Diffusion of Li in olivine. Part I: Experimental observations and a multi species diffusion model
NASA Astrophysics Data System (ADS)
Dohmen, Ralf; Kasemann, Simone A.; Coogan, Laurence; Chakraborty, Sumit
2010-01-01
There are an increasing number of studies that focus on the systematics of the distribution of Li and its isotopes among different geochemical reservoirs. These studies have found that Li is relatively mobile compared to many other elements (e.g., Fe, Mg), and diffusion has been considered as a mechanism to generate large isotopic fractionations even at high temperatures. In order to quantify some of these aspects, we have measured Li diffusion rates experimentally along [0 0 1] of single crystals of olivines from San Carlos, Arizona and Pakistan, at 800-1200 °C at a total pressure of 100 kPa and fO 2 ≈ WM buffer. A complex diffusion behavior of Li is observed, indicating that two mechanisms of diffusion (a fast and a slower one) operate simultaneously. The behavior is well described by a model that partitions Li between two different sites in olivine - an octahedral site (Li Me) and an interstitial site (Li i). Transport of Li is a combination of hopping within and between each of these kinds of sites involving also vacancies on the octahedral site (V Me). It is assumed that the homogeneous reaction (Li Me = V Me + Li i) that maintains equilibrium distribution of Li between the sites is instantaneous compared to the timescales of all other processes associated with diffusive transport. One consequence of this mode of transport of Li in olivine is that the shape and length of diffusion profiles depend on the boundary conditions imposed at the surface of a crystal; i.e., the chemical environment (e.g., fO 2, aLi 4SiO 4), in addition to temperature and pressure. Our model describes the variable experimentally determined Li-profile shapes produced at different temperatures and with different boundary conditions, as well as their time evolution, quantitatively. Modeling the observed isotopic fractionation shows that 6Li diffuses about 5% faster than 7Li on the interstitial site. Inspection of published data on Li distribution in natural olivines that are available
Selzer, D; Hahn, T; Naegel, A; Heisig, M; Kostka, K H; Lehr, C M; Neumann, D; Schaefer, U F; Wittum, G
2013-01-28
This work investigates in vitro finite dose skin absorption of the model compounds flufenamic acid and caffeine experimentally and mathematically. The mass balance in different skin compartments (donor, stratum corneum (SC), deeper skin layers (DSL), lateral skin parts and acceptor) is analyzed as a function of time. For both substances high amounts were found in the lateral skin compartment after 6h of incubation, which emphasizes not to elide these parts in the modeling. Here, three different mathematical models were investigated and tested with the experimental data: a pharmacokinetic model (PK), a detailed microscopic two-dimensional diffusion model (MICRO) and a macroscopic homogenized diffusion model (MACRO). While the PK model was fitted to the experimental data, the MICRO and the MACRO models employed input parameters derived from infinite dose studies to predict the underlying diffusion process. All models could satisfyingly predict or describe the experimental data. The PK model and MACRO model also feature the lateral parts.
Wu, M; Li, J; Ludwig, A; Kharicha, A
2014-09-01
Part 1 of this two-part investigation presented a multiphase solidification model incorporating the finite diffusion kinetics and ternary phase diagram with the macroscopic transport phenomena (Wu et al., 2013). In Part 2, the importance of proper treatment of the finite diffusion kinetics in the calculation of macrosegregation is addressed. Calculations for a two-dimensional (2D) square casting (50 × 50 mm(2)) of Fe-0.45 wt.%C-1.06 wt.%Mn considering thermo-solutal convection and crystal sedimentation are performed. The modeling result indicates that the infinite liquid mixing kinetics as assumed by classical models (e.g., the Gulliver-Scheil or lever rule), which cannot properly consider the solute enrichment of the interdendritic or inter-granular melt at the early stage of solidification, might lead to an erroneous estimation of the macrosegregation. To confirm this statement, further theoretical and experimental evaluations are desired. The pattern and intensity of the flow and crystal sedimentation are dependent on the crystal morphologies (columnar or equiaxed); hence, the potential error of the calculated macrosegregation caused by the assumed growth kinetics depends on the crystal morphology. Finally, an illustrative simulation of an engineering 2.45-ton steel ingot is performed, and the results are compared with experimental results. This example demonstrates the model applicability for engineering castings regarding both the calculation efficiency and functionality.
A new model of diffuse brain injury in rats. Part I: Pathophysiology and biomechanics.
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.
NASA Astrophysics Data System (ADS)
Al-Shakran, Mohammad; Kibler, Ludwig A.; Jacob, Timo; Ibach, Harald; Beltramo, Guillermo L.; Giesen, Margret
2016-09-01
This is Part I of two closely related papers, where we show that the specific adsorption of anions leads to a failure of the nearest-neighbor Ising model to describe island perimeter curvatures on Au(100) electrodes in dilute KBr, HCl and H2SO4 electrolytes and the therewith derived step diffusivity vs. step orientation. This result has major consequences for theoretical studies aiming at the understanding of growth, diffusion and degradation phenomena. Part I focuses on the experimental data. As shown theoretically in detail in Part II (doi:10.1016/j.susc.2016.03.022), a set of nearest-neighbor and next-nearest-neighbor interaction energies (ɛNN, ɛNNN) can uniquely be derived from the diffusivity of steps along <100> and <110>. We find strong repulsive next-nearest neighbor (NNN) interaction in KBr and HCl, whereas NNN interaction is negligibly for H2SO4. The NNN repulsive interaction energy ɛNNN therefore correlates positively with the Gibbs adsorption energy of the anions. We find furthermore that ɛNNN increases with increasing Br- and Cl- coverage. The results for ɛNN and ɛNNN are quantitatively consistent with the coverage dependence of the step line tension. We thereby establish a sound experimental base for theoretical studies on the energetics of steps in the presence of specific adsorption.
Fractal model of anomalous diffusion.
Gmachowski, Lech
2015-12-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
NASA Astrophysics Data System (ADS)
Han, Xuebing; Ouyang, Minggao; Lu, Languang; Li, Jianqiu
2015-03-01
Now the lithium ion batteries are widely used in electrical vehicles (EV). The battery modeling and state estimation is of great significance. The rigorous physic based electrochemical model is too complicated for on-line simulation in vehicle. In this work, the simplification of physics-based model lithium ion battery for application in battery management system (BMS) on real electrical vehicle is proposed. Approximate method for solving the solid phase diffusion and electrolyte concentration distribution problems is introduced. The approximate result is very close to the rigorous model but fewer computations are needed. An extended single particle model is founded based on these approximated results and the on-line state of charge (SOC) estimation algorithm using the extended Kalman filter with this single particle model is discussed. This SOC estimation algorithm could be used in the BMS in real vehicle.
Multispecies diffusion models: A study of uranyl species diffusion
NASA Astrophysics Data System (ADS)
Liu, Chongxuan; Shang, Jianying; Zachara, John M.
2011-12-01
Rigorous numerical description of multispecies diffusion requires coupling of species, charge, and aqueous and surface complexation reactions that collectively affect diffusive fluxes. The applicability of a fully coupled diffusion model is, however, often constrained by the availability of species self-diffusion coefficients, as well as by computational complication in imposing charge conservation. In this study, several diffusion models with variable complexity in charge and species coupling were formulated and compared to describe reactive multispecies diffusion in groundwater. Diffusion of uranyl [U(VI)] species was used as an example in demonstrating the effectiveness of the models in describing multispecies diffusion. Numerical simulations found that a diffusion model with a single, common diffusion coefficient for all species was sufficient to describe multispecies U(VI) diffusion under a steady state condition of major chemical composition, but not under transient chemical conditions. Simulations revealed that for multispecies U(VI) diffusion under transient chemical conditions, a fully coupled diffusion model could be well approximated by a component-based diffusion model when the diffusion coefficient for each chemical component was properly selected. The component-based diffusion model considers the difference in diffusion coefficients between chemical components, but not between the species within each chemical component. This treatment significantly enhanced computational efficiency at the expense of minor charge conservation. The charge balance in the component-based diffusion model can be enforced, if necessary, by adding a secondary migration term resulting from model simplification. The effect of ion activity coefficient gradients on multispecies diffusion is also discussed. The diffusion models were applied to describe U(VI) diffusive mass transfer in intragranular domains in two sediments collected from U.S. Department of Energy's Hanford 300A
Minimal model for anomalous diffusion
NASA Astrophysics Data System (ADS)
Flekkøy, Eirik G.
2017-01-01
A random walk model with a local probability of removal is solved exactly and shown to exhibit subdiffusive behavior with a mean square displacement the evolves as
MODEL OF DIFFUSERS / PERMEATORS FOR HYDROGEN PROCESSING
Hang, T; William Jacobs, W
2007-08-27
Palladium-silver (Pd-Ag) diffusers are mainstays of hydrogen processing. Diffusers separate hydrogen from inert species such as nitrogen, argon or helium. The tubing becomes permeable to hydrogen when heated to more than 250 C and a differential pressure is created across the membrane. The hydrogen diffuses better at higher temperatures. Experimental or experiential results have been the basis for determining or predicting a diffuser's performance. However, the process can be mathematically modeled, and comparison to experimental or other operating data can be utilized to improve the fit of the model. A reliable model-based diffuser system design is the goal which will have impacts on tritium and hydrogen processing. A computer model has been developed to solve the differential equations for diffusion given the operating boundary conditions. The model was compared to operating data for a low pressure diffuser system. The modeling approach and the results are presented in this paper.
Leith diffusion model for homogeneous anisotropic turbulence
Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan
2016-07-19
Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.
Leith diffusion model for homogeneous anisotropic turbulence
Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan
2016-07-19
Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numericalmore » simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.« less
Leith diffusion model for homogeneous anisotropic turbulence
NASA Astrophysics Data System (ADS)
Rubinstein, Robert; Clark, Timothy; Kurien, Susan
2016-11-01
A new spectral closure model for homogeneous anisotropic turbulence is proposed. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.
On modeling pressure diffusion in non-homogeneous shear flows
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Rogers, M. M.; Durbin, P.; Lele, S. K.
1996-01-01
New models are proposed for the 'slow and 'rapid' parts of the pressure diffusive transport based on the examination of DNS databases for plane mixing layers and wakes. The model for the 'slow' part is non-local, but requires the distribution of the triple-velocity correlation as a local source. The latter can be computed accurately for the normal component from standard gradient diffusion models, but such models are inadequate for the cross component. More work is required to remedy this situation.
Modeling of hydrogen diffusion in metals
Yang, K.; Cao, M.Z.; Wan, X.J.; Shi, C.X.
1989-02-01
The study of the diffusion of hydrogen in metals is very important to further understand the hydrogen embrittlement of metals. To describe the diffusion of hydrogen in metals the diffusion equation deduced from Fick's law under an ideal condition has been generally used and the effect of hydrogen trapping in metals has been neglected. In the process of hydrogen diffusion through a metal, hydrogen fills the traps continuously and the fraction of the traps filled by hydrogen, which have only little effect on the diffusion of hydrogen, may be different at different places because the distribution of hydrogen concentration may be different at different places. Thus the hydrogen diffusion coefficient in the metal may also be different at different positions, i.e., the diffusion coefficient should be affected by time in a dynamic process of hydrogen diffusion through a metal. But in the previous analyses, the above fact is not considered and the hydrogen diffusion coefficient is generally taken as a constant. In the present paper a new model of hydrogen diffusion in metals in which the effect of time is taken into account is developed.
Diffusion Background Model for Moving Objects Detection
NASA Astrophysics Data System (ADS)
Vishnyakov, B. V.; Sidyakin, S. V.; Vizilter, Y. V.
2015-05-01
In this paper, we propose a new approach for moving objects detection in video surveillance systems. It is based on construction of the regression diffusion maps for the image sequence. This approach is completely different from the state of the art approaches. We show that the motion analysis method, based on diffusion maps, allows objects that move with different speed or even stop for a short while to be uniformly detected. We show that proposed model is comparable to the most popular modern background models. We also show several ways of speeding up diffusion maps algorithm itself.
Background Error Correlation Modeling with Diffusion Operators
2013-01-01
a general procedure for constructing a BEC model as a rational function of the diffusion operator D is presented and analytic expressions for the...Under the assumption of local homogeneity of D , a heuristic method for computing the diagonal elements of B is proposed. It is shown that the...In this chap- ter, a general procedure for constructing a BEC model as a rational function of the diffusion operator D is presented and analytic
NASA Technical Reports Server (NTRS)
Opila, Elizabeth J.; Smialek, James L.; Robinson, Raymond C.; Fox, Dennis S.; Jacobson, Nathan S.
1998-01-01
In combustion environments, volatilization of SiO2 to Si-O-H(g) species is a critical issue. Available thermochemical data for Si-O-H(g) species were used to calculate boundary layer controlled fluxes from SiO2. Calculated fluxes were compared to volatilization rates Of SiO2 scales grown on SiC which were measured in Part 1 of this paper. Calculated volatilization rates were also compared to those measured in synthetic combustion gas furnace tests. Probable vapor species were identified in both fuel-lean and fuel-rich combustion environments based on the observed pressure, temperature and velocity dependencies as well as the magnitude of the volatility rate. Water vapor is responsible for the degradation of SiO2 in the fuel-lean environment. Silica volatility in fuel-lean combustion environments is attributed primarily to the formation of Si(OH)4(g) with a small contribution of SiO(OH)2(g).
Simple diffusion hopping model with convection
NASA Astrophysics Data System (ADS)
Fitzgerald, Barry W.; Padding, Johan T.; van Santen, Rutger
2017-01-01
We present results from a new variant of a diffusion hopping model, the convective diffusive lattice model, to describe the behavior of a particulate flux around bluff obstacles. Particle interactions are constrained to an underlying square lattice where particles are subject to excluded volume conditions. In an extension to previous models, we impose a real continuous velocity field upon the lattice such that particles have an associated velocity vector. We use this velocity field to mediate the position update of the particles through the use of a convective update after which particles also undergo diffusion. We demonstrate the emergence of an expected wake behind a square obstacle which increases in size with increasing object size. For larger objects we observe the presence of recirculation zones marked by the presence of symmetric vortices in qualitative agreement with experiment and previous simulations.
Mathematical modeling of molecular diffusion through mucus
Cu, Yen; Saltzman, W. Mark
2008-01-01
The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488
Models of anomalous diffusion: the subdiffusive case
NASA Astrophysics Data System (ADS)
Piryatinska, A.; Saichev, A. I.; Woyczynski, W. A.
2005-04-01
The paper discusses a model for anomalous diffusion processes. Their one-point probability density functions (p.d.f.) are exact solutions of fractional diffusion equations. The model reflects the asymptotic behavior of a jump (anomalous random walk) process with random jump sizes and random inter-jump time intervals with infinite means (and variances) which do not satisfy the Law of Large Numbers. In the case when these intervals have a fractional exponential p.d.f., the fractional Komogorov-Feller equation for the corresponding anomalous diffusion is provided and methods of finding its solutions are discussed. Finally, some statistical properties of solutions of the related Langevin equation are studied. The subdiffusive case is explored in detail. The emphasis is on a rigorous presentation which, however, would be accessible to the physical sciences audience.
Diffusion and Advection using Cellular Potts Model
NASA Astrophysics Data System (ADS)
Dan, Debasis; Glazier, James
2005-03-01
The Cellular Potts Model (CPM) is a robust cell level methodology for simulation of biological tissues and morphogenesis. Standard diffusion solvers in the CPM use finite difference methods on the underlying CPM lattice. These methods have difficulty in simulating local advection in the ECM due to physiology and morphogenesis. To circumvent the problem of instabilities we simulate advection-diffusion within the framework of CPM using off-lattice finite-difference methods. We define a set of generalised fluid "cells" or particles which separate advection and diffusion from the lattice. Diffusion occurs between neighboring fluid cells by local averaging rules which approximate the Laplacian. CPM movement of the cells by spin flips handles the advection. The extension allows the CPM to model viscosity explicitly by including a relative velocity constraint on the fluid. The extended CPM correctly reproduces flow profiles of viscous fluids in cylindrical tube, during Stokes flow across a sphere and in flow in concentric cylindrical shells. We illustrate various conditions for diffusion including multiple instantaneous sources, continuous sources, moving sources and different boundary geometries and conditions to validate our approximation by comparing with analytical and established numerical solutions.
Leader in a diffusion competition model
NASA Astrophysics Data System (ADS)
Razzhevaikin, V. N.
2015-03-01
A one-dimensional Cauchy problem is considered for a system of reaction-diffusion equations that, in the point version, generalizes the Volterra competition model. It is proved that the number of the leader in the propagation velocity of nonvanishing solution values at the periphery is independent of nonnegative finite initial distributions.
Modelling Diffusion of a Personalized Learning Framework
ERIC Educational Resources Information Center
Karmeshu; Raman, Raghu; Nedungadi, Prema
2012-01-01
A new modelling approach for diffusion of personalized learning as an educational process innovation in social group comprising adopter-teachers is proposed. An empirical analysis regarding the perception of 261 adopter-teachers from 18 schools in India about a particular personalized learning framework has been made. Based on this analysis,…
A Systems Model for Assessment and Diffusion.
ERIC Educational Resources Information Center
Toomb, Kevin; And Others
The Florida Assessment and Diffusion System (FADS) represents a systematic approach to organizational change, emphasizing the interpersonal communication dimension of the change process. FADS encourages a systems approach to change, but is flexible enough to allow for procedural changes in response to specific user needs. The model assumes a…
Generalized Drift-Diffusion Model In Semiconductors
Mesbah, S.; Bendib-Kalache, K.; Bendib, A.
2008-09-23
A new drift-diffusion model is proposed based on the computation of the stationary nonlocal current density. The semi classical Boltzmann equation is solved keeping all the anisotropies of the distribution function with the use of the continued fractions. The conductivity is calculated in the linear approximation and for arbitrary collision frequency with respect to Kv{sub t} where K{sup -1} is the characteristic length scale of the system and V{sub t} is the thermal velocity. The nonlocal conductivity can be used to close the generalized drift-diffusion equations valid for arbitrary collisionality.
NASA Astrophysics Data System (ADS)
Morgan, D. J.; Chamberlain, K. J.; Kahl, M.; Potts, N. J.; Pankhurst, M. J.; Wilson, C. J. N.
2014-12-01
Over the past 20 years, diffusion chronometers have evolved from a niche tool into one of routine application, with more practitioners, new tools and increasingly large datasets. As we expand the horizons of diffusional geochronometry, it is worth taking stock of developments in methodologies and data acquisition, and taking time to revisit the underpinnings of the technique. Data collected as part of recent projects on Campi Flegrei, the Bishop Tuff and Fimmvörðuháls-Eyjafjallajökull are here used to investigate the initial state assumption, an absolutely vital aspect underpinning most diffusional work and one that is rarely evaluated despite its fundamental importance. To illustrate the nature of the problem we consider two widely-used element-mineral systems for felsic and mafic systems, respectively. First, barium and strontium profiles within sanidine crystals, modelled independently, can give strongly contrasting timescales from the same crystal zone. We can reconcile the datasets only for a situation where the initial boundary within the crystal was not a sharp step function, but relatively fuzzy before diffusion onset. This fuzziness effectively starts both chronometers off with an apparent, and false, pre-existing timescale, impacting the slower-diffusing barium much more strongly than the faster-diffusing strontium, yielding thousands of years of non-existent diffusion history. By combining both elements, a starting width of tens of microns can be shown, shortening the true diffusive timescales from tens of thousands of years to hundreds. Second, in olivine, we encounter different growth-related problems. Here, Fe-Mg interdiffusion occurs at a rate comparable to growth, with the compound nature of zonation making it difficult to extract the diffusion component. This requires a treatment of changing boundary conditions and sequential growth to generate the curvature seen in natural data, in order to recover timescales for anything but the outermost
Coupled chemical and diffusion model for compacted bentonite
Olin, M.; Lehikoinen, J.; Muurinen, A.
1995-12-31
A chemical equilibrium model has been developed for ion-exchange and to a limited extent for other reactions, such as precipitation or dissolution of calcite or gypsum, in compacted bentonite water systems. The model was successfully applied to some bentonite experiments, especially as far as monovalent ions were concerned. The fitted log-binding constants for the exchange of sodium for potassium, magnesium, and calcium were 0.27, 1.50, and 2.10, respectively. In addition, a coupled chemical and diffusion model has been developed to take account of diffusion in pore water, surface diffusion and ion-exchange.d the model was applied to the same experiments as the chemical equilibrium model, and its validation was found partly successful. The above values for binding constants were used also in the coupled model. The apparent (both for anions and cations) and surface diffusion (only for cations) constants yielding the best agreement between calculated and experimental data were 3.0 {times} 10{sup {minus}11} m{sup 2}/s and 6.0 {times} 10{sup {minus}12} m{sup 2}/s, respectively. These values are questionable, however, as experimental results good enough for fitting are currently not available.
A gravitational diffusion model without dark matter
Britten, Roy J.
1998-01-01
In this model, without dark matter, the flat rotation curves of galaxies and the mass-to-light ratios of clusters of galaxies are described quantitatively. The hypothesis is that the agent of gravitational force is propagated as if it were scattered with a mean free path of ≈5 kiloparsecs. As a result, the force between moderately distant masses, separated by more than the mean free path, diminishes as the inverse first power of the distance, following diffusion equations, and describes the flat rotation curves of galaxies. The force between masses separated by <1 kiloparsec diminishes as the inverse square of distance. The excess gravitational force (ratio of 1/r:1/r2) increases with the scale of structures from galaxies to clusters of galaxies. However, there is reduced force at great distances because of the ≈12 billion years that has been available for diffusion to occur. This model with a mean free path of ≈5 kiloparsecs predicts a maximum excess force of a few hundredfold for objects the size of galactic clusters a few megaparsecs in size. With only a single free parameter, the predicted curve for excess gravitational force vs. size of structures fits reasonably well with observations from those for dwarf galaxies through galactic clusters. Under the diffusion model, no matter is proposed in addition to the observed baryons plus radiation and thus the proposed density of the universe is only a few percent of that required for closure. PMID:9520368
A Diffuse Interface Model with Immiscibility Preservation
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
A diffuse interface model with immiscibility preservation
Tiwari, Arpit; Freund, Jonathan B.; Pantano, Carlos
2013-11-01
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.
Creatinine Diffusion Modeling in Capacitive Sensors
NASA Astrophysics Data System (ADS)
Mohabbati-Kalejahi, Elham; Azimirad, Vahid; Bahrami, Manouchehr
2016-12-01
In this paper, creatinine diffusion in capacitive sensors is discussed. The factors influencing the response time of creatinine biosensors are mathematically formulated and then three novel approaches for decreasing the response time are presented. At first, a piezoelectric actuator is used to vibrate the microtube that contains the blood sample, in order to reduce the viscosity of blood, and thus to increase the coefficient of diffusion. Then, the blood sample is assumed to be pushed through a porous medium, and the relevant conditions are investigated. Finally, the effect of the dentate shape of dielectric on response time is studied. The algorithms and the mathematical models are presented and discussed, and the results of simulations are illustrated. The response times for the first, second and third method are 60, 0.036 and about 31 s, respectively. It is also found that pumping results in very fast responses.
A High Diffusive Model for Nanomaterials.
Di Sia, P; Dallacasa, V
2011-12-01
Considerable attention is today devoted to the engineering of films widely used in photocatalytic, solar energy converters, photochemical and photoelectrochemical cells, dye-sensitized solar cells (DSSCs), to optimize electronic time response following photogeneration. However, the precise nature of transport processes in these systems has remained unresolved. To investigate such aspects of carrier dynamics, we have suggested a model for the calculation of correlation functions, expressed as the Fourier transform of the frequency-dependent complex conductivity σ(ω). Results are presented for the velocity correlation functions, the mean square deviation of position and the diffusion coefficient in systems, like TiO2 and doped Si, of large interest in present devices. Fast diffusion occurs in short time intervals of the order of few collision times. Consequences for efficiency of this fast response are discussed in relation to nanostructured devices.
Distributed Energy Resources Market Diffusion Model
Maribu, Karl Magnus; Firestone, Ryan; Marnay, Chris; Siddiqui,Afzal S.
2006-06-16
Distributed generation (DG) technologies, such as gas-fired reciprocating engines and microturbines, have been found to be economically beneficial in meeting commercial-sector electrical, heating, and cooling loads. Even though the electric-only efficiency of DG is lower than that offered by traditional central stations, combined heat and power (CHP) applications using recovered heat can make the overall system energy efficiency of distributed energy resources (DER) greater. From a policy perspective, however, it would be useful to have good estimates of penetration rates of DER under various economic and regulatory scenarios. In order to examine the extent to which DER systems may be adopted at a national level, we model the diffusion of DER in the US commercial building sector under different technical research and technology outreach scenarios. In this context, technology market diffusion is assumed to depend on the system's economic attractiveness and the developer's knowledge about the technology. The latter can be spread both by word-of-mouth and by public outreach programs. To account for regional differences in energy markets and climates, as well as the economic potential for different building types, optimal DER systems are found for several building types and regions. Technology diffusion is then predicted via two scenarios: a baseline scenario and a program scenario, in which more research improves DER performance and stronger technology outreach programs increase DER knowledge. The results depict a large and diverse market where both optimal installed capacity and profitability vary significantly across regions and building types. According to the technology diffusion model, the West region will take the lead in DER installations mainly due to high electricity prices, followed by a later adoption in the Northeast and Midwest regions. Since the DER market is in an early stage, both technology research and outreach programs have the potential to increase
Diffusion through thin membranes: Modeling across scales
NASA Astrophysics Data System (ADS)
Aho, Vesa; Mattila, Keijo; Kühn, Thomas; Kekäläinen, Pekka; Pulkkinen, Otto; Minussi, Roberta Brondani; Vihinen-Ranta, Maija; Timonen, Jussi
2016-04-01
From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesoscopic scheme gives rise to an expression for the permeability of a thin membrane as a function of a mesoscopic transmission parameter. In a microscopic model, the mean waiting time for a passage of a particle through the membrane is in accordance with this permeability. Numerical results computed with the mesoscopic scheme are then compared successfully with analytical solutions derived in a macroscopic scale, and the membrane model introduced here is used to simulate diffusive transport between the cell nucleus and cytoplasm through the nuclear envelope in a realistic cell model based on fluorescence microscopy data. By comparing the simulated fluorophore transport to the experimental one, we determine the permeability of the nuclear envelope of HeLa cells to enhanced yellow fluorescent protein.
Elements of a Model State Education Agency Diffusion System.
ERIC Educational Resources Information Center
Mojkowski, Charles
A study, presented to the National Dissemination Conference, provides a conceptualization of a model diffusion system as it might exist within a state education agency (SEA) and places this diffusion model within the context of the SEA's expanding role as an educational service. Five conclusions were reached regarding a model diffusion system.…
Distributed Wind Diffusion Model Overview (Presentation)
Preus, R.; Drury, E.; Sigrin, B.; Gleason, M.
2014-07-01
Distributed wind market demand is driven by current and future wind price and performance, along with several non-price market factors like financing terms, retail electricity rates and rate structures, future wind incentives, and others. We developed a new distributed wind technology diffusion model for the contiguous United States that combines hourly wind speed data at 200m resolution with high resolution electricity load data for various consumer segments (e.g., residential, commercial, industrial), electricity rates and rate structures for utility service territories, incentive data, and high resolution tree cover. The model first calculates the economics of distributed wind at high spatial resolution for each market segment, and then uses a Bass diffusion framework to estimate the evolution of market demand over time. The model provides a fundamental new tool for characterizing how distributed wind market potential could be impacted by a range of future conditions, such as electricity price escalations, improvements in wind generator performance and installed cost, and new financing structures. This paper describes model methodology and presents sample results for distributed wind market potential in the contiguous U.S. through 2050.
Countercurrent Gaseous Diffusion Model of Oxidation Through a Porous Coating
Holcomb, G.R.
1996-07-01
A countercurrent gaseous diffusion model was developed to describe oxidation through porous coatings and scales. The specific system modeled involved graphite oxidized through a porous alumina (Al{sub 2}O{sub 3}) overcoat between 570 C (1,058 F) and 975 C (1,787 F). The model separated the porous Al{sub 2}O{sub 3} coating into two gas diffusion regions separated by a flame front, where oxygen (O{sub 2}) and carbon monoxide (CO) react to form carbon dioxide (CO{sub 2}). In the outer region O{sub 2} and CO{sub 2} counterdiffused. In the inner region, CO{sub 2} and CO counterdiffused. Concentration gradients of each gaseous specie in the pores of the Al{sub 2}O{sub 3} were determined, and the oxidation rate was calculated. The model was verified by oxidation experiments using graphite through various porous Al{sub 2}O{sub 3} overcoats. The Al{sub 2}O{sub 3} overcoats ranged in fractional porosity and in average pore radius from 0.077 {micro}m (3.0 x 10{sup -6} in., Knudsen diffusion) to 10.0 {micro}m (3.9 x 10{sup -4} in., molecular diffusion). Predicted and measured oxidation rates were shown to have the same dependence upon porosity, pore radius, temperature, and oxygen partial pressure (P{sub O{sub 2}}). Use of the model was proposed for other oxidation systems and for chemical vapor infiltration (CVI). This work was part of the U.S. Bureau of Mines corrosion research program.
Extended source model for diffusive coupling.
González-Ochoa, Héctor O; Flores-Moreno, Roberto; Reyes, Luz M; Femat, Ricardo
2016-01-01
Motivated by the prevailing approach to diffusion coupling phenomena which considers point-like diffusing sources, we derived an analogous expression for the concentration rate of change of diffusively coupled extended containers. The proposed equation, together with expressions based on solutions to the diffusion equation, is intended to be applied to the numerical solution of systems exclusively composed of ordinary differential equations, however is able to account for effects due the finite size of the coupled sources.
Mathematical model for radon diffusion in earthen materials
Nielson, K.K.; Rogers, V.C.
1982-10-01
Radon migration in porous, earthen materials is characterized by diffusion in both the air and water components of the system as well as by the interaction of the radon between the air and water. The size distribution and configuration of the pore spaces and their moisture distributions are key parameters in determining the radon diffusion coefficient for the bulk material. A mathematical model is developed and presented for calculating radon diffusion coefficients solely from the moisture content and pore size distribution of a soil, reducing the need for resorting to radon diffusion measurements. The resulting diffusion coefficients increase with the median pore diameter of the soil and decrease with increasing widths of the pore size distribution. The calculated diffusion coefficients are suitable for use in simple homogeneous-medium diffusion expressions for predicting radon transport and compare well with measured diffusion coefficients and with empirical diffusion coefficient correlations.
GVF-based anisotropic diffusion models.
Yu, Hongchuan; Chua, Chin-Seng
2006-06-01
In this paper, the gradient vector flow fields are introduced in image restoration. Within the context of flow fields, the shock filter, mean curvature flow, and Perona-Malik equation are reformulated. Many advantages over the original models can be obtained; these include numerical stability, large capture range, and high-order derivative estimation. In addition, a fairing process is introduced in the anisotropic diffusion, which contains a fourth-order derivative and is reformulated as the intrinsic Laplacian of curvature under the level set framework. By applying this fairing process, the shape boundaries will become more apparent. In order to overcome numerical errors, the intrinsic Laplacian of curvature is computed from the gradient vector flow fields instead of the observed images.
NASA Astrophysics Data System (ADS)
Wang, Shifang; Wu, Tao; Deng, Yongju; Zheng, Qiusha; Zheng, Qian
2016-08-01
Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging-diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging-diverging effect included is in good agreement with reported experimental data.
Radon diffusion through multilayer earthen covers: Models and simulations
NASA Astrophysics Data System (ADS)
Mayer, D. W.; Oster, C. A.; Nelson, R. W.; Gee, G. W.
