., in top-down diffusion) rather than at the bottom. The large-eddy simulation (LES) data show that this asymmetry is due to a breakdown of the eddy-diffusion concept.A simple updraft-downdraft model of the CBL reveals a physical mechanism that could cause this unexpected behavior. The large, positive skewness of the convectively driven vertical velocity gives an appreciably higher probability of downdrafts than updrafts; this excess probability of downdrafts, interacting with the time changes of the mean mixing ratio caused by the nonstationarity of the bottom-up and top-down diffusion processes, decreases the equilibrium value of mean mixing-ratio jump across the mixed layer in the bottom-up case and increases it in the top-down case. The resulting diffusion asymmetry agrees qualitatively with that found through LES.

Glassy Behavior due to Kinetic Constraints: from Topological Foam to Backgammon

NASA Astrophysics Data System (ADS)

Sherrington, David

A study is reported of a series of simple model systems with only non-interacting Hamiltonians, and hence simple equilibrium thermodynamics, but with constrained kinetics of a type initially suggested by topological considerations of foams and two-dimensional covalent glasses. It is demonstrated that oscopic dynamical features characteristic of real glasses, such as two-time decays in energy and auto-correlation functions, arise and may be understood in terms of annihilation-diffusion concepts and theory. This recognition leads to a sequence of further models which (i) encapsulate the essense but are more readily simulated and open to easier analytic study, and (ii) allow generalization and extension to higher dimension. Fluctuation-dissipation relations are also considered and show novel aspects. The comparison is with strong glasses.

The role of fractional calculus in modeling biological phenomena: A review

NASA Astrophysics Data System (ADS)

Ionescu, C.; Lopes, A.; Copot, D.; Machado, J. A. T.; Bates, J. H. T.

2017-10-01

This review provides the latest developments and trends in the application of fractional calculus (FC) in biomedicine and biology. Nature has often showed to follow rather simple rules that lead to the emergence of complex phenomena as a result. Of these, the paper addresses the properties in respiratory lung tissue, whose natural solutions arise from the midst of FC in the form of non-integer differ-integral solutions and non-integer parametric models. Diffusion of substances in human body, e.g. drug diffusion, is also a phenomena well known to be captured with such mathematical models. FC has been employed in neuroscience to characterize the generation of action potentials and spiking patters but also in characterizing bio-systems (e.g. vegetable tissues). Despite the natural complexity, biological systems belong as well to this class of systems, where FC has offered parsimonious yet accurate models. This review paper is a collection of results and literature reports who are essential to any versed engineer with multidisciplinary applications and bio-medical in particular.

Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios

NASA Astrophysics Data System (ADS)

Fakhari, Abbas; Bolster, Diogo

2017-04-01

We introduce a simple and efficient lattice Boltzmann method for immiscible multiphase flows, capable of handling large density and viscosity contrasts. The model is based on a diffuse-interface phase-field approach. Within this context we propose a new algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. The proposed method has superior computational accuracy compared with the common approach of approximating curved boundaries with stair cases. We test the model by applying it to four benchmark problems: (i) wetting and dewetting of a droplet on a flat surface and (ii) on a cylindrical surface, (iii) multiphase flow past a circular cylinder at an intermediate Reynolds number, and (iv) a droplet falling on hydrophilic and superhydrophobic circular cylinders under differing conditions. Where available, our results show good agreement with analytical solutions and/or existing experimental data, highlighting strengths of this new approach.

Detailed modeling analysis for soot formation and radiation in microgravity gas jet diffusion flames

NASA Technical Reports Server (NTRS)

Ku, Jerry C.; Tong, LI; Greenberg, Paul S.

1995-01-01

Radiation heat transfer in combustion systems has been receiving increasing interest. In the case of hydrocarbon fuels, a significant portion of the radiation comes from soot particles, justifying the need for detailed soot formation model and radiation transfer calculations. For laminar gas jet diffusion flames, results from this project (4/1/91 8/22/95) and another NASA study show that flame shape, soot concentration, and radiation heat fluxes are substantially different under microgravity conditions. Our emphasis is on including detailed soot transport models and a detailed solution for radiation heat transfer, and on coupling them with the flame structure calculations. In this paper, we will discuss the following three specific areas: (1) Comparing two existing soot formation models, and identifying possible improvements; (2) A simple yet reasonably accurate approach to calculating total radiative properties and/or fluxes over the spectral range; and (3) Investigating the convergence of iterations between the flame structure solver and the radiation heat transfer solver.

Estimating front-wave velocity of infectious diseases: a simple, efficient method applied to bluetongue.

PubMed

Pioz, Maryline; Guis, Hélène; Calavas, Didier; Durand, Benoît; Abrial, David; Ducrot, Christian

2011-04-20

Understanding the spatial dynamics of an infectious disease is critical when attempting to predict where and how fast the disease will spread. We illustrate an approach using a trend-surface analysis (TSA) model combined with a spatial error simultaneous autoregressive model (SAR(err) model) to estimate the speed of diffusion of bluetongue (BT), an infectious disease of ruminants caused by bluetongue virus (BTV) and transmitted by Culicoides. In a first step to gain further insight into the spatial transmission characteristics of BTV serotype 8, we used 2007-2008 clinical case reports in France and TSA modelling to identify the major directions and speed of disease diffusion. We accounted for spatial autocorrelation by combining TSA with a SAR(err) model, which led to a trend SAR(err) model. Overall, BT spread from north-eastern to south-western France. The average trend SAR(err)-estimated velocity across the country was 5.6 km/day. However, velocities differed between areas and time periods, varying between 2.1 and 9.3 km/day. For more than 83% of the contaminated municipalities, the trend SAR(err)-estimated velocity was less than 7 km/day. Our study was a first step in describing the diffusion process for BT in France. To our knowledge, it is the first to show that BT spread in France was primarily local and consistent with the active flight of Culicoides and local movements of farm animals. Models such as the trend SAR(err) models are powerful tools to provide information on direction and speed of disease diffusion when the only data available are date and location of cases.

LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions

NASA Astrophysics Data System (ADS)

Cristadoro, Giampaolo

2006-03-01

Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.

Theoretic criteria for antibody penetration into solid tumors and micrometastases.

PubMed

Thurber, Greg M; Zajic, Stefan C; Wittrup, K Dane

2007-06-01

Targeting tumors with antibody-based therapeutics is a complex task presenting multiple kinetic barriers. Antibody internalization and clearance inhibit uptake both in solid tumors, limited by tumor vascular permeability, and in micrometastases, limited by diffusion. A modeling exercise is used to introduce 2 simple criteria that must be less than unity for saturation of both tumors and micrometastases. The clearance modulus and the Thiele modulus are ratios of the plasma clearance rate and antibody catabolism, respectively, to the tumor tissue penetration rate. Even low rates of antigen internalization from constitutive membrane turnover can significantly retard antibody penetration. Rapid clearance of single-chain variable fragments also hinders uptake, often more than counterbalancing their more rapid extravasation and diffusion. The model illustrates that with the large resistance from the tumor capillary, antibodies may be more suitable for targeting micrometastases than vascularized tumors.

Probing the Interplay of Size, Shape, and Solution Environment in Macromolecular Diffusion Using a Simple Refraction Experiment

ERIC Educational Resources Information Center

Mankidy, Bijith D.; Coutinho, Cecil A.; Gupta, Vinay K.

2010-01-01

The diffusion coefficient of polymers is a critical parameter in biomedicine, catalysis, chemical separations, nanotechnology, and other industrial applications. Here, measurement of macromolecular diffusion in solutions is described using a visually instructive, undergraduate-level optical refraction experiment based on Weiner's method. To…

Modeling diffusion control on organic matter decomposition in unsaturated soil pore space

NASA Astrophysics Data System (ADS)

Vogel, Laure; Pot, Valérie; Garnier, Patricia; Vieublé-Gonod, Laure; Nunan, Naoise; Raynaud, Xavier; Chenu, Claire

2014-05-01

Soil Organic Matter decomposition is affected by soil structure and water content, but field and laboratory studies about this issue conclude to highly variable outcomes. Variability could be explained by the discrepancy between the scale at which key processes occur and the measurements scale. We think that physical and biological interactions driving carbon transformation dynamics can be best understood at the pore scale. Because of the spatial disconnection between carbon sources and decomposers, the latter rely on nutrient transport unless they can actively move. In hydrostatic case, diffusion in soil pore space is thus thought to regulate biological activity. In unsaturated conditions, the heterogeneous distribution of water modifies diffusion pathways and rates, thus affects diffusion control on decomposition. Innovative imaging and modeling tools offer new means to address these effects. We have developed a new model based on the association between a 3D Lattice-Boltzmann Model and an adimensional decomposition module. We designed scenarios to study the impact of physical (geometry, saturation, decomposers position) and biological properties on decomposition. The model was applied on porous media with various morphologies. We selected three cubic images of 100 voxels side from µCT-scanned images of an undisturbed soil sample at 68µm resolution. We used LBM to perform phase separation and obtained water phase distributions at equilibrium for different saturation indices. We then simulated the diffusion of a simple soluble substrate (glucose) and its consumption by bacteria. The same mass of glucose was added as a pulse at the beginning of all simulations. Bacteria were placed in few voxels either regularly spaced or concentrated close to or far from the glucose source. We modulated physiological features of decomposers in order to weight them against abiotic conditions. We could evidence several effects creating unequal substrate access conditions for decomposers, hence inducing contrasted decomposition kinetics: position of bacteria relative to the substrate diffusion pathways, diffusion rate and hydraulic connectivity between bacteria and substrate source, local substrate enrichment due to restricted mass transfer. Physiological characteristics had a strong impact on decomposition only when glucose diffused easily but not when diffusion limitation prevailed. This suggests that carbon dynamics should not be considered to derive from decomposers' physiology alone but rather from the interactions of biological and physical processes at the microscale.

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.

Probing Selection Mechanism of the Most Favorable Conformation of a Dipeptide in Chaotropic and Kosmotropic Solution.

PubMed

Jas, Gouri S; Middaugh, C Russell; Kuczera, Krzysztof

2016-07-21

Chaotropes like urea and guanidinium chloride (GdmCl) tend to destabilize, and kosmotropes like proline tend to stabilize folded structures of peptides and proteins. Here, we combine fluorescence anisotropy decay measurements and molecular dynamics simulations to gain a microscopic understanding of the molecular mechanism for shifting conformational preferences in aqueous, GdmCl, urea, and proline solutions of a simple model dipeptide, N-acetyl-tryptophan-amide (NATA). Measured anisotropy decay of NATA as a function of temperature, pH, and cosolvent concentrations showed reorientations moderately slower in GdmCl and urea and substantially slower in proline compared to those of aqueous environment. A small change in pH significantly slows orientation time in water and GdmCl and less markedly in urea. Computationally, we use molecular dynamics with dihedral restraints to separately analyze the motions and interactions of the representative NATA conformers in the four different solvent environments. This novel analysis provides a dissection of the observed overall diffusion rates into contributions from individual dipeptide conformations. The variation of rotational diffusion rates with conformation are quite large. Population-weighted averaging or using properties of the major cluster reproduces the dynamical features of the full unrestrained dynamics. Additionally, we correlate the observable diffusion rates with microscopic features of conformer size, shape, and solvation. This analysis uncovered underlying differences in detailed atomistic behavior of the three cosolvents-urea, GdmCl, and proline. For both urea and the pure water system we find good agreement with hydrodynamic theory, with diffusion rates primarily correlated with conformer size and shape. In contrast, for GdmCl and proline solutions, the variation in conformer diffusion rates was mostly determined by specific interactions with the cosolvents. We also find preferences for different molecular shapes by the three cosolvents, with increased preferential solvation of smaller and more spherical conformers by urea and larger and more elongated conformers by GdmCl and proline. Additionally, our results provide a basis for a simple approximate model of the effects of pH lowering on dipeptide conformational equilibria. The translational diffusion rates of NATA are less sensitive to conformations, but variation with solvation strength is similar to rotational diffusion. Our results, combining experiment and simulation, show that we can identify the individual peptide conformers with definite microscopic properties of shape, size, and solvation, that are responsible for producing physical observables, such as translational and orientational diffusion in the complex solvent environments of denaturants and osmolytes.

Linearized finite-element method solution of the ion-exchange nonlinear diffusion model

NASA Astrophysics Data System (ADS)

Badr, Mohamed M.; Swillam, Mohamed A.

2017-04-01

Ion-exchange process is one of the most common techniques used in glass waveguide fabrication. This has many advantages, such as low cost, ease of implementation, and simple equipment requirements. The technology is based on the substitution of some of the host ions in the glass (typically Na+) with other ions that possess different characteristics in terms of size and polarizability. The newly diffused ions produce a region with a relatively higher refractive index in which the light could be guided. A critical issue arises when it comes to designing such waveguides, which is carefully and precisely determining the resultant index profile. This task has been proven to be hideous as the process is generally governed by a nonlinear diffusion model with no direct general analytical solution. Furthermore, numerical solutions become unreliable-in terms of stability and mean squared error-in some cases, especially the K+-Na+ ion-exchanged waveguide, which is the best candidate to produce waveguides with refractive index differences compatible with those of the commercially available optical fibers. Linearized finite-element method formulations were used to provide a reliable tool that could solve the nonlinear diffusion model of the ion-exchange in both one- and two-dimensional spaces. Additionally, the annealed channel waveguide case has been studied. In all cases, unprecedented stability and minimum mean squared error could be achieved.

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

PubMed

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

2017-03-01

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

Influence of Structural Heterogeneity on Diffusion of CH4 and CO2 in Silicon Carbide-Derived Nanoporous Carbon

PubMed Central

2015-01-01

We investigate the influence of structural heterogeneity on the transport properties of simple gases in a Hybrid Reverse Monte Carlo (HRMC) constructed model of silicon carbide-derived carbon (SiC-DC). The energy landscape of the system is determined based on free energy analysis of the atomistic model. The overall energy barriers of the system for different gases are computed along with important properties, such as Henry constant and differential enthalpy of adsorption at infinite dilution, and indicate hydrophobicity of the SiC-DC structure and its affinity for CO2 and CH4 adsorption. We also study the effect of molecular geometry, pore structure and energy heterogeneity considering different hopping scenarios for diffusion of CO2 and CH4 through ultramicropores using the Nudged Elastic Band (NEB) method. It is shown that the energy barrier of a hopping molecule is very sensitive to the shape of the pore entry. We provide evidence for the influence of structural heterogeneity on self-diffusivity of methane and carbon dioxide using molecular dynamics simulation, based on a maximum in the variation of self-diffusivity with loading. A comparison of the MD simulation results with self-diffusivities from quasi-elastic neutron scattering (QENS) measurements and, with macroscopic uptake-based low-density transport coefficients, reveals the existence of internal barriers not captured in MD simulation and QENS experiments. Nevertheless, the simulation and macroscopic uptake-based diffusion coefficients agree within a factor of 2–3, indicating that our HRMC model structure captures most of the important energy barriers affecting the transport of CH4 in the nanostructure of SiC-DC. PMID:24932319

Influence of Structural Heterogeneity on Diffusion of CH4 and CO2 in Silicon Carbide-Derived Nanoporous Carbon.

PubMed

Farmahini, Amir H; Shahtalebi, Ali; Jobic, Hervé; Bhatia, Suresh K

2014-06-05

We investigate the influence of structural heterogeneity on the transport properties of simple gases in a Hybrid Reverse Monte Carlo (HRMC) constructed model of silicon carbide-derived carbon (SiC-DC). The energy landscape of the system is determined based on free energy analysis of the atomistic model. The overall energy barriers of the system for different gases are computed along with important properties, such as Henry constant and differential enthalpy of adsorption at infinite dilution, and indicate hydrophobicity of the SiC-DC structure and its affinity for CO 2 and CH 4 adsorption. We also study the effect of molecular geometry, pore structure and energy heterogeneity considering different hopping scenarios for diffusion of CO 2 and CH 4 through ultramicropores using the Nudged Elastic Band (NEB) method. It is shown that the energy barrier of a hopping molecule is very sensitive to the shape of the pore entry. We provide evidence for the influence of structural heterogeneity on self-diffusivity of methane and carbon dioxide using molecular dynamics simulation, based on a maximum in the variation of self-diffusivity with loading. A comparison of the MD simulation results with self-diffusivities from quasi-elastic neutron scattering (QENS) measurements and, with macroscopic uptake-based low-density transport coefficients, reveals the existence of internal barriers not captured in MD simulation and QENS experiments. Nevertheless, the simulation and macroscopic uptake-based diffusion coefficients agree within a factor of 2-3, indicating that our HRMC model structure captures most of the important energy barriers affecting the transport of CH 4 in the nanostructure of SiC-DC.

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

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

Ball, W.P.

1990-01-01

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

Counter-extrapolation method for conjugate interfaces in computational heat and mass transfer.

PubMed

Le, Guigao; Oulaid, Othmane; Zhang, Junfeng

2015-03-01

In this paper a conjugate interface method is developed by performing extrapolations along the normal direction. Compared to other existing conjugate models, our method has several technical advantages, including the simple and straightforward algorithm, accurate representation of the interface geometry, applicability to any interface-lattice relative orientation, and availability of the normal gradient. The model is validated by simulating the steady and unsteady convection-diffusion system with a flat interface and the steady diffusion system with a circular interface, and good agreement is observed when comparing the lattice Boltzmann results with respective analytical solutions. A more general system with unsteady convection-diffusion process and a curved interface, i.e., the cooling process of a hot cylinder in a cold flow, is also simulated as an example to illustrate the practical usefulness of our model, and the effects of the cylinder heat capacity and thermal diffusivity on the cooling process are examined. Results show that the cylinder with a larger heat capacity can release more heat energy into the fluid and the cylinder temperature cools down slower, while the enhanced heat conduction inside the cylinder can facilitate the cooling process of the system. Although these findings appear obvious from physical principles, the confirming results demonstrates the application potential of our method in more complex systems. In addition, the basic idea and algorithm of the counter-extrapolation procedure presented here can be readily extended to other lattice Boltzmann models and even other computational technologies for heat and mass transfer systems.

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

PubMed

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

2017-05-16

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

Position-Dependent Dynamics Explain Pore-Averaged Diffusion in Strongly Attractive Adsorptive Systems.

PubMed

Krekelberg, William P; Siderius, Daniel W; Shen, Vincent K; Truskett, Thomas M; Errington, Jeffrey R

2017-12-12

Using molecular simulations, we investigate the relationship between the pore-averaged and position-dependent self-diffusivity of a fluid adsorbed in a strongly attractive pore as a function of loading. Previous work (Krekelberg, W. P.; Siderius, D. W.; Shen, V. K.; Truskett, T. M.; Errington, J. R. Connection between thermodynamics and dynamics of simple fluids in highly attractive pores. Langmuir 2013, 29, 14527-14535, doi: 10.1021/la4037327) established that pore-averaged self-diffusivity in the multilayer adsorption regime, where the fluid exhibits a dense film at the pore surface and a lower density interior pore region, is nearly constant as a function of loading. Here we show that this puzzling behavior can be understood in terms of how loading affects the fraction of particles that reside in the film and interior pore regions as well as their distinct dynamics. Specifically, the insensitivity of pore-averaged diffusivity to loading arises from the approximate cancellation of two factors: an increase in the fraction of particles in the higher diffusivity interior pore region with loading and a corresponding decrease in the particle diffusivity in that region. We also find that the position-dependent self-diffusivities scale with the position-dependent density. We present a model for predicting the pore-average self-diffusivity based on the position-dependent self-diffusivity, which captures the unusual characteristics of pore-averaged self-diffusivity in strongly attractive pores over several orders of magnitude.

Localized Enzymatic Degradation of Polymers: Physics and Scaling Laws

NASA Astrophysics Data System (ADS)

Lalitha Sridhar, Shankar; Vernerey, Franck

2018-03-01

Biodegradable polymers are naturally abundant in living matter and have led to great advances in controlling environmental pollution due to synthetic polymer products, harnessing renewable energy from biofuels, and in the field of biomedicine. One of the most prevalent mechanisms of biodegradation involves enzyme-catalyzed depolymerization by biological agents. Despite numerous studies dedicated to understanding polymer biodegradation in different environments, a simple model that predicts the macroscopic behavior (mass and structural loss) in terms of microphysical processes (enzyme transport and reaction) is lacking. An interesting phenomenon occurs when an enzyme source (released by a biological agent) attacks a tight polymer mesh that restricts free diffusion. A fuzzy interface separating the intact and fully degraded polymer propagates away from the source and into the polymer as the enzymes diffuse and react in time. Understanding the characteristics of this interface will provide crucial insight into the biodegradation process and potential ways to precisely control it. In this work, we present a centrosymmetric model of biodegradation by characterizing the moving fuzzy interface in terms of its speed and width. The model predicts that the characteristics of this interface are governed by two time scales, namely the polymer degradation and enzyme transport times, which in turn depend on four main polymer and enzyme properties. A key finding of this work is simple scaling laws that can be used to guide biodegradation of polymers in different applications.

Alternation in the gap-junctional intercellular communication capacity during the maturation of osteocytes in the embryonic chick calvaria.

PubMed

Wang, Ziyi; Odagaki, Naoya; Tanaka, Tomoyo; Hashimoto, Mana; Nakamura, Masahiro; Hayano, Satoru; Ishihara, Yoshihito; Kawanabe, Noriaki; Kamioka, Hiroshi

2016-10-01

The intercellular network of cell-cell communication among osteocytes is mediated by gap junctions. Gap junctional intercellular communication (GJIC) is thought to play an important role in the integration and synchronization of bone remodeling. To further understand the mechanism of bone development it is important to quantify the difference in the GJIC capacity of young and developmentally mature osteocytes. We first established an embryonic chick calvaria growth model to show the growth of the calvaria in embryos at 13 to 21days of age. We then applied a fluorescence recovery after photobleaching (FRAP) technique to compare the difference in the GJIC capacity of young osteocytes with that of developmentally mature osteocytes. Finally, we quantified the dye (Calcein) diffusion from the FRAP data using a mathematic model of simple diffusion which was also used to identify simple diffusion GJIC pattern cells (fitted model) and accelerated diffusion GJIC pattern cells (non-fitted model). The relationship between the longest medial-lateral length of the calvaria (frontal bone) and the embryonic age fit a logarithmic growth model: length=5.144×ln(day)-11.340. The morphometric data during osteocyte differentiation showed that the cellular body becomes more spindle-shaped and that the cell body volume decreased by approximately 22% with an increase in the length of the processes between the cells. However, there were no significant differences in the cellular body surface area or in the distance between the mass centres of the cells. The dye-displacement rate in young osteocytes was significantly higher than that in developmentally mature osteocytes: dye displacement only occurred in 26.88% of the developmentally mature osteocytes, while it occurred in 64.38% of the young osteocytes. Additionally, in all recovered osteocytes, 36% of the developmentally mature osteocytes comprised non-fitted model cells while 53.19% of the young osteocytes were the non-fitted model, which indicates the active transduction of dye molecules. However, there were no statistically significant differences between the young and developmentally mature osteocytes with regard to the diffusion coefficient, permeability coefficient, or permeance of the osteocyte processes, which were 3.93±3.77 (×10(-8)cm(2)/s), 5.12±4.56 (×10(-5)cm(2)/s) and 2.99±2.47 (×10(-13)cm(2)/s) (mean±SD), respectively. These experiments comprehensively quantified the GJIC capacity in the embryonic chick calvaria and indicated that the cell-cell communication capacity of the osteocytes in the embryonic chick calvaria was related to their development. Copyright © 2016 Elsevier Inc. All rights reserved.

Microperforations significantly enhance diffusion across round window membrane.

PubMed

Kelso, Catherine M; Watanabe, Hirobumi; Wazen, Joseph M; Bucher, Tizian; Qian, Zhen J; Olson, Elizabeth S; Kysar, Jeffrey W; Lalwani, Anil K

2015-04-01

Introduction of microperforations in round window membrane (RWM) will allow reliable and predictable intracochlear delivery of pharmaceutical, molecular, or cellular therapeutic agents. Reliable delivery of medications into the inner ear remains a formidable challenge. The RWM is an attractive target for intracochlear delivery. However, simple diffusion across intact RWM is limited by what material can be delivered, size of material to be delivered, difficulty with precise dosing, timing, and precision of delivery over time. Further, absence of reliable methods for measuring diffusion across RWM in vitro is a significant experimental impediment. A novel model for measuring diffusion across guinea pig RWM, with and without microperforation, was developed and tested: cochleae, sparing the RWM, were embedded in 3D-printed acrylic holders using hybrid dental composite and light cured to adapt the round window niche to 3 ml Franz diffusion cells. Perforations were created with 12.5-μm-diameter needles and examined with light microscopy. Diffusion of 1 mM Rhodamine B across RWM in static diffusion cells was measured via fluorescence microscopy. The diffusion cell apparatus provided reliable and replicable measurements of diffusion across RWM. The permeability of Rhodamine B across intact RWM was 5.1 × 10(9-) m/s. Manual application of microperforation with a 12.5-μm-diameter tip produced an elliptical tear removing 0.22 ± 0.07% of the membrane and was associated with a 35× enhancement in diffusion (P < 0.05). Diffusion cells can be applied to the study of RWM permeability in vitro. Microperforation in RWM is an effective means of increasing diffusion across the RWM.

Estimating hydraulic properties from tidal attenuation in the Northern Guam Lens Aquifer, territory of Guam, USA

USGS Publications Warehouse

Rotzoll, Kolja; Gingerich, Stephen B.; Jenson, John W.; El-Kadi, Aly I.

2013-01-01

Tidal-signal attenuations are analyzed to compute hydraulic diffusivities and estimate regional hydraulic conductivities of the Northern Guam Lens Aquifer, Territory of Guam (Pacific Ocean), USA. The results indicate a significant tidal-damping effect at the coastal boundary. Hydraulic diffusivities computed using a simple analytical solution for well responses to tidal forcings near the periphery of the island are two orders of magnitude lower than for wells in the island’s interior. Based on assigned specific yields of ~0.01–0.4, estimated hydraulic conductivities are ~20–800 m/day for peripheral wells, and ~2,000–90,000 m/day for interior wells. The lower conductivity of the peripheral rocks relative to the interior rocks may best be explained by the effects of karst evolution: (1) dissolutional enhancement of horizontal hydraulic conductivity in the interior; (2) case-hardening and concurrent reduction of local hydraulic conductivity in the cliffs and steeply inclined rocks of the periphery; and (3) the stronger influence of higher-conductivity regional-scale features in the interior relative to the periphery. A simple numerical model calibrated with measured water levels and tidal response estimates values for hydraulic conductivity and storage parameters consistent with the analytical solution. The study demonstrates how simple techniques can be useful for characterizing regional aquifer properties.

Investigating the effect of compression on solute transport through degrading municipal solid waste

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

Woodman, N.D., E-mail: n.d.woodman@soton.ac.uk; Rees-White, T.C.; Stringfellow, A.M.

2014-11-15

Highlights: • The influence of compression on MSW flushing was evaluated using 13 tracer tests. • Compression has little effect on solute diffusion times in MSW. • Lithium tracer was conservative in non-degrading waste but not in degrading waste. • Bromide tracer was conservative, but deuterium was not. - Abstract: The effect of applied compression on the nature of liquid flow and hence the movement of contaminants within municipal solid waste was examined by means of thirteen tracer tests conducted on five separate waste samples. The conservative nature of bromide, lithium and deuterium tracers was evaluated and linked to themore » presence of degradation in the sample. Lithium and deuterium tracers were non-conservative in the presence of degradation, whereas the bromide remained effectively conservative under all conditions. Solute diffusion times into and out of less mobile blocks of waste were compared for each test under the assumption of dominantly dual-porosity flow. Despite the fact that hydraulic conductivity changed strongly with applied stress, the block diffusion times were found to be much less sensitive to compression. A simple conceptual model, whereby flow is dominated by sub-parallel low permeability obstructions which define predominantly horizontally aligned less mobile zones, is able to explain this result. Compression tends to narrow the gap between the obstructions, but not significantly alter the horizontal length scale. Irrespective of knowledge of the true flow pattern, these results show that simple models of solute flushing from landfill which do not include depth dependent changes in solute transport parameters are justified.« less

Natural variability of atmospheric temperatures and geomagnetic intensity over a wide range of time scales.