1981-09-01
A capability to model and analyze the fundamental interactions that influence the diffusion of radon gas through uranium mill tailings and cover systems were investigated. The theoretical basis for modeling radon diffusion and an understanding of the fundamental interactions that influence radon diffusion were developed. The theory was incorporated into three computer models that are used to analyze several tailings and cover configurations. The theoretical basis for modeling radon diffusion and the computer models used to analyze uranium mill tailings and multilayered cover systems are discussed.
Improved input parameters for diffusion models of skin absorption.
Hansen, Steffi; Lehr, Claus-Michael; Schaefer, Ulrich F
2013-02-01
To use a diffusion model for predicting skin absorption requires accurate estimates of input parameters on model geometry, affinity and transport characteristics. This review summarizes methods to obtain input parameters for diffusion models of skin absorption focusing on partition and diffusion coefficients. These include experimental methods, extrapolation approaches, and correlations that relate partition and diffusion coefficients to tabulated physico-chemical solute properties. Exhaustive databases on lipid-water and corneocyte protein-water partition coefficients are presented and analyzed to provide improved approximations to estimate lipid-water and corneocyte protein-water partition coefficients. The most commonly used estimates of lipid and corneocyte diffusion coefficients are also reviewed. In order to improve modeling of skin absorption in the future diffusion models should include the vertical stratum corneum heterogeneity, slow equilibration processes, the absorption from complex non-aqueous formulations, and an improved representation of dermal absorption processes. This will require input parameters for which no suitable estimates are yet available.
Some Problems in Using Diffusion Models for New Products
ERIC Educational Resources Information Center
Bernhardt, Irwin; Mackenzie, Kenneth D.
1972-01-01
Analyzes some of the problems involved in using diffusion models to formulate marketing strategies for introducing new products. Six models, which remove some of the theoretical and methodological restrictions inherent in current models of the adoption and diffusion process, are presented. (Author/JH)
MODIS Solar Diffuser Attenuation Screen Modeling Results
NASA Technical Reports Server (NTRS)
Waluschka, Eugene; Xuong, Xiaoxiong; Guenther, Bruce; Barnes, William
2004-01-01
On-orbit calibration of the reflected solar bands on the EOS Moderate Resolution Imaging Spectroradiometer (MODIS) is accomplished by have the instrument view a high reflectance diffuse surface illuminated by the sun. For some of the spectral bands this proves to be much too bright a signal that results in the saturation of detectors designed for measuring low reflectance (ocean) surfaces signals. A mechanical attenuation device in the form of a pin hole screen is used to reduce the signals to calibrate these bands. The sensor response to solar illumination of the SD with and without the attenuation screen in place will be presented. The MODIS detector response to the solar diffuser is smooth when the attenuation screen is absent, but has structures up to a few percent when the attenuation screen is present. This structure corresponds to non-uniform illumination from the solar diffuser. Each pin hole produces a pin-hole image of the sun on the solar diffuser, and there are very many pin hole images of the sun on the solar diffuser for each MODIS detector. Even though there are very many pin-hole images of the sun on the solar diffuser, it is no longer perfectly uniformly illuminated. This non-uniformly illuminated solar diffuser produces intensity variation on the focal planes. The results of a very detailed simulation will be discussed which show how the illumination of the focal plane changes as a result of the attenuation, and the impacts on the calibration will be discussed.
Comparison of two stochastic models of scalar diffusion in turbulent flow
NASA Astrophysics Data System (ADS)
Rodean, H. C.; Lange, R.; Nasstrom, J. S.; Gavrilov, V. P.
1992-07-01
This report describes and compares two Lagrangian stochastic models for turbulent diffusion: (1) the random velocity increment model based on the Langevin equation; and (2) the random displacement model. We apply both models to identical test problems for one-dimensional (vertical) diffusion, using identical parameterizations of turbulence statistics as inputs. We compare the results and discuss the advantages and disadvantages of each model. This work is part of an effort to improve the ADPIC dispersion model which is based on the eddy diffusivity model. It is also part of a cooperative research effort on the transport and dispersion of hazardous materials in the atmosphere by the Lawrence Livermore National Laboratory and the Institute of Experimental Meteorology (USSR).
A lattice-Boltzman model for noble gas diffusion
NASA Astrophysics Data System (ADS)
Cassata, W. S.; Huber, C.; Renne, P. R.
2010-12-01
Thermochronometry by the 40Ar/39Ar, 4He/3He, and (U-Th)/He techniques provides insights into a array of planetary processes that span immense time and temperature regimes, from rapid and high temperature asteroid impact events to mountain uplift occurring over plate tectonic timescales at near surface temperatures. Thermal modeling has expanded from simple calculations for quantifying diffusion from a single spherical domain or log normal distributions of domains to include crystals having discrete domain distributions, fast diffusion pathways, diffusive anisotropy, complex crystal geometries, alpha damage, and alpha ejection. Despite these advances, our understanding of diffusion within crystals that have complex microstructural features (e.g., exsolution and diffusive sinks) or highly asymmetric concentration gradients remains fragmentary. Improved computational speeds now enable thermochronologists to quantitatively explore many such problems. We have developed a code based on the lattice-Boltzmann (LB) method to model diffusion from a variety of complex 2-D geometries having isotropic, temperature-independent anisotropic, and temperature-dependent anisotropic diffusivity. We utilize the LB diffusion code to examine the effects of non-zero concentration boundaries, fast diffusion pathways, diffusive sinks, exsolution lamellae, asymmetrical concentration distributions, and temperature gradients on calculated diffusion parameters, age data, and inferred thermal histories. Animations and geological examples illustrate the applicability of the code to natural settings.
Radon diffusion through multilayer earthen covers: models and simulations
Mayer, D.W.; Oster, C.A.; Nelson, R.W.; Gee, G.W.
1981-09-01
A capability to model and analyze the fundamental interactions that influence the diffusion of radon gas through uranium mill tailings and cover systems has been investigated. The purpose of this study is to develop the theoretical basis for modeling radon diffusion and to develop an understanding of the fundamental interactions that influence radon diffusion. This study develops the theoretical basis for modeling radon diffusion in one, two and three dimensions. The theory has been incorporated into three computer models that are used to analyze several tailings and cover configurations. This report contains a discussion of the theoretical basis for modeling radon diffusion, a discussion of the computer models used to analyze uranium mill tailings and multilayered cover systems, and presents the results that have been obtained.
A Social Diffusion Model with an Application on Election Simulation
Wang, Fu-Min; Hung, San-Chuan; Kung, Perng-Hwa; Lin, Shou-De
2014-01-01
Issues about opinion diffusion have been studied for decades. It has so far no empirical approach to model the interflow and formation of crowd's opinion in elections due to two reasons. First, unlike the spread of information or flu, individuals have their intrinsic attitudes to election candidates in advance. Second, opinions are generally simply assumed as single values in most diffusion models. However, in this case, an opinion should represent preference toward multiple candidates. Previously done models thus may not intuitively interpret such scenario. This work is to design a diffusion model which is capable of managing the aforementioned scenario. To demonstrate the usefulness of our model, we simulate the diffusion on the network built based on a publicly available bibliography dataset. We compare the proposed model with other well-known models such as independent cascade. It turns out that our model consistently outperforms other models. We additionally investigate electoral issues with our model simulator. PMID:24995351
A social diffusion model with an application on election simulation.
Lou, Jing-Kai; Wang, Fu-Min; Tsai, Chin-Hua; Hung, San-Chuan; Kung, Perng-Hwa; Lin, Shou-De; Chen, Kuan-Ta; Lei, Chin-Laung
2014-01-01
Issues about opinion diffusion have been studied for decades. It has so far no empirical approach to model the interflow and formation of crowd's opinion in elections due to two reasons. First, unlike the spread of information or flu, individuals have their intrinsic attitudes to election candidates in advance. Second, opinions are generally simply assumed as single values in most diffusion models. However, in this case, an opinion should represent preference toward multiple candidates. Previously done models thus may not intuitively interpret such scenario. This work is to design a diffusion model which is capable of managing the aforementioned scenario. To demonstrate the usefulness of our model, we simulate the diffusion on the network built based on a publicly available bibliography dataset. We compare the proposed model with other well-known models such as independent cascade. It turns out that our model consistently outperforms other models. We additionally investigate electoral issues with our model simulator.
Explicit melioration by a neural diffusion model
Simen, Patrick; Cohen, Jonathan D.
2009-01-01
When faced with choices between two sources of reward, animals can rapidly adjust their rates of responding to each so that overall reinforcement increases. Herrnstein's ‘matching law’ provides a simple description of the equilibrium state of this choice allocation process: animals reallocate behavior so that relative rates of responding equal, or match, the relative rates of reinforcement obtained for each response. Herrnstein and colleagues proposed ‘melioration’ as a dynamical process for achieving this equilibrium, but left details of its operation unspecified. Here we examine a way of filling in the details that links the decision-making and operant-conditioning literatures and extends choice-proportion predictions into predictions about inter-response times. Our approach implements melioration in an adaptive version of the drift-diffusion model (DDM), which is widely used in decision-making research to account for response-time distributions. When the drift parameter of the DDM is 0 and its threshold parameters are inversely proportional to reward rates, its choice proportions dynamically track a state of exact matching. A DDM with fixed thresholds and drift that is determined by differences in reward rates can produce similar, but not identical, results. We examine choice probability and inter-response time predictions of these models, separately and in combination, and possible implications for brain organization provided by neural network implementations of them. Results suggest that melioration and matching may derive from synapses that estimate reward rates by a process of leaky integration, and that link together the input and output stages of a two-stage stimulus-response mechanism. PMID:19646968
Parameter Variability and Distributional Assumptions in the Diffusion Model
ERIC Educational Resources Information Center
Ratcliff, Roger
2013-01-01
If the diffusion model (Ratcliff & McKoon, 2008) is to account for the relative speeds of correct responses and errors, it is necessary that the components of processing identified by the model vary across the trials of a task. In standard applications, the rate at which information is accumulated by the diffusion process is assumed to be normally…
A Comparison of Competing Models of the News Diffusion Process.
ERIC Educational Resources Information Center
Mayer, Michael E.; And Others
1990-01-01
Investigates the diffusion of information about the space shuttle Challenger explosion by comparing loglinear models of the diffusion process. Finds that the most parsimonious model with adequate goodness of fit was a linear one in which a person's location affected how the information was heard, which in turn affected when the information was…
Some Problems in Using Diffusion Models for New Products.
ERIC Educational Resources Information Center
Bernhardt, Irwin; Mackenzie, Kenneth D.
This paper analyzes some of the problems of using diffusion models to formulate marketing strategies for new products. Though future work in this area appears justified, many unresolved problems limit its application. There is no theory for adoption and diffusion processes; such a theory is outlined in this paper. The present models are too…
Lévy flight with absorption: A model for diffusing diffusivity with long tails
NASA Astrophysics Data System (ADS)
Jain, Rohit; Sebastian, K. L.
2017-03-01
We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016), 10.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e.,
Varakin, A I; Mazur, V V; Arkhipova, N V; Serianov, Iu V
2009-01-01
Mathematical models of the transfer of charged macromolecules have been constructed on the basis of the classical equations of electromigration diffusion of Helmholtz-Smolukhovskii, Goldman, and Goldman-Hodgkin-Katz. It was shown that ion transfer in placental (mimicking lipid-protein barriers) and muscle barriers occurs by different mechanisms. In placental barriers, the electromigration diffusion occurs along lipid-protein channels formed due to the conformational deformation of phospholipid and protein molecules with the coefficients of diffusion D = (2.6-3.6) x 10(-8) cm2/s. The transfer in muscle barriers is due to the migration across charged interfibrillar channels with the negative diffusion activation energy, which is explained by changes in the structure of muscle fibers and expenditures of thermal energy for the extrusion of Cl- from channel walls with the diffusion coefficient D = (6.0-10.0) x 10(-6) cm2/s.
A memory diffusion model for molecular anisotropic diffusion in siliceous β-zeolite.
Ji, Xiangfei; An, Zhuanzhuan; Yang, Xiaofeng
2016-01-01
A memory diffusion model of molecules on β-zeolite is proposed. In the model, molecular diffusion in β-zeolites is treated as jumping from one adsorption site to its neighbors and the jumping probability is a compound probability which includes that provided by the transitional state theory as well as that derived from the information about which direction the target molecule comes from. The proposed approach reveals that the diffusivities along two crystal axes on β-zeolite are correlated. The model is tested by molecular dynamics simulations on diffusion of benzene and other simple molecules in β-zeolites. The results show that the molecules with larger diameters fit the prediction much better and that the "memory effects" are important in all cases.
An ion diffusion model in semi-permeable clay materials.
Liu, Chongxuan
2007-08-01
Clay materials typically contain negative surface charges that induce electrostatic fields (or diffuse double layers) in electrolytes. During ion diffusion in a porous medium of clay materials, ions dynamically interact with the electrostatic fields associated with individual clay grains by depressing or expanding the electrostatic double layers, which subsequently affects ionic fluxes. Current theory of ion transport in porous media, however, cannot explicitly account for the dynamic interactions. Here we proposed a model by coupling electrodynamics and nonequilibrium thermodynamics (EDNT) to describe ion diffusion in clay materials as a complex function of factors including clay surface charge density, tortuosity, porosity, chemicoosmotic coefficient, and ion self-diffusivity. The model was validated by comparing the calculated and measured apparent ion diffusion coefficients in clay materials as a function of ionic strength. At transitional states, ion diffusive fluxes are dynamically related to the electrostatic fields, which shrink or expand as ion diffusion occurs. At steady states, the electrostatic fields are time-invariant and ion diffusive fluxes conform to flux and concentration gradient relationships; and apparent diffusivity can be approximated by the ion diffusivity in bulk electrolytes corrected by a tortuosity factor and macroscopic concentration discontinuities at the interfaces between clay materials and bulk solutions.
Modeling diffusion and adsorption in compacted bentonite: a critical review
NASA Astrophysics Data System (ADS)
Bourg, Ian C.; Bourg, Alain C. M.; Sposito, Garrison
2003-03-01
The current way of describing diffusive transport through compacted clays is a simple diffusion model coupled to a linear adsorption coefficient ( Kd). To fit the observed results of cation diffusion, this model is usually extended with an adjustable "surface diffusion" coefficient. Description of the negative adsorption of anions calls for a further adjustment through the use of an "effective porosity". The final model thus includes many fitting parameters. This is inconvenient where predictive modeling is called for (e.g., for waste confinement using compacted clay liners). The diffusion/adsorption models in current use have been derived from the common hydrogeological equation of advection/dispersion/adsorption. However, certain simplifications were also borrowed without questioning their applicability to the case of compacted clays. Among these simplifications, the assumption that the volume of the adsorbed phase is negligible should be discussed. We propose a modified diffusion/adsorption model that accounts for the volume of the adsorbed phase. It suggests that diffusion through highly compacted clay takes place through the interlayers (i.e., in the adsorbed phase). Quantitative prediction of the diffusive flux will necessitate more detailed descriptions of surface reactivity and of the mobility of interlayer species.
Dynamic hysteresis modeling including skin effect using diffusion equation model
NASA Astrophysics Data System (ADS)
Hamada, Souad; Louai, Fatima Zohra; Nait-Said, Nasreddine; Benabou, Abdelkader
2016-07-01
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
Exact curvilinear diffusion coefficients in the repton model.
Buhot, A
2005-10-01
The Rubinstein-Duke or repton model is one of the simplest lattice model of reptation for the diffusion of a polymer in a gel or a melt. Recently, a slightly modified model with hardcore interactions between the reptons has been introduced. The curvilinear diffusion coefficients of both models are exactly determined for all chain lengths. The case of periodic boundary conditions is also considered.
1983-03-01
AN ANALYSIS OF A FINITE ELEMENT METHOD FOR CONVECTION- DIFFUSION PROBLEMS PART II: A POSTERIORI ERROR ESTIMATES AND ADAPTIVITY by W. G. Szymczak Y 6a...PERIOD COVERED AN ANALYSIS OF A FINITE ELEMENT METHOD FOR final life of the contract CONVECTION- DIFFUSION PROBLEM S. Part II: A POSTERIORI ERROR ...Element Method for Convection- Diffusion Problems. Part II: A Posteriori Error Estimates and Adaptivity W. G. Szvmczak and I. Babu~ka# Laboratory for
Modeling boron diffusion gettering of iron in silicon solar cells
NASA Astrophysics Data System (ADS)
Haarahiltunen, A.; Talvitie, H.; Savin, H.; Yli-Koski, M.; Asghar, M. I.; Sinkkonen, J.
2008-01-01
In this paper, a model is presented for boron diffusion gettering of iron in silicon during thermal processing. In the model, both the segregation of iron due to high boron doping concentration and heterogeneous precipitation of iron to the surface of the wafer are taken into account. It is shown, by comparing simulated results with experimental ones, that this model can be used to estimate boron diffusion gettering efficiency of iron under a variety of processing conditions. Finally, the application of the model to phosphorus diffusion gettering is discussed.
Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-12-15
Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber.
Anisotropy-resolving models for predicting separation in 3--D asymmetric diffusers
NASA Astrophysics Data System (ADS)
Jeyapaul, Elbert; Durbin, Paul
2011-11-01
All linear eddy-viscosity models are qualitatively incorrect in predicting separation in 3-D asymmetric diffusers. The failure to predict normal stress and shear stress anisotropy at high production-dissipation ratios is the cause. The Explicit algebraic Reynolds stress model (Wallin and Johansson, 2000) predicts the mean flow field in the diffuser accurately, but not the wall pressure and Reynolds stresses. Recalibrating the coefficients of the rapid part of pressure-strain model improves the wall pressure prediction. Including the convective, diffusive, streamline curvature effects on anisotropy has not been beneficial. The model has been tested using a family of diffusers having the same nominal streamwise pressure gradient, LES data is used as a reference. Professor
A computational kinetic model of diffusion for molecular systems
NASA Astrophysics Data System (ADS)
Teo, Ivan; Schulten, Klaus
2013-09-01
Regulation of biomolecular transport in cells involves intra-protein steps like gating and passage through channels, but these steps are preceded by extra-protein steps, namely, diffusive approach and admittance of solutes. The extra-protein steps develop over a 10-100 nm length scale typically in a highly particular environment, characterized through the protein's geometry, surrounding electrostatic field, and location. In order to account for solute energetics and mobility of solutes in this environment at a relevant resolution, we propose a particle-based kinetic model of diffusion based on a Markov State Model framework. Prerequisite input data consist of diffusion coefficient and potential of mean force maps generated from extensive molecular dynamics simulations of proteins and their environment that sample multi-nanosecond durations. The suggested diffusion model can describe transport processes beyond microsecond duration, relevant for biological function and beyond the realm of molecular dynamics simulation. For this purpose the systems are represented by a discrete set of states specified by the positions, volumes, and surface elements of Voronoi grid cells distributed according to a density function resolving the often intricate relevant diffusion space. Validation tests carried out for generic diffusion spaces show that the model and the associated Brownian motion algorithm are viable over a large range of parameter values such as time step, diffusion coefficient, and grid density. A concrete application of the method is demonstrated for ion diffusion around and through the Eschericia coli mechanosensitive channel of small conductance ecMscS.
A computational kinetic model of diffusion for molecular systems
Teo, Ivan; Schulten, Klaus
2013-01-01
Regulation of biomolecular transport in cells involves intra-protein steps like gating and passage through channels, but these steps are preceded by extra-protein steps, namely, diffusive approach and admittance of solutes. The extra-protein steps develop over a 10–100 nm length scale typically in a highly particular environment, characterized through the protein's geometry, surrounding electrostatic field, and location. In order to account for solute energetics and mobility of solutes in this environment at a relevant resolution, we propose a particle-based kinetic model of diffusion based on a Markov State Model framework. Prerequisite input data consist of diffusion coefficient and potential of mean force maps generated from extensive molecular dynamics simulations of proteins and their environment that sample multi-nanosecond durations. The suggested diffusion model can describe transport processes beyond microsecond duration, relevant for biological function and beyond the realm of molecular dynamics simulation. For this purpose the systems are represented by a discrete set of states specified by the positions, volumes, and surface elements of Voronoi grid cells distributed according to a density function resolving the often intricate relevant diffusion space. Validation tests carried out for generic diffusion spaces show that the model and the associated Brownian motion algorithm are viable over a large range of parameter values such as time step, diffusion coefficient, and grid density. A concrete application of the method is demonstrated for ion diffusion around and through the Eschericia coli mechanosensitive channel of small conductance ecMscS. PMID:24089741
Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models
NASA Technical Reports Server (NTRS)
Yoder, Dennis A.
2016-01-01
This paper will include a detailed comparison of heat transfer models that rely upon the thermal diffusivity. The goals are to inform users of the development history of the various models and the resulting differences in model formulations, as well as to evaluate the models on a variety of validation cases so that users might better understand which models are more broadly applicable.
Diffusion in different models of active Brownian motion
NASA Astrophysics Data System (ADS)
Lindner, B.; Nicola, E. M.
2008-04-01
Active Brownian particles (ABP) have served as phenomenological models of self-propelled motion in biology. We study the effective diffusion coefficient of two one-dimensional ABP models (simplified depot model and Rayleigh-Helmholtz model) differing in their nonlinear friction functions. Depending on the choice of the friction function the diffusion coefficient does or does not attain a minimum as a function of noise intensity. We furthermore discuss the case of an additional bias breaking the left-right symmetry of the system. We show that this bias induces a drift and that it generally reduces the diffusion coefficient. For a finite range of values of the bias, both models can exhibit a maximum in the diffusion coefficient vs. noise intensity.
Improved knowledge diffusion model based on the collaboration hypernetwork
NASA Astrophysics Data System (ADS)
Wang, Jiang-Pan; Guo, Qiang; Yang, Guang-Yong; Liu, Jian-Guo
2015-06-01
The process for absorbing knowledge becomes an essential element for innovation in firms and in adapting to changes in the competitive environment. In this paper, we present an improved knowledge diffusion hypernetwork (IKDH) model based on the idea that knowledge will spread from the target node to all its neighbors in terms of the hyperedge and knowledge stock. We apply the average knowledge stock V(t) , the variable σ2(t) , and the variance coefficient c(t) to evaluate the performance of knowledge diffusion. By analyzing different knowledge diffusion ways, selection ways of the highly knowledgeable nodes, hypernetwork sizes and hypernetwork structures for the performance of knowledge diffusion, results show that the diffusion speed of IKDH model is 3.64 times faster than that of traditional knowledge diffusion (TKDH) model. Besides, it is three times faster to diffuse knowledge by randomly selecting "expert" nodes than that by selecting large-hyperdegree nodes as "expert" nodes. Furthermore, either the closer network structure or smaller network size results in the faster knowledge diffusion.
Net diffusivity in ocean general circulation models with nonuniform grids
NASA Technical Reports Server (NTRS)
Yin, F. L.; Fung, I. Y.
1991-01-01
The numerical vertical diffusivity K(num), embedded in a numerical ocean general circulation model with nonuniform vertical grid, is estimated. It is shown that in a downwelling region, K(num) is negative for a grid with grid size increasing with depth. When the grid size increment, or the downward vertical velocity, is large, K(num) may exceed the vertical diffusivity specified and may result in a negative effective vertical diffusivity. Therefore care needs to be taken to specify the vertical diffusivity in a numerical model with nonuniform grid, and a lower bound is generally imposed in order to avoid an unphysical negative value. Some possible effects of the negative effective diffusivity are discussed.
Modeling Intragranular Diffusion in Low-Connectivity Granular Media
Ewing, Robert G.; Liu, Chongxuan; Hu, Qinhong
2012-03-20
Diffusive exchange of solutes between bulk water in an aquifer and water in the intragranular pores of the solid phase remains confusing after decades of study. In a previous paper, we reviewed some of the explanations, and suggested that the disparities between observation and theory were largely due to low connectivity of the intragranular pores. Low connectivity indicates that a useful conceptual framework is percolation theory, which guided our analysis. The present study was initiated to improve the finite difference (FD) model presented in the previous paper, and to test that new model rigorously against new random walk (RW) simulations of diffusion in low-connectivity porous spheres starting from non-equilibrium. The new FD model calculates diffusion separately in the infinite cluster and the finite clusters, and closely matches the new, more complex RW results. The percolation-theory based description of the new model is fairly simple, and can readily be incorporated into existing FD models. The simulations showed that the combination of low intragranular pore connectivity, and out-diffusion initiated at diffusive non-equilibrium, can produce diffusive behavior that appears as if the solute had undergone slow sorption, even in the absence of any sorption process. This mechanism may help explain some hitherto confusing aspects of intragranular diffusion.
BF{sub 3} PIII modeling: Implantation, amorphisation and diffusion
Essa, Z.; Cristiano, F.; Spiegel, Y.; Boulenc, P.; Qiu, Y.; Quillec, M.; Taleb, N.; Burenkov, A.; Hackenberg, M.; Bedel-Pereira, E.; Mortet, V.; Torregrosa, Frank; Tavernier, C.
2012-11-06
In the race for highly doped ultra-shallow junctions (USJs) in complementary metal oxide semi-conductor (CMOS) technologies, plasma immersion ion implantation (PIII) is a promising alternative to traditional beamline implantation. Currently, no commercial technology computer aided design (TCAD) process simulator allows modeling the complete USJ fabrication process by PIII, including as-implanted dopant profiles, damage formation, dopant diffusion and activation. In this work, a full simulation of a p-type BF{sub 3} PIII USJ has been carried out. In order to investigate the various physical phenomena mentioned above, process conditions included a high energy/high dose case (10 kV, 5 Multiplication-Sign 10{sup 15} cm{sup -2}), specifically designed to increase damage formation, as well as more technology relevant implant conditions (0.5 kV) for comparison. All implanted samples were annealed at different temperatures and times. As implanted profiles for both boron and fluorine in BF{sub 3} implants were modeled and compared to Secondary Ion Mass Spectrometry (SIMS) measurements. Amorphous/crystalline (a/c) interface depths were measured by transmission electron microscopy (TEM) and successfully simulated. Diffused profiles simulations agreed with SIMS data at low thermal budgets. A boron peak behind the a/c interface was observed in all annealed SIMS profiles for the 10 kV case, indicating boron trapping from EOR defects in this region even after high thermal budgets. TEM measurements on the annealed samples showed an end of range (EOR) defects survival behind the a/c interface, including large dislocation loops (DLs) lying on (001) plane parallel to the surface. In the last part of this work, activation simulations were compared to Hall measurements and confirmed the need to develop a (001) large BICs model.
Postural control model interpretation of stabilogram diffusion analysis
NASA Technical Reports Server (NTRS)
Peterka, R. J.
2000-01-01
Collins and De Luca [Collins JJ. De Luca CJ (1993) Exp Brain Res 95: 308-318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior.
A universal model of restricted diffusion for fluorescence correlation spectroscopy.
Piskorz, Tomasz K; Ochab-Marcinek, Anna
2014-05-08
Fluorescence correlation spectroscopy (FCS) is frequently used to study the processes of restricted diffusion. The most important quantity to determine is the size of the structures that hinder the Brownian motion of the molecules. We study three qualitatively different models of restricted diffusion, widely applied in biophysics and material science: Diffusion constrained by elastic force (i), walking confined diffusion (ii), and hop diffusion (iii). They cover the diversity of statistical behaviors, from purely Gaussian (i) to sharply non-Gaussian on intermediate time scales (ii) and, additionally, discrete (iii). We test whether one can use the Gaussian approximation of the FCS autocorrelation function to interpret the non-Gaussian data. We show that (i-iii) have approximately the same mean square displacements. Using simulations, we show that the FCS data suspected of restricted diffusion can be reliably interpreted using one archetypal model (i). Even if the underlying mechanism of the restriction is different or unknown, the accuracy of fitting the confinement size is excellent, and diffusion coefficients are also estimated with a good accuracy. This study gives a physical insight into the statistical behavior of different types of restricted diffusion and into the ability of fluorescence correlation spectroscopy to distinguish between them.
Modeling diffuse reflectance measurements of light scattered by layered tissues
NASA Astrophysics Data System (ADS)
Rohde, Shelley B.
In this dissertation, we first present a model for the diffuse reflectance due to a continuous beam incident normally on a half space composed of a uniform scattering and absorbing medium. This model is the result of an asymptotic analysis of the radiative transport equation for strong scattering, weak absorption and a defined beam width. Through comparison with the diffuse reflectance computed using the numerical solution of the radiative transport equation, we show that this diffuse reflectance model gives results that are accurate for small source-detector separation distances. We then present an explicit model for the diffuse reflectance due to a collimated beam of light incident normally on layered tissues. This model is derived using the corrected diffusion approximation applied to a layered medium, and it takes the form of a convolution with an explicit kernel and the incident beam profile. This model corrects the standard diffusion approximation over all source-detector separation distances provided the beam is sufficiently wide compared to the scattering mean-free path. We validate this model through comparison with Monte Carlo simulations. Then we use this model to estimate the optical properties of an epithelial layer from Monte Carlo simulation data. Using measurements at small source-detector separations and this model, we are able to estimate the absorption coefficient, scattering coefficient and anisotropy factor of epithelial tissues efficiently with reasonable accuracy. Finally, we present an extension of the corrected diffusion approximation for an obliquely incident beam. This model is formed through a Fourier Series representation in the azimuthal angle which allows us to exhibit the break in axisymmetry when combined with the previous analysis. We validate this model with Monte Carlo simulations. This model can also be written in the form of a convolution of an explicit kernel with the incident beam profile. Additionally, it can be used to
Modelling oxygen self-diffusion in UO2 under pressure
Cooper, Michael William D.; Grimes, R. W.; Fitzpatrick, M. E.; ...
2015-10-22
Access to values for oxygen self-diffusion over a range of temperatures and pressures in UO2 is important to nuclear fuel applications. Here, elastic and expansivity data are used in the framework of a thermodynamic model, the cBΩ model, to derive the oxygen self-diffusion coefficient in UO2 over a range of pressures (0–10 GPa) and temperatures (300–1900 K). Furthermore, the significant reduction in oxygen self-diffusion as a function of increasing hydrostatic pressure, and the associated increase in activation energy, is identified.
The Defect Diffusion Model of Glass-Forming Liquids
NASA Astrophysics Data System (ADS)
Fontanella, John; Bendler, John; Wintersgill, Mary; Shlesinger, Michael
2013-03-01
The defect diffusion model (DDM) provides an explanation of many properties of glass-forming liquids. For example, it has been used to interpret dielectric relaxation (alpha and beta relaxations and the boson peak), viscosity, ionic conductivity, (including the effects of temperature and pressure) positron annihilation lifetime spectroscopy data, the physical basis of fragility, scaling, the ratio of the apparent isochoric activation energy to the isobaric activation enthalpy and its relationship to monomer volume, and correlation lengths. In the model, the glass transition, Tg, occurs because of rigidity percolation. In addition the transition at TB (or TLL) is associated with mobility percolation. In the simplest form of the DDM, a supercooled liquid contains mobile single defects (MSDs) and immobile, clustered single defects (ICSDs). Consequently, dynamic heterogeneity is a natural feature of the model. If the glass transition did not intervene, all MSDs would disappear at a critical temperature Tc. In the present talk, the model will be used to comment on the change of heat capacity, thermal expansion coefficient and compressibility at Tg. Work supported in part by the Office of Naval Research
Wang, Hsin; Porter, Wallace D; Bottner, Harold; Konig, Jan; Chen, Lidong; Bai, Shengqiang; Tritt, Terry M.; Mayolett, Alex; Senawiratne, Jayantha; Smith, Charlene; Harris, Fred; Gilbert, Partricia; Sharp, J; Lo, Jason; Keinke, Holger; Kiss, Laszlo I.
2013-01-01
For bulk thermoelectrics, figure-of-merit, ZT, still needs to improve from the current value of 1.0 - 1.5 to above 2 to be competitive to other alternative technologies. In recent years, the most significant improvements in ZT were mainly due to successful reduction of thermal conductivity. However, thermal conductivity cannot be measured directly at high temperatures. The combined measurements of thermal diffusivity and specific heat and density are required. It has been shown that thermal conductivity is the property with the greatest uncertainty and has a direct influence on the accuracy of the figure of merit. The International Energy Agency (IEA) group under the implementing agreement for Advanced Materials for Transportation (AMT) has conducted two international round-robins since 2009. This paper is Part II of the international round-robin testing of transport properties of bulk bismuth telluride. The main focuses in Part II are on thermal diffusivity, specific heat and thermal conductivity.
Evaluating the accuracy of diffusion MRI models in white matter.
Rokem, Ariel; Yeatman, Jason D; Pestilli, Franco; Kay, Kendrick N; Mezer, Aviv; van der Walt, Stefan; Wandell, Brian A
2015-01-01
Models of diffusion MRI within a voxel are useful for making inferences about the properties of the tissue and inferring fiber orientation distribution used by tractography algorithms. A useful model must fit the data accurately. However, evaluations of model-accuracy of commonly used models have not been published before. Here, we evaluate model-accuracy of the two main classes of diffusion MRI models. The diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian distribution. Sparse fascicle models (SFM) summarize the signal as a sum of signals originating from a collection of fascicles oriented in different directions. We use cross-validation to assess model-accuracy at different gradient amplitudes (b-values) throughout the white matter. Specifically, we fit each model to all the white matter voxels in one data set and then use the model to predict a second, independent data set. This is the first evaluation of model-accuracy of these models. In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM model-accuracy, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations. The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking.
Dighe, Manjiri; Barr, Richard; Bojunga, Jörg; Cantisani, Vito; Chammas, Maria Cristina; Cosgrove, David; Cui, Xin Wu; Dong, Yi; Fenner, Franziska; Radzina, Maija; Vinayak, Sudhir; Xu, Jun Mei; Dietrich, Christoph F
2017-01-31
Accurate differentiation of focal thyroid nodules (FTL) and thyroid abnormalities is pivotal for proper diagnostic and therapeutic work-up. In these two part articles, the role of ultrasound techniques in the characterization of FTL and evaluation of diffuse thyroid diseases is described to expand on the recently published World Federation in Ultrasound and Medicine (WFUMB) thyroid elastography guidelines and review how this guideline fits into a complete thyroid ultrasound exam.
Theoretical model of blood flow measurement by diffuse correlation spectroscopy
NASA Astrophysics Data System (ADS)
Sakadžić, Sava; Boas, David A.; Carp, Stefan
2017-02-01
Diffuse correlation spectroscopy (DCS) is a noninvasive method to quantify tissue perfusion from measurements of the intensity temporal autocorrelation function of diffusely scattered light. However, DCS autocorrelation function measurements in tissue better match theoretical predictions based on the diffusive motion of the scatterers than those based on a model where the advective nature of blood flow dominates the stochastic properties of the scattered light. We have recently shown using Monte Carlo (MC) simulations and assuming a simplistic vascular geometry and laminar flow profile that the diffusive nature of the DCS autocorrelation function decay is likely a result of the shear-induced diffusion of the red blood cells. Here, we provide theoretical derivations supporting and generalizing the previous MC results. Based on the theory of diffusing-wave spectroscopy, we derive an expression for the autocorrelation function along the photon path through a vessel that takes into account both diffusive and advective scatterer motion, and we provide the solution for the DCS autocorrelation function in a semi-infinite geometry. We also derive the correlation diffusion and correlation transfer equation, which can be applied for an arbitrary sample geometry. Further, we propose a method to take into account realistic vascular morphology and flow profile.
NASA Astrophysics Data System (ADS)
Guillory, J. U.; Terry, R. E.
1984-07-01
This report describes work done under DNA Contract 001-79-C-0189 from February 1982 to June 1983, and some more recent work. Part 1 includes treatments of a simple zero-D implosion code, analytic but very approximate scaling laws for radiation, and a discussion of preliminary work on nonlinear field penetration of plasma. Part 2 contains a discussion of electrodiffusive 1D modeling of annular plasma implosions. The thermoelectrical field, its role in field penetrations, the nonlocal constraints required in field diffusion (and some arising from field diffusion), flux limits and the acceleration process for annular plasmas are discussed.
Extreme Events and Their Predictability in a Branching Diffusion Model
NASA Astrophysics Data System (ADS)
Gabrielov, A.; Zaliapin, I.; Keilis-Borok, V.
2009-05-01
Studies in prediction of extreme events, based on real observations and numerical modeling of complex systems, suggest universal patterns of system's behavior signaling approach of an extreme event. These patterns include deviation from self-similarity, increase in background activity, clustering, and long-range correlation. In the absence of a closed theory describing critical transitions in complex systems, and with insufficient and noisy observations, numerical parameters of the patterns have to be data-fitted, creating the risk of self-deception ("With four exponents I can fit the elephant" - J. von Neumann). Here, we introduce a model which provides analytical definition of at least two parameters, intensity and deviation from self-similarity. That drastically reduces non-uniqueness of parametrization, suggesting a simple universal mechanism of premonitory patterns and natural framework for their analytical study. Major conceptual parts of the model - direct cascading or fragmentation, spatial dynamics, and external driving - are combined in a classical age-dependent multi-type branching diffusion process with immigration. A complete analytic description of the size- and space-dependent distributions of particles and their correlations is derived using the generating function approach.
Innovation Diffusion Model in Higher Education: Case Study of E-Learning Diffusion
ERIC Educational Resources Information Center
Buc, Sanjana; Divjak, Blaženka
2015-01-01
The diffusion of innovation (DOI) is critical for any organization and especially nowadays for higher education institutions (HEIs) in the light of vast pressure of emerging educational technologies as well as of the demand of economy and society. DOI takes into account the initial and the implementation phase. The conceptual model of DOI in…
Reaction-diffusion-branching models of stock price fluctuations
NASA Astrophysics Data System (ADS)
Tang, Lei-Han; Tian, Guang-Shan
Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior ( H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.
Modeling cation diffusion in compacted water-saturated sodium bentonite at low ionic strength.
Bourg, Ian C; Sposito, Garrison; Bourg, Alain C M
2007-12-01
Sodium bentonites are used as barrier materials for the isolation of landfills and are under consideration for a similar use in the subsurface storage of high-level radioactive waste. The performance of these barriers is determined in large part by molecular diffusion in the bentonite pore space. We tested two current models of cation diffusion in bentonite against experimental data on the relative apparent diffusion coefficients of two representative cations, sodium and strontium. On the "macropore/nanopore" model, solute molecules are divided into two categories, with unequal pore-scale diffusion coefficients, based on location: in macropores or in interlayer nanopores. On the "surface diffusion" model, solute molecules are divided into categories based on chemical speciation: dissolved or adsorbed. The macropore/nanopore model agrees with all experimental data at partial montmorillonite dry densities ranging from 0.2 (a dilute bentonite gel) to 1.7 kg dm(-3) (a highly compacted bentonite with most of its pore space located in interlayer nanopores), whereas the surface diffusion model fails at partial montmorillonite dry densities greater than about 1.3 kg dm(-3).
Modeling cation diffusion in compacted water-saturatedNa-bentonite at low ionic strength
Bourg, Ian C.; Sposito, Garrison; Bourg, Alain C.M.
2007-08-28
Sodium bentonites are used as barrier materials for the isolation of landfills and are under consideration for a similar use in the subsurface storage of high-level radioactive waste. The performance of these barriers is determined in large part by molecular diffusion in the bentonite pore space. We tested two current models of cation diffusion in bentonite against experimental data on the relative apparent diffusion coefficients of two representative cations, sodium and strontium. On the 'macropore/nanopore' model, solute molecules are divided into two categories, with unequal pore-scale diffusion coefficients, based on location: in macropores or in interlayer nanopores. On the 'surface diffusion' model, solute molecules are divided into categories based on chemical speciation: dissolved or adsorbed. The macropore/nanopore model agrees with all experimental data at partial montmorillonite dry densities ranging from 0.2 (a dilute bentonite gel) to 1.7 kg dm{sup -3} (a highly compacted bentonite with most of its pore space located in interlayer nanopores), whereas the surface diffusion model fails at partial montmorillonite dry densities greater than about 1.2 kg dm{sup -3}.
Update on Advection-Diffusion Purge Flow Model
NASA Technical Reports Server (NTRS)
Brieda, Lubos
2015-01-01
Gaseous purge is commonly used in sensitive spacecraft optical or electronic instruments to prevent infiltration of contaminants and/or water vapor. Typically, purge is sized using simplistic zero-dimensional models that do not take into account instrument geometry, surface effects, and the dependence of diffusive flux on the concentration gradient. For this reason, an axisymmetric computational fluid dynamics (CFD) simulation was recently developed to model contaminant infiltration and removal by purge. The solver uses a combined Navier-Stokes and Advection-Diffusion approach. In this talk, we report on updates in the model, namely inclusion of a particulate transport model.
SOLVING THE TWO-DIMENSIONAL DIFFUSION FLOW MODEL.
Hromadka, T.V.; Lai, Chintu
1985-01-01
A simplification of the two-dimensional (2-D) continuity and momentum equations is the diffusion equation. To investigate its capability, the numerical model using the diffusion approach is applied to a hypothetical failure problem of a regional water reservoir. The model is based on an explicit, integrated finite-difference scheme, and the floodplain is simulated by a popular home computer which supports 64K FORTRAN. Though simple, the 2-D model can simulate some interesting flooding effects that a 1-D full dynamic model cannot.
Evolution Nonlinear Diffusion-Convection PDE Models for Spectrogram Enhancement
NASA Astrophysics Data System (ADS)
Dugnol, B.; Fernández, C.; Galiano, G.; Velasco, J.
2008-09-01
In previous works we studied the application of PDE-based image processing techniques applied to the spectrogram of audio signals in order to improve the readability of the signal. In particular we considered the implementation of the nonlinear diffusive model proposed by Álvarez, Lions and Morel [1](ALM) combined with a convective term inspired by the differential reassignment proposed by Chassandre-Mottin, Daubechies, Auger and Flandrin [2]-[3]. In this work we consider the possibility of replacing the diffusive model of ALM by diffusive terms in divergence form. In particular we implement finite element approximations of nonlinear diffusive terms studied by Chen, Levine, Rao [4] and Antontsev, Shmarev [5]-[8] with a convective term.
Evolution of a simple inhomogeneous anisotropic cosmological model with diffusion
Shogin, Dmitry; Hervik, Sigbjørn E-mail: sigbjorn.hervik@uis.no
2013-10-01
We investigate a simple inhomogeneous anisotropic cosmology (plane symmetric G{sub 2} model) filled with a tilted perfect fluid undergoing velocity diffusion on a scalar field. Considered are two types of fluid: dust and radiation. We solve the system of Einstein field equations and diffusion equations numerically and demonstrate how the universe evolves towards its future asymptotic state. Also, typical time scales of characteristic processes are determined. The obtained results for dust- and radiation-filled cosmologies are compared to each other and to those in the diffusionless case, giving a hint on which effects can be the result of including diffusion in more complicated models. For example, diffusion causes the accelerated expansion stage to arrive at later times.
Laminar flamelet modeling of turbulent diffusion flames
NASA Astrophysics Data System (ADS)
Mell, W. E.; Kosaly, G.; Planche, O.; Poinsot, T.; Ferziger, J. H.
1990-12-01
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.
Mesoscale modelling of crack-induced diffusivity in concrete
NASA Astrophysics Data System (ADS)
Nilenius, Filip; Larsson, Fredrik; Lundgren, Karin; Runesson, Kenneth
2015-02-01
Cracks have large impact on the diffusivity of concrete since they provide low-resistance pathways for moisture and chloride ions to migrate through the material. In this work, crack-induced diffusivity in concrete is modelled on the heterogeneous mesoscale and computationally homogenized to obtain macroscale diffusivity properties. Computations are carried out using the finite element method on three-dimensional statistical volume elements (SVEs) comprising the mesoscale constituents in terms of cement paste, aggregates and the interfacial transition zone (ITZ). The SVEs are subjected to uni-axial tension loading and cracks are simulated by use of an isotropic damage model. In a damaged finite element, the crack plane is assumed to be perpendicular to the largest principle strain, and diffusivity properties are assigned to the element only in the in-plane direction of the crack by anisotropic constitutive modelling. The numerical results show that the macroscale diffusivity of concrete can be correlated to the applied mechanical straining of the SVE and that the macroscale diffusivity increases mainly in the transversal direction relative to the axis of imposed mechanical straining.
A pesticide emission model (PEM) Part II: model evaluation
NASA Astrophysics Data System (ADS)
Scholtz, M. T.; Voldner, E.; Van Heyst, B. J.; McMillan, A. C.; Pattey, E.
In the first part of the paper, the development of a numerical pesticide emission model (PEM) is described for predicting the volatilization of pesticides applied to agricultural soils and crops through soil incorporation, surface spraying, or in the furrow at the time of planting. In this paper the results of three steps toward the evaluation of PEM are reported. The evaluation involves: (i) verifying the numerical algorithms and computer code through comparison of PEM simulations with an available analytical solution of the advection/diffusion equation for semi-volatile solutes in soil; (ii) comparing hourly heat, moisture and emission fluxes of trifluralin and triallate modeled by PEM with fluxes measured using the relaxed eddy-accumulation technique; and (iii) comparison of the PEM predictions of persistence half-life for 29 pesticides with the ranges of persistence found in the literature. The overall conclusion from this limited evaluation study is that PEM is a useful model for estimating the volatilization rates of pesticides from agricultural soils and crops. The lack of reliable estimates of chemical and photochemical degradation rates of pesticide on foliage, however, introduces large uncertainties in the estimates from any model of the volatilization of pesticide that impacts the canopy.
Shao, Yuan; Ramachandran, Sandhya; Arnold, Susan; Ramachandran, Gurumurthy
2017-03-01
The use of the turbulent eddy diffusion model and its variants in exposure assessment is limited due to the lack of knowledge regarding the isotropic eddy diffusion coefficient, DT. But some studies have suggested a possible relationship between DT and the air changes per hour (ACH) through a room. The main goal of this study was to accurately estimate DT for a range of ACH values by minimizing the difference between the concentrations measured and predicted by eddy diffusion model. We constructed an experimental chamber with a spatial concentration gradient away from the contaminant source, and conducted 27 3-hr long experiments using toluene and acetone under different air flow conditions (0.43-2.89 ACHs). An eddy diffusion model accounting for chamber boundary, general ventilation, and advection was developed. A mathematical expression for the slope based on the geometrical parameters of the ventilation system was also derived. There is a strong linear relationship between DT and ACH, providing a surrogate parameter for estimating DT in real-life settings. For the first time, a mathematical expression for the relationship between DT and ACH has been derived that also corrects for non-ideal conditions, and the calculated value of the slope between these two parameters is very close to the experimentally determined value. The values of DT obtained from the experiments are generally consistent with values reported in the literature. They are also independent of averaging time of measurements, allowing for comparison of values obtained from different measurement settings. These findings make the use of turbulent eddy diffusion models for exposure assessment in workplace/indoor environments more practical.
Structure and Mixing of a Turbulent Meandering Plume Part 2: Turbulent Mixing and Eddy-Diffusivity
NASA Astrophysics Data System (ADS)
Webster, D. R.; Young, D. L.; Larsson, A. I.
2016-11-01
Turbulent mixing in a meandering non-buoyant chemical plume is far less understood than in a straight plume - partially due to the difficulty separating the plume meander fluctuations from the turbulent fluctuations. In this study we present high resolution measurements of the covariance of the turbulent fluctuations of velocity and concentration in a phase-locked meandering plume, acquired by combining simultaneous PTV velocity and LIF concentration measurements. The effectiveness of the eddy-diffusivity model for predicting the turbulent flux is assessed. Analysis of the data reveals that the spatial distribution of the turbulent flux is governed by the large-scale alternating-sign vortices that induce the plume meander. Further, regions of high turbulent flux are co-located with areas of large phase-averaged concentration gradients. As a result, the eddy-diffusivity framework models the turbulent flux effectively. As expected from turbulent mixing theory, the eddy-diffusivity coefficient plateaus at a constant value once the plume width reaches the size of the largest eddies (i.e., the scale of the water depth in this open channel flow). However, when the plume width is less than the water depth the eddy-diffusivity coefficient scales with the plume width to the 3/4 power. This differs from the theoretical 4/3 scaling that results from the assumption of an inertial subrange. The extent of the inertial subrange is extremely limited in the current moderate-Re open channel flow.
A Novel Restricted Diffusion Model of Evoked Dopamine
2015-01-01
In vivo fast-scan cyclic voltammetry provides high-fidelity recordings of electrically evoked dopamine release in the rat striatum. The evoked responses are suitable targets for numerical modeling because the frequency and duration of the stimulus are exactly known. Responses recorded in the dorsal and ventral striatum of the rat do not bear out the predictions of a numerical model that assumes the presence of a diffusion gap interposed between the recording electrode and nearby dopamine terminals. Recent findings, however, suggest that dopamine may be subject to restricted diffusion processes in brain extracellular space. A numerical model cast to account for restricted diffusion produces excellent agreement between simulated and observed responses recorded under a broad range of anatomical, stimulus, and pharmacological conditions. The numerical model requires four, and in some cases only three, adjustable parameters and produces meaningful kinetic parameter values. PMID:24983330
Guideline for fluid modeling of atmospheric diffusion
NASA Astrophysics Data System (ADS)
Snyder, W. H.
1981-04-01
The usefulness of fluid models are evaluated from both scientific and engineering viewpoints. Because many detailed decisions must be made during the design and execution of each model study, and because the fundamental principles frequency do not provide enough guidance, extensive discussion of the details of the most common types of modeling problems are provided. The hardware requirements are also discussed. This guidance is intended to be of use both to scientists and engineering involved in operating fluid modeling facilities and to air pollution control officials in evaluating the quality and credibility of the reports from such studies.
Modeling phosphorus diffusion gettering of iron in single crystal silicon
NASA Astrophysics Data System (ADS)
Haarahiltunen, A.; Savin, H.; Yli-Koski, M.; Talvitie, H.; Sinkkonen, J.
2009-01-01
We propose a quantitative model for phosphorus diffusion gettering (PDG) of iron in silicon, which is based on a special fitting procedure to experimental data. We discuss the possibilities of the underlying physics of the segregation coefficient. Finally, we show that the proposed PDG model allows quantitative analysis of gettering efficiency of iron at various processing conditions.
Restabilizing Forcing for a Diffusive Prey-Predator Model
NASA Astrophysics Data System (ADS)
Buonomo, Bruno; Rionero, Salvatore
2008-04-01
We consider a diffusive prey-predator model and find conditions under which a relevant non trivial equilibrium undergoes to Turing bifurcation. Then, a forcing is applied to the model and values of forcing able to regain the (nonlinear) stability are detected. A maximal restabilizing region is derived.
An Urban Diffusion Simulation Model for Carbon Monoxide
ERIC Educational Resources Information Center
Johnson, W. B.; And Others
1973-01-01
A relatively simple Gaussian-type diffusion simulation model for calculating urban carbon (CO) concentrations as a function of local meteorology and the distribution of traffic is described. The model can be used in two ways: in the synoptic mode and in the climatological mode. (Author/BL)
A combinatorial model of malware diffusion via bluetooth connections.
Merler, Stefano; Jurman, Giuseppe
2013-01-01
We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy) and closed form (more complex but efficiently computable) expression.
A Diffusion Model Account of the Lexical Decision Task
ERIC Educational Resources Information Center
Ratcliff, Roger; Gomez, Pablo; McKoon, Gail
2004-01-01
The diffusion model for 2-choice decisions (R. Ratcliff, 1978) was applied to data from lexical decision experiments in which word frequency, proportion of high- versus low-frequency words, and type of nonword were manipulated. The model gave a good account of all of the dependent variables--accuracy, correct and error response times, and their…
A three-dimensional spin-diffusion model for micromagnetics.
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter
2015-10-07
We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation.
A three-dimensional spin-diffusion model for micromagnetics
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter
2015-01-01
We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation. PMID:26442796
A molecular diffusion based utility model for Drosophila larval phototaxis
2012-01-01
Background Generally, utility based decision making models focus on experimental outcomes. In this paper we propose a utility model based on molecular diffusion to simulate the choice behavior of Drosophila larvae exposed to different light conditions. Methods In this paper, light/dark choice-based Drosophila larval phototaxis is analyzed with our molecular diffusion based model. An ISCEM algorithm is developed to estimate the model parameters. Results By applying this behavioral utility model to light intensity and phototaxis data, we show that this model fits the experimental data very well. Conclusions Our model provides new insights into decision making mechanisms in general. From an engineering viewpoint, we propose that the model could be applied to a wider range of decision making practices. PMID:22300450
Relaxation and diffusion models with non-singular kernels
NASA Astrophysics Data System (ADS)
Sun, HongGuang; Hao, Xiaoxiao; Zhang, Yong; Baleanu, Dumitru
2017-02-01
Anomalous relaxation and diffusion processes have been widely quantified by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to its limitation in describing different kinds of non-exponential decays (e.g. stretched exponential decay). Meanwhile, many efforts by mathematicians and engineers have been made to overcome the singularity of power function kernel in its definition. This study first explores physical properties of relaxation and diffusion models where the temporal derivative was defined recently using an exponential kernel. Analytical analysis shows that the Caputo type derivative model with an exponential kernel cannot characterize non-exponential dynamics well-documented in anomalous relaxation and diffusion. A legitimate extension of the previous derivative is then proposed by replacing the exponential kernel with a stretched exponential kernel. Numerical tests show that the Caputo type derivative model with the stretched exponential kernel can describe a much wider range of anomalous diffusion than the exponential kernel, implying the potential applicability of the new derivative in quantifying real-world, anomalous relaxation and diffusion processes.
Notes on the Langevin model for turbulent diffusion of ``marked`` particles
Rodean, H.C.
1994-01-26
Three models for scalar diffusion in turbulent flow (eddy diffusivity, random displacement, and on the Langevin equation) are briefly described. These models random velocity increment based Fokker-Planck equation is introduced as are then examined in more detail in the reverse order. The Fokker-Planck equation is the Eulerian equivalent of the Lagrangian Langevin equation, and the derivation of e outlined. The procedure for obtaining the deterministic and stochastic components of the Langevin equation from Kolmogorov`s 1941 inertial range theory and the Fokker-Planck equation is described. it is noted that a unique form of the Langevin equation can be determined for diffusion in one dimension but not in two or three. The Langevin equation for vertical diffusion in the non-Gaussian convective boundary layer is presented and successively simplified for Gaussian inhomogeneous turbulence and Gaussian homogeneous turbulence in turn. The Langevin equation for Gaussian inhomogeneous turbulence is mathematically transformed into the random displacement model. It is shown how the Fokker-Planck equation for the random displacement model is identical in form to the partial differential equation for the eddy diffusivity model. It is noted that the Langevin model is applicable in two cases in which the other two are not valid: (1) very close in time and distance to the point of scalar release and (2) the non-Gaussian convective boundary layer. The two- and three-dimensional cases are considered in Part III.
q-Space Deep Learning: Twelve-Fold Shorter and Model-Free Diffusion MRI Scans.
Golkov, Vladimir; Dosovitskiy, Alexey; Sperl, Jonathan I; Menzel, Marion I; Czisch, Michael; Samann, Philipp; Brox, Thomas; Cremers, Daniel
2016-05-01
Numerous scientific fields rely on elaborate but partly suboptimal data processing pipelines. An example is diffusion magnetic resonance imaging (diffusion MRI), a non-invasive microstructure assessment method with a prominent application in neuroimaging. Advanced diffusion models providing accurate microstructural characterization so far have required long acquisition times and thus have been inapplicable for children and adults who are uncooperative, uncomfortable, or unwell. We show that the long scan time requirements are mainly due to disadvantages of classical data processing. We demonstrate how deep learning, a group of algorithms based on recent advances in the field of artificial neural networks, can be applied to reduce diffusion MRI data processing to a single optimized step. This modification allows obtaining scalar measures from advanced models at twelve-fold reduced scan time and detecting abnormalities without using diffusion models. We set a new state of the art by estimating diffusion kurtosis measures from only 12 data points and neurite orientation dispersion and density measures from only 8 data points. This allows unprecedentedly fast and robust protocols facilitating clinical routine and demonstrates how classical data processing can be streamlined by means of deep learning.
NASA Technical Reports Server (NTRS)
Srinivasan, R. Srini; Gerth, Wayne A.; Powell, Michael R.; Paloski, William H. (Technical Monitor)
2000-01-01
A three-region mathematical model of gas bubble dynamics has been shown suitable for describing diffusion-limited dynamics of more than one bubble in a given volume of extravascular tissue. The model is based on the dynamics of gas exchange between a bubble and a well-stirred tissue region through an intervening unperfused diffusion region previously assumed to have constant thickness and uniform gas diffusivity. As a result, the gas content of the diffusion region remains constant as the volume of the region increases with bubble growth, causing dissolved gas in the region to violate Henry's law. Earlier work also neglected the relationship between the varying diffusion region volume and the fixed total tissue volume, because only cases in which the diffusion region volume is a small fraction of the overall tissue volume were considered. We herein extend the three-region model to correct these theoretical inconsistencies by allowing both the thickness and gas content of the diffusion region to vary during bubble evolution. A postulated difference in gas diffusivity between an infinitesimally thin layer at the bubble surface and the remainder of the diffusion region leads to variation in diffusion region gas content and thickness during bubble growth and resolution. This variable thickness, differential diffusivity (VTDD) model can yield bubble lifetimes considerably longer than those yielded by earlier three-region models for given model and decompression parameters, and meets a need for theoretically consistent but relatively simple bubble dynamics models for use in studies of decompression sickness (DCS) in human subjects, Keywords: decompression sickness, gas diffusion in tissue, diffusivity
MESOI: an interactive Lagrangian trajectory puff diffusion model
Ramsdell, J.V.; Athey, G.F.
1981-12-01
MESOI is an interactive Lagrangian trajectory puff diffusion model based on an earlier model by Start and Wendell at the Air Resources Laboratory Field Office at Idaho Falls, Idaho. Puff trajectories are determined using spatially and temporally varying wind fields. Diffusion in the puffs is computed as a function of distance traveled and atmospheric stability. Exposures are computed at nodes of a 31 by 31 grid. There is also provision for interpolation of short term exposures at off-grid locations. This report discusses: the theoretical bases of the model, the numerical approach used in the model, and the sensitivity and accuracy of the model. It contains a description of the computer program and a listing of the code. MESOI is written in FORTRAN. A companion report (Athey, Allwine and Ramsdell, 1981) contains a user's guide to MESOI and documents utility programs that maintain the data files needed by the model.
THE SEPARATION OF URANIUM ISOTOPES BY GASEOUS DIFFUSION: A LINEAR PROGRAMMING MODEL,
URANIUM, ISOTOPE SEPARATION), (*GASEOUS DIFFUSION SEPARATION, LINEAR PROGRAMMING ), (* LINEAR PROGRAMMING , GASEOUS DIFFUSION SEPARATION), MATHEMATICAL MODELS, GAS FLOW, NUCLEAR REACTORS, OPERATIONS RESEARCH
An effective diffusivity model based on Koopman mode decomposition
NASA Astrophysics Data System (ADS)
Arbabi, Hassan; Mezic, Igor
2016-11-01
In the previous work, we had shown that the Koopman mode decomposition (KMD) can be used to analyze mixing of passive tracers in time-dependent flows. In this talk, we discuss the extension of this type of analysis to the case of advection-diffusion transport for passive scalar fields. Application of KMD to flows with complex time-dependence yields a decomposition of the flow into mean, periodic and chaotic components. We briefly discuss the computation of these components using a combination of harmonic averaging and Discrete Fourier Transform. We propose a new effective diffusivity model in which the advection is dominated by mean and periodic components whereas the effect of chaotic motion is absorbed into an effective diffusivity tensor. The performance of this model is investigated in the case of lid-driven cavity flow.
Some Approaches to Modeling Diffuse Flow at Mid-Ocean Ridges
NASA Astrophysics Data System (ADS)
Farough, A.; Lowell, R. P.; Craft, K.; Germanovich, L. N.
2011-12-01
To obtain a sound understanding of subsurface temperatures and the extent of the subsurface biosphere in young oceanic crust, one must understand the mechanisms of diffuse flow at oceanic spreading centers. Mathematical modeling of diffuse flow at oceanic spreading centers has received relatively little attention compared to high-temperature black smoker discharge, in part because the temperature and fluid flow data required to constrain the models are scarce. We review a number of different approaches to modelling diffuse flow: (1) The simplest method considers 1-D steady-state uniform upflow from below subject to a heat transfer boundary condition at the surface, which represents the effects of mixing of hydrothermal fluid with seawater. These models, in which the heat transfer coefficient and the velocity of the ascending fluid are constrained by observed diffuse flow vent temperature and heat flux, typically result in a steep temperature gradient near the seafloor and subsurface biological activity may be limited to the upper few cm of the crust. (2) A related method uses data on the partitioning of heat flux between focused and diffuse flow and chemical data from the focused and diffuse flow components in a two-limb single pass modeling approach to determine the fraction of high-temperature fluid that is incorporated in the diffuse flow. Using data available from EPR 950', the Main Endeavour Field, and ASHES vent field at Axial Volcano on the Juan de Fuca Ridge in conjunction with Mg as a passive tracer, we find that the mixing ratio of high temperature in diffuse flow is <10%. The high-temperature contribution to the diffuse heat flux remains large, however, and high-temperature vent fluid ultimately contributes ~ 90% of the total heat output from the vent field. In these models mixing between high-temperature fluid and seawater may occur over a considerable depth, and the subsurface biosphere may be ~ 100 m deep beneath diffuse flow sites. (3) Finally, in
Computer modelling of nanoscale diffusion phenomena at epitaxial interfaces
NASA Astrophysics Data System (ADS)
Michailov, M.; Ranguelov, B.
2014-05-01
The present study outlines an important area in the application of computer modelling to interface phenomena. Being relevant to the fundamental physical problem of competing atomic interactions in systems with reduced dimensionality, these phenomena attract special academic attention. On the other hand, from a technological point of view, detailed knowledge of the fine atomic structure of surfaces and interfaces correlates with a large number of practical problems in materials science. Typical examples are formation of nanoscale surface patterns, two-dimensional superlattices, atomic intermixing at an epitaxial interface, atomic transport phenomena, structure and stability of quantum wires on surfaces. We discuss here a variety of diffusion mechanisms that control surface-confined atomic exchange, formation of alloyed atomic stripes and islands, relaxation of pure and alloyed atomic terraces, diffusion of clusters and their stability in an external field. The computational model refines important details of diffusion of adatoms and clusters accounting for the energy barriers at specific atomic sites: smooth domains, terraces, steps and kinks. The diffusion kinetics, integrity and decomposition of atomic islands in an external field are considered in detail and assigned to specific energy regions depending on the cluster stability in mass transport processes. The presented ensemble of diffusion scenarios opens a way for nanoscale surface design towards regular atomic interface patterns with exotic physical features.
NASA Astrophysics Data System (ADS)
Chau, J. F.; Or, D.; Jones, S.; Sukop, M.
2004-05-01
Liquid distribution in unsaturated porous media under different gravitational forces and resulting gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. Different fluid behavior in plant growth media under microgravity conditions as compared to earth presents a challenge to plant growth in long duration space exploration missions. Our primary objective was to provide qualitative description and quantitative measures of the role of reduced gravity on hydraulic and gaseous transport properties in simulated porous media. We implemented a multi-phase lattice Boltzmann code for equilibrium distribution of liquid in an idealized two-dimensional porous medium under microgravity and "normal" gravity conditions. The information was then used to provide boundary conditions for simulation of gaseous diffusion through the equilibrium domains (considering diffusion through liquid phase negligibly small). The models were tested by comparison with several analytical solutions to the diffusion equation, with excellent results. The relative diffusion coefficient for both series of simulations (with and without gravity) as functions of air-filled porosity was in good agreement with established models of Millington-Quirk. Liquid distribution under earth's gravity featured increased water content at the lower part of the medium relative to the distribution in reduced gravity, which resulted in decreased gas diffusion through a vertically oriented column of a porous medium. Simulation results for larger domains under various orientations will be presented.