PubMed

Pelletier, Jon D

2002-02-19

The majority of numerical models in climatology and geomagnetism rely on deterministic finite-difference techniques and attempt to include as many empirical constraints on the many processes and boundary conditions applicable to their very complex systems. Despite their sophistication, many of these models are unable to reproduce basic aspects of climatic or geomagnetic dynamics. We show that a simple stochastic model, which treats the flux of heat energy in the atmosphere by convective instabilities with random advection and diffusive mixing, does a remarkable job at matching the observed power spectrum of historical and proxy records for atmospheric temperatures from time scales of one day to one million years (Myr). With this approach distinct changes in the power-spectral form can be associated with characteristic time scales of ocean mixing and radiative damping. Similarly, a simple model of the diffusion of magnetic intensity in Earth's core coupled with amplification and destruction of the local intensity can reproduce the observed 1/f noise behavior of Earth's geomagnetic intensity from time scales of 1 (Myr) to 100 yr. In addition, the statistics of the fluctuations in the polarity reversal rate from time scales of 1 Myr to 100 Myr are consistent with the hypothesis that reversals are the result of variations in 1/f noise geomagnetic intensity above a certain threshold, suggesting that reversals may be associated with internal fluctuations rather than changes in mantle thermal or magnetic boundary conditions.

Natural variability of atmospheric temperatures and geomagnetic intensity over a wide range of time scales

PubMed Central

Pelletier, Jon D.

2002-01-01

The majority of numerical models in climatology and geomagnetism rely on deterministic finite-difference techniques and attempt to include as many empirical constraints on the many processes and boundary conditions applicable to their very complex systems. Despite their sophistication, many of these models are unable to reproduce basic aspects of climatic or geomagnetic dynamics. We show that a simple stochastic model, which treats the flux of heat energy in the atmosphere by convective instabilities with random advection and diffusive mixing, does a remarkable job at matching the observed power spectrum of historical and proxy records for atmospheric temperatures from time scales of one day to one million years (Myr). With this approach distinct changes in the power-spectral form can be associated with characteristic time scales of ocean mixing and radiative damping. Similarly, a simple model of the diffusion of magnetic intensity in Earth's core coupled with amplification and destruction of the local intensity can reproduce the observed 1/f noise behavior of Earth's geomagnetic intensity from time scales of 1 (Myr) to 100 yr. In addition, the statistics of the fluctuations in the polarity reversal rate from time scales of 1 Myr to 100 Myr are consistent with the hypothesis that reversals are the result of variations in 1/f noise geomagnetic intensity above a certain threshold, suggesting that reversals may be associated with internal fluctuations rather than changes in mantle thermal or magnetic boundary conditions. PMID:11875208

A new model of diffuse brain injury in rats. Part I: Pathophysiology and biomechanics.

PubMed

Marmarou, A; Foda, M A; van den Brink, W; Campbell, J; Kita, H; Demetriadou, K

1994-02-01

This report describes the development of an experimental head injury model capable of producing diffuse brain injury in the rodent. A total of 161 anesthetized adult rats were injured utilizing a simple weight-drop device consisting of a segmented brass weight free-falling through a Plexiglas guide tube. Skull fracture was prevented by cementing a small stainless-steel disc on the calvaria. Two groups of rats were tested: Group 1, consisting of 54 rats, to establish fracture threshold; and Group 2, consisting of 107 animals, to determine the primary cause of death at severe injury levels. Data from Group 1 animals showed that a 450-gm weight falling from a 2-m height (0.9 kg-m) resulted in a mortality rate of 44% with a low incidence (12.5%) of skull fracture. Impact was followed by apnea, convulsions, and moderate hypertension. The surviving rats developed decortication flexion deformity of the forelimbs, with behavioral depression and loss of muscle tone. Data from Group 2 animals suggested that the cause of death was due to central respiratory depression; the mortality rate decreased markedly in animals mechanically ventilated during the impact. Analysis of mathematical models showed that this mass-height combination resulted in a brain acceleration of 900 G and a brain compression gradient of 0.28 mm. It is concluded that this simple model is capable of producing a graded brain injury in the rodent without a massive hypertensive surge or excessive brain-stem damage.

Emergent spatial synaptic structure from diffusive plasticity.

PubMed

Sweeney, Yann; Clopath, Claudia

2017-04-01

Some neurotransmitters can diffuse freely across cell membranes, influencing neighbouring neurons regardless of their synaptic coupling. This provides a means of neural communication, alternative to synaptic transmission, which can influence the way in which neural networks process information. Here, we ask whether diffusive neurotransmission can also influence the structure of synaptic connectivity in a network undergoing plasticity. We propose a form of Hebbian synaptic plasticity which is mediated by a diffusive neurotransmitter. Whenever a synapse is modified at an individual neuron through our proposed mechanism, similar but smaller modifications occur in synapses connecting to neighbouring neurons. The effects of this diffusive plasticity are explored in networks of rate-based neurons. This leads to the emergence of spatial structure in the synaptic connectivity of the network. We show that this spatial structure can coexist with other forms of structure in the synaptic connectivity, such as with groups of strongly interconnected neurons that form in response to correlated external drive. Finally, we explore diffusive plasticity in a simple feedforward network model of receptive field development. We show that, as widely observed across sensory cortex, the preferred stimulus identity of neurons in our network become spatially correlated due to diffusion. Our proposed mechanism of diffusive plasticity provides an efficient mechanism for generating these spatial correlations in stimulus preference which can flexibly interact with other forms of synaptic organisation. © 2016 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.

Conservative Exposure Predictions for Rapid Risk Assessment of Phase-Separated Additives in Medical Device Polymers.

PubMed

Chandrasekar, Vaishnavi; Janes, Dustin W; Saylor, David M; Hood, Alan; Bajaj, Akhil; Duncan, Timothy V; Zheng, Jiwen; Isayeva, Irada S; Forrey, Christopher; Casey, Brendan J

2018-01-01

A novel approach for rapid risk assessment of targeted leachables in medical device polymers is proposed and validated. Risk evaluation involves understanding the potential of these additives to migrate out of the polymer, and comparing their exposure to a toxicological threshold value. In this study, we propose that a simple diffusive transport model can be used to provide conservative exposure estimates for phase separated color additives in device polymers. This model has been illustrated using a representative phthalocyanine color additive (manganese phthalocyanine, MnPC) and polymer (PEBAX 2533) system. Sorption experiments of MnPC into PEBAX were conducted in order to experimentally determine the diffusion coefficient, D = (1.6 ± 0.5) × 10 -11  cm 2 /s, and matrix solubility limit, C s  = 0.089 wt.%, and model predicted exposure values were validated by extraction experiments. Exposure values for the color additive were compared to a toxicological threshold for a sample risk assessment. Results from this study indicate that a diffusion model-based approach to predict exposure has considerable potential for use as a rapid, screening-level tool to assess the risk of color additives and other small molecule additives in medical device polymers.

Evaluating the multimedia fate of organic chemicals: A level III fugacity model

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

Mackay, D.; Paterson, S.

A multimedia model is developed and applied to selected organic chemicals in evaluative and real regional environments. The model employs the fugacity concept and treats four bulk compartments: air, water, soil, and bottom sediment, which consist of subcompartments of varying proportions of air, water, and mineral and organic matter. Chemical equilibrium is assumed to apply within (but not between) each bulk compartment. Expressions are included for emissions, advective flows, degrading reactions, and interphase transport by diffusive and non-diffusive processes. Input to the model consists of a description of the environment, the physical-chemical and reaction properties of the chemical, and emissionmore » rates. For steady-state conditions the solution is a simple algebraic expression. The model is applied to six chemicals in the region of southern Ontario and the calculated fate and concentrations are compared with observations. The results suggest that the model may be used to determine the processes that control the environmental fate of chemicals in a region and provide approximate estimates of relative media concentrations.« less

Applicability of ASHRAE clear-sky model based on solar-radiation measurements in Saudi Arabia

NASA Astrophysics Data System (ADS)

Abouhashish, Mohamed

2017-06-01

The constants of the ASHRAE clear sky model predict high values of the hourly beam radiation and very low values of the hourly diffuse radiation when used for locations in Saudi Arabia. Eight measurement stations in different locations are used to obtain new clearness factors for the model. The procedure depends on the comparison of monthly direct normal radiation (DNI) and diffuse horizontal radiation (DHI) between the measurement and the calculated values. Two factors are obtained CNb, CNd for every month to adjust the calculated clear sky radiation in order to consider the effects of local weather conditions. A simple and practical simulation model for solar geometry is designed using Microsoft Visual Basic platform, the model simulates the solar angles and radiation components according to ASHRAE model. The comparison of the calculated data with the first year of measurements indicate that the attenuation of site clearness is variable across the locations and from month to month, showing the clearest skies in the north and northwestern parts of the Kingdom especially during summer months.

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.

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

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

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

2005-08-10

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

Tracing compartment exchange by NMR diffusometry: Water in lithium-exchanged low-silica X zeolites

NASA Astrophysics Data System (ADS)

Lauerer, A.; Kurzhals, R.; Toufar, H.; Freude, D.; Kärger, J.

2018-04-01

The two-region model for analyzing signal attenuation in pulsed field gradient (PFG) NMR diffusion studies with molecules in compartmented media implies that, on their trajectory, molecules get from one region (one type of compartment) into the other one with a constant (i.e. a time-invariant) probability. This pattern has proved to serve as a good approach for considering guest diffusion in beds of nanoporous host materials, with the two regions ("compartments") identified as the intra- and intercrystalline pore spaces. It is obvious, however, that the requirements of the application of the two-region model are not strictly fulfilled given the correlation between the covered diffusion path lengths in the intracrystalline pore space and the probability of molecular "escape" from the individual crystallites. On considering water diffusion in lithium-exchanged low-silica X zeolite, we are now assuming a different position since this type of material is known to offer "traps" in the trajectories of the water molecules. Now, on attributing the water molecules in the traps and outside of the traps to these two types of regions, we perfectly comply with the requirements of the two-region model. We do, moreover, benefit from the option of high-resolution measurements owing to the combination of magic angle spinning (MAS) with PFG NMR. Data analysis via the two-region model under inclusion of the influence of nuclear magnetic relaxation yields satisfactory agreement between experimental evidence and theoretical estimates. Limitations in accuracy are shown to result from the fact that mass transfer outside of the traps is too complicated for being adequately reflected by simple Fick's laws with but one diffusivity.

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

USGS Publications Warehouse

Ding, Xin; Kennedy, B. Mack.; Evans, William C.; Stonestrom, David A.

2016-01-01

The noble gases, which are chemically inert under normal terrestrial conditions but vary systematically across a wide range of atomic mass and diffusivity, offer a multicomponent approach to investigating gas dynamics in unsaturated soil horizons, including transfer of gas between saturated zones, unsaturated zones, and the atmosphere. To evaluate the degree to which fractionation of noble gases in the presence of an advective–diffusive flux agrees with existing theory, a simple laboratory sand column experiment was conducted. Pure CO2 was injected at the base of the column, providing a series of constant CO2 fluxes through the column. At five fixed sampling depths within the system, samples were collected for CO2 and noble gas analyses, and ambient pressures were measured. Both the advection–diffusion and dusty gas models were used to simulate the behavior of CO2 and noble gases under the experimental conditions, and the simulations were compared with the measured depth-dependent concentration profiles of the gases. Given the relatively high permeability of the sand column (5 ´ 10−11 m2), Knudsen diffusion terms were small, and both the dusty gas model and the advection–diffusion model accurately predicted the concentration profiles of the CO2 and atmospheric noble gases across a range of CO2 flux from ?700 to 10,000 g m−2 d−1. The agreement between predicted and measured gas concentrations demonstrated that, when applied to natural systems, the multi-component capability provided by the noble gases can be exploited to constrain component and total gas fluxes of non-conserved (CO2) and conserved (noble gas) species or attributes of the soil column relevant to gas transport, such as porosity, tortuosity, and gas saturation.

Following fluctuating signs: Anomalous active superdiffusion of swimmers in anisotropic media

NASA Astrophysics Data System (ADS)

Toner, John; Löwen, Hartmut; Wensink, Henricus H.

2016-06-01

Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic nematic background. While the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is superdiffusive, with an anomalous scaling proportional to t lnt of the mean-square displacement with time t . This behavior is predicted by an analytical theory that we present here and is corroborated by numerical simulation of active particle diffusion in a simple lattice model for a nematic liquid crystal. It is universal for any collection of self-propelled elements (e.g., bacteria or active rods) moving in a nematic background, provided only that the swimmers are sufficiently dilute that their interactions with each other can be neglected and that they do not perform hairpin turns.

Numerical convergence of the self-diffusion coefficient and viscosity obtained with Thomas-Fermi-Dirac molecular dynamics.

PubMed

Danel, J-F; Kazandjian, L; Zérah, G

2012-06-01

Computations of the self-diffusion coefficient and viscosity in warm dense matter are presented with an emphasis on obtaining numerical convergence and a careful evaluation of the standard deviation. The transport coefficients are computed with the Green-Kubo relation and orbital-free molecular dynamics at the Thomas-Fermi-Dirac level. The numerical parameters are varied until the Green-Kubo integral is equal to a constant in the t→+∞ limit; the transport coefficients are deduced from this constant and not by extrapolation of the Green-Kubo integral. The latter method, which gives rise to an unknown error, is tested for the computation of viscosity; it appears that it should be used with caution. In the large domain of coupling constant considered, both the self-diffusion coefficient and viscosity turn out to be well approximated by simple analytical laws using a single effective atomic number calculated in the average-atom model.

Numerical convergence of the self-diffusion coefficient and viscosity obtained with Thomas-Fermi-Dirac molecular dynamics

NASA Astrophysics Data System (ADS)

Danel, J.-F.; Kazandjian, L.; Zérah, G.

2012-06-01

Computations of the self-diffusion coefficient and viscosity in warm dense matter are presented with an emphasis on obtaining numerical convergence and a careful evaluation of the standard deviation. The transport coefficients are computed with the Green-Kubo relation and orbital-free molecular dynamics at the Thomas-Fermi-Dirac level. The numerical parameters are varied until the Green-Kubo integral is equal to a constant in the t→+∞ limit; the transport coefficients are deduced from this constant and not by extrapolation of the Green-Kubo integral. The latter method, which gives rise to an unknown error, is tested for the computation of viscosity; it appears that it should be used with caution. In the large domain of coupling constant considered, both the self-diffusion coefficient and viscosity turn out to be well approximated by simple analytical laws using a single effective atomic number calculated in the average-atom model.

Purging of multilayer insulation by gas diffusion

NASA Technical Reports Server (NTRS)

Sumner, I. E.; Spuckler, C. M.