GIS-BASED 1-D DIFFUSIVE WAVE OVERLAND FLOW MODEL
KALYANAPU, ALFRED; MCPHERSON, TIMOTHY N.; BURIAN, STEVEN J.
2007-01-17
This paper presents a GIS-based 1-d distributed overland flow model and summarizes an application to simulate a flood event. The model estimates infiltration using the Green-Ampt approach and routes excess rainfall using the 1-d diffusive wave approximation. The model was designed to use readily available topographic, soils, and land use/land cover data and rainfall predictions from a meteorological model. An assessment of model performance was performed for a small catchment and a large watershed, both in urban environments. Simulated runoff hydrographs were compared to observations for a selected set of validation events. Results confirmed the model provides reasonable predictions in a short period of time.
Approximating nonequilibrium processes using a collection of surrogate diffusion models
NASA Astrophysics Data System (ADS)
Calderon, Christopher P.; Chelli, Riccardo
2008-04-01
The surrogate process approximation (SPA) is applied to model the nonequilibrium dynamics of a reaction coordinate (RC) associated with the unfolding and refolding processes of a deca-alanine peptide at 300K. The RC dynamics, which correspond to the evolution of the end-to-end distance of the polypeptide, are produced by steered molecular dynamics (SMD) simulations and approximated using overdamped diffusion models. We show that the collection of (estimated) SPA models contain structural information "orthogonal" to the RC monitored in this study. Functional data analysis ideas are used to correlate functions associated with the fitted SPA models with the work done on the system in SMD simulations. It is demonstrated that the shape of the nonequilibrium work distributions for the unfolding and refolding processes of deca-alanine can be predicted with functional data analysis ideas using a relatively small number of simulated SMD paths for calibrating the SPA diffusion models.
Mathematical properties of models of the reaction-diffusion type
NASA Astrophysics Data System (ADS)
Beccaria, M.; Soliani, G.
Nonlinear systems of the reaction-diffusion (RD) type, including Gierer-Meinhardt models of autocatalysis, are studied using Lie algebras coming from their prolongation structure. Depending on the form of the functions of the fields characterizing the reactions among them, we consider both quadratic and cubic RD equations. On the basis of the prolongation algebra associated with a given RD model, we distinguish the model as a completely linearizable or a partially linearizable system. In this classification a crucial role is played by the relative sign of the diffusion coefficients, which strongly influence the properties of the system. In correspondence to the above situations, different algebraic characterizations, together with exact and approximate solutions, are found. Interesting examples are the quadratic RD model, which admits an exact solution in terms of the elliptic Weierstrass function, and the cubic Gierer-Meinhardt model, whose prolongation algebra leads to the similitude group in the plane.
Cosmic ray anisotropy in fractional differential models of anomalous diffusion
Uchaikin, V. V.
2013-06-15
The problem of galactic cosmic ray anisotropy is considered in two versions of the fractional differential model for anomalous diffusion. The simplest problem of cosmic ray propagation from a point instantaneous source in an unbounded medium is used as an example to show that the transition from the standard diffusion model to the Lagutin-Uchaikin fractional differential model (with characteristic exponent {alpha} = 3/5 and a finite velocity of free particle motion), which gives rise to a knee in the energy spectrum at 10{sup 6} GeV, increases the anisotropy coefficient only by 20%, while the anisotropy coefficient in the Lagutin-Tyumentsev model (with exponents {alpha} = 0.3 and {beta} = 0.8, a long stay of particles in traps, and an infinite velocity of their jumps) is close to one. This is because the parameters of the Lagutin-Tyumentsev model have been chosen improperly.
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.
Decomposing Task-Switching Costs with the Diffusion Model
ERIC Educational Resources Information Center
Schmitz, Florian; Voss, Andreas
2012-01-01
In four experiments, task-switching processes were investigated with variants of the alternating runs paradigm and the explicit cueing paradigm. The classical diffusion model for binary decisions (Ratcliff, 1978) was used to dissociate different components of task-switching costs. Findings can be reconciled with the view that task-switching…
Modeling development of inhibition zones in an agar diffusion bioassay.
Chandrasekar, Vaishnavi; Knabel, Stephen J; Anantheswaran, Ramaswamy C
2015-09-01
A two-temperature agar diffusion bioassay is commonly used to quantify the concentration of nisin using Micrococcus luteus as the indicator microorganism. A finite element computational model based on Fick's second law of diffusion was used to predict the radius of the inhibition zone in this diffusion bioassay. The model developed was used to calculate nisin concentration profiles as a function of time and position within the agar. The minimum inhibitory concentration (MIC) of nisin against M. luteus was determined experimentally. The critical time (T c) for growth of M. luteus within the agar diffusion bioassay was experimentally determined using incubation studies with nisin. The radius of the inhibition zone was predicted from the computational model as the location where the predicted nisin concentration at T c was equal to MIC. The MIC was experimentally determined to be 0.156 μg mL(-1), and T c was determined to be 7 h. Good agreement (R (2) = 0.984) was obtained between model-predicted and experimentally determined inhibition zone radii.
Reaction Diffusion Modeling of Calcium Dynamics with Realistic ER Geometry
Means, Shawn; Smith, Alexander J.; Shepherd, Jason; Shadid, John; Fowler, John; Wojcikiewicz, Richard J. H.; Mazel, Tomas; Smith, Gregory D.; Wilson, Bridget S.
2006-01-01
We describe a finite-element model of mast cell calcium dynamics that incorporates the endoplasmic reticulum's complex geometry. The model is built upon a three-dimensional reconstruction of the endoplasmic reticulum (ER) from an electron tomographic tilt series. Tetrahedral meshes provide volumetric representations of the ER lumen, ER membrane, cytoplasm, and plasma membrane. The reaction-diffusion model simultaneously tracks changes in cytoplasmic and ER intraluminal calcium concentrations and includes luminal and cytoplasmic protein buffers. Transport fluxes via PMCA, SERCA, ER leakage, and Type II IP3 receptors are also represented. Unique features of the model include stochastic behavior of IP3 receptor calcium channels and comparisons of channel open times when diffusely distributed or aggregated in clusters on the ER surface. Simulations show that IP3R channels in close proximity modulate activity of their neighbors through local Ca2+ feedback effects. Cytoplasmic calcium levels rise higher, and ER luminal calcium concentrations drop lower, after IP3-mediated release from receptors in the diffuse configuration. Simulation results also suggest that the buffering capacity of the ER, and not restricted diffusion, is the predominant factor influencing average luminal calcium concentrations. PMID:16617072
A simple reaction-rate model for turbulent diffusion flames
NASA Technical Reports Server (NTRS)
Bangert, L. H.
1975-01-01
A simple reaction rate model is proposed for turbulent diffusion flames in which the reaction rate is proportional to the turbulence mixing rate. The reaction rate is also dependent on the mean mass fraction and the mean square fluctuation of mass fraction of each reactant. Calculations are compared with experimental data and are generally successful in predicting the measured quantities.
User's Manual for the APRAC-1A Urban Diffusion Model Computer Program.
ERIC Educational Resources Information Center
Mancuso, R. L.; And Others
The APRAC-1A diffusion model was developed as a versatile and practical model for computing the concentrations of pollutants at any point within a city. The model calculates pollutant contributions from diffusion on various scales, including: extra-urban diffusion, mainly from sources in upwind cities; intra-urban diffusion from freeway, arterial,…
ZGB surface reaction model with high diffusion rates
NASA Astrophysics Data System (ADS)
Evans, J. W.
1993-02-01
The diffusionless ZGB (monomer-dimer) surface reaction model exhibits a discontinuous transition to a monomer-poisoned state when the fraction of monomer adsorption attempts exceeds 0.525. It has been claimed that this transition shifts to 2/3 with introduction of rapid diffusion of the monomer species, or of both species. We show this is not the case, 2/3 representing the spinodal rather than the transition point. For equal diffusion rates of both species, we find that the transition only shifts to 0.5951±0.0002.
ZGB surface reaction model with high diffusion rates
Evans, J.W. )
1993-02-01
The diffusionless ZGB (monomer--dimer) surface reaction model exhibits a discontinuous transition to a monomer-poisoned state when the fraction of monomer adsorption attempts exceeds 0.525. It has been claimed that this transition shifts to 2/3 with introduction of rapid diffusion of the monomer species, or of both species. We show this is not the case, 2/3 representing the spinodal rather than the transition point. For equal diffusion rates of both species, we find that the transition only shifts to 0.5951[plus minus]0.0002.
Modeling the diffusion of phosphorus in silicon in 3-D
Baker, K.R.
1994-12-31
The use of matrix preconditioning in semiconductor process simulation is examined. The simplified nonlinear single-species model for the diffusion of phosphorus into silicon is considered. The experimental three-dimensional simulator, PEPPER3, which uses finite differences and the numerical method of lines to implement the reaction-diffusion equation is modified to allow NSPCG to be called to solve the linear system in the inner Newton loop. Use of NSPCG allowed various accelerators such as Generalized Minimal Residual (GMRES) and Conjugate Gradient (CG) to be used in conjunction with preconditioners such as Richardson, Jacobi, and Incomplete Cholesky.
Pressure swing adsorption processes: Intraparticle diffusion/convection models
Lu, Zuping; Loureiro, J.M.; LeVan, M.D. . Dept. of Chemical Engineering); Rodrigues, A.E. . School of Engineering)
1993-11-01
The dynamic behavior of a three-step one-column isothermal PSA process is assessed by simulation; three models are used: equilibrium, intraparticle diffusion, and intraparticle diffusion/convection. Two process performance parameters, product enrichment and recovery of the light component, are used to measure the separation performance. The effects of several operating variables on the process performance are addressed. Higher pressure ratios (P[sub h]/P[sub l]) and higher adsorption capacities increase the process performance. The process performance is practically independent of the step rates, although it can decrease if high feed rates are used together with large feed duration times. The limiting performance of the system is found in the absence of mass-transfer resistances. Intraparticle convection, enhancing mass transfer inside particles, increases the process performance relative to intraparticle diffusion alone; the improvement is limited by the equilibrium situation.
Diffusion models in experimental psychology: a practical introduction.
Voss, Andreas; Nagler, Markus; Lerche, Veronika
2013-01-01
Stochastic diffusion models (Ratcliff, 1978) can be used to analyze response time data from binary decision tasks. They provide detailed information about cognitive processes underlying the performance in such tasks. Most importantly, different parameters are estimated from the response time distributions of correct responses and errors that map (1) the speed of information uptake, (2) the amount of information used to make a decision, (3) possible decision biases, and (4) the duration of nondecisional processes. Although this kind of model can be applied to many experimental paradigms and provides much more insight than the analysis of mean response times can, it is still rarely used in cognitive psychology. In the present paper, we provide comprehensive information on the theory of the diffusion model, as well as on practical issues that have to be considered for implementing the model.
Transport Corrections in Nodal Diffusion Codes for HTR Modeling
Abderrafi M. Ougouag; Frederick N. Gleicher
2010-08-01
The cores and reflectors of High Temperature Reactors (HTRs) of the Next Generation Nuclear Plant (NGNP) type are dominantly diffusive media from the point of view of behavior of the neutrons and their migration between the various structures of the reactor. This means that neutron diffusion theory is sufficient for modeling most features of such reactors and transport theory may not be needed for most applications. Of course, the above statement assumes the availability of homogenized diffusion theory data. The statement is true for most situations but not all. Two features of NGNP-type HTRs require that the diffusion theory-based solution be corrected for local transport effects. These two cases are the treatment of burnable poisons (BP) in the case of the prismatic block reactors and, for both pebble bed reactor (PBR) and prismatic block reactor (PMR) designs, that of control rods (CR) embedded in non-multiplying regions near the interface between fueled zones and said non-multiplying zones. The need for transport correction arises because diffusion theory-based solutions appear not to provide sufficient fidelity in these situations.
The effect of a realistic thermal diffusivity on numerical model of a subducting slab
NASA Astrophysics Data System (ADS)
Maierova, P.; Steinle-Neumann, G.; Cadek, O.
2010-12-01
A number of numerical studies of subducting slab assume simplified (constant or only depth-dependent) models of thermal conductivity. The available mineral physics data indicate, however, that thermal diffusivity is strongly temperature- and pressure-dependent and may also vary among different mantle materials. In the present study, we examine the influence of realistic thermal properties of mantle materials on the thermal state of the upper mantle and the dynamics of subducting slabs. On the basis of the data published in mineral physics literature we compile analytical relationships that approximate the pressure and temperature dependence of thermal diffusivity for major mineral phases of the mantle (olivine, wadsleyite, ringwoodite, garnet, clinopyroxenes, stishovite and perovskite). We propose a simplified composition of mineral assemblages predominating in the subducting slab and the surrounding mantle (pyrolite, mid-ocean ridge basalt, harzburgite) and we estimate their thermal diffusivity using the Hashin-Shtrikman bounds. The resulting complex formula for the diffusivity of each aggregate is then approximated by a simpler analytical relationship that is used in our numerical model as an input parameter. For the numerical modeling we use the Elmer software (open source finite element software for multiphysical problems, see http://www.csc.fi/english/pages/elmer). We set up a 2D Cartesian thermo-mechanical steady-state model of a subducting slab. The model is partly kinematic as the flow is driven by a boundary condition on velocity that is prescribed on the top of the subducting lithospheric plate. Reology of the material is non-linear and is coupled with the thermal equation. Using the realistic relationship for thermal diffusivity of mantle materials, we compute the thermal and flow fields for different input velocity and age of the subducting plate and we compare the results against the models assuming a constant thermal diffusivity. The importance of the
A skewed PDF combustion model for jet diffusion flames. [Probability density function (PDF)
Abou-Ellail, M.M.M.; Salem, H. )
1990-11-01
A combustion model based on restricted chemical equilibrium is described. A transport equation for the skewness of the mixture fraction is derived. It contains two adjustable constants. The computed values of the mean mixture fraction (f) and its variance and skewness (g and s) for a jet diffusion methane flame are used to obtain the shape of a shewed pdf. The skewed pdf is split into a turbulent part (beta function) and a nonturbulent part (delta function) at f = 0. The contribution of each part is directly related to the values of f, g, and s. The inclusion of intermittency in the skewed pdf appreciably improves the numerical predictions obtained for a turbulent jet diffusion methane flame for which experimental data are available.
Toxicological Models Part B: Environmental Models
NASA Astrophysics Data System (ADS)
Garric, Jeanne; Thybaud, Eric
Assessment of ecotoxicological risks due to chemical substances is based in part on establishing concentration-response relationships for different organisms, including plants, invertebrates, and vertebrates living on land, fresh water, or sea water. European regulations for assessing the risks due to chemical products thus recommend the measurement of toxic effects on at least three taxons (algae, crustacea, fish) [1]. The assessment becomes more relevant when based upon a variety of different organisms, with a range of different biological and ecological features (autotrophic or heterotrophic, benthic or pelagic habitat, and different modes of reproduction, growth, respiration, or feeding, etc.), but also when it describes the effects of contaminants on sensitive physiological functions such as growth and reproduction, which determine the balance of populations of terrestrial and aquatic species in their environment.
Numerical modelling and image reconstruction in diffuse optical tomography
Dehghani, Hamid; Srinivasan, Subhadra; Pogue, Brian W.; Gibson, Adam
2009-01-01
The development of diffuse optical tomography as a functional imaging modality has relied largely on the use of model-based image reconstruction. The recovery of optical parameters from boundary measurements of light propagation within tissue is inherently a difficult one, because the problem is nonlinear, ill-posed and ill-conditioned. Additionally, although the measured near-infrared signals of light transmission through tissue provide high imaging contrast, the reconstructed images suffer from poor spatial resolution due to the diffuse propagation of light in biological tissue. The application of model-based image reconstruction is reviewed in this paper, together with a numerical modelling approach to light propagation in tissue as well as generalized image reconstruction using boundary data. A comprehensive review and details of the basis for using spatial and structural prior information are also discussed, whereby the use of spectral and dual-modality systems can improve contrast and spatial resolution. PMID:19581256
Modeling aerosol formation in opposed-flow diffusion flames.
Violi, Angela; D'Anna, Andrea; D'Alessio, Antonio; Sarofim, Adel F
2003-06-01
The microstructures of atmospheric pressure, counter-flow, sooting, flat, laminar ethylene diffusion flames have been studied numerically by using a new kinetic model developed for hydrocarbon oxidation and pyrolysis. Modeling results are in reasonable agreement with experimental data in terms of concentration profiles of stable species and gas-phase aromatic compounds. Modeling results are used to analyze the controlling steps of aromatic formation and soot growth in counter-flow configurations. The formation of high molecular mass aromatics in diffusion controlled conditions is restricted to a narrow area close to the flame front where these species reach a molecular weight of about 1000 u. Depending on the flame configuration, soot formation is controlled by the coagulation of nanoparticles or by the addition of PAH to soot nuclei.
Semiparametric Bayesian local functional models for diffusion tensor tract statistics☆
Hua, Zhaowei; Dunson, David B.; Gilmore, John H.; Styner, Martin A.; Zhu, Hongtu
2012-01-01
We propose a semiparametric Bayesian local functional model (BFM) for the analysis of multiple diffusion properties (e.g., fractional anisotropy) along white matter fiber bundles with a set of covariates of interest, such as age and gender. BFM accounts for heterogeneity in the shape of the fiber bundle diffusion properties among subjects, while allowing the impact of the covariates to vary across subjects. A nonparametric Bayesian LPP2 prior facilitates global and local borrowings of information among subjects, while an infinite factor model flexibly represents low-dimensional structure. Local hypothesis testing and credible bands are developed to identify fiber segments, along which multiple diffusion properties are significantly associated with covariates of interest, while controlling for multiple comparisons. Moreover, BFM naturally group subjects into more homogeneous clusters. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of BFM. We apply BFM to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment in new born infants. PMID:22732565
Characterization and modeling of thermal diffusion and aggregation in nanofluids.
Gharagozloo, Patricia E.; Goodson, Kenneth E.
2010-05-01
Fluids with higher thermal conductivities are sought for fluidic cooling systems in applications including microprocessors and high-power lasers. By adding high thermal conductivity nanoscale metal and metal oxide particles to a fluid the thermal conductivity of the fluid is enhanced. While particle aggregates play a central role in recent models for the thermal conductivity of nanofluids, the effect of particle diffusion in a temperature field on the aggregation and transport has yet to be studied in depth. The present work separates the effects of particle aggregation and diffusion using parallel plate experiments, infrared microscopy, light scattering, Monte Carlo simulations, and rate equations for particle and heat transport in a well dispersed nanofluid. Experimental data show non-uniform temporal increases in thermal conductivity above effective medium theory and can be well described through simulation of the combination of particle aggregation and diffusion. The simulation shows large concentration distributions due to thermal diffusion causing variations in aggregation, thermal conductivity and viscosity. Static light scattering shows aggregates form more quickly at higher concentrations and temperatures, which explains the increased enhancement with temperature reported by other research groups. The permanent aggregates in the nanofluid are found to have a fractal dimension of 2.4 and the aggregate formations that grow over time are found to have a fractal dimension of 1.8, which is consistent with diffusion limited aggregation. Calculations show as aggregates grow the viscosity increases at a faster rate than thermal conductivity making the highly aggregated nanofluids unfavorable, especially at the low fractal dimension of 1.8. An optimum nanoparticle diameter for these particular fluid properties is calculated to be 130 nm to optimize the fluid stability by reducing settling, thermal diffusion and aggregation.
Majda, Andrew J; Gershgorin, Boris
2013-01-13
This paper motivates, develops and reviews elementary models for turbulent tracers with a background mean gradient which, despite their simplicity, have complex statistical features mimicking crucial aspects of laboratory experiments and atmospheric observations. These statistical features include exact formulas for tracer eddy diffusivity which is non-local in space and time, exact formulas and simple numerics for the tracer variance spectrum in a statistical steady state, and the transition to intermittent scalar probability density functions with fat exponential tails as certain variances of the advecting mean velocity are increased while satisfying important physical constraints. The recent use of such simple models with complex statistics as unambiguous test models for central contemporary issues in both climate change science and the real-time filtering of turbulent tracers from sparse noisy observations is highlighted throughout the paper.
Performance of turbulence models for transonic flows in a diffuser
NASA Astrophysics Data System (ADS)
Liu, Yangwei; Wu, Jianuo; Lu, Lipeng
2016-09-01
Eight turbulence models frequently used in aerodynamics have been employed in the detailed numerical investigations for transonic flows in the Sajben diffuser, to assess the predictive capabilities of the turbulence models for shock wave/turbulent boundary layer interactions (SWTBLI) in internal flows. The eight turbulence models include: the Spalart-Allmaras model, the standard k - 𝜀 model, the RNG k - 𝜀 model, the realizable k - 𝜀 model, the standard k - ω model, the SST k - ω model, the v2¯ - f model and the Reynolds stress model. The performance of the different turbulence models adopted has been systematically assessed by comparing the numerical results with the available experimental data. The comparisons show that the predictive performance becomes worse as the shock wave becomes stronger. The v2¯ - f model and the SST k - ω model perform much better than other models, and the SST k - ω model predicts a little better than the v2¯ - f model for pressure on walls and velocity profile, whereas the v2¯ - f model predicts a little better than the SST k - ω model for separation location, reattachment location and separation length for strong shock case.
Modeling of diffuse-diffuse photon coupling via a nonscattering region: a comparative study.
Lee, Jae Hoon; Kim, Seunghwan; Kim, Youn Tae
2004-06-20
It is well established that diffusion approximation is valid for light propagation in highly scattering media, but it breaks down in nonscattering regions. The previous methods that manipulate nonscattering regions are essentially boundary-to-boundary coupling (BBC) methods through a nonscattering void region based on the radiosity theory. We present a boundary-to-interior coupling (BIC) method. BIC is based on the fact that the collimated pencil beam incident on the medium can be replaced by an isotropic point source positioned at one reduced scattering length inside the medium from an illuminated point. A similar replacement is possible for the nondiffuse lights that enter the diffuse medium through the void, and it is formulated as the BIC method. We implemented both coupling methods using the finite element method (FEM) and tested for the circle with a void gap and for a four-layer adult head model. For mean time of flight, the BIC shows better agreement with Monte Carlo (MC) simulation results than BBC. For intensity, BIC shows a comparable match with MC data compared with that of BBC. The effect of absorption of the clear layer in the adult head model was investigated. Both mean time and intensity decrease as absorption of the clear layer increases.
Most current electrostatic surface complexation models describing ionic binding at the particle/water interface rely on the use of Poisson - Boltzmann (PB) theory for relating diffuse layer charge densities to diffuse layer electrostatic potentials. PB theory is known to contain ...
Experimental exploration of diffusion panel labyrinth in scale model
NASA Astrophysics Data System (ADS)
Vance, Mandi M.
Small rehearsal and performance venues often lack the rich reverberation found in larger spaces. Higini Arau-Puchades has designed and implemented a system of diffusion panels in the Orchestra Rehearsal Room at the Great Theatre Liceu and the Tonhalle St. Gallen that lengthen the reverberation time. These panels defy traditional room acoustics theory which holds that adding material to a room will shorten the reverberation time. This work explores several versions of Arau-Puchades' panels and room characteristics in scale model. Reverberation times are taken from room impulse response measurements in order to better understand the unusual phenomenon. Scale modeling enables many tests but has limitations in its accuracy due to the higher frequency range involved. Further investigations are necessary to establish how the sound energy interacts with the diffusion panels and confirm their validity in a range of applications.
Thermomechanics of damageable materials under diffusion: modelling and analysis
NASA Astrophysics Data System (ADS)
Roubíček, Tomáš; Tomassetti, Giuseppe
2015-12-01
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat generation/consumption/transfer is considered. Damage is modelled as rate-independent. The applications include metal-hydrogen systems with metal/hydride phase transformation, poroelastic rocks, structural and ferro/para-magnetic phase transformation, water and heat transport in concrete, and if diffusion is neglected, plasticity with damage and viscoelasticity, etc. For the ensuing system of partial differential equations and inclusions, we prove existence of solutions by a carefully devised semi-implicit approximation scheme of the fractional-step type.
Forecasting Diffusion of Technology by using Bass Model
NASA Astrophysics Data System (ADS)
Kim, Do-Hoi; Shin, Young-Geun; Park, Sang-Sung; Jang, Dong-Sik
2009-08-01
Generally, researching method of technology forecasting has been depended on intuition of expert until now. So there were many defects like consuming much time and money and so on. In this paper, we forecast diffusion of technology by using Bass model that is one of the quantitative analysis methods. We applied this model at technology market. And for input data of experiment, we use patent data that is representing each technology in technology market. We expect this research will be suggest new possibility that patent data can be applied in Bass model.
Reaction-diffusion processes and metapopulation models on duplex networks
NASA Astrophysics Data System (ADS)
Xuan, Qi; Du, Fang; Yu, Li; Chen, Guanrong
2013-03-01
Reaction-diffusion processes, used to model various spatially distributed dynamics such as epidemics, have been studied mostly on regular lattices or complex networks with simplex links that are identical and invariant in transferring different kinds of particles. However, in many self-organized systems, different particles may have their own private channels to keep their purities. Such division of links often significantly influences the underlying reaction-diffusion dynamics and thus needs to be carefully investigated. This article studies a special reaction-diffusion process, named susceptible-infected-susceptible (SIS) dynamics, given by the reaction steps β→α and α+β→2β, on duplex networks where links are classified into two groups: α and β links used to transfer α and β particles, which, along with the corresponding nodes, consist of an α subnetwork and a β subnetwork, respectively. It is found that the critical point of particle density to sustain reaction activity is independent of the network topology if there is no correlation between the degree sequences of the two subnetworks, and this critical value is suppressed or extended if the two degree sequences are positively or negatively correlated, respectively. Based on the obtained results, it is predicted that epidemic spreading may be promoted on positive correlated traffic networks but may be suppressed on networks with modules composed of different types of diffusion links.
Modeling diffusive transport with a fractional derivative without singular kernel
NASA Astrophysics Data System (ADS)
Gómez-Aguilar, J. F.; López-López, M. G.; Alvarado-Martínez, V. M.; Reyes-Reyes, J.; Adam-Medina, M.
2016-04-01
In this paper we present an alternative representation of the diffusion equation and the diffusion-advection equation using the fractional calculus approach, the spatial-time derivatives are approximated using the fractional definition recently introduced by Caputo and Fabrizio in the range β , γ ∈(0 ; 2 ] for the space and time domain respectively. In this representation two auxiliary parameters σx and σt are introduced, these parameters related to equation results in a fractal space-time geometry provide an entire new family of solutions for the diffusion processes. The numerical results showed different behaviors when compared with classical model solutions. In the range β , γ ∈(0 ; 1) , the concentration exhibits the non-Markovian Lévy flights and the subdiffusion phenomena; when β = γ = 1 the classical case is recovered; when β , γ ∈(1 ; 2 ] the concentration exhibits the Markovian Lévy flights and the superdiffusion phenomena; finally when β = γ = 2 the concentration is anomalous dispersive and we found ballistic diffusion.
Modelling of diffusion and conductivity relaxation of oxide ceramics
NASA Astrophysics Data System (ADS)
Preis, Wolfgang
2016-12-01
A two-dimensional square grain model has been applied to simulate simultaneously the diffusion process and relaxation of the dc conduction of polycrystalline oxide materials due to a sudden change of the oxygen partial pressure of the surrounding gas phase. The numerical calculations are performed by employing the finite element approach. The grains are squares of equal side length (average grain size) and the grain boundaries may consist of thin slabs of uniform thickness. An additional (space charge) layer adjacent to the grain boundary cores (thin slabs) either blocking (depletion layer) or highly conductive for electronic charge carriers may surround the grains. The electronic transport number of the mixed ionic-electronic conducting oxide ceramics may be close to unity (predominant electronic conduction). If the chemical diffusion coefficient of the neutral mobile component (oxygen) of the grain boundary core regions is assumed to be higher by many orders of magnitude than that in the bulk, the simulated relaxation curves for mass transport (diffusion) and dc conduction can deviate remarkably from each other. Deviations between the relaxation of mass transport and dc conduction are found in the case of considerably different electronic conductivities of grain boundary core regions, space charge layers, and bulk. On the contrary, the relaxation curves of mass transport and electronic conductivity are in perfect coincidence, when either effective medium diffusion occurs or the effective conductivity is unaffected by the individual conductivities of core regions and possible space charge layers, i.e. the grain boundary resistivity is negligible.
Consistent flamelet modeling of differential molecular diffusion for turbulent non-premixed flames
NASA Astrophysics Data System (ADS)
Wang, Haifeng
2016-03-01
Treating differential molecular diffusion correctly and accurately remains as a great challenge to the modeling of turbulent non-premixed combustion. The aim of this paper is to develop consistent modeling strategies for differential molecular diffusion in flamelet models. Two types of differential molecular diffusion models are introduced, linear differential diffusion models and nonlinear differential diffusion models. A multi-component turbulent mixing layer problem is analyzed in detail to gain insights into differential molecular diffusion and its characteristics, particularly the dependence of differential molecular diffusion on the Reynolds number and the Lewis number. These characteristics are then used to validate the differential molecular diffusion models. Finally, the new models are applied to the modeling of a series of laboratory-scale turbulent non-premixed jet flames with different Reynolds number (Sandia Flames B, C, and D) to further assess the models' performance.
Modeling of Diffusion in Liquid Ge and Its Alloys
NASA Technical Reports Server (NTRS)
Stroud, David G.
1998-01-01
This report summarizes progress made on NASA Grant NAG3-1437, Modeling of diffusion in Liquid Ge and Its Alloys, which was in effect from January 15, 1993 through July 10, 1997. It briefly describes the purpose of the grant, and the work accomplished in simulations and other studies of thermophysical properties of liquid semiconductors and related materials. A list of publications completed with the support of the grant is also given.
Particle Tracking Model Transport Process Verification: Diffusion Algorithm
2015-07-01
requires the input of hydrodynamics (i.e., water surface elevation and velocities), defined upon a bathymetry grid that is provided through an external...without the computational overhead of regenerating flow conditions for each hydrodynamic run. PTM operates within the Surface- water Modeling System (SMS...particle’s vertical position in the water column (m). It is seen that the vertical eddy diffusivity has a parabolic dependence upon the vertical
THE LOS ALAMOS NATIONAL LABORATORY ATMOSPHERIC TRANSPORT AND DIFFUSION MODELS
M. WILLIAMS
1999-08-01
The LANL atmospheric transport and diffusion models are composed of two state-of-the-art computer codes. The first is an atmospheric wind model called HOThlAC, Higher Order Turbulence Model for Atmospheric circulations. HOTMAC generates wind and turbulence fields by solving a set of atmospheric dynamic equations. The second is an atmospheric diffusion model called RAPTAD, Random Particle Transport And Diffusion. RAPTAD uses the wind and turbulence output from HOTMAC to compute particle trajectories and concentration at any location downwind from a source. Both of these models, originally developed as research codes on supercomputers, have been modified to run on microcomputers. Because the capability of microcomputers is advancing so rapidly, the expectation is that they will eventually become as good as today's supercomputers. Now both models are run on desktop or deskside computers, such as an IBM PC/AT with an Opus Pm 350-32 bit coprocessor board and a SUN workstation. Codes have also been modified so that high level graphics, NCAR Graphics, of the output from both models are displayed on the desktop computer monitors and plotted on a laser printer. Two programs, HOTPLT and RAPLOT, produce wind vector plots of the output from HOTMAC and particle trajectory plots of the output from RAPTAD, respectively. A third CONPLT provides concentration contour plots. Section II describes step-by-step operational procedures, specifically for a SUN-4 desk side computer, on how to run main programs HOTMAC and RAPTAD, and graphics programs to display the results. Governing equations, boundary conditions and initial values of HOTMAC and RAPTAD are discussed in Section III. Finite-difference representations of the governing equations, numerical solution procedures, and a grid system are given in Section IV.