1976-01-01

An experimental investigation was conducted to determine the time required to purge a multilayer insulation (MLI) panel with gaseous helium by means of gas diffusion to obtain a condensable (nitrogen) gas concentration of less than 1 percent within the panel. Two flat, rectangular MLI panel configurations, one incorporating a butt joint, were tested. The insulation panels consisted of 15 double-aluminized Mylar radiation shields separated by double silk net spacers. The test results indicated that the rate which the condensable gas concentration at the edge or at the butt joint of an MLI panel was reduced was a significant factor in the total time required to reduce the condensable gas concentration within the panel to less than 1 percent. The experimental data agreed well with analytical predictions made by using a simple, one-dimensional gas diffusion model in which the boundary conditions at the edge of the MLI panel were time dependent.

Two-dimensional enzyme diffusion in laterally confined DNA monolayers.

PubMed

Castronovo, Matteo; Lucesoli, Agnese; Parisse, Pietro; Kurnikova, Anastasia; Malhotra, Aseem; Grassi, Mario; Grassi, Gabriele; Scaggiante, Bruna; Casalis, Loredana; Scoles, Giacinto

2011-01-01

Addressing the effects of confinement and crowding on biomolecular function may provide insight into molecular mechanisms within living organisms, and may promote the development of novel biotechnology tools. Here, using molecular manipulation methods, we investigate restriction enzyme reactions with double-stranded (ds)DNA oligomers confined in relatively large (and flat) brushy matrices of monolayer patches of controlled, variable density. We show that enzymes from the contacting solution cannot access the dsDNAs from the top-matrix interface, and instead enter at the matrix sides to diffuse two-dimensionally in the gap between top- and bottom-matrix interfaces. This is achieved by limiting lateral access with a barrier made of high-density molecules that arrest enzyme diffusion. We put forward, as a possible explanation, a simple and general model that relates these data to the steric hindrance in the matrix, and we briefly discuss the implications and applications of this strikingly new phenomenon.

An ion displacement membrame model.

PubMed

Hladky, S B; Harris, J D

1967-09-01

The usual assumption in treating the diffusion of ions in an electric field has been that the movement of each ion is independent of the movement of the others. The resulting equation for diffusion by a succession of spontaneous jumps has been well stated by Parlin and Eyring. This paper will consider one simple case in which a different assumption is reasonable. Diffusion of monovalent positive ions is considered as a series of jumps from one fixed negative site to another. The sites are assumed to be full (electrical neutrality). Interaction occurs by the displacement of one ion by another. An ion leaves a site if and only if another ion, not necessarily of the same species, attempts to occupy the same site. Flux ratios and net fluxes are given as functions of the electrical potential, concentration ratios, and number of sites encountered in crossing the membrane. Quantitative comparisons with observations of Hodgkin and Keynes are presented.

Stochastic lattice model of synaptic membrane protein domains.

PubMed

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

2017-05-01

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

Cross-diffusion-driven hydrodynamic instabilities in a double-layer system: General classification and nonlinear simulations

NASA Astrophysics Data System (ADS)

Budroni, M. A.

2015-12-01

Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.

Discovery of Diffuse Hard X-ray Emission associated with Jupiter

NASA Astrophysics Data System (ADS)

Ezoe, Y.; Miyoshi, Y.; Ishikawa, K.; Ohashi, T.; Terada, N.; Uchiyama, Y.; Negoro, H.

2009-12-01

Our discovery of diffuse hard (1-5 keV) X-ray emission around Jupiter is reported. Recent Chandra and XMM-Newton observations revealed several types of X-rays in the vicinity of Jupiter such as auroral and disk emission from Jupiter and faint diffuse X-rays from the Io Plasma Torus (see Bhardwaj et al. 2007 for review). To investigate possible diffuse hard X-ray emission around Jupiter with the highest sensitivity, we conducted data analysis of Suzaku XIS observations of Jupiter on Feb 2006. After removing satellite and planetary orbital motions, we detected a significant diffuse X-ray emission extending to ~6 x 3 arcmin with the 1-5 keV X-ray luminosity of ~3e15 erg/s. The emitting region very well coincided with the Jupiter's radiation belts. The 1-5 keV X-ray spectrum was represented by a simple power law model with a photon index of 1.4. Such a flat continuum strongly suggests non-thermal origin. Although such an emission can be originated from multiple background point sources, its possibility is quite low. We hence examined three mechanisms, assuming that the emission is truly diffuse: bremsstrahlung by keV electrons, synchrotron emission by TeV electrons, and inverse Compton scattering of solar photons by MeV electrons. The former two can be rejected because of the X-ray spectral shape and implausible existence of TeV electrons around Jupiter, respectively. The last possibility was found to be possible because tens MeV electrons, which have been confirmed in inner radiation belts (Bolton et al. 2002), can kick solar photons to the keV energy range and provide a simple power-law continuum. We estimated an average electron density from the X-ray luminosity assuming the oblate spheroid shaped emitting region with 8 x 8 x 4 Jovian radii. The necessary density was 0.02 1/cm3 for 50 MeV electrons. Hence, our results may suggest a new particle acceleration phenomenon around Jupiter.

How to Detect the Location and Time of a Covert Chemical Attack: A Bayesian Approach

DTIC Science & Technology

2009-12-01

Inverse Problems, Design and Optimization Symposium 2004. Rio de Janeiro , Brazil. Chan, R., and Yee, E. (1997). A simple model for the probability...sensor interpretation applications and has been successfully applied, for example, to estimate the source strength of pollutant releases in multi...coagulation, and second-order pollutant diffusion in sorption- desorption, are not linear. Furthermore, wide uncertainty bounds exist for several of

NDE Research At Nondestructive Measurement Science At NASA Langley

DTIC Science & Technology

1989-06-01

our staff include: ultrasonics, nonlinear acoustics , thermal acoustics and diffusion, magnetics , fiber optics, and x-ray tomography . We have a...based on the simple assumption that acoustic waves interact with the sample and reveal "important" properties . In practice, such assumptions have...between the acoustic wave and the media. The most useful models can generally be inverted to determine the physical properties or geometry of the

A simple model of the effect of ocean ventilation on ocean heat uptake

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

Nadiga, Balasubramanya T.; Urban, Nathan Mark

Presentation includes slides on Earth System Models vs. Simple Climate Models; A Popular SCM: Energy Balance Model of Anomalies; On calibrating against one ESM experiment, the SCM correctly captures that ESM's surface warming response with other forcings; Multi-Model Analysis: Multiple ESMs, Single SCM; Posterior Distributions of ECS; However In Excess of 90% of TOA Energy Imbalance is Sequestered in the World Oceans; Heat Storage in the Two Layer Model; Heat Storage in the Two Layer Model; Including TOA Rad. Imbalance and Ocean Heat in Calibration Improves Repr., but Significant Errors Persist; Improved Vertical Resolution Does Not Fix Problem; A Seriesmore » of Expts. Confirms That Anomaly-Diffusing Models Cannot Properly Represent Ocean Heat Uptake; Physics of the Thermocline; Outcropping Isopycnals and Horizontally-Averaged Layers; Local interactions between outcropping isopycnals leads to non-local interactions between horizontally-averaged layers; Both Surface Warming and Ocean Heat are Well Represented With Just 4 Layers; A Series of Expts. Confirms That When Non-Local Interactions are Allowed, the SCMs Can Represent Both Surface Warming and Ocean Heat Uptake; and Summary and Conclusions.« less

Threshold effect with stochastic fluctuation in bacteria-colony-like proliferation dynamics as analyzed through a comparative study of reaction-diffusion equations and cellular automata

NASA Astrophysics Data System (ADS)

Odagiri, Kenta; Takatsuka, Kazuo

2009-02-01

We report a comparative study on pattern formation between the methods of cellular automata (CA) and reaction-diffusion equations (RD) applying to a morphology of bacterial colony formation. To do so, we began the study with setting an extremely simple model, which was designed to realize autocatalytic proliferation of bacteria (denoted as X ) fed with nutrition (N) and their inactive state (prespore state) P1 due to starvation: X+N→2X and X→P1 , respectively. It was found numerically that while the CA could successfully generate rich patterns ranging from the circular fat structure to the viscous-finger-like complicated one, the naive RD reproduced only the circular pattern but failed to give a finger structure. Augmenting the RD equations by adding two physical factors, (i) a threshold effect in the dynamics of X+N→2X (breaking the continuity limit of RD) and (ii) internal noise with onset threshold (breaking the inherent symmetry of RD), we have found that the viscous-finger-like realistic patterns are indeed recovered by thus modified RD. This highlights the important difference between CA and RD, and at the same time, clarifies the necessary factors for the complicated patterns to emerge in such a surprisingly simple model system.

Exploring the Dynamics of Cell Processes through Simulations of Fluorescence Microscopy Experiments

PubMed Central

Angiolini, Juan; Plachta, Nicolas; Mocskos, Esteban; Levi, Valeria

2015-01-01

Fluorescence correlation spectroscopy (FCS) methods are powerful tools for unveiling the dynamical organization of cells. For simple cases, such as molecules passively moving in a homogeneous media, FCS analysis yields analytical functions that can be fitted to the experimental data to recover the phenomenological rate parameters. Unfortunately, many dynamical processes in cells do not follow these simple models, and in many instances it is not possible to obtain an analytical function through a theoretical analysis of a more complex model. In such cases, experimental analysis can be combined with Monte Carlo simulations to aid in interpretation of the data. In response to this need, we developed a method called FERNET (Fluorescence Emission Recipes and Numerical routines Toolkit) based on Monte Carlo simulations and the MCell-Blender platform, which was designed to treat the reaction-diffusion problem under realistic scenarios. This method enables us to set complex geometries of the simulation space, distribute molecules among different compartments, and define interspecies reactions with selected kinetic constants, diffusion coefficients, and species brightness. We apply this method to simulate single- and multiple-point FCS, photon-counting histogram analysis, raster image correlation spectroscopy, and two-color fluorescence cross-correlation spectroscopy. We believe that this new program could be very useful for predicting and understanding the output of fluorescence microscopy experiments. PMID:26039162

Radial diffusion with outer boundary determined by geosynchronous measurements: Storm and post-storm intervals

NASA Astrophysics Data System (ADS)

Chu, F.; Haines, P.; Hudson, M.; Kress, B.; Freidel, R.; Kanekal, S.

2007-12-01

Work is underway by several groups to quantify diffusive radial transport of radiation belt electrons, including a model for pitch angle scattering losses to the atmosphere. The radial diffusion model conserves the first and second adiabatic invariants and breaks the third invariant. We have developed a radial diffusion code which uses the Crank Nicholson method with a variable outer boundary condition. For the radial diffusion coefficient, DLL, we have several choices, including the Brautigam and Albert (JGR, 2000) diffusion coefficient parameterized by Kp, which provides an ad hoc measure of the power level at ULF wave frequencies in the range of electron drift (mHz), breaking the third invariant. Other diffusion coefficient models are Kp-independent, fixed in time but explicitly dependent on the first invariant, or energy at a fixed L, such as calculated by Elkington et al. (JGR, 2003) and Perry et al. (JGR, 2006) based on ULF wave model fields. We analyzed three periods of electron flux and phase space density (PSD) enhancements inside of geosynchronous orbit: March 31 - May 31, 1991, and July 2004 and Nov 2004 storm intervals. The radial diffusion calculation is initialized with a computed phase space density profile for the 1991 interval using differential flux values from the CRRES High Energy Electron Fluxmeter instrument, covering 0.65 - 7.5 MeV. To calculate the initial phase space density, we convert Roederer L* to McIlwain's L- parameter using the ONERA-DESP program. A time averaged model developed by Vampola1 from the entire 14 month CRRES data set is applied to the July 2004 and Nov 2004 storms. The online CRESS data for specific orbits and the Vampola-model flux are both expressed in McIlwain L-shell, while conversion to L* conserves phase space density in a distorted non-dipolar magnetic field model. A Tsyganenko (T04) magnetic field model is used for conversion between L* and L. The outer boundary PSD is updated using LANL GEO satellite fluxes. After calculating the phase space density time evolution for the two storms and post-injection interval (March 31 - May 31, 1991), we compare results with SAMPEX measurements. A better match with SAMPEX measurements is obtained with a variable outer boundary, also with a Kp-dependent diffusion coefficient, and finally with an energy and L-dependent loss term (Summers et al., JGR, 2004), than with a time-independent diffusion coefficient and a simple Kp-parametrized loss rate and location of the plasmapause. Addition of a varying outer boundary which incorporates measured fluxes at geosynchronous orbit using L* has the biggest effect of the three parametrized variations studied. 1Vampola, A.L., 1996, The ESA Outer Zone Electron Model Update, Environment Modelling for Spaced-based Applications, ESA SP-392, ESTEC, Nordwijk, NL, pp. 151-158, W. Burke and T.-D. Guyenne, eds.

Thirty years since diffuse sound reflection by maximum length

NASA Astrophysics Data System (ADS)

Cox, Trevor J.; D'Antonio, Peter

2005-09-01

This year celebrates the 30th anniversary of Schroeder's seminal paper on sound scattering from maximum length sequences. This paper, along with Schroeder's subsequent publication on quadratic residue diffusers, broke new ground, because they contained simple recipes for designing diffusers with known acoustic performance. So, what has happened in the intervening years? As with most areas of engineering, the room acoustic diffuser has been greatly influenced by the rise of digital computing technologies. Numerical methods have become much more powerful, and this has enabled predictions of surface scattering to greater accuracy and for larger scale surfaces than previously possible. Architecture has also gone through a revolution where the forms of buildings have become more extreme and sculptural. Acoustic diffuser designs have had to keep pace with this to produce shapes and forms that are desirable to architects. To achieve this, design methodologies have moved away from Schroeder's simple equations to brute force optimization algorithms. This paper will look back at the past development of the modern diffuser, explaining how the principles of diffuser design have been devised and revised over the decades. The paper will also look at the present state-of-the art, and dreams for the future.

Inferring nonlinear mantle rheology from the shape of the Hawaiian swell.

PubMed

Asaadi, N; Ribe, N M; Sobouti, F

2011-05-26

The convective circulation generated within the Earth's mantle by buoyancy forces of thermal and compositional origin is intimately controlled by the rheology of the rocks that compose it. These can deform either by the diffusion of point defects (diffusion creep, with a linear relationship between strain rate and stress) or by the movement of intracrystalline dislocations (nonlinear dislocation creep). However, there is still no reliable map showing where in the mantle each of these mechanisms is dominant, and so it is important to identify regions where the operative mechanism can be inferred directly from surface geophysical observations. Here we identify a new observable quantity--the rate of downstream decay of the anomalous seafloor topography (swell) produced by a mantle plume--which depends only on the value of the exponent in the strain rate versus stress relationship that defines the difference between diffusion and dislocation creep. Comparison of the Hawaiian swell topography with the predictions of a simple fluid mechanical model shows that the swell shape is poorly explained by diffusion creep, and requires a dislocation creep rheology. The rheology predicted by the model is reasonably consistent with laboratory deformation data for both olivine and clinopyroxene, suggesting that the source of Hawaiian lavas could contain either or both of these components.