Analysis of diffusion models for protein adsorption to porous anion-exchange adsorbent.
Chen, Wei-Dong; Dong, Xiao-Yan; Sun, Yan
2002-07-12
The ion-exchange adsorption kinetics of bovine serum albumin (BSA) and gamma-globulin to an anion exchanger, DEAE Spherodex M, has been studied by batch adsorption experiments. Various diffusion models, that is, pore diffusion, surface diffusion, homogeneous diffusion and parallel diffusion models, are analyzed for their suitabilities to depict the adsorption kinetics. Protein diffusivities are estimated by matching the models with the experimental data. The dependence of the diffusivities on initial protein concentration is observed and discussed. The adsorption isotherm of BSA is nearly rectangular, so there is little surface diffusion. As a result, the surface and homogeneous diffusion models do not fit to the kinetic data of BSA adsorption. The adsorption isotherm of gamma-globulin is less favorable, and the surface diffusion contributes greatly to the mass transport. Consequently, both the surface and homogeneous diffusion models fit to the kinetic data of gamma-globulin well. The adsorption kinetics of BSA and gamma-globulin can be very well fitted by parallel diffusion model, because the model reflects correctly the intraparticle mass transfer mechanism. In addition, for both the favorably bound proteins, the pore diffusion model fits the adsorption kinetics reasonably well. The results here indicate that the pore diffusion model can be used as a good approximate to depict protein adsorption kinetics for protein adsorption systems from rectangular to linear isotherms.
NASA Astrophysics Data System (ADS)
Dohmen, Ralf; Chakraborty, Sumit
2007-08-01
Analysis of existing data and models on point defects in pure (Fe,Mg)-olivine (Phys Chem Miner 10:27 37,1983; Phys Chem Miner 29:680 694, 2002) shows that it is necessary to consider thermodynamic non-ideality of mixing to adequately describe the concentration of point defects over the range of measurement. In spite of different sources of uncertainties, the concentrations of vacancies in octahedral sites in (Fe,Mg)-olivine are on the order of 10-4 per atomic formula unit at 1,000 1,200 °C according to both the studies. We provide the first explicit plots of vacancy concentrations in olivine as a function of temperature and oxygen fugacity according to the two models. It is found that in contrast to absolute concentrations at ˜1,100 °C and dependence on fO2, there is considerable uncertainty in our knowledge of temperature dependence of vacancy concentrations. This needs to be considered in discussing the transport properties such as diffusion coefficients. Moreover, these defect models in pure (Fe,Mg)-olivine need to be extended by considering aliovalent impurities such as Al, Cr to describe the behavior of natural olivine. We have developed such a formulation, and used it to analyze the considerable database of diffusion coefficients in olivine from Dohmen et al. (Phys Chem Miner this volume, 2007) (Part - I) and older data in the literature. The analysis documents unequivocally for the first time a change of diffusion mechanism in a silicate mineral—from the transition metal extrinsic (TaMED) to the purely extrinsic (PED) domain, at fO2 below 10-10 Pa, and consequently, temperatures below 900 °C. The change of diffusion mechanism manifests itself in a change in fO2 dependence of diffusivity and a slight change in activation energy of diffusion—the activation energy increases at lower temperatures. These are consistent with the predictions of Chakraborty (J Geophys Res 102(B6):12317 12331, 1997). Defect formation enthalpies in the TaMED regime (distinct
Stochastic Functional Data Analysis: A Diffusion Model-based Approach
Zhu, Bin; Song, Peter X.-K.; Taylor, Jeremy M.G.
2011-01-01
Summary This paper presents a new modeling strategy in functional data analysis. We consider the problem of estimating an unknown smooth function given functional data with noise. The unknown function is treated as the realization of a stochastic process, which is incorporated into a diffusion model. The method of smoothing spline estimation is connected to a special case of this approach. The resulting models offer great flexibility to capture the dynamic features of functional data, and allow straightforward and meaningful interpretation. The likelihood of the models is derived with Euler approximation and data augmentation. A unified Bayesian inference method is carried out via a Markov Chain Monte Carlo algorithm including a simulation smoother. The proposed models and methods are illustrated on some prostate specific antigen data, where we also show how the models can be used for forecasting. PMID:21418053
Jun, K S; Kang, J W; Lee, K S
2007-01-01
Diffuse pollution sources along a stream reach are very difficult to both monitor and estimate. In this paper, a systematic method using an optimal estimation algorithm is presented for simultaneous estimation of diffuse pollution and model parameters in a stream water quality model. It was applied with the QUAL2E model to the South Han River in South Korea for optimal estimation of kinetic constants and diffuse loads along the river. Initial calibration results for kinetic constants selected from a sensitivity analysis reveal that diffuse source inputs for nitrogen and phosphorus are essential to satisfy the system mass balance. Diffuse loads for total nitrogen and total phosphorus were estimated by solving the expanded inverse problem. Comparison of kinetic constants estimated simultaneously with diffuse sources to those estimated without diffuse loads, suggests that diffuse sources must be included in the optimization not only for its own estimation but also for adequate estimation of the model parameters. Application of the optimization method to river water quality modeling is discussed in terms of the sensitivity coefficient matrix structure.
A Temporal Model of Technology Diffusion into Small Firms in Wales.
ERIC Educational Resources Information Center
Thomas, Brychan; Packham, Gary; Miller, Chris
2001-01-01
Discusses technology diffusion through formal and informal networks. Develops a model that includes channels and mechanisms involved in transferring technology into innovative small businesses. The model depicts influences that increase or slow the rate of diffusion. (SK)
Estimation of kinetic model parameters in fluorescence optical diffusion tomography.
Milstein, Adam B; Webb, Kevin J; Bouman, Charles A
2005-07-01
We present a technique for reconstructing the spatially dependent dynamics of a fluorescent contrast agent in turbid media. The dynamic behavior is described by linear and nonlinear parameters of a compartmental model or some other model with a deterministic functional form. The method extends our previous work in fluorescence optical diffusion tomography by parametrically reconstructing the time-dependent fluorescent yield. The reconstruction uses a Bayesian framework and parametric iterative coordinate descent optimization, which is closely related to Gauss-Seidel methods. We demonstrate the method with a simulation study.
Affinity based information diffusion model in social networks
NASA Astrophysics Data System (ADS)
Liu, Hongli; Xie, Yun; Hu, Haibo; Chen, Zhigao
2014-12-01
There is a widespread intuitive sense that people prefer participating in spreading the information in which they are interested. The affinity of people with information disseminated can affect the information propagation in social networks. In this paper, we propose an information diffusion model incorporating the mechanism of affinity of people with information which considers the fitness of affinity values of people with affinity threshold of the information. We find that the final size of information diffusion is affected by affinity threshold of the information, average degree of the network and the probability of people's losing their interest in the information. We also explore the effects of other factors on information spreading by numerical simulations and find that the probabilities of people's questioning and confirming the information can affect the propagation speed, but not the final scope.
Diffusive Models of Membrane Permeation with Explicit Orientational Freedom.
Comer, Jeffrey; Schulten, Klaus; Chipot, Christophe
2014-07-08
Accurate calculation of permeabilities from first-principles has been a long-standing challenge for computer simulations, notably in the context of drug discovery, as a route to predict the propensity of small, organic molecules to spontaneously translocate biological membranes. Of equal importance is the understanding of the permeation process and the pathway followed by the permeant from the aqueous medium to the interior of the lipid bilayer, and back out again. A convenient framework for the computation of permeabilities is provided by the solubility-diffusion model, which requires knowledge of the underlying free-energy and diffusivity landscapes. Here, we develop a formalism that includes an explicit description of the orientational motion of the solute as it diffuses across the membrane. Toward this end, we have generalized a recently proposed method that reconciles thermodynamics and kinetics in importance-sampling simulations by means of a Bayesian-inference scheme to reverse-solve the underlying Smoluchowski equation. Performance of the proposed formalism is examined in the model cases of a water and an ethanol molecule crossing a fully hydrated lipid bilayer. Our analysis reveals a conspicuous dependence of the free-energy and rotational diffusivity on the orientation of ethanol when it lies within the headgroup region of the bilayer. Specifically, orientations for which the hydroxyl group lies among the polar lipid head groups, while the ethyl group recedes toward the hydrophobic interior are associated with free-energy minima ∼2kBT deep, as well as significantly slower orientational kinetics compared to the bulk solution or the core of the bilayer. The conspicuous orientational anisotropy of ethanol at the aqueous interface is suggestive of a complete rotation of the permeant as it crosses the hydrophobic interior of the membrane.
Marinak, M. )
1990-02-01
The problem of deducing {chi}{sub e} from measurements of the propagation of a monopole heatpulse is considered. An extended diffusive model, which takes into account perturbed sources and sinks is extended to the case of a monopole heat input. {chi}{sub e} is expressed as a function of two observables, the heat pulse velocity and the radial damping rate. Two simple expressions valid for two different ranges of the radius of the poloidal waist of the beam power profile are given. The expressions are valid in the heat pulse measurement region, extending radially 0.05a beyond the beam power waist to near 0.6a. The inferred {chi}{sub e} is a local value, not an average value of the radial {chi}{sub e} profile. 7 refs., 6 figs., 1 tab.
A Discrete Model to Study Reaction-Diffusion-Mechanics Systems
Weise, Louis D.; Nash, Martyn P.; Panfilov, Alexander V.
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. PMID:21804911
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Boussinesq modeling of HB06 tracer releases Part 2: Tracer plumes
NASA Astrophysics Data System (ADS)
Clark, D. B.; Feddersen, F.; Guza, R. T.
2010-12-01
Tracer plumes simulated with a Boussinesq surfzone model (funwaveC) are compared with 5 plumes observed during the HB06 experiment (Huntington Beach, Fall 2006). Surfzone tracer plumes were formed by continuously releasing dye tracer into the wave-driven alongshore current. Bulk cross-shore eddy diffusivities, O(1 m2 s-1), were estimated from the observed plumes and agreed best with a mixing-length scaling based on large 2D eddies [Clark et al., JGR, in press 2010]. The mechanisms for surfzone cross-shore tracer dispersion are not well known, and are explored here with the time-dependent, wave and horizontal eddy resolving, funwaveC model. The funwaveC model is run with observed bathymetry, and initialized in 4m depth with the observed obliquely incident and directionally spread waves. Modeled and observed waves and currents are similar, and discussed in Part 1. Model tracer is dispersed by the surfzone horizontal eddy field, a breaking wave eddy diffusivity, and a small O(0.01 m2 s-1) background diffusivity. Modeled and observed mean plume structures agree, but can be degraded by a mismatch between observed and modeled alongshore currents, especially near the tracer source. Bulk tracer eddy diffusivities agree with HB06 observations, and the long narrow plume assumption (used for diffusion analysis) is discussed with modeled tracer fluxes. The model suggests that cross-shore mixing at time scales of many wave periods is dominated by horizontal eddies, not by the breaking eddy diffusivity.
Pieruschka, Roland; Schurr, Ulrich; Jensen, Manfred; Wolff, Wilfried F; Jahnke, Siegfried
2006-01-01
Gas exchange is generally regarded to occur between the leaf interior and ambient air, i.e. in vertical (anticlinal) directions of leaf blades. However, inside homobaric leaves, gas movement occurs also in lateral directions. The aim of the present study was to ascertain whether lateral CO2 diffusion affects leaf photosynthesis when illuminated leaves are partially shaded. Measurements using gas exchange and chlorophyll fluorescence imaging techniques were performed on homobaric leaves of Vicia faba and Nicotiana tabacum or on heterobaric leaves of Glycine max and Phaseolus vulgaris. For homobaric leaves, gas exchange inside a clamp-on leaf chamber was affected by shading the leaf outside the chamber. The quantum yield of photosystem II (Phi(PSII)) was highest directly adjacent to a light/shade border (LSB). Phi(PSII) decreased in the illuminated leaf parts with distance from the LSB, while the opposite was observed for nonphotochemical quenching. These effects became most pronounced at low stomatal conductance. They were not observed in heterobaric leaves. The results suggest that plants with homobaric leaves can benefit from lateral CO2 flux, in particular when stomata are closed (e.g. under drought stress). This may enhance photosynthetic, instead of nonphotochemical, processes near LSBs in such leaves and reduce the photoinhibitory effects of excess light.
A simple diffusion-reaction model for resid hydroprocessing catalysts
Adkins, B.D.; Limmer, K.R. )
1990-08-01
It is commonly accepted that the intraparticle diffusion characteristics of resid hydroprocessing catalysts can play an important role in determining their performance. It is also commonly accepted that diffusion characteristics are determined by properties of the catalyst which are at least partially reflected in measurements such as surface area and pore size. One approach to experimentally determine the appropriate region on the diffusion-reaction curve is to vary V{sub P}/S{sub P} for a fixed pore structure. One example (among many) of this approach is the paper of Gosselink and Stork in which the authors modeled the fixed-bed HDS performance of Shell 444 catalyst on heavy gasoil in crushed (particle diameter 0.2 mm) and uncrushed (1.5 mm) form. The method has the advantage of minimizing unaccountable differences in pore structures, but is susceptible to major variations in external mass and heat transfer. An alternative is to vary the pore structure widely while exploring only commercially meaningful variations in V{sub P}/S{sub P}. This is the approach used in the study.
Diffusion models for innovation: s-curves, networks, power laws, catastrophes, and entropy.
Jacobsen, Joseph J; Guastello, Stephen J
2011-04-01
This article considers models for the diffusion of innovation would be most relevant to the dynamics of early 21st century technologies. The article presents an overview of diffusion models and examines the adoption S-curve, network theories, difference models, influence models, geographical models, a cusp catastrophe model, and self-organizing dynamics that emanate from principles of network configuration and principles of heat diffusion. The diffusion dynamics that are relevant to information technologies and energy-efficient technologies are compared. Finally, principles of nonlinear dynamics for innovation diffusion that could be used to rehabilitate the global economic situation are discussed.
Bayesian Model Selection with Network Based Diffusion Analysis
Whalen, Andrew; Hoppitt, William J. E.
2016-01-01
A number of recent studies have used Network Based Diffusion Analysis (NBDA) to detect the role of social transmission in the spread of a novel behavior through a population. In this paper we present a unified framework for performing NBDA in a Bayesian setting, and demonstrate how the Watanabe Akaike Information Criteria (WAIC) can be used for model selection. We present a specific example of applying this method to Time to Acquisition Diffusion Analysis (TADA). To examine the robustness of this technique, we performed a large scale simulation study and found that NBDA using WAIC could recover the correct model of social transmission under a wide range of cases, including under the presence of random effects, individual level variables, and alternative models of social transmission. This work suggests that NBDA is an effective and widely applicable tool for uncovering whether social transmission underpins the spread of a novel behavior, and may still provide accurate results even when key model assumptions are relaxed. PMID:27092089
A Reaction-Diffusion Model of Cholinergic Retinal Waves
Lansdell, Benjamin; Ford, Kevin; Kutz, J. Nathan
2014-01-01
Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability. PMID:25474327
Anomalous diffusion in neutral evolution of model proteins
NASA Astrophysics Data System (ADS)
Nelson, Erik D.; Grishin, Nick V.
2015-06-01
Protein evolution is frequently explored using minimalist polymer models, however, little attention has been given to the problem of structural drift, or diffusion. Here, we study neutral evolution of small protein motifs using an off-lattice heteropolymer model in which individual monomers interact as low-resolution amino acids. In contrast to most earlier models, both the length and folded structure of the polymers are permitted to change. To describe structural change, we compute the mean-square distance (MSD) between monomers in homologous folds separated by n neutral mutations. We find that structural change is episodic, and, averaged over lineages (for example, those extending from a single sequence), exhibits a power-law dependence on n . We show that this exponent depends on the alignment method used, and we analyze the distribution of waiting times between neutral mutations. The latter are more disperse than for models required to maintain a specific fold, but exhibit a similar power-law tail.
Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
NASA Astrophysics Data System (ADS)
Flegg, Mark B.; Rüdiger, Sten; Erban, Radek
2013-04-01
The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While stochasticity in the gating transition of ion channels has been incorporated into many models, the distribution of calcium is usually described by deterministic reaction-diffusion equations. Here we test the validity of the latter modeling approach by using two different models to calculate the frequency of localized calcium signals (calcium puffs) from clustered IP3 receptor channels. The complexity of the full calcium system is here limited to the basic opening mechanism of the ion channels and, in the mathematical reduction simplifies to the calculation of a first passage time. Two models are then studied: (i) a hybrid model, where channel gating is treated stochastically, while calcium concentration is deterministic and (ii) a fully stochastic model with noisy channel gating and Brownian calcium ion motion. The second model utilises the recently developed two-regime method [M. B. Flegg, S. J. Chapman, and R. Erban, "The two-regime method for optimizing stochastic reaction-diffusion simulations," J. R. Soc., Interface 9, 859-868 (2012)], 10.1098/rsif.2011.0574 in order to simulate a large domain with precision required only near the Ca2+ absorbing channels. The expected time for a first channel opening that results in a calcium puff event is calculated. It is found that for a large diffusion constant, predictions of the interpuff time are significantly overestimated using the model (i) with a deterministic non-spatial calcium variable. It is thus demonstrated that the presence of diffusive noise in local concentrations of intracellular Ca2+ ions can substantially influence the occurrence of calcium signals. The presented approach and results may also be relevant for other cell-physiological first-passage time problems with
NASA Astrophysics Data System (ADS)
Wang, Wei; Ma, Wanbiao; Lai, Xiulan
2017-01-01
From a biological perspective, a diffusive virus infection dynamic model with nonlinear functional response, absorption effect and chemotaxis is proposed. In the model, the diffusion of virus consists of two parts, the random diffusion and the chemotactic movement. The chemotaxis flux of virus depends not only on their own density, but also on the density of infected cells, and the density gradient of infected cells. The well posedness of the proposed model is deeply investigated. For the proposed model, the linear stabilities of the infection-free steady state E0 and the infection steady state E* are extensively performed. We show that the threshold dynamics can be expressed by the basic reproduction number R0 of the model without chemotaxis. That is, the infection-free steady state E0 is globally asymptotically stable if R0 < 1, and the virus is uniformly persistent if R0 > 1. In addition, we use the cross iteration method and the Schauder's fixed point theorem to prove the existence of travelling wave solutions connecting the infection-free steady state E0 and the infection steady state E* by constructing a pair of upper-lower solutions. At last, numerical simulations are presented to confirm theoretical findings.
A study of hydrogen diffusion flames using PDF turbulence model
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1991-01-01
The application of probability density function (pdf) turbulence models is addressed. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional computational fluid dynamic (CFD) flow solver with the Monte Carlo simulation of the pdf evolution equation was developed. The algorithm was validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames was carried out using this algorithm. Numerical results compared favorably with experimental data. The computations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.
Reading and a Diffusion Model Analysis of Reaction Time
Naples, Adam; Katz, Leonard; Grigorenko, Elena L.
2012-01-01
Processing speed is associated with reading performance. However, the literature is not clear either on the definition of processing speed or on why and how it contributes to reading performance. In this study we demonstrated that processing speed, as measured by reaction time, is not a unitary construct. Using the diffusion model of two-choice reaction time, we assessed processing speed in a series of same-different reaction time tasks for letter and number strings. We demonstrated that the association between reaction time and reading performance is driven by processing speed for reading-related information, but not motor or sensory encoding speed. PMID:22612543
SHIR competitive information diffusion model for online social media
NASA Astrophysics Data System (ADS)
Liu, Yun; Diao, Su-Meng; Zhu, Yi-Xiang; Liu, Qing
2016-11-01
In online social media, opinion divergences and differentiations generally exist as a result of individuals' extensive participation and personalization. In this paper, a Susceptible-Hesitated-Infected-Removed (SHIR) model is proposed to study the dynamics of competitive dual information diffusion. The proposed model extends the classical SIR model by adding hesitators as a neutralized state of dual information competition. It is both hesitators and stable spreaders that facilitate information dissemination. Researching on the impacts of diffusion parameters, it is found that the final density of stiflers increases monotonically as infection rate increases and removal rate decreases. And the advantage information with larger stable transition rate takes control of whole influence of dual information. The density of disadvantage information spreaders slightly grows with the increase of its stable transition rate, while whole spreaders of dual information and the relaxation time remain almost unchanged. Moreover, simulations imply that the final result of competition is closely related to the ratio of stable transition rates of dual information. If the stable transition rates of dual information are nearly the same, a slightly reduction of the smaller one brings out a significant disadvantage in its propagation coverage. Additionally, the relationship of the ratio of final stiflers versus the ratio of stable transition rates presents power characteristic.
A chaotic model for advertising diffusion problem with competition
NASA Astrophysics Data System (ADS)
Ip, W. H.; Yung, K. L.; Wang, Dingwei
2012-08-01
In this article, the author extends Dawid and Feichtinger's chaotic advertising diffusion model into the duopoly case. A computer simulation system is used to test this enhanced model. Based on the analysis of simulation results, it is found that the best advertising strategy in duopoly is to increase the advertising investment to reach the best Win-Win situation where the oscillation of market portion will not occur. In order to effectively arrive at the best situation, we define a synthetic index and two thresholds. An estimation method for the parameters of the index and thresholds is proposed in this research. We can reach the Win-Win situation by simply selecting the control parameters to make the synthetic index close to the threshold of min-oscillation state. The numerical example and computational results indicated that the proposed chaotic model is useful to describe and analyse advertising diffusion process in duopoly, it is an efficient tool for the selection and optimisation of advertising strategy.
Modeling the Determinants Influencing the Diffusion of Mobile Internet
NASA Astrophysics Data System (ADS)
Alwahaishi, Saleh; Snášel, Václav
2013-04-01
Understanding individual acceptance and use of Information and Communication Technology (ICT) is one of the most mature streams of information systems research. In Information Technology and Information System research, numerous theories are used to understand users' adoption of new technologies. Various models were developed including the Innovation Diffusion Theory, Theory of Reasoned Action, Theory of Planned Behavior, Technology Acceptance Model, and recently, the Unified Theory of Acceptance and Use of Technology. This research composes a new hybrid theoretical framework to identify the factors affecting the acceptance and use of Mobile Internet -as an ICT application- in a consumer context. The proposed model incorporates eight constructs: Performance Expectancy (PE), Effort Expectancy (EE), Facilitating Conditions (FC), Social Influences (SI), Perceived Value (PV), Perceived Playfulness (PP), Attention Focus (AF), and Behavioral intention (BI). Individual differences-namely, age, gender, education, income, and experience are moderating the effects of these constructs on behavioral intention and technology use.
Effect of numerical diffusion on the water mass transformation in eddy-resolving models
NASA Astrophysics Data System (ADS)
Urakawa, L. Shogo; Hasumi, Hiroyasu
2014-02-01
This study investigates the effect of numerical diffusion associated with advection schemes on water mass transformation in an eddy-resolving model. The effect of numerical diffusion is evaluated as a residual between the total water mass transformation and the explicit water mass transformation: the former is calculated as the sum of meridional streamfunction and the temporal change rate of an isopycnal surface depth, and the latter is directly calculated with the use of the tendency equation of density. This method is used for investigating a dependency of numerical diffusion on explicit diffusivity. It is found that idealized channel experiments are categorized into three regimes according to a magnitude of explicit diffusivity: numerical diffusion, transitional, and explicit diffusion regimes. The numerical diffusion regime is defined as the regime where explicit diffusion changes do not significantly impact the solution. The magnitude of numerical diffusion is independent of the explicit diffusivity there. In the transitional regime, explicit (numerical) diffusion works more (less) with higher explicit diffusivity. Explicit and numerical diffusions are comparably important there. The explicit diffusion becomes significantly large and the numerical diffusion is almost negligible in the explicit diffusion regime. The total diffusion effect on water mass transformation there is considerably larger than those in the two other regimes. Two experiments are conducted with a Southern Ocean model under a realistic configuration. These belong to the numerical diffusion and transitional regimes. The model becomes a little too diffusive in the latter experiment. This result and results of channel experiments indicate that it is not an adequate option for a realistic Southern Ocean simulation that we adopt a diffusion coefficient in the explicit diffusion regime in order to reduce levels of numerical diffusion. It indicates that numerical diffusion is inevitable for eddy
Hybrid approaches for multiple-species stochastic reaction–diffusion models
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen
2015-10-15
Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.
Analysis of a diffuse interface model of multispecies tumor growth
NASA Astrophysics Data System (ADS)
Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E.
2017-04-01
We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726–54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn–Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity \\mathbf{u} satisfies \\mathbf{u}\\centerdot ν >0 , where ν is the outer normal to the boundary of the domain.
Pharmacokinetic modeling of ascorbate diffusion through normal and tumor tissue.
Kuiper, Caroline; Vissers, Margreet C M; Hicks, Kevin O
2014-12-01
Ascorbate is delivered to cells via the vasculature, but its ability to penetrate into tissues remote from blood vessels is unknown. This is particularly relevant to solid tumors, which often contain regions with dysfunctional vasculature, with impaired oxygen and nutrient delivery, resulting in upregulation of the hypoxic response and also the likely depletion of essential plasma-derived biomolecules, such as ascorbate. In this study, we have utilized a well-established multicell-layered, three-dimensional pharmacokinetic model to measure ascorbate diffusion and transport parameters through dense tissue in vitro. Ascorbate was found to penetrate the tissue at a slightly lower rate than mannitol and to travel via the paracellular route. Uptake parameters into the cells were also determined. These data were fitted to the diffusion model, and simulations of ascorbate pharmacokinetics in normal tissue and in hypoxic tumor tissue were performed with varying input concentrations, ranging from normal dietary plasma levels (10-100 μM) to pharmacological levels (>1 mM) as seen with intravenous infusion. The data and simulations demonstrate heterogeneous distribution of ascorbate in tumor tissue at physiological blood levels and provide insight into the range of plasma ascorbate concentrations and exposure times needed to saturate all regions of a tumor. The predictions suggest that supraphysiological plasma ascorbate concentrations (>100 μM) are required to achieve effective delivery of ascorbate to poorly vascularized tumor tissue.
Diffusion dynamics in the disordered Bose Hubbard model
NASA Astrophysics Data System (ADS)
Wadleigh, Laura; Russ, Philip; Demarco, Brian
2016-05-01
We explore the dynamics of diffusion for out-of-equilibrium superfluid, Mott insulator, and Bose glass states using an atomic realization of the disordered Bose Hubbard (DBH) model. Dynamics in strongly correlated systems, especially far from equilibrium, are not well understood. The introduction of disorder further complicates these systems. We realize the DBH model--which has been central to our understanding of quantum phase transitions in disordered systems--using ultracold Rubidium-87 atoms trapped in a cubic disordered optical lattice. By tightly focusing a beam into the center of the gas, we create a hole in the atomic density profile. We achieve Mott insulator, superfluid, or Bose glass states by varying the interaction and disorder strength, and measure the time evolution of the density profile after removing the central barrier. This allows us to infer diffusion rates from the velocities at the edge of the hole and to look for signatures of superfluid puddles in the Bose glass state. We acknowledge funding from NSF Grant PHY 15-05468, NSF Grant DGE-1144245, and ARO Grant W911NF-12-1-0462.
Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models
NASA Technical Reports Server (NTRS)
Yoder, Dennis A.
2016-01-01
In this study, several variable turbulent Prandtl number formulations are examined for boundary layers, pipe flow, and axisymmetric jets. The model formulations include simple algebraic relations between the thermal diffusivity and turbulent viscosity as well as more complex models that solve transport equations for the thermal variance and its dissipation rate. Results are compared with available data for wall heat transfer and profile measurements of mean temperature, the root-mean-square (RMS) fluctuating temperature, turbulent heat flux and turbulent Prandtl number. For wall-bounded problems, the algebraic models are found to best predict the rise in turbulent Prandtl number near the wall as well as the log-layer temperature profile, while the thermal variance models provide a good representation of the RMS temperature fluctuations. In jet flows, the algebraic models provide no benefit over a constant turbulent Prandtl number approach. Application of the thermal variance models finds that some significantly overpredict the temperature variance in the plume and most underpredict the thermal growth rate of the jet. The models yield very similar fluctuating temperature intensities in jets from straight pipes and smooth contraction nozzles, in contrast to data that indicate the latter should have noticeably higher values. For the particular low subsonic heated jet cases examined, changes in the turbulent Prandtl number had no effect on the centerline velocity decay.
On Modeling Viral Diffusion in Heterogeneous Wireless Networks
NASA Astrophysics Data System (ADS)
Nguyen, Hoai-Nam; Shinoda, Yoichi
Smart phones and computers now are able to co-work in a wireless environment where malware can propagate. Although many investigations have modeled the spread of malware, little has been done to take into account different characteristics of items to see how they affect disease diffusion in an ad hoc network. We have therefore developed a novel framework, consisting of two models, which consider diversity of objects as well as interactions between their different classes. Our framework is able to produce a huge result space thus makes it appropriate to describe many viral proliferating scenarios. Additionally, we have developed a formula to calculate the possible average number of newly infected devices in the considered system. An important contribution of our work is the comprehension of item diversity, which states that a mixture of device types causes a bigger malware spread as the number of device types in the network increases.
A self-consistent spin-diffusion model for micromagnetics.
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Manchon, Aurelien; Praetorius, Dirk; Suess, Dieter
2016-12-01
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
NASA Astrophysics Data System (ADS)
Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio
2016-07-01
A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.
An HBV model with diffusion and time delay.
Xu, Rui; Ma, Zhien
2009-04-07
In this paper, a hepatitis B virus (HBV) model with spatial diffusion and saturation response of the infection rate is investigated, in which the intracellular incubation period is modelled by a discrete time delay. By analyzing the corresponding characteristic equations, the local stability of an infected steady state and an uninfected steady state is discussed. By comparison arguments, it is proved that if the basic reproductive number is less than unity, the uninfected steady state is globally asymptotically stable. If the basic reproductive number is greater than unity, by successively modifying the coupled lower-upper solution pairs, sufficient conditions are obtained for the global stability of the infected steady state. Numerical simulations are carried out to illustrate the main results.
Modeling Periodic Impulsive Effects on Online TV Series Diffusion
Fang, Qiwen; Wang, Xi
2016-01-01
Background Online broadcasting substantially affects the production, distribution, and profit of TV series. In addition, online word-of-mouth significantly affects the diffusion of TV series. Because on-demand streaming rates are the most important factor that influences the earnings of online video suppliers, streaming statistics and forecasting trends are valuable. In this paper, we investigate the effects of periodic impulsive stimulation and pre-launch promotion on on-demand streaming dynamics. We consider imbalanced audience feverish distribution using an impulsive susceptible-infected-removed(SIR)-like model. In addition, we perform a correlation analysis of online buzz volume based on Baidu Index data. Methods We propose a PI-SIR model to evolve audience dynamics and translate them into on-demand streaming fluctuations, which can be observed and comprehended by online video suppliers. Six South Korean TV series datasets are used to test the model. We develop a coarse-to-fine two-step fitting scheme to estimate the model parameters, first by fitting inter-period accumulation and then by fitting inner-period feverish distribution. Results We find that audience members display similar viewing habits. That is, they seek new episodes every update day but fade away. This outcome means that impulsive intensity plays a crucial role in on-demand streaming diffusion. In addition, the initial audience size and online buzz are significant factors. On-demand streaming fluctuation is highly correlated with online buzz fluctuation. Conclusion To stimulate audience attention and interpersonal diffusion, it is worthwhile to invest in promotion near update days. Strong pre-launch promotion is also a good marketing tool to improve overall performance. It is not advisable for online video providers to promote several popular TV series on the same update day. Inter-period accumulation is a feasible forecasting tool to predict the future trend of the on-demand streaming amount
Mukhopadhyay, B; Bhattacharyya, R
2006-02-01
The paper is concerned with the effect of variable dispersal rates on Turing instability of a non-Lotka-Volterra reaction-diffusion system. In ecological applications, the dispersal rates of different species tends to oscillate in time. This oscillation is modeled by temporal variation in the diffusion coefficient with large as well as small periodicity. The case of large periodicity is analyzed using the theory of Floquet multipliers and that of the small periodicity by using Hill's equation. The effect of such variation on the resulting Turing space is studied. A comparative analysis of the Turing spaces with constant diffusivity and variable diffusivities is performed. Numerical simulations are carried out to support analytical findings.
An intravoxel oriented flow model for diffusion-weighted imaging of the kidney.
Hilbert, Fabian; Bock, Maximilian; Neubauer, Henning; Veldhoen, Simon; Wech, Tobias; Bley, Thorsten Alexander; Köstler, Herbert
2016-10-01
By combining intravoxel incoherent motion (IVIM) and diffusion tensor imaging (DTI) we introduce a new diffusion model called intravoxel oriented flow (IVOF) that accounts for anisotropy of diffusion and the flow-related signal. An IVOF model using a simplified apparent flow fraction tensor (IVOFf ) is applied to diffusion-weighted imaging of human kidneys. The kidneys of 13 healthy volunteers were examined on a 3 T scanner. Diffusion-weighted images were acquired with six b values between 0 and 800 s/mm(2) and 30 diffusion directions. Diffusivity and flow fraction were calculated for different diffusion models. The Akaike information criterion was used to compare the model fit of the proposed IVOFf model to IVIM and DTI. In the majority of voxels the proposed IVOFf model with a simplified apparent flow fraction tensor performs better than IVIM and DTI. Mean diffusivity is significantly higher in DTI compared with models that account for the flow-related signal. The fractional anisotropy of diffusion is significantly reduced when flow fraction is considered to be anisotropic. Anisotropy of the apparent flow fraction tensor is significantly higher in the renal medulla than in the cortex region. The IVOFf model describes diffusion-weighted data in the human kidney more accurately than IVIM or DTI. The apparent flow fraction in the kidney proved to be anisotropic.
Mechanism of diffusive transport in molecular spider models
NASA Astrophysics Data System (ADS)
Semenov, Oleg; Olah, Mark J.; Stefanovic, Darko
2011-02-01
Recent advances in single-molecule chemistry have led to designs for artificial multipedal walkers that follow tracks of chemicals. We investigate the motion of a class of walkers, called molecular spiders, which consist of a rigid chemically inert body and several flexible enzymatic legs. The legs can reversibly bind to chemical substrates on a surface and through their enzymatic action convert them to products. The legs can also reversibly bind to products, but at a different rate. Antal and Krapivsky have proposed a model for molecular spider motion over regular one-dimensional lattices [T. Antal and P. L. Krapivsky, Phys. Rev. ENATUAS1539-375510.1103/PhysRevE.76.021121 76, 021121 (2007).]. In the model the legs hop from site to site under constraints imposed by connection to a common body. The first time a leg visits a site, the site is an uncleaved substrate, and the leg hops from this site only once it has cleaved it into a product. This cleavage happens at a rate r<1, slower than dissociation from a product site, r=1. The effect of cleavage is to slow down the hopping rate for legs that visit a site for the first time. Along with the constraints imposed on the legs, this leads to an effective bias in the direction of unvisited sites that decreases the average time needed to visit n sites. The overall motion, however, remains diffusive in the long time limit. We have reformulated the Antal-Krapivsky model as a continuous-time Markov process and simulated many traces of this process using kinetic Monte Carlo techniques. Our simulations show a previously unpredicted transient behavior wherein spiders with small r values move superdiffusively over significant distances and times. We explain this transient period of superdiffusive behavior by describing the spider process as switching between two metastates: a diffusive state D wherein the spider moves in an unbiased manner over previously visited sites, and a boundary state B wherein the spider is on the
Modeling geomagnetic storms on prompt and diffusive time scales
NASA Astrophysics Data System (ADS)
Li, Zhao
The discovery of the Van Allen radiation belts in the 1958 was the first major discovery of the Space Age. There are two belts of energetic particles. The inner belt is very stable, but the outer belt is extremely variable, especially during geomagnetic storms. As the energetic particles are hazardous to spacecraft, understanding the source of these particles and their dynamic behavior driven by solar activity has great practical importance. In this thesis, the effects of magnetic storms on the evolution of the electron radiation belts, in particular the outer zone, is studied using two types of numerical simulation: radial diffusion and magnetohydrodynamics (MHD) test-particle simulation. A radial diffusion code has been developed at Dartmouth, applying satellite measurements to model flux as an outer boundary condition, exploring several options for the diffusion coefficient and electron loss time. Electron phase space density is analyzed for July 2004 coronal mass ejection (CME) driven storms and March-April 2008 co-rotating interaction region (CIR) driven storms, and compared with Global Positioning System (GPS) satellite measurements within 5 degrees of the magnetic equator at L=4.16. A case study of a month-long interval in the Van Allen Probes satellite era, March 2013, confirms that electron phase space density is well described by radial diffusion for the whole month at low first invariant <400~MeV/G, but peaks in phase space density observed by the ECT instrument suite at higher first invariant are not reproduced by radial transport from a source at higher L. A 3D guiding center code with plasmasheet injection is used to simulate particle motion in time-dependent MHD fields calculated from the Lyon-Fedder-Mobarry global MHD code, as an extension of the Hudson et al. (2012) study of the Whole Heliosphere Interval of CIR-driven storms in March-April 2008. Direct comparison with measured fluxes at GOES show improved comparison with observations relative to
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.
Analytical model of diffuse reflectance spectrum of skin tissue
Lisenko, S A; Kugeiko, M M; Firago, V A; Sobchuk, A N
2014-01-31
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. (biophotonics)
Ohashi, Hidenori; Tamaki, Takanori; Yamaguchi, Takeo
2011-12-29
Molecular collisions, which are the microscopic origin of molecular diffusive motion, are affected by both the molecular surface area and the distance between molecules. Their product can be regarded as the free space around a penetrant molecule defined as the "shell-like free volume" and can be taken as a characteristic of molecular collisions. On the basis of this notion, a new diffusion theory has been developed. The model can predict molecular diffusivity in polymeric systems using only well-defined single-component parameters of molecular volume, molecular surface area, free volume, and pre-exponential factors. By consideration of the physical description of the model, the actual body moved and which neighbor molecules are collided with are the volume and the surface area of the penetrant molecular core. In the present study, a semiempirical quantum chemical calculation was used to calculate both of these parameters. The model and the newly developed parameters offer fairly good predictive ability.
A model for the diffuse attenuation coefficient of downwelling irradiance
NASA Astrophysics Data System (ADS)
Lee, Zhong-Ping; Du, Ke-Ping; Arnone, Robert
2005-02-01
The diffuse attenuation coefficient for downwelling irradiance (Kd) is an important parameter for ocean studies. For the vast ocean the only feasible means to get fine-scale measurements of Kd is by ocean color remote sensing. At present, values of Kd from remote sensing are estimated using empirical algorithms. Such an approach is insufficient to provide an understanding regarding the variation of Kd and contains large uncertainties in the derived values. In this study a semianalytical model for Kd is developed based on the radiative transfer equation, with values of the model parameters derived from Hydrolight simulations using the averaged particle phase function. The model is further tested with data simulated using significantly different particle phase functions, and the modeled Kd are found matching Hydrolight Kd very well (˜2% average error and ˜12% maximum error). Such a model provides an improved interpretation about the variation of Kd and a basis to more accurately determine Kd (especially using data from remote sensing).
Reactor-Diffusion Models For Cartilage Pattern Formation
NASA Astrophysics Data System (ADS)
Glimm, Tilmann; Hentschel, H. G. E.
2004-03-01
In the early stages of the development of the embryonic chick limb, the sites of future skeletal elements are marked by a prepattern formed by condensations of precartilage cells. A number of different theories have been proposed as to what mechanism determines the characteristic size, shape and number of these condensations. Nevertheless, there is still little definite knowledge on this question. In this talk, we present a model of the limb based on recent experiments and additional hypotheses. In this model, it is a ``reactor-diffusion'' mechanism which gives rise to precartilage condensation. The model consists of a system of nonlinear partial differential equations which govern the spatiotemporal distribution of various types of mesenchymal cells and relevant biomolecules. These biomolecules include Fibroblast growth factors (FGFs), transforming growth factor-betas (TGF-βs), the extracellular matrix protein Fibronectin, as well as a laterally-acting inhibitor. We present the results of numerical simulations for the system of PDEs. Also addressed are preliminary results on how this PDE model can be tied in with more biologically realistic cellular automata based models.
Weak solutions for a non-Newtonian diffuse interface model with different densities
NASA Astrophysics Data System (ADS)
Abels, Helmut; Breit, Dominic
2016-11-01
We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard equation. For the Cahn-Hilliard part a smooth free energy density and a constant, positive mobility is assumed. Using the {{L}∞} -truncation method we prove existence of weak solutions for a power-law exponent p>\\frac{2d+2}{d+2} , d = 2, 3.
Hall, Matt G; Bongers, Andre; Sved, Paul; Watson, Geoffrey; Bourne, Roger M
2015-04-01
Non-Gaussian diffusion dynamics was investigated in the two distinct water populations identified by a biexponential model of diffusion in prostate tissue. Diffusion-weighted MRI (DWI) signal attenuation was measured ex vivo in two formalin-fixed prostates at 9.4 T with diffusion times Δ = 10, 20 and 40 ms, and b values in the range 0.017-8.2 ms/µm(2) . A conventional biexponential model was compared with models in which either the lower diffusivity component or both of the components of the biexponential were stretched. Models were compared using Akaike's Information Criterion (AIC) and a leave-one-out (LOO) test of model prediction accuracy. The doubly stretched (SS) model had the highest LOO prediction accuracy and lowest AIC (highest information content) in the majority of voxels at Δ = 10 and 20 ms. The lower diffusivity stretching factor (α2 ) of the SS model was consistently lower (range ~0.3-0.9) than the higher diffusivity stretching factor (α1 , range ~0.7-1.1), indicating a high degree of diffusion heterogeneity in the lower diffusivity environment, and nearly Gaussian diffusion in the higher diffusivity environment. Stretched biexponential models demonstrate that, in prostate tissue, the two distinct water populations identified by the simple biexponential model individually exhibit non-Gaussian diffusion dynamics.
Mathematical model for silicon electrode - Part I. 2-d model
NASA Astrophysics Data System (ADS)
Sikha, Godfrey; De, Sumitava; Gordon, Joseph
2014-09-01
This paper presents a 2-dimensional transient numerical model to simulate the electrochemical lithium insertion in a silicon nanowire (Si NW) electrode. The model geometry is a cylindrical Si NW electrode anchored to a copper current collector (Cu CC) substrate. The model solves for diffusion of lithium in Si NW, stress generation in the Si NW due to chemical and elastic strains, stress generation in the Cu CC due to elastic strain, and volume expansion in the Si NW and Cu CC geometries. The evolution of stress components, i.e., radial, axial and tangential stresses in different regions in the Si NW are presented and discussed. The effect of radius of Si NW and lithiation rate, on the maximum stresses developed in the Si NW are also discussed.
The small ice cap instability in diffusive climate models
NASA Technical Reports Server (NTRS)
North, G. R.
1984-01-01
Simple climate models which invoke diffusive heat transport and ice cap albedo feedback have equilibrium solutions with no stable ice cap smaller than a radius of about 20 deg on a great circle. Attention is presently given to a solution of this phenomenon which is physically appealing. The ice-free solution has a thermal minimum, and if the minimum temperature is just above the critical value for ice formation, then the artificial addition of a patch of ice leads to a widespread depression of the temperature below the critical freezing temperature. A second stable solution will then exist whose spatial extent is determined by the range of the influence function of a point sink of heat, due to the albedo shift in the patch.
A reaction-diffusion model of cytosolic hydrogen peroxide.
Lim, Joseph B; Langford, Troy F; Huang, Beijing K; Deen, William M; Sikes, Hadley D
2016-01-01
As a signaling molecule in mammalian cells, hydrogen peroxide (H2O2) determines the thiol/disulfide oxidation state of several key proteins in the cytosol. Localization is a key concept in redox signaling; the concentrations of signaling molecules within the cell are expected to vary in time and in space in manner that is essential for function. However, as a simplification, all theoretical studies of intracellular hydrogen peroxide and many experimental studies to date have treated the cytosol as a well-mixed compartment. In this work, we incorporate our previously reported reduced kinetic model of the network of reactions that metabolize hydrogen peroxide in the cytosol into a model that explicitly treats diffusion along with reaction. We modeled a bolus addition experiment, solved the model analytically, and used the resulting equations to quantify the spatiotemporal variations in intracellular H2O2 that result from this kind of perturbation to the extracellular H2O2 concentration. We predict that micromolar bolus additions of H2O2 to suspensions of HeLa cells (0.8 × 10(9)cells/l) result in increases in the intracellular concentration that are localized near the membrane. These findings challenge the assumption that intracellular concentrations of H2O2 are increased uniformly throughout the cell during bolus addition experiments and provide a theoretical basis for differing phenotypic responses of cells to intracellular versus extracellular perturbations to H2O2 levels.
Stochastic fire-diffuse-fire model with realistic cluster dynamics
NASA Astrophysics Data System (ADS)
Calabrese, Ana; Fraiman, Daniel; Zysman, Daniel; Ponce Dawson, Silvina
2010-09-01
Living organisms use waves that propagate through excitable media to transport information. Ca2+ waves are a paradigmatic example of this type of processes. A large hierarchy of Ca2+ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, Ca2+ release occurs trough inositol 1,4,5-trisphosphate receptors (IP3Rs) which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of IP3R ’s that replicates the experimental observations reported in [D. Fraiman , Biophys. J. 90, 3897 (2006)10.1529/biophysj.105.075911]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the IP3 concentration is increased.
Random shearing direction models for isotropic turbulent diffusion
NASA Astrophysics Data System (ADS)
Majda, Andrew J.
1994-06-01
Recently, a rigorous renormalization theory for various scalar statistics has been developed for special modes of random advection diffusion involving random shear layer velocity fields with long-range spatiotemporal correlations. New random shearing direction models for isotropic turbulent diffusion are introduced here. In these models the velocity field has the spatial second-order statistics of an arbitrary prescribed stationary incompressible isotropic random field including long-range spatial correlations with infrared divergence, but the temporal correlations have finite range. The explicit theory of renormalization for the mean and second-order statistics is developed here. With ɛ the spectral parameter, for -∞<ɛ<4 and measuring the strength of the infrared divergence of the spatial spectrum, the scalar mean statistics rigorously exhibit a phase transition from mean-field behavior for ɛ<2 to anomalous behavior for ɛ with 2<ɛ<4 as conjectured earlier by Avellaneda and the author. The universal inertial range renormalization for the second-order scalar statistics exhibits a phase transition from a covariance with a Gaussian functional form for ɛ with ɛ<2 to an explicit family with a non-Gaussian covariance for ɛ with 2<ɛ<4. These non-Gaussian distributions have tails that are broader than Gaussian as ɛ varies with 2<ɛ<4 and behave for large values like exp(- C c | x|4-ɛ), with C c an explicit constant. Also, here the attractive general principle is formulated and proved that every steady, stationary, zero-mean, isotropic, incompressible Gaussian random velocity field is well approximated by a suitable superposition of random shear layers.
NASA Astrophysics Data System (ADS)
Martelli, Fabrizio; Ninni, Paola Di; Zaccanti, Giovanni; Contini, Davide; Spinelli, Lorenzo; Torricelli, Alessandro; Cubeddu, Rinaldo; Wabnitz, Heidrun; Mazurenka, Mikhail; Macdonald, Rainer; Sassaroli, Angelo; Pifferi, Antonio
2014-07-01
We present the experimental implementation and validation of a phantom for diffuse optical imaging based on totally absorbing objects for which, in the previous paper [J. Biomed. Opt. 18(6), 066014, (2013)], we have provided the basic theory. Totally absorbing objects have been manufactured as black polyvinyl chloride (PVC) cylinders and the phantom is a water dilution of intralipid-20% as the diffusive medium and India ink as the absorber, filled into a black scattering cell made of PVC. By means of time-domain measurements and of Monte Carlo simulations, we have shown the reliability, the accuracy, and the robustness of such a phantom in mimicking typical absorbing perturbations of diffuse optical imaging. In particular, we show that such a phantom can be used to generate any absorption perturbation by changing the volume and position of the totally absorbing inclusion.
Diffusion bonding and its application to manufacturing. [for joining of metal parts
NASA Technical Reports Server (NTRS)
Spurgeon, W. M.
1972-01-01
In its simplest form diffusion bonding is accomplished by placing clean metal surfaces together under a sufficient load and heating. The natural interatomic attractive force between atoms transforms the interface into a natural grain boundary. Therefore, in principle, the properties of the bond area are identical to those of the parent metal. Other advantages of diffusion bonding over conventional methods of bonding include freedom from residual stresses, excessive deformation, foreign metals, or changed crystal structures. Stainless steels, nickel-base superalloys, and aluminum alloys have all been successfully joined. Complex hardware, including integrated flueric devices, jet engine servovalves, and porous woven structures have been fabricated. The processing involved is discussed, along with such theoretical considerations as the role of metal surfaces, the formation of metal contact junctions, and the mechanisms of material transport in diffusion bonding.
Modeling of tower relief dynamics: Part 2
Cassata, J.R.; Dasgupta, S.; Gandhi, S.L. )
1993-11-01
Dynamic simulations of individual towers or systems of distillations columns overcome limitations of steady-state models by rigorously determining dynamic responses. These will lead to a realistic quantification of relief header and flare system load and identify the design-setting relief scenario. Determination of distillation tower relief loads based on steady-state simulations or recognized methods of approximation can lead to over designing relief systems by large margins. This can result in unnecessary capital expenditure for relief headers and flare systems that can significantly alter the economics of a proposed project. Such overly conservative requirements may even cause potentially attractive projects to be unnecessarily canceled. In addition, approximate methods or analyses based on steady-state simulations sometimes do not identify the design-setting relief mode. Part 1 introduced the PRV and tower dynamic models. Different strategies were shown that can simplify these models. These strategies include tower segmentation, tray lumping and component lumping. Two case studies illustrate the advantages of dynamic models. The two studies are a depentanizer tower relief study and a delthanizer tower relief study.
Partly conditional survival models for longitudinal data.
Zheng, Yingye; Heagerty, Patrick J
2005-06-01
It is common in longitudinal studies to collect information on the time until a key clinical event, such as death, and to measure markers of patient health at multiple follow-up times. One approach to the joint analysis of survival and repeated measures data adopts a time-varying covariate regression model for the event time hazard. Using this standard approach, the instantaneous risk of death at time t is specified as a possibly semi-parametric function of covariate information that has accrued through time t. In this manuscript, we decouple the time scale for modeling the hazard from the time scale for accrual of available longitudinal covariate information. Specifically, we propose a class of models that condition on the covariate information through time s and then specifies the conditional hazard for times t, where t > s. Our approach parallels the "partly conditional" models proposed by Pepe and Couper (1997, Journal of the American Statistical Association 92, 991-998) for pure repeated measures applications. Estimation is based on the use of estimating equations applied to clusters of data formed through the creation of derived survival times that measure the time from measurement of covariates to the end of follow-up. Patient follow-up may be terminated either by the occurrence of the event or by censoring. The proposed methods allow a flexible characterization of the association between a longitudinal covariate process and a survival time, and facilitate the direct prediction of survival probabilities in the time-varying covariate setting.
Protein folding dynamics: the diffusion-collision model and experimental data.
Karplus, M.; Weaver, D. L.
1994-01-01
The diffusion-collision model of protein folding is assessed. A description is given of the qualitative aspects and quantitative results of the diffusion-collision model and their relation to available experimental data. We consider alternative mechanisms for folding and point out their relationship to the diffusion-collision model. We show that the diffusion-collision model is supported by a growing body of experimental and theoretical evidence, and we outline future directions for developing the model and its applications. PMID:8003983
NASA/MSFC multilayer diffusion models and computer programs, version 5
NASA Technical Reports Server (NTRS)
Dumbauld, R. K.; Bjorklund, J. R.
1975-01-01
The transport and diffusion models and algorithms developed for use by NASA in predicting concentrations and dosages downwind from normal and abnormal launches of rocket vehicles are described along with the associated computer programs for use in performing the calculations. Topics discussed include: the mathematical specifications and procedures used in the Preprocessor Program to calculate rocket exhaust cloud rise, cloud dimensions, and other input parameters to the transport and diffusion models; the revised mathematical specifications for the Multilayer Diffusion Models; users' instructions for implementing the Preprocessor and Multilayer Diffusion Models Programs; and worked example problems illustrating the use of the models and computer programs.
NASA Astrophysics Data System (ADS)
Simpson, Matthew J.; Baker, Ruth E.; McCue, Scott W.
2011-02-01
Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multiscale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (PME). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the PME to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.
A reaction-diffusion model for long bones growth.
Garzón-Alvarado, D A; García-Aznar, J M; Doblaré, M
2009-10-01
Bone development is characterized by differentiation and growth of chondrocytes from the proliferation zone to the hypertrophying one. These two cellular processes are controlled by a complex signalling regulatory loop between different biochemical signals, whose production depends on the current cell density, constituting a coupled cell-chemical system. In this work, a mathematical model of the process of early bone growth is presented, extending and generalizing other earlier approaches on the same topic. A reaction-diffusion regulatory loop between two chemical factors: parathyroid hormone-related peptide (PTHrP) and Indian hedgehog (Ihh) is hypothesized, where PTHrP is activated by Ihh and inhibits Ihh production. Chondrocytes proliferation and hypertrophy are described by means of population equations being both regulated by the PTHrP and Ihh concentrations. In the initial stage of bone growth, these two cellular proceses are considered to be directionally dependent, modelling the well known column cell formation, characteristic of endochondral ossification. This coupled set of equations is solved within a finite element framework, getting an estimation of the chondrocytes spatial distribution, growth of the diaphysis and formation of the epiphysis of a long bone. The results obtained are qualitatively similar to the actual physiological ones and quantitatively close to some available experimental data. Finally, this extended approach allows finding important relations between the model parameters to get stability of the physiological process and getting additional insight on the spatial and directional distribution of cells and paracrine factors.
The dynamics of multimodal integration: The averaging diffusion model.
Turner, Brandon M; Gao, Juan; Koenig, Scott; Palfy, Dylan; L McClelland, James
2017-03-08
We combine extant theories of evidence accumulation and multi-modal integration to develop an integrated framework for modeling multimodal integration as a process that unfolds in real time. Many studies have formulated sensory processing as a dynamic process where noisy samples of evidence are accumulated until a decision is made. However, these studies are often limited to a single sensory modality. Studies of multimodal stimulus integration have focused on how best to combine different sources of information to elicit a judgment. These studies are often limited to a single time point, typically after the integration process has occurred. We address these limitations by combining the two approaches. Experimentally, we present data that allow us to study the time course of evidence accumulation within each of the visual and auditory domains as well as in a bimodal condition. Theoretically, we develop a new Averaging Diffusion Model in which the decision variable is the mean rather than the sum of evidence samples and use it as a base for comparing three alternative models of multimodal integration, allowing us to assess the optimality of this integration. The outcome reveals rich individual differences in multimodal integration: while some subjects' data are consistent with adaptive optimal integration, reweighting sources of evidence as their relative reliability changes during evidence integration, others exhibit patterns inconsistent with optimality.
Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation
2010-01-01
1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is
Random walks models with intermediate fractional diffusion asymptotics
NASA Astrophysics Data System (ADS)
Saichev, Alexander I.; Utkin, Sergei G.
2004-05-01
Random walk process was investigated with PDF of random time intervals similar to fractional exponential law on small times and to regular exponential law on long times. Generalized fractional Kolmogorov-Feller equation was derived for such kind of process. Asymptotics of its PDF in the long time limit and for intermediate times were found. They obey standard diffusion law or fractional diffusion law respectively. Exact solutions of mentioned equations were numerically calculated, demonstrating crossover of fractional diffusion law into the linear one.
Performance of a TKE diffusion scheme in ECMWF IFS Single Column Model
NASA Astrophysics Data System (ADS)
Svensson, Jacob; Bazile, Eric; Sandu, Irina; Svensson, Gunilla
2015-04-01
Numerical Weather Prediction models (NWP) as well as climate models are used for decision making on all levels in society and their performance and accuracy are of great importance for both economical and safety reasons. Today's extensive use of weather apps and websites that directly uses model output even more highlights the importance of realistic output parameters. The turbulent atmospheric boundary layer (ABL) includes many physical processes which occur on a subgrid scale and need to be parameterized. As the absolute major part of the biosphere is located in the ABL, it is of great importance that these subgrid processes are parametrized so that they give realistic values of e.g. temperature and wind on the levels close to the surface. GEWEX (Global Energy and Water Exchange Project) Atmospheric Boundary Layer Study (GABLS), has the overall objective to improve the understanding and the representation of the atmospheric boundary layers in climate models. The study has pointed out that there is a need for a better understanding and representation of stable atmospheric boundary layers (SBL). Therefore four test cases have been designed to highlight the performance of and differences between a number of climate models and NWP:s in SBL. In the experiments, most global NWP and climate models have shown to be too diffusive in stable conditions and thus give too weak temperature gradients, too strong momentum mixing and too weak ageostrophic Ekman flow. The reason for this is that the models need enhanced diffusion to create enough friction for the large scale weather systems, which otherwise would be too fast and too active. In the GABLS test cases, turbulence schemes that use Turbulent Kinetic Energy (TKE) have shown to be more skilful than schemes that only use stability and gradients. TKE as a prognostic variable allows for advection both vertically and horizontally and gives a "memory" from previous time steps. Therefore, e.g. the ECMWF-GABLS workshop in 2011
NASA Astrophysics Data System (ADS)
Debure, Mathieu; De Windt, Laurent; Frugier, Pierre; Gin, Stéphane
2013-11-01
The influence of diffusion of reactive species in aqueous solutions on the alteration rate of borosilicate glass of nuclear interest in the presence of magnesium carbonate (hydromagnesite: 4MgCO3·Mg(OH)2·4H2O) is investigated together with the ability of coupled chemistry/transport models to simulate the processes involved. Diffusion cells in which the solids are separated by an inert stainless steel sintered filter were used to establish parameters for direct comparison with batch experiments in which solids are intimately mixed. The chemistry of the solution and solid phases was monitored over time by various analytical techniques including ICP-AES, XRD, and SEM. The primary mechanism controlling the geochemical evolution of the system remains the consumption of silicon from the glass by precipitation of magnesium silicates. The solution chemistry and the dissolution and precipitation of solid phases are correctly described by 2D modeling with the GRAAL model implemented in the HYTEC reactive transport code. The spatial symmetry of the boron concentrations in both compartments of the cells results from dissolution coupled with simple diffusion, whereas the spatial asymmetry of the silicon and magnesium concentrations is due to strong coupling between dissolution, diffusion, and precipitation of secondary phases. A sensitivity analysis on the modeling of glass alteration shows that the choice of these phases and their thermodynamic constants have only a moderate impact whereas the thickness of the filter has a greater barrier effect.
Capone, Florinda; De Cataldis, Valentina; De Luca, Roberta
2015-11-01
A reaction-diffusion system modeling cholera epidemic in a non-homogeneously mixed population is introduced. The interaction between population and toxigenic Vibrio cholerae concentration in contaminated water has been taken into account. The existence of biologically meaningful equilibria is investigated together with their linear and nonlinear stability. Using the data collected during the Haiti cholera epidemic, a numerical simulation is performed.
Hybrid approaches for multiple-species stochastic reaction–diffusion models
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen
2015-01-01
Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. PMID:26478601
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen
2015-10-15
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Hybrid approaches for multiple-species stochastic reaction-diffusion models
NASA Astrophysics Data System (ADS)
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Development of Spray on Bag for manufacturing of large composites parts: Diffusivity analysis
NASA Astrophysics Data System (ADS)
Dempah, Maxime Joseph
Bagging materials are utilized in many composites manufacturing processes. The selection is mainly driven by cost, temperature requirements, chemical compatibility and tear properties of the bag. The air barrier properties of the bag are assumed to be adequate or in many cases are not considered at all. However, the gas barrier property of a bag is the most critical parameter, as it can negatively affect the quality of the final laminate. The barrier property is a function of the bag material, uniformity, thickness and temperature. Improved barrier properties are needed for large parts, high pressure consolidated components and structures where air stays entrapped on the part surface. The air resistance property of the film is defined as permeability and is investigated in this thesis. A model was developed to evaluate the gas transport through the film and an experimental cell was implemented to characterize various commercial films. Understanding and characterizing the transport phenomena through the film allows optimization of the bagging material for various manufacturing processes. Spray-on-Bag is a scalable alternative bagging method compared to standard films. The approach allows in-situ fabrication of the bag on large and complex geometry structures where optimization of the bag properties can be varied on a local level. An experimental setup was developed and implemented using a six axis robot and an automated spraying system. Experiments were performed on a flat surface and specimens were characterized and compared to conventional films. Air barrier properties were within range of standard film approaches showing the potential to fabricate net shape bagging structures in an automated process.
JPEG-2000 Part 10 Verification Model
Mniszewski, Susan; Rivenburgh, Reid; Brislawn, Chris
2003-03-04
VM10 is a research software implementation of the ISO/IEC JPEG-2000 Still Image Coding standard (ISO international Standard 15444). JPEG-2000 image coding involves subband codiing and compression of digital raster images to facilitate storage and transmission of such imagery. Images are decomposed into space/scale subbands using cascades of two-dimensional (tensor product) discrete wavelet transforms. The wavelet transforms can be either reversible (integer-to-integer) transforms or irreversible (integer-to-float). The subbands in each resolution level are quantized by uniform scalar quantization in the irreversible case. The resulting integer subbands in each resolution level are partitioned into spatially localized code blocks to facilitate localized entropy decoding. Code blocks are encoded and packaged into an embedded bitstream using binary arithmetic bitplane coding (the MQ Coder algorithm applied to hierarchical bitplane coding (the MQ coder algorithm applied to hierachical bitplane context modeling). The resultant compressed bitstream is configured for use with the JPIP interactive client-server protocol (JPEG-2000 part 9). VM10 is written in ANSI C++ using the Biltz++ array class library. To enable development of multidimensional image coding algorithms, VM10 is templated on the dimension of the array containers. It was developed with the GNU g++ compiler on both Linux (Red Hat) and Windows/cygwin platforms, although it should compile and run under other ANSI C++ compilers as well. Software design is highly modular and object-oriented in order to facilitate rapid development and frequent revision and experimentation. No attempt has been made to optimize the run-time performance of the code. The software performs both the encoding and decoding operations involved in JPEG-2000 image coding, as implemented in apps/compress/main.cpp and apps/expand/main.cpp. VM10 implements all of the JPEG-2000 baseline (Part 1, ISO 15444-1) and portions of the published
Diffusion Models of the Flanker Task: Discrete versus Gradual Attentional Selection
ERIC Educational Resources Information Center
White, Corey N.; Ratcliff, Roger; Starns, Jeffrey J.