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

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

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro

2017-04-01

We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Stressed Oxidation Life Prediction for C/SiC Composites

NASA Technical Reports Server (NTRS)

Levine, Stanley R.

2004-01-01

The residual strength and life of C/SiC is dominated by carbon interface and fiber oxidation if seal coat and matrix cracks are open to allow oxygen ingress. Crack opening is determined by the combination of thermal, mechanical and thermal expansion mismatch induced stresses. When cracks are open, life can be predicted by simple oxidation based models with reaction controlled kinetics at low temperature, and by gas phase diffusion controlled kinetics at high temperatures. Key life governing variables in these models include temperature, stress, initial strength, oxygen partial pressure, and total pressure. These models are described in this paper.

Coupled electromagnetic-thermodynamic simulations of microwave heating problems using the FDTD algorithm.

PubMed

Kopyt, Paweł; Celuch, Małgorzata

2007-01-01

A practical implementation of a hybrid simulation system capable of modeling coupled electromagnetic-thermodynamic problems typical in microwave heating is described. The paper presents two approaches to modeling such problems. Both are based on an FDTD-based commercial electromagnetic solver coupled to an external thermodynamic analysis tool required for calculations of heat diffusion. The first approach utilizes a simple FDTD-based thermal solver while in the second it is replaced by a universal commercial CFD solver. The accuracy of the two modeling systems is verified against the original experimental data as well as the measurement results available in literature.

Diffusion mechanism of non-interacting Brownian particles through a deformed substrate

NASA Astrophysics Data System (ADS)

Arfa, Lahcen; Ouahmane, Mehdi; El Arroum, Lahcen

2018-02-01

We study the diffusion mechanism of non-interacting Brownian particles through a deformed substrate. The study is done at low temperature for different values of the friction. The deformed substrate is represented by a periodic Remoissenet-Peyrard potential with deformability parameter s. In this potential, the particles (impurity, adatoms…) can diffuse. We ignore the interactions between these mobile particles consider them merely as non-interacting Brownian particles and this system is described by a Fokker-Planck equation. We solve this equation numerically using the matrix continued fraction method to calculate the dynamic structure factor S(q , ω) . From S(q , ω) some relevant correlation functions are also calculated. In particular, we determine the half-width line λ(q) of the peak of the quasi-elastic dynamic structure factor S(q , ω) and the diffusion coefficient D. Our numerical results show that the diffusion mechanism is described, depending on the structure of the potential, either by a simple jump diffusion process with jump length close to the lattice constant a or by a combination of a jump diffusion model with jump length close to lattice constant a and a liquid-like motion inside the unit cell. It shows also that, for different friction regimes and various potential shapes, the friction attenuates the diffusion mechanism. It is found that, in the high friction regime, the diffusion process is more important through a deformed substrate than through a non-deformed one.

Adsorptive Removal of Toxic Chromium from Waste-Water Using Wheat Straw and Eupatorium adenophorum

PubMed Central

Song, Dagang; Pan, Kaiwen; Tariq, Akash; Azizullah, Azizullah; Sun, Feng; Li, Zilong; Xiong, Qinli

2016-01-01

Environmental pollution with heavy metals is a serious issue worldwide posing threats to humans, animals and plants and to the stability of overall ecosystem. Chromium (Cr) is one of most hazardous heavy metals with a high carcinogenic and recalcitrant nature. Aim of the present study was to select low-cost biosorbent using wheat straw and Eupatorium adenophorum through simple carbonization process, capable of removing Cr (VI) efficiently from wastewater. From studied plants a low cost adsorbent was prepared for removing Cr (VI) from aqueous solution following very simple carbonization method excluding activation process. Several factors such as pH, contact time, sorbent dosage and temperature were investigated for attaining ideal condition. For analysis of adsorption equilibrium isotherm data, Langmuir, Freundlich and Temkin models were used while pseudo-first-order, pseudo-second-order, external diffusion and intra-particle diffusion models were used for the analysis of kinetic data. The obtained results revealed that 99.9% of Cr (VI) removal was observed in the solution with a pH of 1.0. Among all the tested models Langmuir model fitted more closely according to the data obtained. Increase in adsorption capacity was observed with increasing temperature revealing endothermic nature of Cr (VI). The maximum Cr (VI) adsorption potential of E. adenophorum and wheat straw was 89.22 mg per 1 gram adsorbent at 308K. Kinetic data of absorption precisely followed pseudo-second-order model. Present study revealed highest potential of E. adenophorum and wheat straw for producing low cost adsorbent and to remove Cr (VI) from contaminated water. PMID:27911906

Adsorptive Removal of Toxic Chromium from Waste-Water Using Wheat Straw and Eupatorium adenophorum.

PubMed

Song, Dagang; Pan, Kaiwen; Tariq, Akash; Azizullah, Azizullah; Sun, Feng; Li, Zilong; Xiong, Qinli

2016-01-01

Environmental pollution with heavy metals is a serious issue worldwide posing threats to humans, animals and plants and to the stability of overall ecosystem. Chromium (Cr) is one of most hazardous heavy metals with a high carcinogenic and recalcitrant nature. Aim of the present study was to select low-cost biosorbent using wheat straw and Eupatorium adenophorum through simple carbonization process, capable of removing Cr (VI) efficiently from wastewater. From studied plants a low cost adsorbent was prepared for removing Cr (VI) from aqueous solution following very simple carbonization method excluding activation process. Several factors such as pH, contact time, sorbent dosage and temperature were investigated for attaining ideal condition. For analysis of adsorption equilibrium isotherm data, Langmuir, Freundlich and Temkin models were used while pseudo-first-order, pseudo-second-order, external diffusion and intra-particle diffusion models were used for the analysis of kinetic data. The obtained results revealed that 99.9% of Cr (VI) removal was observed in the solution with a pH of 1.0. Among all the tested models Langmuir model fitted more closely according to the data obtained. Increase in adsorption capacity was observed with increasing temperature revealing endothermic nature of Cr (VI). The maximum Cr (VI) adsorption potential of E. adenophorum and wheat straw was 89.22 mg per 1 gram adsorbent at 308K. Kinetic data of absorption precisely followed pseudo-second-order model. Present study revealed highest potential of E. adenophorum and wheat straw for producing low cost adsorbent and to remove Cr (VI) from contaminated water.

Diffusion with social reinforcement: The role of individual preferences

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Characterization of Tissue Structure at Varying Length Scales Using Temporal Diffusion Spectroscopy

PubMed Central

Gore, John C.; Xu, Junzhong; Colvin, Daniel C.; Yankeelov, Thomas E.; Parsons, Edward C.; Does, Mark D.

2011-01-01

The concepts, theoretical behavior and experimental applications of temporal diffusion spectroscopy are reviewed and illustrated. Temporal diffusion spectra are obtained by using oscillating gradient waveforms in diffusion-weighted measurements, and represent the manner in which various spectral components of molecular velocity correlations vary in different geometrical structures that restrict or hinder free movements. Measurements made at different gradient frequencies reveal information on the scale of restrictions or hindrances to free diffusion, and the shape of a spectrum reveals the relative contributions of spatial restrictions at different distance scales. Such spectra differ from other so-called diffusion spectra which depict spatial frequencies and are defined at a fixed diffusion time. Experimentally, oscillating gradients at moderate frequency are more feasible for exploring restrictions at very short distances, which in tissues correspond to structures smaller than cells. We describe the underlying concepts of temporal diffusion spectra and provide analytical expressions for the behavior of the diffusion coefficient as a function of gradient frequency in simple geometries with different dimensions. Diffusion in more complex model media that mimic tissues has been simulated using numerical methods. Experimental measurements of diffusion spectra have been obtained in suspensions of particles and cells, as well as in vivo in intact animals. An observation of particular interest is the increased contrast and heterogeneity observed in tumors using oscillating gradients at moderate frequency compared to conventional pulse gradient methods, and the potential for detecting changes in tumors early in their response to treatment. Computer simulations suggest that diffusion spectral measurements may be sensitive to intracellular structures such as nuclear size, and that changes in tissue diffusion properties may be measured before there are changes in cell density. PMID:20677208

Causal Loop Analysis of coastal geomorphological systems

NASA Astrophysics Data System (ADS)

Payo, Andres; Hall, Jim W.; French, Jon; Sutherland, James; van Maanen, Barend; Nicholls, Robert J.; Reeve, Dominic E.

2016-03-01

As geomorphologists embrace ever more sophisticated theoretical frameworks that shift from simple notions of evolution towards single steady equilibria to recognise the possibility of multiple response pathways and outcomes, morphodynamic modellers are facing the problem of how to keep track of an ever-greater number of system feedbacks. Within coastal geomorphology, capturing these feedbacks is critically important, especially as the focus of activity shifts from reductionist models founded on sediment transport fundamentals to more synthesist ones intended to resolve emergent behaviours at decadal to centennial scales. This paper addresses the challenge of mapping the feedback structure of processes controlling geomorphic system behaviour with reference to illustrative applications of Causal Loop Analysis at two study cases: (1) the erosion-accretion behaviour of graded (mixed) sediment beds, and (2) the local alongshore sediment fluxes of sand-rich shorelines. These case study examples are chosen on account of their central role in the quantitative modelling of geomorphological futures and as they illustrate different types of causation. Causal loop diagrams, a form of directed graph, are used to distil the feedback structure to reveal, in advance of more quantitative modelling, multi-response pathways and multiple outcomes. In the case of graded sediment bed, up to three different outcomes (no response, and two disequilibrium states) can be derived from a simple qualitative stability analysis. For the sand-rich local shoreline behaviour case, two fundamentally different responses of the shoreline (diffusive and anti-diffusive), triggered by small changes of the shoreline cross-shore position, can be inferred purely through analysis of the causal pathways. Explicit depiction of feedback-structure diagrams is beneficial when developing numerical models to explore coastal morphological futures. By explicitly mapping the feedbacks included and neglected within a model, the modeller can readily assess if critical feedback loops are included.

Test of electical resistivity and current diffusion modelling on MAST and JET

NASA Astrophysics Data System (ADS)

Keeling, D. L.; Challis, C. D.; Jenkins, I.; Hawkes, N. C.; Lupelli, I.; Michael, C.; de Bock, M. F. M.; the MAST Team; contributors, JET

2018-01-01

Experiments have been carried out on the MAST and JET tokamaks intended to compare the electrical resistivity of the plasma with theoretical formulations. The tests consist of obtaining motional stark effect (MSE) measurements in MHD-free plasmas during plasma current ramp-up (JET and MAST), ramp-down (MAST) and in stationary state (JET and MAST). Simulations of these plasmas are then performed in which the current profile evolution is calculated according to the poloidal field diffusion equation (PFDE) with classical or neoclassical resistivity. Synthetic MSE data are produced in the simulations for direct comparison with the experimental data. It is found that the toroidal current profile evolution modelled using neoclassical resistivity did not match the experimental observations on either device during current ramp-up or ramp-down as concluded from comparison of experimental and synthetic MSE profiles. In these phases, use of neoclassical resistivity in the modelling systematically overestimates the rate of current profile evolution. During the stationary state however, the modelled toroidal current profile matched experimental observations to a high degree of accuracy on both devices using neoclassical resistivity. Whilst no solution to the mismatch in the dynamic phases of the plasma is proposed, it is suggested that some physical process other than MHD which is not captured by the simple diffusive model of current profile evolution is responsible.

Anisotropic diffusion and capture on surfaces: Time dependent modeling and visualization in 2 dimensions

NASA Astrophysics Data System (ADS)

Yang, Pu

Since the application of nanowires may lead to a new generation of electronic, optoelectronic and magnetic devices, there is much research on understanding the growth mechanism of various "self assembled" nanowires on semiconductor surfaces. The motivation of the present work is to use theoretical modeling to study the conditions required to form and grow elongated islands and nanowires. In this work, a modeling method is developed to study the time-dependent anisotropic diffusion and growth in two dimensions for an array of rectangular islands. This method uses discrete Fast Fourier Transformation (FFT) to solve the time-dependent diffusion equation on the surface. The ad-particles are captured and incorporated to the island edge to simulate island growth. Implemented in MATLABRTM programs, this model produces expected faceted shapes; the calculation runs very fast on a common personal computer. Time-dependent island growth and the evolving diffusion field have been visualized using simple MATLABRTM functions and can be made into MATLABRTM movies. This modeling method is applied to simulate elongated island and nanowire growth by incorporating anisotropic bonding at the island edge. When there is a full sink in one direction and partial sink in the other direction at the island edge, the model results in the growth of an elongated island with an aspect ratio that stabilizes after it reaches a certain value. This result agrees with experimental data on "endotaxial" nanowire growth. For the island edge with a full sink in one direction and no sink in the other direction, the island grows in length with constant width, which is comparable to experimental data on Bi nanoline and rare-earth metal nanowire growth.

A Theory for Stability and Buzz Pulsation Amplitude in Ram Jets and an Experimental Investigation Including Scale Effects

NASA Technical Reports Server (NTRS)

Trimpi, Robert L

1956-01-01

From a theory developed on a quasi-one-dimensional-flow basis, it is found that the stability of the ram jet is dependent upon the instantaneous values of mass flow and total pressure recovery of the supersonic diffuser and immediate neighboring subsonic diffuser. Conditions for stable and unstable flow are presented. The theory developed in the report is in agreement with the experimental data of NACA-TN-3506 and NACA-RM-L50K30. A simple theory for predicting the approximate amplitude of small pressure pulsation in terms of mass-flow decrement from minimum-stable mass flow is developed and found to agree with experiments. Cold-flow tests at a Mach number of 1.94 of ram-jet models having scale factors of 3.15:1 and Reynolds number ratios of 4.75:1 with several supersonic diffuser configurations showed only small variations in performance between geometrically similar models. The predominant variation in steady-flow performance resulted from the larger boundary layer in the combustion chamber of the low Reynolds number models. The conditions at which buzz originated were nearly the same for the same supersonic diffuser (cowling-position angle) configurations in both large and small diameter models. There was no appreciable variation in stability limits of any of the models when the combustion-chamber length was increased by a factor of three. The unsteady-flow performance and wave patterns were also similar when considered on a reduced-frequency basis determined from the relative lengths of the model. The negligible effect of Reynolds number on stability of the off-design configurations was not anticipated in view of the importance of boundary layer to stability, and this result should not be construed to be generally applicable. (author)

Metapopulation models for historical inference.