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…
A diffuse interface model of grain boundary faceting
NASA Astrophysics Data System (ADS)
Abdeljawad, Fadi; Medlin, Douglas; Zimmerman, Jonathan; Hattar, Khalid; Foiles, Stephen
Incorporating anisotropy into thermodynamic treatments of interfaces dates back to over a century ago. For a given orientation of two abutting grains in a pure metal, depressions in the grain boundary (GB) energy may exist as a function of GB inclination, defined by the plane normal. Therefore, an initially flat GB may facet resulting in a hill-and-valley structure. Herein, we present a diffuse interface model of GB faceting that is capable of capturing anisotropic GB energies and mobilities, and accounting for the excess energy due to facet junctions and their non-local interactions. The hallmark of our approach is the ability to independently examine the role of each of the interface properties on the faceting behavior. As a demonstration, we consider the Σ 5 < 001 > tilt GB in iron, where faceting along the { 310 } and { 210 } planes was experimentally observed. Linear stability analysis and numerical examples highlight the role of junction energy and associated non-local interactions on the resulting facet length scales. On the whole, our modeling approach provides a general framework to examine the spatio-temporal evolution of highly anisotropic GBs in polycrystalline metals. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under Contract DE-AC04-94AL85000.
Subgrid models for mass and thermal diffusion in turbulent mixing
Sharp, David H; Lim, Hyunkyung; Li, Xiao - Lin; Gilmm, James G
2008-01-01
We are concerned with the chaotic flow fields of turbulent mixing. Chaotic flow is found in an extreme form in multiply shocked Richtmyer-Meshkov unstable flows. The goal of a converged simulation for this problem is twofold: to obtain converged solutions for macro solution features, such as the trajectories of the principal shock waves, mixing zone edges, and mean densities and velocities within each phase, and also for such micro solution features as the joint probability distributions of the temperature and species concentration. We introduce parameterized subgrid models of mass and thermal diffusion, to define large eddy simulations (LES) that replicate the micro features observed in the direct numerical simulation (DNS). The Schmidt numbers and Prandtl numbers are chosen to represent typical liquid, gas and plasma parameter values. Our main result is to explore the variation of the Schmidt, Prandtl and Reynolds numbers by three orders of magnitude, and the mesh by a factor of 8 per linear dimension (up to 3200 cells per dimension), to allow exploration of both DNS and LES regimes and verification of the simulations for both macro and micro observables. We find mesh convergence for key properties describing the molecular level of mixing, including chemical reaction rates between the distinct fluid species. We find results nearly independent of Reynolds number for Re 300, 6000, 600K . Methodologically, the results are also new. In common with the shock capturing community, we allow and maintain sharp solution gradients, and we enhance these gradients through use of front tracking. In common with the turbulence modeling community, we include subgrid scale models with no adjustable parameters for LES. To the authors' knowledge, these two methodologies have not been previously combined. In contrast to both of these methodologies, our use of Front Tracking, with DNS or LES resolution of the momentum equation at or near the Kolmogorov scale, but without resolving the
Ndanou, S. Favrie, N. Gavrilyuk, S.
2015-08-15
We extend the model of diffuse solid–fluid interfaces developed earlier by authors of this paper to the case of arbitrary number of interacting hyperelastic solids. Plastic transformations of solids are taken into account through a Maxwell type model. The specific energy of each solid is given in separable form: it is the sum of a hydrodynamic part of the energy depending only on the density and the entropy, and an elastic part of the energy which is unaffected by the volume change. It allows us to naturally pass to the fluid description in the limit of vanishing shear modulus. In spite of a large number of governing equations, the model has a quite simple mathematical structure: it is a duplication of a single visco-elastic model. The model is well posed both mathematically and thermodynamically: it is hyperbolic and compatible with the second law of thermodynamics. The resulting model can be applied in the situations involving an arbitrary number of fluids and solids. In particular, we show the ability of the model to describe spallation and penetration phenomena occurring during high velocity impacts.
Perceptual decision making: drift-diffusion model is equivalent to a Bayesian model
Bitzer, Sebastian; Park, Hame; Blankenburg, Felix; Kiebel, Stefan J.
2014-01-01
Behavioral data obtained with perceptual decision making experiments are typically analyzed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence toward a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses. PMID:24616689
Monte Carlo Modeling of Diffuse Scattering from Single Crystals: The Program ZMC
Goossens, D.J.; Heerdegen, A.P.; Chan, E.J.; Welberry, T.R.
2012-04-30
Diffuse scattering probes the local ordering in a crystal, whereas Bragg peaks are descriptive of the average long-range ordering. The population of local configurations can be explored by modeling the three-dimensional distribution of diffuse scattering. Local configurations are not constrained by the average crystallographic symmetry, so one way of modeling diffuse scattering is by modeling a disordered (short-range-ordered) structure and then calculating its diffuse scattering. The structure must contain enough unit cells to give a statistically valid model of the populations of local configurations, and so requirements for a program to model this ordering are very different from programs that model average crystal structures (used to fit the Bragg diffraction). ZMC is a program that has been developed to model diffuse scattering, particularly from molecular crystals. The strategies used to tackle the problem and the way in which they are implemented will be discussed.
Spatiotemporal Patterns Induced by Cross-Diffusion in a Three-Species Food Chain Model
NASA Astrophysics Data System (ADS)
Ma, Zhan-Ping; Li, Wan-Tong; Wang, Yu-Xia
This paper focuses on a three-species Lotka-Volterra food chain model with cross-diffusion under homogeneous Neumann boundary conditions. The known results indicate that no spatiotemporal patterns happen in the corresponding reaction-diffusion system. When some cross-diffusion terms are introduced in the system, the existence of nonconstant positive steady-states as well as the Hopf bifurcation is studied. Our result shows that cross-diffusion plays a crucial role in the formation of spatiotemporal patterns, that is, it can create not only stationary patterns but also spatially inhomogeneous periodic oscillatory patterns, which is a strong contrast to the case without cross-diffusion.
Model Complexity in Diffusion Modeling: Benefits of Making the Model More Parsimonious
Lerche, Veronika; Voss, Andreas
2016-01-01
The diffusion model (Ratcliff, 1978) takes into account the reaction time distributions of both correct and erroneous responses from binary decision tasks. This high degree of information usage allows the estimation of different parameters mapping cognitive components such as speed of information accumulation or decision bias. For three of the four main parameters (drift rate, starting point, and non-decision time) trial-to-trial variability is allowed. We investigated the influence of these variability parameters both drawing on simulation studies and on data from an empirical test-retest study using different optimization criteria and different trial numbers. Our results suggest that less complex models (fixing intertrial variabilities of the drift rate and the starting point at zero) can improve the estimation of the psychologically most interesting parameters (drift rate, threshold separation, starting point, and non-decision time). PMID:27679585
NASA Astrophysics Data System (ADS)
Verdecchia, K.; Diop, M.; St. Lawrence, K.
2015-03-01
Diffuse correlation spectroscopy (DCS) is a non-invasive optical technique capable of monitoring tissue perfusion changes, particularly in the brain. The normalized temporal intensity autocorrelation function generated by DCS is typically characterized by assuming that the movement of erythrocytes can be modeled as a Brownian diffusion-like process instead of the expected random flow model. Carp et al. [Biomedical Optics Express, 2011] proposed a hybrid model, referred to as the hydrodynamic diffusion model, to capture both the random ballistic and diffusive nature of erythrocyte motion. The purpose of this study was to compare how well the Brownian diffusion and the hydrodynamic diffusion models characterized DCS data acquired directly on the brain, avoiding the confounding effects of scalp and skull. Data were acquired from seven pigs during normocapnia (39.9 +/- 0.7 mmHg) and hypocapnia (22.1 +/- 1.6 mmHg) with the DCS fibers placed 7 mm apart, directly on the cerebral cortex. The hydrodynamic diffusion model was found to provide a consistently better fit to the autocorrelation functions compared to the Brownian diffusion model and was less sensitive to the chosen start and end time points used in the fitting. However, the decrease in cerebral blood flow from normocapnia to hypocapnia determined was similar for the two models (-42.6 +/- 8.6 % for the Brownian model and -42.2 +/- 10.2 % for the hydrodynamic model), suggesting that the latter is reasonable for monitoring flow changes.
NASA Astrophysics Data System (ADS)
Wang, Hsin; Porter, Wallace D.; Böttner, Harald; König, Jan; Chen, Lidong; Bai, Shengqiang; Tritt, Terry M.; Mayolet, Alex; Senawiratne, Jayantha; Smith, Charlene; Harris, Fred; Gilbert, Patricia; Sharp, Jeff; Lo, Jason; Kleinke, Holger; Kiss, Laszlo
2013-06-01
For bulk thermoelectrics, improvement of the figure of merit ZT to above 2 from the current values of 1.0 to 1.5 would enhance their competitiveness with alternative technologies. In recent years, the most significant improvements in ZT have mainly been due to successful reduction of thermal conductivity. However, thermal conductivity is difficult to measure directly at high temperatures. Combined measurements of thermal diffusivity, specific heat, and mass density are a widely used alternative to direct measurement of thermal conductivity. In this work, thermal conductivity is shown to be the factor in the calculation of ZT with the greatest measurement uncertainty. The International Energy Agency (IEA) group, under the implementing agreement for Advanced Materials for Transportation (AMT), has conducted two international round-robins since 2009. This paper, part II of our report on the international round-robin testing of transport properties of bulk bismuth telluride, focuses on thermal diffusivity, specific heat, and thermal conductivity measurements.
Developing A Laser Shockwave Model For Characterizing Diffusion Bonded Interfaces
James A. Smith; Jeffrey M. Lacy; Barry H. Rabin
2014-07-01
12. Other advances in QNDE and related topics: Preferred Session Laser-ultrasonics Developing A Laser Shockwave Model For Characterizing Diffusion Bonded Interfaces 41st Annual Review of Progress in Quantitative Nondestructive Evaluation Conference QNDE Conference July 20-25, 2014 Boise Centre 850 West Front Street Boise, Idaho 83702 James A. Smith, Jeffrey M. Lacy, Barry H. Rabin, Idaho National Laboratory, Idaho Falls, ID ABSTRACT: The US National Nuclear Security Agency has a Global Threat Reduction Initiative (GTRI) which is assigned with reducing the worldwide use of high-enriched uranium (HEU). A salient component of that initiative is the conversion of research reactors from HEU to low enriched uranium (LEU) fuels. An innovative fuel is being developed to replace HEU. The new LEU fuel is based on a monolithic fuel made from a U-Mo alloy foil encapsulated in Al-6061 cladding. In order to complete the fuel qualification process, the laser shock technique is being developed to characterize the clad-clad and fuel-clad interface strengths in fresh and irradiated fuel plates. The Laser Shockwave Technique (LST) is being investigated to characterize interface strength in fuel plates. LST is a non-contact method that uses lasers for the generation and detection of large amplitude acoustic waves to characterize interfaces in nuclear fuel plates. However the deposition of laser energy into the containment layer on specimen’s surface is intractably complex. The shock wave energy is inferred from the velocity on the backside and the depth of the impression left on the surface from the high pressure plasma pulse created by the shock laser. To help quantify the stresses and strengths at the interface, a finite element model is being developed and validated by comparing numerical and experimental results for back face velocities and front face depressions with experimental results. This paper will report on initial efforts to develop a finite element model for laser
Reaction time in ankle movements: a diffusion model analysis
Michmizos, Konstantinos P.; Krebs, Hermano Igo
2015-01-01
Reaction time (RT) is one of the most commonly used measures of neurological function and dysfunction. Despite the extensive studies on it, no study has ever examined the RT in the ankle. Twenty-two subjects were recruited to perform simple, 2- and 4-choice RT tasks by visually guiding a cursor inside a rectangular target with their ankle. RT did not change with spatial accuracy constraints imposed by different target widths in the direction of the movement. RT increased as a linear function of potential target stimuli, as would be predicted by Hick–Hyman law. Although the slopes of the regressions were similar, the intercept in dorsal–plantar (DP) direction was significantly smaller than the intercept in inversion–eversion (IE) direction. To explain this difference, we used a hierarchical Bayesian estimation of the Ratcliff's (Psychol Rev 85:59, 1978) diffusion model parameters and divided processing time into cognitive components. The model gave a good account of RTs, their distribution and accuracy values, and hence provided a testimony that the non-decision processing time (overlap of posterior distributions between DP and IE < 0.045), the boundary separation (overlap of the posterior distributions < 0.1) and the evidence accumulation rate (overlap of the posterior distributions < 0.01) components of the RT accounted for the intercept difference between DP and IE. The model also proposed that there was no systematic change in non-decision processing time or drift rate when spatial accuracy constraints were altered. The results were in agreement with the memory drum hypothesis and could be further justified neurophysiologically by the larger innervation of the muscles controlling DP movements. This study might contribute to assessing deficits in sensorimotor control of the ankle and enlighten a possible target for correction in the framework of our on-going effort to develop robotic therapeutic interventions to the ankle of children with cerebral palsy
Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong
2016-01-01
Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R2 = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer. PMID:27934928
Y genetic data support the Neolithic demic diffusion model.
Chikhi, Lounes; Nichols, Richard A; Barbujani, Guido; Beaumont, Mark A
2002-08-20
There still is no general agreement on the origins of the European gene pool, even though Europe has been more thoroughly investigated than any other continent. In particular, there is continuing controversy about the relative contributions of European Palaeolithic hunter-gatherers and of migrant Near Eastern Neolithic farmers, who brought agriculture to Europe. Here, we apply a statistical framework that we have developed to obtain direct estimates of the contribution of these two groups at the time they met. We analyze a large dataset of 22 binary markers from the non-recombining region of the Y chromosome (NRY), by using a genealogical likelihood-based approach. The results reveal a significantly larger genetic contribution from Neolithic farmers than did previous indirect approaches based on the distribution of haplotypes selected by using post hoc criteria. We detect a significant decrease in admixture across the entire range between the Near East and Western Europe. We also argue that local hunter-gatherers contributed less than 30% in the original settlements. This finding leads us to reject a predominantly cultural transmission of agriculture. Instead, we argue that the demic diffusion model introduced by Ammerman and Cavalli-Sforza [Ammerman, A. J. & Cavalli-Sforza, L. L. (1984) The Neolithic Transition and the Genetics of Populations in Europe (Princeton Univ. Press, Princeton)] captures the major features of this dramatic episode in European prehistory.
An electrodynamics-based model for ion diffusion in microbial polysaccharides.
Liu, Chongxuan; Zachara, John M; Felmy, Andrew; Gorby, Yuri
2004-10-10
An electrodynamics-based model was formulated for simulation of ion diffusion in microbial polysaccharides. The fixed charges and electrostatic double layers that may associate with microbial polysaccharides and their effects on ion diffusion were explicitly built into the model. The model extends a common multicomponent ion diffusion formulation that is based on irreversible thermodynamics under a zero ionic charge flux condition, which is only applicable to the regions without fixed charges and electrostatic double layers. An efficient numerical procedure was presented to solve the differential equations in the model. The model well described key features of experimental observations of ion diffusion in negatively charged microbial polysaccharides including accelerated diffusive transport of cations, exclusion of anions, and increased rate of cation transport with increasing negative charge density. The simulated diffusive fluxes of cations and anions were consistent with a cation exchange diffusion concept in negatively charged polysaccharides at the interface of plant roots and soils; and the developed model allows to mathematically study such diffusion phenomena. An illustrative example was also provided to simulate dynamic behavior of ionic current during ion diffusion within a charged bacterial cell wall polysaccharide and the effects of the ionic current on the compression or expansion of the bacterial electrostatic double layer at the interface of the cell wall and bulk solution.
NASA Astrophysics Data System (ADS)
Mekkaoui, Imen; Moulin, Kevin; Croisille, Pierre; Pousin, Jerome; Viallon, Magalie
2016-08-01
Cardiac motion presents a major challenge in diffusion weighted MRI, often leading to large signal losses that necessitate repeated measurements. The diffusion process in the myocardium is difficult to investigate because of the unqualified sensitivity of diffusion measurements to cardiac motion. A rigorous mathematical formalism is introduced to quantify the effect of tissue motion in diffusion imaging. The presented mathematical model, based on the Bloch-Torrey equations, takes into account deformations according to the laws of continuum mechanics. Approximating this mathematical model by using finite elements method, numerical simulations can predict the sensitivity of the diffusion signal to cardiac motion. Different diffusion encoding schemes are considered and the diffusion weighted MR signals, computed numerically, are compared to available results in literature. Our numerical model can identify the existence of two time points in the cardiac cycle, at which the diffusion is unaffected by myocardial strain and cardiac motion. Of course, these time points depend on the type of diffusion encoding scheme. Our numerical results also show that the motion sensitivity of the diffusion sequence can be reduced by using either spin echo technique with acceleration motion compensation diffusion gradients or stimulated echo acquisition mode with unipolar and bipolar diffusion gradients.
Mekkaoui, Imen; Moulin, Kevin; Croisille, Pierre; Pousin, Jerome; Viallon, Magalie
2016-08-07
Cardiac motion presents a major challenge in diffusion weighted MRI, often leading to large signal losses that necessitate repeated measurements. The diffusion process in the myocardium is difficult to investigate because of the unqualified sensitivity of diffusion measurements to cardiac motion. A rigorous mathematical formalism is introduced to quantify the effect of tissue motion in diffusion imaging. The presented mathematical model, based on the Bloch-Torrey equations, takes into account deformations according to the laws of continuum mechanics. Approximating this mathematical model by using finite elements method, numerical simulations can predict the sensitivity of the diffusion signal to cardiac motion. Different diffusion encoding schemes are considered and the diffusion weighted MR signals, computed numerically, are compared to available results in literature. Our numerical model can identify the existence of two time points in the cardiac cycle, at which the diffusion is unaffected by myocardial strain and cardiac motion. Of course, these time points depend on the type of diffusion encoding scheme. Our numerical results also show that the motion sensitivity of the diffusion sequence can be reduced by using either spin echo technique with acceleration motion compensation diffusion gradients or stimulated echo acquisition mode with unipolar and bipolar diffusion gradients.
A Numerical Model for Coupling of Neutron Diffusion and Thermomechanics in Fast Burst Reactors
Samet Y. Kadioglu; Dana A. Knoll; Cassiano De Oliveira
2008-11-01
We develop a numerical model for coupling of neutron diffusion adn termomechanics in order to stimulate transient behavior of a fast burst reactor. The problem involves solving a set of non-linear different equations which approximate neutron diffusion, temperature change, and material behavior. With this equation set we will model the transition from a supercritical to subcritical state and possible mechanical vibration.
Baup, S; Wolbert, D; Laplanche, A
2002-10-01
Three pesticides (atrazine, bromoxynil and diuron) and two granular activated carbons are involved in equilibrium and kinetic adsorption experiments. Equilibrium is represented by Freundlich isotherm law and kinetic is described by the Homogeneous Surface Diffusion Model, based on external mass transfer and intraparticle surface diffusion. Equilibrium and long-term experiments are conducted to compare Powdered Activated Carbon and Granular Activated Carbon. These first investigations show that crushing GAC into PAC improves the accessibility of the adsorption sites without increasing the number of these sites. In a second part, kinetics experiments are carried out using a Differential Column Batch Reactor. Thanks to this experimental device, the external mass transfer coefficient k(f) is calculated from empirical correlation and the effect of external mass transfer on adsorption is likely to be minimized. In order to obtain the intraparticle surface diffusion coefficient D. for these pesticides, comparisons between experimental kinetic data and simulations are conducted and the best agreement leads to the Ds coefficient. This procedure appears to be an efficient way to acquire surface diffusion coefficients for the adsorption of pesticides onto GAC. Finally it points out the role of surface diffusivity in the adsorption rate. As a matter of fact, even if the amount of the target-compound that could be potentially adsorbed is really important, its surface diffusion coefficient may be small, so that its adsorption may not have enough contact time to be totally achieved.
Boundedness in a chemotaxis-haptotaxis model with nonlinear diffusion
NASA Astrophysics Data System (ADS)
Li, Yan; Lankeit, Johannes
2016-05-01
This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion under homogeneous Neumann boundary conditions in a bounded smooth domain Ω \\subset {{{R}}n} , n = 2, 3, 4, where χ,ξ and μ are given nonnegative parameters. The diffusivity D(u) is assumed to satisfy D(u)≥slant δ {{u}m-1} for all u > 0 with some δ >0 . It is proved that for sufficiently regular initial data global bounded solutions exist whenever m>2-\\frac{2}{n} . For the case of non-degenerate diffusion (i.e. D(0) > 0) the solutions are classical; for the case of possibly degenerate diffusion (D(0)≥slant 0 ), the existence of bounded weak solutions is shown.
NASA Astrophysics Data System (ADS)
Poornesh, K. K.; Cho, C. D.; Lee, G. B.; Tak, Y. S.
In PEM fuel cell, gas-diffusion electrode (GDE) plays very significant role in force transmission from bipolar plate to the membrane. This paper investigates the effects of geometrical heterogeneities of gas-diffusion electrode layer (gas-diffusion layer (GDL) and catalyst layer (CL)) on mechanical damage evolution and propagation. We present a structural integrity principle of membrane electrode assembly (MEA) based on the interlayer stress transfer capacity and corresponding cell layer material response. Commonly observable damages such as rupture of hydrophobic coating and breakage of carbon fiber in gas-diffusion layer are attributed to the ductile to brittle phase transition within a single carbon fiber. Effect of material inhomogeneity on change in modulus, hardness, contact stiffness, and electrical contact resistance is also discussed. Fracture statistics of carbon fiber and variations in flexural strength of GDL are studied. The damage propagation in CL is perceived to be influenced by the type of gradation and the vicinity from which crack originates. Cohesive zone model has been proposed based on the traction-separation law to investigate the damage propagation throughout the two interfaces (carbon fiber/CL and CL/membrane).
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.
Modeling Simple Driving Tasks with a One-Boundary Diffusion Model
Ratcliff, Roger; Strayer, David
2014-01-01
A one-boundary diffusion model was applied to the data from two experiments in which subjects were performing a simple simulated driving task. In the first experiment, the same subjects were tested on two driving tasks using a PC-based driving simulator and the psychomotor vigilance test (PVT). The diffusion model fit the response time (RT) distributions for each task and individual subject well. Model parameters were found to correlate across tasks which suggests common component processes were being tapped in the three tasks. The model was also fit to a distracted driving experiment of Cooper and Strayer (2008). Results showed that distraction altered performance by affecting the rate of evidence accumulation (drift rate) and/or increasing the boundary settings. This provides an interpretation of cognitive distraction whereby conversing on a cell phone diverts attention from the normal accumulation of information in the driving environment. PMID:24297620
Modeling simple driving tasks with a one-boundary diffusion model.
Ratcliff, Roger; Strayer, David
2014-06-01
A one-boundary diffusion model was applied to the data from two experiments in which subjects were performing a simple simulated driving task. In the first experiment, the same subjects were tested on two driving tasks using a PC-based driving simulator and the psychomotor vigilance test. The diffusion model fit the response time distributions for each task and individual subject well. Model parameters were found to correlate across tasks, which suggests that common component processes were being tapped in the three tasks. The model was also fit to a distracted driving experiment of Cooper and Strayer (Human Factors, 50, 893-902, 2008). Results showed that distraction altered performance by affecting the rate of evidence accumulation (drift rate) and/or increasing the boundary settings. This provides an interpretation of cognitive distraction whereby conversing on a cell phone diverts attention from the normal accumulation of information in the driving environment.
Phantoms for diffuse optical imaging based on totally absorbing objects, part 1: Basic concepts.
Martelli, Fabrizio; Pifferi, Antonio; Contini, Davide; Spinelli, Lorenzo; Torricelli, Alessandro; Wabnitz, Heidrun; Macdonald, Rainer; Sassaroli, Angelo; Zaccanti, Giovanni
2013-06-01
The design of inhomogeneous phantoms for diffuse optical imaging purposes using totally absorbing objects embedded in a diffusive medium is proposed and validated. From time-resolved and continuous-wave Monte Carlo simulations, it is shown that a given or desired perturbation strength caused by a realistic absorbing inhomogeneity of a certain absorption and volume can be approximately mimicked by a small totally absorbing object of a so-called equivalent black volume (equivalence relation). This concept can be useful in two ways. First, it can be exploited to design realistic inhomogeneous phantoms with different perturbation strengths simply using a set of black objects with different volumes. Further, it permits one to grade physiological or pathological changes on a reproducible scale of perturbation strengths given as equivalent black volumes, thus facilitating the performance assessment of clinical instruments. A set of plots and interpolating functions to derive the equivalent black volume corresponding to a given absorption change is provided. The application of the equivalent black volume concept for grading different optical perturbations is demonstrated for some examples.
The development of a through-diffusion model with a parent-daughter decay chain.
Chen, Chin-Lung; Wang, Tsing-Hai; Lee, Ching-Hor; Teng, Shi-Ping
2012-09-01
A valid performance assessment of radioactive waste repositories strongly depends on the reliability of nuclide transport parameters, including distribution and diffusion coefficients. To reduce the waste produced and time spent conducting diffusion experiments, a robust model is required to accurately interpret the experiment results. Therefore, we developed a through-diffusion model with parent-daughter nuclide decay chain. We validated our model through comparisons with the Moridis model (Moridis, 1999) and Bharat model (Bharat et al., 2009), assessing our model and these two models using the distribution of parent nuclide concentrations. This strongly supports the rationality and functionality of extending our proposed model to daughter nuclides. In this study, we derived analytical solutions for the parent nuclides of the through-diffusion experiment using the multicompartment (MC) model. We also propose a simplified formula for estimating the apparent diffusion coefficient of parent nuclides based on the analytical solutions. Through numerical experiments, we verified the feasibility of the formula. Our models are useful for determining the apparent diffusion coefficient of daughter nuclides when conducting through-diffusion experiments with parent-daughter nuclide decay chains. Additionally, the proposed models offer the advantages of saving time and reducing experimental waste.
Diffusion-controlled reactions modeling in Geant4-DNA
Karamitros, M.; Luan, S.; Bernal, M.A.; Allison, J.; Baldacchino, G.; Davidkova, M.; Francis, Z.; Friedland, W.; Ivantchenko, V.; Ivantchenko, A.; Mantero, A.; Nieminem, P.; Santin, G.; Tran, H.N.; Stepan, V.; Incerti, S.
2014-10-01
Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k–d tree data structure for quickly locating, for a given molecule, its closest reactants. The
Diffusion-controlled reactions modeling in Geant4-DNA
NASA Astrophysics Data System (ADS)
Karamitros, M.; Luan, S.; Bernal, M. A.; Allison, J.; Baldacchino, G.; Davidkova, M.; Francis, Z.; Friedland, W.; Ivantchenko, V.; Ivantchenko, A.; Mantero, A.; Nieminem, P.; Santin, G.; Tran, H. N.; Stepan, V.; Incerti, S.
2014-10-01
Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k-d tree data structure for quickly locating, for a given molecule, its closest reactants. The
[A study of brain inner tissue water molecule self-diffusion model based on Monte Carlo simulation].
Wu, Zhanxiong; Zhu, Shanan; Bin, He
2010-06-01
The study of water molecule self-diffusion process is of importance not only for getting anatomical information of brain inner tissue, but also for shedding light on the diffusion process of some medicine in brain tissue. In this paper, we summarized the self-diffusion model of water molecule in brain inner tissue, and calculated the self-diffusion coefficient based on Monte Carlo simulation under different conditions. The comparison between this result and that of Latour model showed that the two self-diffusion coefficients were getting closer when the diffusion time became longer, and that the Latour model was a long time-depended self-diffusion model.
Color diffusion model for active contours - an application to skin lesion segmentation.
Ivanovici, Mihai; Stoica, Diana
2012-01-01
Most of the existing diffusion models are defined for gray-scale images. We propose a diffusion model for color images to be used as external energy for active contours. Our diffusion model is based on the first-order moment of the correlation integral expressed using ΔE distances in the CIE Lab color space. We use a multi-scale approach for active contours, the diffusion being independently computed at various scales. We validate the model on synthetic images, including multi-fractal color textures, as well as medical images representing melanoma. We conclude that the proposed diffusion model is valid for use in skin lesion segmentation in color images using active contours.
NASA Technical Reports Server (NTRS)
Allgood, Daniel C.; Graham, Jason S.; Ahuja, Vineet; Hosangadi, Ashvin
2008-01-01
Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence
NASA Technical Reports Server (NTRS)
Allgood, Daniel C.; Graham, Jason S.; Ahuja, Vineet; Hosangadi, Ashvin
2010-01-01
Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence
NASA Astrophysics Data System (ADS)
Naglič, Peter; Vidovič, Luka; Milanič, Matija; Randeberg, Lise L.; Majaron, Boris
2014-03-01
Light propagation in highly scattering biological tissues is often treated in the so-called diffusion approximation (DA). Although the analytical solutions derived within the DA are known to be inaccurate near tissue boundaries and absorbing layers, their use in quantitative analysis of diffuse reflectance spectra (DRS) is quite common. We analyze the artifacts in assessed tissue properties which occur in fitting of numerically simulated DRS with the DA solutions for a three-layer skin model. In addition, we introduce an original procedure which significantly improves the accuracy of such an inverse analysis of DRS. This procedure involves a single comparison run of a Monte Carlo (MC) numerical model, yet avoids the need to implement and run an inverse MC. This approach is tested also in analysis of experimental DRS from human skin.
NASA Astrophysics Data System (ADS)
Hay, M. B.; Stoliker, D. L.; Johnson, K. J.; Curtis, G. P.; Kent, D. B.; Davis, J. A.
2008-12-01
The mobility of U(VI) in contaminated aquifers is limited by adsorption to mineral surfaces. While the chemical sorption step proceeds rapidly, the achievement of equilibrium can be kinetically limited by the diffusion of U(VI) through soil aggregates, grain fractures, and mineral coatings. The diffusion kinetics are in turn dependent on the adsorption equilibrium, due to the sorptive retardation effect that occurs within the intragranular diffusion regime. Since adsorption equilibrium is dependent on chemical conditions (e.g., pH, alkalinity, Ca concentration), diffusion of these chemical species as solution conditions change may also affect U(VI) kinetics. These coupled effects are difficult to capture in generic rate models that do not explicitly include a diffusion mechanism, particularly when the diffusion regime is heterogeneous. We present a grain-scale diffusion model for contaminated sediments from Naturita, CO and Hanford, WA, constrained by kinetic U(VI) desorption data and non-reactive tracer uptake and release measurements with tritiated water. Batch and column-scale tracer results are modeled using a multi-rate mass transfer scheme to extract intragranular diffusion parameters. These results suggest a high degree of heterogeneity in the diffusivity of the intragranular pore space, as indicated by a wide, bi/multimodal distribution of mass transfer rates. These results are used to constrain a U(VI) diffusion model with surface complexation and multicomponent diffusion that can be incorporated into field-scale reactive transport models. Preliminary results suggest that the sorptive retardation effect is significant; U(VI) batch-scale diffusion kinetics requiring hundreds to thousands of hours for equilibration appear to be controlled by intragranular pore space that requires less than 24 hours for equilibration of a non-reactive tracer.
NASA Astrophysics Data System (ADS)
Ge, J.; Everett, M. E.; Weiss, C. J.
2012-12-01
A 2.5D finite difference (FD) frequency-domain modeling algorithm based on the theory of fractional diffusion of electromagnetic (EM) fields generated by a loop source lying above a fractured geological medium is addressed in this paper. The presence of fractures in the subsurface, usually containing highly conductive pore fluids, gives rise to spatially hierarchical flow paths of induced EM eddy currents. The diffusion of EM eddy currents in such formations is anomalous, generalizing the classical Gaussian process described by the conventional Maxwell equations. Based on the continuous time random walk (CTRW) theory, the diffusion of EM eddy currents in a rough medium is governed by the fractional Maxwell equations. Here, we model the EM response of a 2D subsurface containing fractured zones, with a 3D loop source, which results the so-called 2.5D model geometry. The governing equation in the frequency domain is converted using Fourier transform into k domain along the strike direction (along which the model conductivity doesn't vary). The resulting equation system is solved by the multifrontal massively parallel solver (MUMPS). The data obtained is then converted back to spatial domain and the time domain. We find excellent agreement between the FD and analytic solutions for a rough halfspace model. Then FD solutions are calculated for a 2D fault zone model with variable conductivity and roughness. We compare the results with responses from several classical models and explore the relationship between the roughness and the spatial density of the fracture distribution.