PubMed

Wakeley, John

2004-04-01

The genealogical process for a sample from a metapopulation, in which local populations are connected by migration and can undergo extinction and subsequent recolonization, is shown to have a relatively simple structure in the limit as the number of populations in the metapopulation approaches infinity. The result, which is an approximation to the ancestral behaviour of samples from a metapopulation with a large number of populations, is the same as that previously described for other metapopulation models, namely that the genealogical process is closely related to Kingman's unstructured coalescent. The present work considers a more general class of models that includes two kinds of extinction and recolonization, and the possibility that gamete production precedes extinction. In addition, following other recent work, this result for a metapopulation divided into many populations is shown to hold both for finite population sizes and in the usual diffusion limit, which assumes that population sizes are large. Examples illustrate when the usual diffusion limit is appropriate and when it is not. Some shortcomings and extensions of the model are considered, and the relevance of such models to understanding human history is discussed.

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Application of the isotope-dilution principle to the analysis of factors affecting the incorporation of [3H]uridine and [3H]cytidine into cultured lymphocytes. Evaluation of pools in serum and culture media

PubMed Central

Forsdyke, D. R.

1971-01-01

1. Rat lymph-node cells were incubated in serum and medium 199 with [5-3H]uridine or [5-3H]cytidine and acid-precipitable radioactivity was measured. Results were interpreted in terms of an isotope-dilution model. 2. Both serum and medium 199 contained pools that inhibited radioactive labelling in a competitive manner. The serum activity was diffusible and inhibited labelling with [3H]cytidine more than with [3H]uridine; in these respects the activity resembled cytidine (14μm). 3. The pools in serum and plasma were the same size; however, the rate of labelling was greater in plasma, owing to a diffusible factor. 4. Paradoxically, relatively simple media (Earle's salts and Eagle's minimum essential) appeared to have a larger pool than the more complex pyrimidine-containing medium 199; this suggests a contribution to the pool by cells in the simple media. 5. In the absence of pools the average cell was capable of incorporating 2000 radioactive nucleoside molecules/s. PMID:4947658

Phase-field crystal modeling of heteroepitaxy and exotic modes of crystal nucleation

NASA Astrophysics Data System (ADS)

Podmaniczky, Frigyes; Tóth, Gyula I.; Tegze, György; Pusztai, Tamás; Gránásy, László

2017-01-01

We review recent advances made in modeling heteroepitaxy, two-step nucleation, and nucleation at the growth front within the framework of a simple dynamical density functional theory, the Phase-Field Crystal (PFC) model. The crystalline substrate is represented by spatially confined periodic potentials. We investigate the misfit dependence of the critical thickness in the StranskiKrastanov growth mode in isothermal studies. Apparently, the simulation results for stress release via the misfit dislocations fit better to the PeopleBean model than to the one by Matthews and Blakeslee. Next, we investigate structural aspects of two-step crystal nucleation at high undercoolings, where an amorphous precursor forms in the first stage. Finally, we present results for the formation of new grains at the solid-liquid interface at high supersaturations/supercoolings, a phenomenon termed Growth Front Nucleation (GFN). Results obtained with diffusive dynamics (applicable to colloids) and with a hydrodynamic extension of the PFC theory (HPFC, developed for simple liquids) will be compared. The HPFC simulations indicate two possible mechanisms for GFN.

Analysis of bacterial migration. 2: Studies with multiple attractant gradients

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

Strauss, I.; Frymier, P.D.; Hahn, C.M.

1995-02-01

Many motile bacteria exhibit chemotaxis, the ability to bias their random motion toward or away from increasing concentrations of chemical substances which benefit or inhibit their survival, respectively. Since bacteria encounter numerous chemical concentration gradients simultaneously in natural surroundings, it is necessary to know quantitatively how a bacterial population responds in the presence of more than one chemical stimulus to develop predictive mathematical models describing bacterial migration in natural systems. This work evaluates three hypothetical models describing the integration of chemical signals from multiple stimuli: high sensitivity, maximum signal, and simple additivity. An expression for the tumbling probability for individualmore » stimuli is modified according to the proposed models and incorporated into the cell balance equation for a 1-D attractant gradient. Random motility and chemotactic sensitivity coefficients, required input parameters for the model, are measured for single stimulus responses. Theoretical predictions with the three signal integration models are compared to the net chemotactic response of Escherichia coli to co- and antidirectional gradients of D-fucose and [alpha]-methylaspartate in the stopped-flow diffusion chamber assay. Results eliminate the high-sensitivity model and favor the simple additivity over the maximum signal. None of the simple models, however, accurately predict the observed behavior, suggesting a more complex model with more steps in the signal processing mechanism is required to predict responses to multiple stimuli.« less

Dynamics of two-dimensional monolayer water confined in hydrophobic and charged environments.

PubMed

Kumar, Pradeep; Han, Sungho

2012-09-21

We perform molecular dynamics simulations to study the effect of charged surfaces on the intermediate and long time dynamics of water in nanoconfinements. Here, we use the transferable interaction potential with five points (TIP5P) model of a water molecule confined in both hydrophobic and charged surfaces. For a single molecular layer of water between the surfaces, we find that the temperature dependence of the lateral diffusion constant of water up to very high temperatures remains Arrhenius with a high activation energy. In case of charged surfaces, however, the dynamics of water in the intermediate time regime is drastically modified presumably due to the transient coupling of dipoles of water molecules with electric field fluctuations induced by charges on the confining surfaces. Specifically, the lateral mean square displacements display a distinct super-diffusive behavior at intermediate time scale, defined as the time scale between ballistic and diffusive regimes. This change in the intermediate time-scale dynamics in the charged confinement leads to the enhancement of long-time dynamics as reflected in increasing diffusion constant. We introduce a simple model for a possible explanation of the super-diffusive behavior and find it to be in good agreement with our simulation results. Furthermore, we find that confinement and the surface polarity enhance the low frequency vibration in confinement compared to bulk water. By introducing a new effective length scale of coupling between translational and orientational motions, we find that the length scale increases with the increasing strength of the surface polarity. Further, we calculate the correlation between the diffusion constant and the excess entropy and find a disordering effect of polar surfaces on the structure of water. Finally, we find that the empirical relation between the diffusion constant and the excess entropy holds for a monolayer of water in nanoconfinement.

Scaling for the SOL/separatrix χ ⊥ following from the heuristic drift model for the power scrape-off layer width

NASA Astrophysics Data System (ADS)

Huber, A.; Chankin, A. V.

2017-06-01

A simple two-point representation of the tokamak scrape-off layer (SOL) in the conduction limited regime, based on the parallel and perpendicular energy balance equations in combination with the heat flux width predicted by a heuristic drift-based model, was used to derive a scaling for the cross-field thermal diffusivity {χ }\\perp . For fixed plasma shape and neglecting weak power dependence indexes 1/8, the scaling {χ }\\perp \\propto {P}{{S}{{O}}{{L}}}/(n{B}θ {R}2) is derived.

Diffusion of a new intermediate product in a simple 'classical-Schumpeterian' model.

PubMed

Haas, David

2018-05-01

This paper deals with the problem of new intermediate products within a simple model, where production is circular and goods enter into the production of other goods. It studies the process by which the new good is absorbed into the economy and the structural transformation that goes with it. By means of a long-period method the forces of structural transformation are examined, in particular the shift of existing means of production towards the innovation and the mechanism of differential growth in terms of alternative techniques and their associated systems of production. We treat two important Schumpeterian topics: the question of technological unemployment and the problem of 'forced saving' and the related problem of an involuntary reduction of real consumption per capita. It is shown that both phenomena are potential by-products of the transformation process.

Mathematical Modeling the Geometric Regularity in Proteus Mirabilis Colonies

NASA Astrophysics Data System (ADS)

Zhang, Bin; Jiang, Yi; Minsu Kim Collaboration

Proteus Mirabilis colony exhibits striking spatiotemporal regularity, with concentric ring patterns with alternative high and low bacteria density in space, and periodicity for repetition process of growth and swarm in time. We present a simple mathematical model to explain the spatiotemporal regularity of P. Mirabilis colonies. We study a one-dimensional system. Using a reaction-diffusion model with thresholds in cell density and nutrient concentration, we recreated periodic growth and spread patterns, suggesting that the nutrient constraint and cell density regulation might be sufficient to explain the spatiotemporal periodicity in P. Mirabilis colonies. We further verify this result using a cell based model.

Generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

18O-tracer diffusion along nanoscaled Sc2O3/yttria stabilized zirconia (YSZ) multilayers: on the influence of strain

PubMed Central

Aydin, Halit; Korte, Carsten; Janek, Jürgen

2013-01-01

The oxygen tracer diffusion coefficient describing transport along nano-/microscaled YSZ/Sc2O3 multilayers as a function of the thick­ness of the ion-conducting YSZ layers has been measured by isotope exchange depth profiling (IEDP), using secondary ion mass spec­trometry (SIMS). The multilayer samples were prepared by pulsed laser deposition (PLD) on (0001) Al2O3 single crystalline substrates. The values for the oxygen tracer diffusion coefficient were analyzed as a combination of contributions from bulk and interface contributions and compared with results from YSZ/Y2O3-multilayers with similar microstructure. Using the Nernst–Einstein equation as the relation between diffusivity and electrical conductivity we find very good agreement between conductivity and diffusion data, and we exclude substantial electronic conductivity in the multilayers. The effect of hetero-interface transport can be well explained by a simple interface strain model. As the multilayer samples consist of columnar film crystallites with a defined inter­face structure and texture, we also discuss the influence of this particular microstructure on the interfacial strain. PMID:27877580

Communication: Diverse nanoscale cluster dynamics: Diffusion of 2D epitaxial clusters

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

Lai, King C.; Evans, James W.; Liu, Da -Jiang

The dynamics of nanoscale clusters can be distinct from macroscale behavior described by continuum formalisms. For diffusion of 2D clusters of N atoms in homoepitaxial systems mediated by edge atom hopping, macroscale theory predicts simple monotonic size scaling of the diffusion coefficient, D N ~ N –β, with β = 3/2. However, modeling for nanoclusters on metal(100) surfaces reveals that slow nucleation-mediated diffusion displaying weak size scaling β < 1 occurs for “perfect” sizes N p = L 2 and L(L+1) for integer L = 3,4,… (with unique square or near-square ground state shapes), and also for N p+3, Nmore » p+4,…. In contrast, fast facile nucleation-free diffusion displaying strong size scaling β ≈ 2.5 occurs for sizes N p+1 and N p+2. D N versus N oscillates strongly between the slowest branch (for N p+3) and the fastest branch (for N p+1). All branches merge for N = O(10 2), but macroscale behavior is only achieved for much larger N = O(10 3). Here, this analysis reveals the unprecedented diversity of behavior on the nanoscale.« less

Communication: Diverse nanoscale cluster dynamics: Diffusion of 2D epitaxial clusters

DOE PAGES

Lai, King C.; Evans, James W.; Liu, Da -Jiang

2017-11-27

The dynamics of nanoscale clusters can be distinct from macroscale behavior described by continuum formalisms. For diffusion of 2D clusters of N atoms in homoepitaxial systems mediated by edge atom hopping, macroscale theory predicts simple monotonic size scaling of the diffusion coefficient, D N ~ N –β, with β = 3/2. However, modeling for nanoclusters on metal(100) surfaces reveals that slow nucleation-mediated diffusion displaying weak size scaling β < 1 occurs for “perfect” sizes N p = L 2 and L(L+1) for integer L = 3,4,… (with unique square or near-square ground state shapes), and also for N p+3, Nmore » p+4,…. In contrast, fast facile nucleation-free diffusion displaying strong size scaling β ≈ 2.5 occurs for sizes N p+1 and N p+2. D N versus N oscillates strongly between the slowest branch (for N p+3) and the fastest branch (for N p+1). All branches merge for N = O(10 2), but macroscale behavior is only achieved for much larger N = O(10 3). Here, this analysis reveals the unprecedented diversity of behavior on the nanoscale.« less

Twin-domain size and bulk oxygen in-diffusion kinetics of YBa 2Cu 3O 6+x studied by neutron powder diffraction and gas volumetry

NASA Astrophysics Data System (ADS)

Poulsen, H. F.; Andersen, N. H.; Lebech, B.

1991-02-01

We report experimental results of twin-domain size and bulk oxygen in-diffusion kinetics of YBa 2Cu 3O 6+ x, which supplement a previous and simultaneous study of the structural phase diagram and oxygen equilibrium partial pressure. Analysis of neutron powder diffraction peak broadening show features which are identified to result from temperature independent twin-domain formation in to different orthorhombic phases with domain sizes and 250 and 350Å, respectively. The oxygen in-diffusion flow shows simple relaxation type behaviour J=J 0 exp( {-t}/{τ}) despite a rather broad particle size distribution. At higher temperatures, τ is activated with activation energies 0.55 and 0.25 eV in the tetragonal and orthorhombic phases, respectively. Comparison between twin-domain sizes and bulk oxygen in-diffusion time constants indicates that the twin-domain boundaries may contribute to the effective bulk oxygen in-diffusion. All our results may be interpreted in terms of the 2D ASYNNNI model description of the oxygen basal plane ordering, and they suggest that recent first principles interaction parameters should be modified.

Startup analysis for a high temperature gas loaded heat pipe

NASA Technical Reports Server (NTRS)

Sockol, P. M.

1973-01-01

A model for the rapid startup of a high-temperature gas-loaded heat pipe is presented. A two-dimensional diffusion analysis is used to determine the rate of energy transport by the vapor between the hot and cold zones of the pipe. The vapor transport rate is then incorporated in a simple thermal model of the startup of a radiation-cooled heat pipe. Numerical results for an argon-lithium system show that radial diffusion to the cold wall can produce large vapor flow rates during a rapid startup. The results also show that startup is not initiated until the vapor pressure p sub v in the hot zone reaches a precise value proportional to the initial gas pressure p sub i. Through proper choice of p sub i, startup can be delayed until p sub v is large enough to support a heat-transfer rate sufficient to overcome a thermal load on the heat pipe.

Fuzzy Neural Network Applied to Gene Expression Profiling for Predicting the Prognosis of Diffuse Large B‐cell Lymphoma

PubMed Central

Ando, Tatsuya; Suguro, Miyuki; Hanai, Taizo; Kobayashi, Takeshi; Seto, Masao

2002-01-01

Diffuse large B‐cell lymphoma (DLBCL) is the largest category of aggressive lymphomas. Less than 50% of patients can be cured by combination chemotherapy. Microarray technologies have recently shown that the response to chemotherapy reflects the molecular heterogeneity in DLBCL. On the basis of published microarray data, we attempted to develop a long‐overdue method for the precise and simple prediction of survival of DLBCL patients. We developed a fuzzy neural network (FNN) model to analyze gene expression profiling data for DLBCL. From data on 5857 genes, this model identified four genes (CD10, AA807551, AA805611 and IRF‐4) that could be used to predict prognosis with 93% accuracy. FNNs are powerful tools for extracting significant biological markers affecting prognosis, and are applicable to various kinds of expression profiling data for any malignancy. PMID:12460461

Statistical mechanics of an ideal active fluid confined in a channel

NASA Astrophysics Data System (ADS)

Wagner, Caleb; Baskaran, Aparna; Hagan, Michael

The statistical mechanics of ideal active Brownian particles (ABPs) confined in a channel is studied by obtaining the exact solution of the steady-state Smoluchowski equation for the 1-particle distribution function. The solution is derived using results from the theory of two-way diffusion equations, combined with an iterative procedure that is justified by numerical results. Using this solution, we quantify the effects of confinement on the spatial and orientational order of the ensemble. Moreover, we rigorously show that both the bulk density and the fraction of particles on the channel walls obey simple scaling relations as a function of channel width. By considering a constant-flux steady state, an effective diffusivity for ABPs is derived which shows signatures of the persistent motion that characterizes ABP trajectories. Finally, we discuss how our techniques generalize to other active models, including systems whose activity is modeled in terms of an Ornstein-Uhlenbeck process.

The predictive power of zero intelligence in financial markets.

PubMed

Farmer, J Doyne; Patelli, Paolo; Zovko, Ilija I

2005-02-08

Standard models in economics stress the role of intelligent agents who maximize utility. However, there may be situations where constraints imposed by market institutions dominate strategic agent behavior. We use data from the London Stock Exchange to test a simple model in which minimally intelligent agents place orders to trade at random. The model treats the statistical mechanics of order placement, price formation, and the accumulation of revealed supply and demand within the context of the continuous double auction and yields simple laws relating order-arrival rates to statistical properties of the market. We test the validity of these laws in explaining cross-sectional variation for 11 stocks. The model explains 96% of the variance of the gap between the best buying and selling prices (the spread) and 76% of the variance of the price diffusion rate, with only one free parameter. We also study the market impact function, describing the response of quoted prices to the arrival of new orders. The nondimensional coordinates dictated by the model approximately collapse data from different stocks onto a single curve. This work is important from a practical point of view, because it demonstrates the existence of simple laws relating prices to order flows and, in a broader context, suggests there are circumstances where the strategic behavior of agents may be dominated by other considerations.

A model of return intervals between earthquake events

NASA Astrophysics Data System (ADS)

Zhou, Yu; Chechkin, Aleksei; Sokolov, Igor M.; Kantz, Holger

2016-06-01

Application of the diffusion entropy analysis and the standard deviation analysis to the time sequence of the southern California earthquake events from 1976 to 2002 uncovered scaling behavior typical for anomalous diffusion. However, the origin of such behavior is still under debate. Some studies attribute the scaling behavior to the correlations in the return intervals, or waiting times, between aftershocks or mainshocks. To elucidate a nature of the scaling, we applied specific reshulffling techniques to eliminate correlations between different types of events and then examined how it affects the scaling behavior. We demonstrate that the origin of the scaling behavior observed is the interplay between mainshock waiting time distribution and the structure of clusters of aftershocks, but not correlations in waiting times between the mainshocks and aftershocks themselves. Our findings are corroborated by numerical simulations of a simple model showing a very similar behavior. The mainshocks are modeled by a renewal process with a power-law waiting time distribution between events, and aftershocks follow a nonhomogeneous Poisson process with the rate governed by Omori's law.

Cancerous tumor: the high frequency of a rare event.

PubMed

Galam, S; Radomski, J P

2001-05-01

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

Heat localization for targeted tumor treatment with nanoscale near-infrared radiation absorbers

PubMed Central

Xie, Bin; Singh, Ravi; Torti, F. M.; Keblinski, Pawel; Torti, Suzy

2012-01-01

Focusing heat delivery while minimizing collateral damage to normal tissues is essential for successful nanoparticle-mediated laser-induced thermal cancer therapy. We present thermal maps obtained via magnetic resonance imaging (MRI) characterizing laser heating of a phantom tissue containing a multiwalled carbon nanotube inclusion. The data demonstrate that heating continuously over tens of seconds leads to poor localization (~ 0.5 cm) of the elevated temperature region. By contrast, for the same energy input, heat localization can be reduced to the millimeter rather than centimeter range by increasing the laser power and shortening the pulse duration. The experimental data can be well understood within a simple diffusive heat conduction model. Analysis of the model indicates that to achieve 1 mm or better resolution, heating pulses of ~ 2s or less need to be used with appropriately higher heating power. Modeling these data using a diffusive heat conduction analysis predicts parameters for optimal targeted delivery of heat for ablative therapy. PMID:22948207

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

NASA Astrophysics Data System (ADS)

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

2005-05-01

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

Growing surfaces with anomalous diffusion: Results for the fractal Kardar-Parisi-Zhang equation

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2003-09-01

In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. It is shown that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, the self-consistent expansion (SCE) is used to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the fractal KPZ equation is suggested and the upper critical dimension of this model is discussed.

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

NASA Astrophysics Data System (ADS)

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

2010-12-01

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

A Simple Parameterization of Mixing of Passive Scalars in Turbulent Flows

NASA Astrophysics Data System (ADS)

Nithianantham, Ajithshanthar; Venayagamoorthy, Karan

2015-11-01

A practical model for quantifying the turbulent diascalar diffusivity is proposed as Ks = 1 . 1γ'LTk 1 / 2 , where LT is defined as the Thorpe length scale, k is the turbulent kinetic energy and γ' is one-half of the mechanical to scalar time scale ratio, which was shown by previous researchers to be approximately 0 . 7 . The novelty of the proposed model lies in the use of LT, which is a widely used length scale in stably stratified flows (almost exclusively used in oceanography), for quantifying turbulent mixing in unstratified flows. LT can be readily obtained in the field using a Conductivity, Temperature and Depth (CTD) profiler. The turbulent kinetic energy is mostly contained in the large scales of the flow field and hence can be measured in the field or modeled in numerical simulations. Comparisons using DNS data show remarkably good agreement between the predicted and exact diffusivities. Office of Naval Research and National Science Foundation.

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

NASA Astrophysics Data System (ADS)

Newton, P. K.; Meiburg, Eckart

1991-05-01

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

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).

Strange kinetics of bulk-mediated diffusion on lipid bilayers

PubMed Central

Campagnola, Grace; Nepal, Kanti; Peersen, Olve B.

2016-01-01

Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide rich complexities. In particular, bulk-mediated diffusion occurs when molecules are transiently released from the surface to perform three-dimensional excursions into the liquid bulk. This phenomenon bears the dichotomy where a molecule always return to the surface but the mean jump length is infinite. Such behavior is associated with a breakdown of the central limit theorem and weak ergodicity breaking. Here, we use single-particle tracking to study the statistics of bulk-mediated diffusion on a supported lipid bilayer. We find that the time-averaged mean square displacement (MSD) of individual trajectories, the archetypal measure in diffusion processes, does not converge to the ensemble MSD but it remains a random variable, even in the long observation-time limit. The distribution of time averages is shown to agree with a Lévy flight model. Our results also unravel intriguing anomalies in the statistics of displacements. The time averaged MSD is shown to depend on experimental time and investigations of fractional moments show a scaling 〈|r(t)|q〉 ∼ tqv(q) with non-linear exponents, i.e. v(q) ≠ const. This type of behavior is termed strong anomalous diffusion and is rare among experimental observations. PMID:27095275

Confinement Regulates Complex Biochemical Networks: Initiation of Blood Clotting by “Diffusion Acting”

PubMed Central

Shen, Feng; Pompano, Rebecca R.; Kastrup, Christian J.; Ismagilov, Rustem F.

2009-01-01

Abstract This study shows that environmental confinement strongly affects the activation of nonlinear reaction networks, such as blood coagulation (clotting), by small quantities of activators. Blood coagulation is sensitive to the local concentration of soluble activators, initiating only when the activators surpass a threshold concentration, and therefore is regulated by mass transport phenomena such as flow and diffusion. Here, diffusion was limited by decreasing the size of microfluidic chambers, and it was found that microparticles carrying either the classical stimulus, tissue factor, or a bacterial stimulus, Bacillus cereus, initiated coagulation of human platelet-poor plasma only when confined. A simple analytical argument and numerical model were used to describe the mechanism for this phenomenon: confinement causes diffusible activators to accumulate locally and surpass the threshold concentration. To interpret the results, a dimensionless confinement number, Cn, was used to describe whether a stimulus was confined, and a Damköhler number, Da2, was used to describe whether a subthreshold stimulus could initiate coagulation. In the context of initiation of coagulation by bacteria, this mechanism can be thought of as “diffusion acting”, which is distinct from “diffusion sensing”. The ability of confinement and diffusion acting to change the outcome of coagulation suggests that confinement should also regulate other biological “on” and “off” processes that are controlled by thresholds. PMID:19843446

An improved strip FRAP method for estimating diffusion coefficients: correcting for the degree of photobleaching.

PubMed

Yang, J; Köhler, K; Davis, D M; Burroughs, N J

2010-06-01

Fluorescence recovery after photobleaching is a widely established method for the estimation of diffusion coefficients, strip bleaching with an associated recovery curve analysis being one of the simplest techniques. However, its implementation requires near 100% bleaching in the region of interest with negligible fluorescence loss outside, both constraints being hard to achieve concomitantly for fast diffusing molecules. We demonstrate that when these requirements are not met there is an error in the estimation of the diffusion coefficient D, either an under- or overestimation depending on which assumption is violated the most. We propose a simple modification to the recovery curve analysis incorporating the concept of the relative bleached mass m giving a revised recovery time parametrization tau=m(2)w(2)/4piD for a strip of width w. This modified model removes the requirement of 100% bleaching in the region of interest and allows for limited diffusion of the fluorophore during bleaching. We validate our method by estimating the (volume) diffusion coefficient of FITC-labelled IgG in 60% glycerol solution, D= 4.09 +/- 0.21 microm(2) s(-1), and the (surface) diffusion coefficient of a green-fluorescent protein-tagged class I MHC protein expressed at the surface of a human B cell line, D= 0.32 +/- 0.03 microm(2) s(-1) for a population of cells.

Role of boundary layer diffusion in vapor deposition growth of chalcogenide nanosheets: the case of GeS.

PubMed

Li, Chun; Huang, Liang; Snigdha, Gayatri Pongur; Yu, Yifei; Cao, Linyou

2012-10-23

We report a synthesis of single-crystalline two-dimensional GeS nanosheets using vapor deposition processes and show that the growth behavior of the nanosheet is substantially different from those of other nanomaterials and thin films grown by vapor depositions. The nanosheet growth is subject to strong influences of the diffusion of source materials through the boundary layer of gas flows. This boundary layer diffusion is found to be the rate-determining step of the growth under typical experimental conditions, evidenced by a substantial dependence of the nanosheet's size on diffusion fluxes. We also find that high-quality GeS nanosheets can grow only in the diffusion-limited regime, as the crystalline quality substantially deteriorates when the rate-determining step is changed away from the boundary layer diffusion. We establish a simple model to analyze the diffusion dynamics in experiments. Our analysis uncovers an intuitive correlation of diffusion flux with the partial pressure of source materials, the flow rate of carrier gas, and the total pressure in the synthetic setup. The observed significant role of boundary layer diffusions in the growth is unique for nanosheets. It may be correlated with the high growth rate of GeS nanosheets, ~3-5 μm/min, which is 1 order of magnitude higher than other nanomaterials (such as nanowires) and thin films. This fundamental understanding of the effect of boundary layer diffusions may generally apply to other chalcogenide nanosheets that can grow rapidly. It can provide useful guidance for the development of general paradigms to control the synthesis of nanosheets.

Flow interaction in the combustor-diffusor system of industrial gas turbines

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

Agrawal, A.K.; Kapat, J.S.; Yang, T.

1996-05-01

This paper presents an experimental/computational study of cold flow in the combustor-diffuser system of industrial gas turbines to address issues relating to flow interactions and pressure losses in the pre- and dump diffusers. The present configuration with can annular combustors differs substantially from the aircraft engines which typically use a 360 degree annular combustor. Experiments were conducted in a one-third scale, annular 360-degree model using several can combustors equispaced around the turbine axis. A 3-D computational fluid dynamics analysis employing the multidomain procedure was performed to supplement the flow measurements. The measured data correlated well with the computations. The airflowmore » in the dump diffuser adversely affected the prediffuser flow by causing it to accelerate in the outer region at the prediffuser exit. This phenomenon referred to as the sink-effect also caused a large fraction of the flow to bypass much of the dump diffuser and go directly from the prediffuser exit to the bypass air holes on the combustor casing, thereby, rendering the dump diffuser ineffective in diffusing the flow. The dump diffuser was occupied by a large recirculation region which dissipated the flow kinetic energy. Approximately 1.2 dynamic head at the prediffuser inlet was lost in the combustor-diffuser system; much of it in the dump diffuser where the fluid passed through the narrow gaps and pathways. Strong flow interactions in the combustor-diffuser system indicate the need for design modifications which could not be addressed by empirical correlations based on simple flow configurations.« less

A 3-Component System of Competition and Diffusion.

DTIC Science & Technology

1983-08-01

assume * that the distribution of the populations are determined by competition of’ Lotka - Volterra - * Gause type and simple diffusion. Suppose ui(t,x...diffusive Lotka - Volterra system with three species can have a stable non-constant equilibrium solutions. J. Math. Biol., (in press). [7] Kishimoto, K., Mimura...M. and Yoshida, K., Stable spatlo-temporal oscillations of diffusive Lotka - Volterra systems with three or more species, to appear in J. Math. Biol

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

PubMed

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

2014-08-01

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

Point-particle method to compute diffusion-limited cellular uptake.

PubMed

Sozza, A; Piazza, F; Cencini, M; De Lillo, F; Boffetta, G

2018-02-01

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of the method by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences.

BRDF Calibration of Sintered PTFE in the SWIR

NASA Technical Reports Server (NTRS)

Georgiev, Georgi T.; Butler, James J.

2009-01-01

Satellite instruments operating in the reflective solar wavelength region often require accurate and precise determination of the Bidirectional Reflectance Distribution Function (BRDF) of laboratory-based diffusers used in their pre-flight calibrations and ground-based support of on-orbit remote sensing instruments. The Diffuser Calibration Facility at NASA's Goddard Space Flight Center is a secondary diffuser calibration standard after NEST for over two decades, providing numerous NASA projects with BRDF data in the UV, Visible and the NIR spectral regions. Currently the Diffuser Calibration Facility extended the covered spectral range from 900 nm up to 1.7 microns. The measurements were made using the existing scatterometer by replacing the Si photodiode based receiver with an InGaAs-based one. The BRDF data was recorded at normal incidence and scatter zenith angles from 10 to 60 deg. Tunable coherent light source was setup. Broadband light source application is under development. Gray-scale sintered PTFE samples were used at these first trials, illuminated with P and S polarized incident light. The results are discussed and compared to empirically generated BRDF data from simple model based on 8 deg directional/hemispherical measurements.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

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

Ottino, J.M.

1991-05-01

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of microstructures'' whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context ofmore » the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.« less

Theory and Experiment of Binary Diffusion Coefficient of n-Alkanes in Dilute Gases.

PubMed

Liu, Changran; McGivern, W Sean; Manion, Jeffrey A; Wang, Hai

2016-10-10

Binary diffusion coefficients were measured for n-pentane, n-hexane, and n-octane in helium and of n-pentane in nitrogen over the temperature range of 300 to 600 K, using reversed-flow gas chromatography. A generalized, analytical theory is proposed for the binary diffusion coefficients of long-chain molecules in simple diluent gases, taking advantage of a recently developed gas-kinetic theory of the transport properties of nanoslender bodies in dilute free-molecular flows. The theory addresses the long-standing question about the applicability of the Chapman-Enskog theory in describing the transport properties of nonspherical molecular structures, or equivalently, the use of isotropic potentials of interaction for a roughly cylindrical molecular structure such as large normal alkanes. An approximate potential energy function is proposed for the intermolecular interaction of long-chain n-alkane with typical bath gases. Using this potential and the analytical theory for nanoslender bodies, we show that the diffusion coefficients of n-alkanes in typical bath gases can be treated by the resulting analytical model accurately, especially for compounds larger than n-butane.

Lipid diffusion in the distal and proximal leaflets of supported lipid bilayer membranes studied by single particle tracking

NASA Astrophysics Data System (ADS)

Schoch, Rafael L.; Barel, Itay; Brown, Frank L. H.; Haran, Gilad

2018-03-01

Supported lipid bilayers (SLBs) have been studied extensively as simple but powerful models for cellular membranes. Yet, potential differences in the dynamics of the two leaflets of a SLB remain poorly understood. Here, using single particle tracking, we obtain a detailed picture of bilayer dynamics. We observe two clearly separate diffusing populations, fast and slow, that we associate with motion in the distal and proximal leaflets of the SLB, respectively, based on fluorescence quenching experiments. We estimate diffusion coefficients using standard techniques as well as a new method based on the blur of images due to motion. Fitting the observed diffusion coefficients to a two-leaflet membrane hydrodynamic model allows for the simultaneous determination of the intermonolayer friction coefficient and the substrate-membrane friction coefficient, without any prior assumptions on the strengths of the relevant interactions. Remarkably, our calculations suggest that the viscosity of the interfacial water confined between the membrane and the substrate is elevated by ˜104 as compared to bulk water. Using hidden Markov model analysis, we then obtain insight into the transbilayer movement of lipids. We find that lipid flip-flop dynamics are very fast, with half times in the range of seconds. Importantly, we find little evidence for membrane defect mediated lipid flip-flop for SLBs at temperatures well above the solid-to-liquid transition, though defects seem to be involved when the SLBs are cooled down. Our work thus shows that the combination of single particle tracking and advanced hydrodynamic modeling provides a powerful means to obtain insight into membrane dynamics.

The effect of ambient pressure on the evaporation rate of materials

NASA Technical Reports Server (NTRS)

Naumann, R. J.; Russell, W. M.

1972-01-01

A simple expression is obtained using a diffusion model for the effect of ambient pressure on the outgassing or evaporation rate of materials. The correctness of the expression is demonstrated by comparing the estimates from this expression with actual weight loss measurements. It is shown that the rate of mass loss is governed by the ratio of mean free path to the characteristic dimension of the surface in question.

The Kinetics of Dissolution Revisited

NASA Astrophysics Data System (ADS)

Antonel, Paula S.; Hoijemberg, Pablo A.; Maiante, Leandro M.; Lagorio, M. Gabriela

2003-09-01

An experiment analyzing the kinetics of dissolution of a solid with cylindrical geometry in water is presented. The dissolution process is followed by measuring the solid mass and its size parameters (thickness and diameter) as a function of time. It is verified that the dissolution rate follows the Nernst model. Data treatment is compared with the dissolution of a spherical solid previously described. Kinetics, diffusion concepts, and polynomial fitting of experimental data are combined in this simple experiment.

MRI Simulation Study Investigating Effects of Vessel Topology, Diffusion, and Susceptibility on Transverse Relaxation Rates Using a Cylinder Fork Model.

PubMed

Shazeeb, Mohammed Salman; Kalpathy-Cramer, Jayashree; Issa, Bashar

2017-11-24

Brain vasculature is conventionally represented as straight cylinders when simulating blood oxygenation level dependent (BOLD) contrast effects in functional magnetic resonance imaging (fMRI). In reality, the vasculature is more complicated with branching and coiling especially in tumors. Diffusion and susceptibility changes can also introduce variations in the relaxation mechanisms within tumors. This study introduces a simple cylinder fork model (CFM) and investigates the effects of vessel topology, diffusion, and susceptibility on the transverse relaxation rates R2* and R2. Simulations using Monte Carlo methods were performed to quantify R2* and R2 by manipulating the CFM at different orientations, bifurcation angles, and rotation angles. Other parameters of the CFM were chosen based on physiologically relevant values: vessel diameters (~2‒10 µm), diffusion rates (1 × 10 -11 ‒1 × 10 -9  m 2 /s), and susceptibility values (3 × 10 -8 -4 × 10 -7 cgs units). R2* and R2 measurements showed a significant dependence on the bifurcation and rotation angles in several scenarios using different vessel diameters, orientations, diffusion rates, and susceptibility values. The angular dependence of R2* and R2 using the CFM could potentially be exploited as a tool to differentiate between normal and tumor vessels. The CFM can also serve as the elementary building block to simulate a capillary network reflecting realistic topological features.

The Influence of Feedback on Task-Switching Performance: A Drift Diffusion Modeling Account.

PubMed

Cohen Hoffing, Russell; Karvelis, Povilas; Rupprechter, Samuel; Seriès, Peggy; Seitz, Aaron R

2018-01-01

Task-switching is an important cognitive skill that facilitates our ability to choose appropriate behavior in a varied and changing environment. Task-switching training studies have sought to improve this ability by practicing switching between multiple tasks. However, an efficacious training paradigm has been difficult to develop in part due to findings that small differences in task parameters influence switching behavior in a non-trivial manner. Here, for the first time we employ the Drift Diffusion Model (DDM) to understand the influence of feedback on task-switching and investigate how drift diffusion parameters change over the course of task switch training. We trained 316 participants on a simple task where they alternated sorting stimuli by color or by shape. Feedback differed in six different ways between subjects groups, ranging from No Feedback (NFB) to a variety of manipulations addressing trial-wise vs. Block Feedback (BFB), rewards vs. punishments, payment bonuses and different payouts depending upon the trial type (switch/non-switch). While overall performance was found to be affected by feedback, no effect of feedback was found on task-switching learning. Drift Diffusion Modeling revealed that the reductions in reaction time (RT) switch cost over the course of training were driven by a continually decreasing decision boundary. Furthermore, feedback effects on RT switch cost were also driven by differences in decision boundary, but not in drift rate. These results reveal that participants systematically modified their task-switching performance without yielding an overall gain in performance.

Transport of volatile organic compounds across the capillary fringe

USGS Publications Warehouse

McCarthy, Kathleen A.; Johnson, Richard L.

1993-01-01

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

Thermal and non-thermal X-rays from the Galactic supernova remnant G348.5+0.1

NASA Astrophysics Data System (ADS)

Yamauchi, Shigeo; Minami, Sari; Ota, Naomi; Koyama, Katsuji

2014-02-01

We report on Suzaku results of the two distinct regions in the Galactic supernova remnant G348.5+0.1: extended thermal X-rays ("soft diffuse") at the north-east region and non-thermal X-rays (CXOU J171419.8-383023) at the north-west region. The X-ray spectrum of the soft diffuse X-rays can be fitted with neither an ionization equilibrium nor a non-equilibrium (ionizing) plasma model, leaving saw- tooth residuals in the 1.5-3 keV energy band. The residual structures can be produced when free electrons are recombined to the K-shells of highly ionized Mg and Si ions. In fact, the X-ray spectrum is nicely fitted with a recombination-dominant plasma model. We propose a scenario whereby the plasma in a nearly fully ionized state at high temperature quickly changed to a recombining phase due to selective cooling of electrons to a lower temperature of ˜ 0.5 keV. The spectrum of CXOU J171419.8-383023 is well explained by a simple power-law model with a photon index of 1.9, nearly equal to the typical value for pulsar wind nebulae. Since the distance is estimated to be the same as that of the soft diffuse radiation, we infer that both the soft diffuse X-rays and CXOU J171419.8-383023 are associated with the same object, SNR G348.5+0.1.

Interaction dynamics of two diffusing particles: contact times and influence of nearby surfaces.

PubMed

Tränkle, B; Ruh, D; Rohrbach, A

2016-03-14

Interactions of diffusing particles are governed by hydrodynamics on different length and timescales. The local hydrodynamics can be influenced substantially by simple interfaces. Here, we investigate the interaction dynamics of two micron-sized spheres close to plane interfaces to mimic more complex biological systems or microfluidic environments. Using scanned line optical tweezers and fast 3D interferometric particle tracking, we are able to track the motion of each bead with precisions of a few nanometers and at a rate of 10 kilohertz. From the recorded trajectories, all spatial and temporal information is accessible. This way, we measure diffusion coefficients for two coupling particles at varying distances h to one or two glass interfaces. We analyze their coupling strength and length by cross-correlation analysis relative to h and find a significant decrease in the coupling length when a second particle diffuses nearby. By analysing the times the particles are in close contact, we find that the influence of nearby surfaces and interaction potentials reduce the diffusivity strongly, although we found that the diffusivity hardly affects the contact times and the binding probability between the particles. All experimental results are compared to a theoretical model, which is based on the number of possible diffusion paths following the Catalan numbers and a diffusion probability, which is biased by the spheres' surface potential. The theoretical and experimental results agree very well and therefore enable a better understanding of hydrodynamically coupled interaction processes.

Cu-Zn binary phase diagram and diffusion couples

NASA Technical Reports Server (NTRS)

Mccoy, Robert A.

1992-01-01

The objectives of this paper are to learn: (1) what information a binary phase diagram can yield; (2) how to construct and heat treat a simple diffusion couple; (3) how to prepare a metallographic sample; (4) how to operate a metallograph; (5) how to correlate phases found in the diffusion couple with phases predicted by the phase diagram; (6) how diffusion couples held at various temperatures could be used to construct a phase diagram; (7) the relation between the thickness of an intermetallic phase layer and the diffusion time; and (8) the effect of one species of atoms diffusing faster than another species in a diffusion couple.

Numerical Solution of the Extended Nernst-Planck Model.

PubMed

Samson; Marchand

1999-07-01

The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst-Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed. Copyright 1999 Academic Press.

Valuation of exotic options in the framework of Levy processes

NASA Astrophysics Data System (ADS)

Milev, Mariyan; Georgieva, Svetla; Markovska, Veneta

2013-12-01

In this paper we explore a straightforward procedure to price derivatives by using the Monte Carlo approach when the underlying process is a jump-diffusion. We have compared the Black-Scholes model with one of its extensions that is the Merton model. The latter model is better in capturing the market's phenomena and is comparative to stochastic volatility models in terms of pricing accuracy. We have presented simulations of asset paths and pricing of barrier options for both Geometric Brownian motion and exponential Levy processes as it is the concrete case of the Merton model. A desired level of accuracy is obtained with simple computer operations in MATLAB for efficient computational time.

Ion-Exchange Interdiffusion Model with Potential Application to Long-Term Nuclear Waste Glass Performance

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

Neeway, James Joseph; Kerisit, Sebastien N.; Liu, Jia

2016-05-05

Abstract: Ion exchange is an integral mechanism influencing the corrosion of glasses. Due to the formation of alteration layers in aqueous conditions, it is difficult to conclusively deconvolute the process of ion exchange from other processes, principally dissolution of the glass matrix. Therefore, we have developed a method to isolate alkali diffusion that involves contacting glass coupons with a solution of 6LiCl dissolved in functionally inert dimethyl sulfoxide. We employ the method at temperatures ranging from 25 to 150 °C with various glass formulations. Glass compositions include simulant nuclear waste glasses, such as SON68 and the international simple glass (ISG),more » glasses in which the nature of the alkali element was varied, and glasses that contained more than one alkali element. An interdiffusion model based on Fick’s second law was developed and applied to all experiments to extract diffusion coefficients. The model expands established models of interdiffusion to the case where multiple types of alkali sites are present in the glass. Activation energies for alkali ion exchange were calculated and the results are in agreement with those obtained in glass strengthening experiments but are nearly five times higher than values reported for diffusion-controlled processes in nuclear waste glass corrosion experiments. A discussion of the root causes for this apparent discrepancy is provided. The interdiffusion model derived from laboratory experiments is expected to be useful for modeling glass corrosion in a geological repository when the silicon concentration is high.« less

Air-Parcel Residence Times Within Forest Canopies

NASA Astrophysics Data System (ADS)

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

2017-10-01

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