Model for radon diffusion through the lunar regolith.
NASA Technical Reports Server (NTRS)
Friesen, L. J.; Heymann, D.
1972-01-01
Description of a model for radon diffusion through the lunar regolith in which the atom migrates by random walk. The regolith is represented by a system of randomly oriented baffles in which the mean distance which the atom travels between two collisions takes on the role of a mean free path. The effective mean time between two collisions depends on two entities: the actual mean time-of-flight and the mean sticking time on grain surfaces for one collision. The latter depends strongly on the temperature and the heat of adsorption of radon on regolith materials. Both the mean free path as well as the heat of adsorption are either poorly known or unknown for the lunar regolith; hence these quantities are treated as free parameters. Because of the greatly different mean lifetimes against radioactive decay of Rn219, Rn220, and Rn222, the regolith acts as a powerful 'filter' for these species. Rn222 escape is significant (32%) even for a mean free path of 1 micron, a heat of adsorption of 7.0 kcal/mole and a regolith depth of 4 m. Calculations of radon escape from a 4 m thick regolith, using mean free paths of 1, 10, and 80 microns and heats of adsorption of 4.0, 5.2, and 7.0 kcal/mole show that the Rn222/Rn220 escape ratio can be as small as 7.7 and as large as, or larger than 47. The small value of 7.7 is of particular interest, because it is nearly equal to the escape ratio inferred by Turkevich et al. (1970) from their Surveyor 5 results.
Quantum-corrected drift-diffusion models for transport in semiconductor devices
De Falco, Carlo; Gatti, Emilio; Lacaita, Andrea L.; Sacco, Riccardo . E-mail: riccardo.sacco@mate.polimi.it
2005-04-10
In this paper, we propose a unified framework for Quantum-corrected drift-diffusion (QCDD) models in nanoscale semiconductor device simulation. QCDD models are presented as a suitable generalization of the classical drift-diffusion (DD) system, each particular model being identified by the constitutive relation for the quantum-correction to the electric potential. We examine two special, and relevant, examples of QCDD models; the first one is the modified DD model named Schroedinger-Poisson-drift-diffusion, and the second one is the quantum-drift-diffusion (QDD) model. For the decoupled solution of the two models, we introduce a functional iteration technique that extends the classical Gummel algorithm widely used in the iterative solution of the DD system. We discuss the finite element discretization of the various differential subsystems, with special emphasis on their stability properties, and illustrate the performance of the proposed algorithms and models on the numerical simulation of nanoscale devices in two spatial dimensions.
NASA Astrophysics Data System (ADS)
Huber, Christian; Cassata, William S.; Renne, Paul R.
2011-04-01
Thermochronometry based on radiogenic noble gases is critically dependent upon accurate knowledge of the kinetics of diffusion. With few exceptions, complex natural crystals are represented by ideal geometries such as infinite sheets, infinite cylinders, or spheres, and diffusivity is assumed to be isotropic. However, the physical boundaries of crystals generally do not conform to ideal geometries and diffusion within some crystals is known to be anisotropic. Our failure to incorporate such complexities into diffusive models leads to inaccuracies in both thermal histories and diffusion parameters calculated from fractional release data. To address these shortcomings we developed a code based on the lattice Boltzmann (LB) method to model diffusion from complex 3D geometries having isotropic, temperature-independent anisotropic, and temperature-dependent anisotropic diffusivity. In this paper we outline the theoretical basis for the LB code and highlight several advantages of this model relative to more traditional finite difference approaches. The LB code, along with existing analytical solutions for diffusion from simple geometries, is used to investigate the affect of intrinsic crystallographic features (e.g., crystal topology and diffusion anisotropy) on calculated diffusion parameters and a novel method for approximating thermal histories from crystals with complex topologies and diffusive anisotropy is presented.
An Electrodynamics-Based Model for Ion Diffusion in Microbial Polysaccharides
Liu, Chongxuan; Zachara, John M.; Felmy, Andrew R.; Gorby, Yuri A.
2004-08-03
An electrodynamics-based model was formulated for simulation of ion diffusion in microbial polysaccharides with fixed charges and electrostatic double layers. The model extends a common multicomponent ion diffusion model that is based on irreversible thermodynamics under a zero ionic charge flux condition, which is only applicable to the regions without fixed charges and electrostatic double layers. An efficient numerical procedure was presented to solve the differential equations in the model. The model well described key features of experimental observations of ion diffusion in negatively charged microbial polysaccharides including accelerated diffusive transport of cations, exclusion of anions, and increased rate of cation transport with increasing negative charge density. The simulated diffusive fluxes of cations and anions were consistent with a classic exchange diffusion concept in negatively charged polysaccharides at the interface of plant roots and soils; and the developed model allows to mathematically study such diffusion phenomena. Numerical simulations also showed that ion diffusive transport within a bacterial cell wall polysaccharide may induce an ionic current that compresses or expands the bacterial electrostatic double layer at the interface of the cell wall and bulk solution.
Bass-SIR model for diffusion of new products in social networks.
Fibich, Gadi
2016-09-01
We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the susceptible-infected-recovered (SIR) model, but rather by a new model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from nonadopters to adopters is described by a nonstandard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Moreover, unlike the SIR model, there is no threshold value above which the diffusion will peter out. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.
Bass-SIR model for diffusion of new products in social networks
NASA Astrophysics Data System (ADS)
Fibich, Gadi
2016-09-01
We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the susceptible-infected-recovered (SIR) model, but rather by a new model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from nonadopters to adopters is described by a nonstandard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Moreover, unlike the SIR model, there is no threshold value above which the diffusion will peter out. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.
NASA Astrophysics Data System (ADS)
Rothfischer, Ramona; Grosenick, Dirk; Macdonald, Rainer
2015-07-01
We discuss the determination of optical properties of thick scattering media from measurements of time-resolved transmittance by diffusion theory using Monte Carlo simulations as a gold standard to model photon migration. Our theoretical and experimental investigations reveal differences between calculated distributions of times of flight (DTOFs) of photons from both models which result in an overestimation of the absorption and the reduced scattering coefficient by diffusion theory which becomes larger for small scattering coefficients. By introducing a temporal shift in the DTOFs obtained with the diffusion model as additional fit parameter, the deviation in the absorption coefficient can be compensated almost completely. If the scattering medium is additionally covered by transparent layers (e.g. glass plates) the deviation between the DTOFs from both models is even larger which mainly effects the determination of the reduced scattering coefficient by diffusion theory. A temporal shift improves the accuracy of the optical properties derived by diffusion theory in this case as well.
Climate stability for a Sellers-type model. [atmospheric diffusive energy balance model
NASA Technical Reports Server (NTRS)
Ghil, M.
1976-01-01
We study a diffusive energy-balance climate model governed by a nonlinear parabolic partial differential equation. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. We consider also models similar to the main one studied, and determine the number of their steady states. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The diffusion is taken to be nonlinear as well as linear. We investigate the stability under small perturbations of the main model's climates. A stability criterion is derived, and its application shows that the 'present climate' and the 'deep freeze' are stable, whereas the model's glacial is unstable. A variational principle is introduced to confirm the results of this stability analysis. For a sufficient decrease in solar radiation (about 2%) the glacial and interglacial solutions disappear, leaving the ice-covered earth as the only possible climate.
Modeling the flow in diffuse interface methods of solidification
NASA Astrophysics Data System (ADS)
Subhedar, A.; Steinbach, I.; Varnik, F.
2015-08-01
Fluid dynamical equations in the presence of a diffuse solid-liquid interface are investigated via a volume averaging approach. The resulting equations exhibit the same structure as the standard Navier-Stokes equation for a Newtonian fluid with a constant viscosity, the effect of the solid phase fraction appearing in the drag force only. This considerably simplifies the use of the lattice Boltzmann method as a fluid dynamics solver in solidification simulations. Galilean invariance is also satisfied within this approach. Further, we investigate deviations between the diffuse and sharp interface flow profiles via both quasiexact numerical integration and lattice Boltzmann simulations. It emerges from these studies that the freedom in choosing the solid-liquid coupling parameter h provides a flexible way of optimizing the diffuse interface-flow simulations. Once h is adapted for a given spatial resolution, the simulated flow profiles reach an accuracy comparable to quasiexact numerical simulations.
NASA Astrophysics Data System (ADS)
Aminfar, Habib; Mohammadpourfard, Mousa; Khajeh, Kosar
2017-03-01
It is well-known that the Low Density Lipoprotein (LDL) can accumulate and penetrate into the arterial wall. Here, we have investigated the diffusion rate of macromolecules across the porous layer of blood vessel under the effects of magnetic force. By using a finite volume technique, it was found that magnetic field makes alterations in diffusion rate of LDLs, also surface concentration of macromolecules on the walls. As well, the influence of different value of Re and Sc number in the presence of a magnetic field have shown as nondimensional concentration profiles. Magnetic field considered as a body force, porous layer simulated by using Darcy's law and the blood regarded as nano fluid which was examined as a single phase model.
Utrillas, María P; Marín, María J; Esteve, Anna R; Estellés, Victor; Tena, Fernando; Cañada, Javier; Martínez-Lozano, José A
2009-01-01
Values of measured and modeled diffuse UV erythemal irradiance (UVER) for all sky conditions are compared on planes inclined at 40 degrees and oriented north, south, east and west. The models used for simulating diffuse UVER are of the geometric-type, mainly the Isotropic, Klucher, Hay, Muneer, Reindl and Schauberger models. To analyze the precision of the models, some statistical estimators were used such as root mean square deviation, mean absolute deviation and mean bias deviation. It was seen that all the analyzed models reproduce adequately the diffuse UVER on the south-facing plane, with greater discrepancies for the other inclined planes. When the models are applied to cloud-free conditions, the errors obtained are higher because the anisotropy of the sky dome acquires more importance and the models do not provide the estimation of diffuse UVER accurately.
NASA Astrophysics Data System (ADS)
Wu, Yixiang; Zou, Xingfu
2016-10-01
Mass action and standard incidence are two major infection mechanisms in modelling spread of infectious diseases. Spatial heterogeneity plays an important role in spread of infectious diseases, and hence, motivates and advocates diffusive models for disease dynamics. By analyzing a diffusive SIS model with the standard incidence infection mechanism, some recent works [2,12] have investigated the asymptotical profiles of the endemic steady state for large and small diffusion rates, and the results show that controlling the diffusion rate of the susceptible individuals can help eradicate the infection, while controlling the diffusion rate of the infectious individuals cannot. This paper aims to reveal the difference between the two infection mechanisms in a spatially heterogeneous environment. To this end, we consider a diffusive SIS model of the same structure but with the mass action infection adopted, and explore the asymptotic profiles of the endemic steady state for small and large diffusion rates. It turns out that the new model poses some new challenges due to the nonlocal term in the equilibrium problem and the unboundedness of the nonlinear term. Our results on this new model reveal some fundamental differences between the two transmission mechanisms in such spatial models, which may provide some implications on disease modelling and controls.
Diffusion Dynamics and Creative Destruction in a Simple Classical Model
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
Kee, Kerk F; Sparks, Lisa; Struppa, Daniele C; Mannucci, Mirco A; Damiano, Alberto
2016-01-01
By integrating the simplicial model of social aggregation with existing research on opinion leadership and diffusion networks, this article introduces the constructs of simplicial diffusers (mathematically defined as nodes embedded in simplexes; a simplex is a socially bonded cluster) and simplicial diffusing sets (mathematically defined as minimal covers of a simplicial complex; a simplicial complex is a social aggregation in which socially bonded clusters are embedded) to propose a strategic approach for information diffusion of cancer screenings as a health intervention on Facebook for community cancer prevention and control. This approach is novel in its incorporation of interpersonally bonded clusters, culturally distinct subgroups, and different united social entities that coexist within a larger community into a computational simulation to select sets of simplicial diffusers with the highest degree of information diffusion for health intervention dissemination. The unique contributions of the article also include seven propositions and five algorithmic steps for computationally modeling the simplicial model with Facebook data.
Modeling of the magnetic free energy of self-diffusion in bcc Fe
NASA Astrophysics Data System (ADS)
Sandberg, N.; Chang, Z.; Messina, L.; Olsson, P.; Korzhavyi, P.
2015-11-01
A first-principles based approach to calculating self-diffusion rates in bcc Fe is discussed with particular focus on the magnetic free energy associated with diffusion activation. First, the enthalpies and entropies of vacancy formation and migration in ferromagnetic bcc Fe are calculated from standard density functional theory methods in combination with transition state theory. Next, the shift in diffusion activation energy when going from the ferromagnetic to the paramagnetic state is estimated by averaging over random spin states. Classical and quantum mechanical Monte Carlo simulations within the Heisenberg model are used to study the effect of spin disordering on the vacancy formation and migration free energy. Finally, a quasiempirical model of the magnetic contribution to the diffusion activation free energy is applied in order to connect the current first-principles results to experimental data. The importance of the zero-point magnon energy in modeling of diffusion in bcc Fe is stressed.
Scrape-off layer modeling with kinetic or diffusion description of charge-exchange atoms
NASA Astrophysics Data System (ADS)
Tokar, M. Z.
2016-12-01
Hydrogen isotope atoms, generated by charge-exchange (c-x) of neutral particles recycling from the first wall of a fusion reactor, are described either kinetically or in a diffusion approximation. In a one-dimensional (1-D) geometry, kinetic calculations are accelerated enormously by applying an approximate pass method for the assessment of integrals in the velocity space. This permits to perform an exhaustive comparison of calculations done with both approaches. The diffusion approximation is deduced directly from the velocity distribution function of c-x atoms in the limit of charge-exchanges with ions occurring much more frequently than ionization by electrons. The profiles across the flux surfaces of the plasma parameters averaged along the main part of the scrape-off layer (SOL), beyond the X-point and divertor regions, are calculated from the one-dimensional equations where parallel flows of charged particles and energy towards the divertor are taken into account as additional loss terms. It is demonstrated that the heat losses can be firmly estimated from the SOL averaged parameters only; for the particle loss the conditions in the divertor are of importance and the sensitivity of the results to the so-called "divertor impact factor" is investigated. The coupled 1-D models for neutral and charged species, with c-x atoms described either kinetically or in the diffusion approximation, are applied to assess the SOL conditions in a fusion reactor, with the input parameters from the European DEMO project. It is shown that the diffusion approximation provides practically the same profiles across the flux surfaces for the plasma density, electron, and ion temperatures, as those obtained with the kinetic description for c-x atoms. The main difference between the two approaches is observed in the characteristics of these species themselves. In particular, their energy flux onto the wall is underestimated in calculations with the diffusion approximation by 20 % - 30
Employing a Modified Diffuser Momentum Model to Simulate Ventilation of the Orion CEV
NASA Technical Reports Server (NTRS)
Straus, John; Lewis, John F.
2011-01-01
The Ansys CFX CFD modeling tool was used to support the design efforts of the ventilation system for the Orion CEV. CFD modeling was used to establish the flow field within the cabin for several supply configurations. A mesh and turbulence model sensitivity study was performed before the design studies. Results were post-processed for comparison with performance requirements. Most configurations employed straight vaned diffusers to direct and throw the flow. To manage the size of the models, the diffuser vanes were not resolved. Instead, a momentum model was employed to account for the effect of the diffusers. The momentum model was tested against a separate, vane-resolved side study. Results are presented for a single diffuser configuration for a low supply flow case.
NASA Astrophysics Data System (ADS)
Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.
2016-10-01
Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the
Solving the advection-diffusion equations in biological contexts using the cellular Potts model
NASA Astrophysics Data System (ADS)
Dan, Debasis; Mueller, Chris; Chen, Kun; Glazier, James A.
2005-10-01
The cellular Potts model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or matrix (ECM). Standard diffusion solvers applied to the cellular potts model use finite difference methods on the underlying CPM lattice. However, these methods produce a diffusing field tied to the underlying lattice, which is inaccurate in many biological situations in which cell or ECM movement causes advection rapid compared to diffusion. Finite difference schemes suffer numerical instabilities solving the resulting advection-diffusion equations. To circumvent these problems we simulate advection diffusion within the framework of the CPM using off-lattice finite-difference methods. We define a set of generalized fluid particles which detach advection and diffusion from the lattice. Diffusion occurs between neighboring fluid particles by local averaging rules which approximate the Laplacian. Directed spin flips in the CPM handle the advective movement of the fluid particles. A constraint on relative velocities in the fluid explicitly accounts for fluid viscosity. We use the CPM to solve various diffusion examples including multiple instantaneous sources, continuous sources, moving sources, and different boundary geometries and conditions to validate our approximation against analytical and established numerical solutions. We also verify the CPM results for Poiseuille flow and Taylor-Aris dispersion.
Diffusion within the Cytoplasm: A Mesoscale Model of Interacting Macromolecules
Trovato, Fabio; Tozzini, Valentina
2014-01-01
Recent experiments carried out in the dense cytoplasm of living cells have highlighted the importance of proteome composition and nonspecific intermolecular interactions in regulating macromolecule diffusion and organization. Despite this, the dependence of diffusion-interaction on physicochemical properties such as the degree of poly-dispersity and the balance between steric repulsion and nonspecific attraction among macromolecules was not systematically addressed. In this work, we study the problem of diffusion-interaction in the bacterial cytoplasm, combining theory and experimental data to build a minimal coarse-grained representation of the cytoplasm, which also includes, for the first time to our knowledge, the nucleoid. With stochastic molecular-dynamics simulations of a virtual cytoplasm we are able to track the single biomolecule motion, sizing from 3 to 80 nm, on submillisecond-long trajectories. We demonstrate that the size dependence of diffusion coefficients, anomalous exponents, and the effective viscosity experienced by biomolecules in the cytoplasm is fine-tuned by the intermolecular interactions. Accounting only for excluded volume in these potentials gives a weaker size-dependence than that expected from experimental data. On the contrary, adding nonspecific attraction in the range of 1–10 thermal energy units produces a stronger variation of the transport properties at growing biopolymer sizes. Normal and anomalous diffusive regimes emerge straightforwardly from the combination of high macromolecular concentration, poly-dispersity, stochasticity, and weak nonspecific interactions. As a result, small biopolymers experience a viscous cytoplasm, while the motion of big ones is jammed because the entanglements produced by the network of interactions and the entropic effects caused by poly-dispersity are stronger. PMID:25468337
Modeling of band-3 protein diffusion in the normal and defective red blood cell membrane.
Li, He; Zhang, Yihao; Ha, Vi; Lykotrafitis, George
2016-04-21
We employ a two-component red blood cell (RBC) membrane model to simulate lateral diffusion of band-3 proteins in the normal RBC and in the RBC with defective membrane proteins. The defects reduce the connectivity between the lipid bilayer and the membrane skeleton (vertical connectivity), or the connectivity of the membrane skeleton itself (horizontal connectivity), and are associated with the blood disorders of hereditary spherocytosis (HS) and hereditary elliptocytosis (HE) respectively. Initially, we demonstrate that the cytoskeleton limits band-3 lateral mobility by measuring the band-3 macroscopic diffusion coefficients in the normal RBC membrane and in a lipid bilayer without the cytoskeleton. Then, we study band-3 diffusion in the defective RBC membrane and quantify the relation between band-3 diffusion coefficients and percentage of protein defects in HE RBCs. In addition, we illustrate that at low spectrin network connectivity (horizontal connectivity) band-3 subdiffusion can be approximated as anomalous diffusion, while at high horizontal connectivity band-3 diffusion is characterized as confined diffusion. Our simulations show that the band-3 anomalous diffusion exponent depends on the percentage of protein defects in the membrane cytoskeleton. We also confirm that the introduction of attraction between the lipid bilayer and the spectrin network reduces band-3 diffusion, but we show that this reduction is lower than predicted by the percolation theory. Furthermore, we predict that the attractive force between the spectrin filament and the lipid bilayer is at least 20 times smaller than the binding forces at band-3 and glycophorin C, the two major membrane binding sites. Finally, we explore diffusion of band-3 particles in the RBC membrane with defects related to vertical connectivity. We demonstrate that in this case band-3 diffusion can be approximated as confined diffusion for all attraction levels between the spectrin network and the lipid bilayer
Diffusion on a hypersphere: application to the Wright-Fisher model
NASA Astrophysics Data System (ADS)
Maruyama, Kishiko; Itoh, Yoshiaki
2016-04-01
The eigenfunction expansion by Gegenbauer polynomials for the diffusion on a hypersphere is transformed into the diffusion for the Wright-Fisher model with a particular mutation rate. We use the Ito calculus considering stochastic differential equations. The expansion gives a simple interpretation of the Griffiths eigenfunction expansion for the Wright-Fisher model. Our representation is useful to simulate the Wright-Fisher model as well as Brownian motion on a hypersphere.
NASA Astrophysics Data System (ADS)
Boyer, D.; Romo-Cruz, J. C. R.
2014-10-01
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random-walk model with long-range memory for which not only the mean-square displacement (MSD) but also the propagator can be obtained exactly in the asymptotic limit. The model consists of a random walker on a lattice, which, at a constant rate, stochastically relocates at a site occupied at some earlier time. This time in the past is chosen randomly according to a memory kernel, whose temporal decay can be varied via an exponent parameter. In the weakly non-Markovian regime, memory reduces the diffusion coefficient from the bare value. When the mean backward jump in time diverges, the diffusion coefficient vanishes and a transition to an anomalous subdiffusive regime occurs. Paradoxically, at the transition, the process is an anticorrelated Lévy flight. Although in the subdiffusive regime the model exhibits some features of the continuous time random walk with infinite mean waiting time, it belongs to another universality class. If memory is very long-ranged, a second transition takes place to a regime characterized by a logarithmic growth of the MSD with time. In this case the process is asymptotically Gaussian and effectively described as a scaled Brownian motion with a diffusion coefficient decaying as 1 /t .
Goossens, D. J.
2015-01-01
Diffuse scattering from a crystal contains valuable information about the two-body correlations (related to the nanoscale order) in the material. Despite years of development, the detailed analysis of single crystal diffuse scattering (SCDS) has yet to become part of the everyday toolbox of the structural scientist. Recent decades have seen the pair distribution function approach to diffuse scattering (in fact, total scattering) from powders become a relatively routine tool. However, analysing the detailed, complex, and often highly anisotropic three-dimensional distribution of SCDS remains valuable yet rare because there is no routine method for undertaking the analysis. At present, analysis requires significant investment of time to develop specialist expertise, which means that the analysis of diffuse scattering, which has much to offer, is not incorporated thorough studies of many compounds even though it has the potential to be a very useful adjunct to existing techniques. This article endeavours to outline in some detail how the diffuse scattering from a molecular crystal can be modelled relatively quickly and largely using existing software tools. It is hoped this will provide a template for other studies. To enable this, the entire simulation is included as deposited material.
Goossens, D. J.
2015-01-01
Diffuse scattering from a crystal contains valuable information about the two-body correlations (related to the nanoscale order) in the material. Despite years of development, the detailed analysis of single crystal diffuse scattering (SCDS) has yet to become part of the everyday toolbox of the structural scientist. Recent decades have seen the pair distribution function approach to diffuse scattering (in fact, total scattering) from powders become a relatively routine tool. However, analysing the detailed, complex, and often highly anisotropic three-dimensional distribution of SCDS remains valuable yet rare because there is no routine method for undertaking the analysis. At present, analysis requiresmore » significant investment of time to develop specialist expertise, which means that the analysis of diffuse scattering, which has much to offer, is not incorporated thorough studies of many compounds even though it has the potential to be a very useful adjunct to existing techniques. This article endeavours to outline in some detail how the diffuse scattering from a molecular crystal can be modelled relatively quickly and largely using existing software tools. It is hoped this will provide a template for other studies. To enable this, the entire simulation is included as deposited material.« less
12 CFR Appendix B to Part 1002 - Model Application Forms
Code of Federal Regulations, 2013 CFR
2013-01-01
... 12 Banks and Banking 8 2013-01-01 2013-01-01 false Model Application Forms B Appendix B to Part... B) Pt. 1002, App. B Appendix B to Part 1002—Model Application Forms 1. This appendix contains five... form. 3. If a creditor uses an appropriate appendix B model form, or modifies a form in accordance...
12 CFR Appendix B to Part 202 - Model Application Forms
Code of Federal Regulations, 2012 CFR
2012-01-01
... 12 Banks and Banking 2 2012-01-01 2012-01-01 false Model Application Forms B Appendix B to Part... CREDIT OPPORTUNITY ACT (REGULATION B) Pt. 202, App. B Appendix B to Part 202—Model Application Forms 1... appear on the creditor's form. 3. If a creditor uses an appropriate Appendix B model form, or modifies...
12 CFR Appendix B to Part 202 - Model Application Forms
Code of Federal Regulations, 2013 CFR
2013-01-01
... 12 Banks and Banking 2 2013-01-01 2013-01-01 false Model Application Forms B Appendix B to Part... CREDIT OPPORTUNITY ACT (REGULATION B) Pt. 202, App. B Appendix B to Part 202—Model Application Forms 1... appear on the creditor's form. 3. If a creditor uses an appropriate appendix B model form, or modifies...
12 CFR Appendix B to Part 202 - Model Application Forms
Code of Federal Regulations, 2011 CFR
2011-01-01
... 12 Banks and Banking 2 2011-01-01 2011-01-01 false Model Application Forms B Appendix B to Part... CREDIT OPPORTUNITY ACT (REGULATION B) Pt. 202, App. B Appendix B to Part 202—Model Application Forms 1... appear on the creditor's form. 3. If a creditor uses an appropriate Appendix B model form, or modifies...
12 CFR Appendix B to Part 1002 - Model Application Forms
Code of Federal Regulations, 2012 CFR
2012-01-01
... 12 Banks and Banking 8 2012-01-01 2012-01-01 false Model Application Forms B Appendix B to Part... B) Pt. 1002, App. B Appendix B to Part 1002—Model Application Forms 1. This Appendix contains five... form. 3. If a creditor uses an appropriate Appendix B model form, or modifies a form in accordance...
12 CFR Appendix B to Part 1002 - Model Application Forms
Code of Federal Regulations, 2014 CFR
2014-01-01
... 12 Banks and Banking 8 2014-01-01 2014-01-01 false Model Application Forms B Appendix B to Part... B) Pt. 1002, App. B Appendix B to Part 1002—Model Application Forms 1. This appendix contains five... form. 3. If a creditor uses an appropriate appendix B model form, or modifies a form in accordance...
12 CFR Appendix B to Part 202 - Model Application Forms
Code of Federal Regulations, 2010 CFR
2010-01-01
... 12 Banks and Banking 2 2010-01-01 2010-01-01 false Model Application Forms B Appendix B to Part 202 Banks and Banking FEDERAL RESERVE SYSTEM BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM EQUAL CREDIT OPPORTUNITY ACT (REGULATION B) Pt. 202, App. B Appendix B to Part 202—Model Application Forms 1. This appendix contains five model...
12 CFR Appendix B to Part 202 - Model Application Forms
Code of Federal Regulations, 2014 CFR
2014-01-01
... 12 Banks and Banking 2 2014-01-01 2014-01-01 false Model Application Forms B Appendix B to Part... CREDIT OPPORTUNITY ACT (REGULATION B) Pt. 202, App. B Appendix B to Part 202—Model Application Forms 1... appear on the creditor's form. 3. If a creditor uses an appropriate Appendix B model form, or modifies...
Modelling the Mach bands illusion by means of a diffusion model.
Geier, Janos; Hudák, Mariann
2014-01-01
First, we criticize the validity of the principle of lateral inhibition. Second, on the basis of illusory phenomena and stabilized retinal images, we point out that the retina does not code the absolute luminance; the retina forwards a relative luminance sketch towards higher levels of the visual system. However, at the level of conscious processing the perceptual counterpart of absolute luminance, brightness, is available. Therefore, it is reasonable to assume that a reconstruction process is carried out by the visual system, which recovers the inner representation that corresponds to the retinal light distribution from the coded relative luminance sketch. We provide an illustrative description of a computational model of this reconstruction process. The basis of the reconstruction is a mathematically provable theorem, according to which if image P is produced from image I by Laplacian filtering, and then P is used as the sources and sinks of a homogeneous linear diffusion process, then the equilibrium of the diffusion will be identical to the original image I. We have illustrated this by a one-dimensional heat diffusion example, and by a series of test tubes connected to each other, also in one dimension. Brightness illusions are considered as a side effect of this diffusion-based reconstruction process. If the diffusion process deviates from the principle of homogeneous linearity, then the result of the reconstruction will deviate from the original image I. We showed a concrete illustration of this with regards to the Mach bands illusion: here we violated the principle of homogeneous linearity by means of inserting a small vertical tube serving as a serial resistance between each test tube and the horizontal connecting tube. This violation resulted in a change of water level in the source and the sink test tubes corresponding to the Mach bands illusion.
Nie, Qi-Yang; Maurer, Mara; Müller, Hermann J; Conci, Markus
2016-05-01
Illusory Kanizsa figures demonstrate that a perceptually completed whole is more than the sum of its composite parts. In the current study, we explored part/whole relationships in object completion using the configural superiority effect (CSE) with illusory figures (Pomerantz & Portillo, 2011). In particular, we investigated to which extent the CSE is modulated by closure in target and distractor configurations. Our results demonstrated a typical CSE, with detection of a configural whole being more efficient than the detection of a corresponding part-level target. Moreover, the CSE was more pronounced when grouped objects were presented in distractors rather than in the target. A follow-up experiment systematically manipulated closure in whole target or, respectively, distractor configurations. The results revealed the effect of closure to be again stronger in distractor, rather than in target configurations, suggesting that closure primarily affects the inhibition of distractors, and to a lesser extent the selection of the target. In addition, a drift-diffusion model analysis of our data revealed that efficient distractor inhibition expedites the rate of evidence accumulation, with closure in distractors particularly speeding the drift toward the decision boundary. In sum, our findings demonstrate that the CSE in Kanizsa figures derives primarily from the inhibition of closed distractor objects, rather than being driven by a conspicuous target configuration. Altogether, these results support a fundamental role of inhibition in driving configural superiority effects in visual search.
Hierarchical Bass model: a product diffusion model considering a diversity of sensitivity to fashion
NASA Astrophysics Data System (ADS)
Tashiro, Tohru
2016-11-01
We propose a new product diffusion model including the number of how many adopters or advertisements a non-adopter met until he/she adopts the product, where (non-)adopters mean people (not) possessing it. By this effect not considered in the Bass model, we can depict a diversity of sensitivity to fashion. As an application, we utilize the model to fit the iPod and the iPhone unit sales data, and so the better agreement is obtained than the Bass model for the iPod data. We also present a new method to estimate the number of advertisements in a society from fitting parameters of the Bass model and this new model.
Diffusive flux in a model of stochastically gated oxygen transport in insect respiration
NASA Astrophysics Data System (ADS)
Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.
2016-05-01
Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.
Xu, X; Sumption, M D
2016-01-12
In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb3Sn superconductors. In the first part, the governing equations for the bulk diffusion and inter-phase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether it is the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that "frozen" bulk diffusion leads to unique composition characteristics that the bulk composition of a compound layer remains unchanged after its initial formation instead of varying with the diffusion reaction system; here the model is modified for the case of grain boundary diffusion. Finally, we apply this model to the Nb3Sn superconductors and propose approaches to control their compositions.
Xu, X.; Sumption, M. D.
2016-01-12
In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb_{3}Sn superconductors. In the first part, the governing equations for the bulk diffusion and interphase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether it is the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that “frozen” bulk diffusion leads to unique composition characteristics that the bulk composition of a compound layer remains unchanged after its initial formation instead of varying with the diffusion reaction system; here the model is modified for the case of grain boundary diffusion. Lastly, we apply this model to the Nb_{3}Sn superconductors and propose approaches to control their compositions.
Xu, X.; Sumption, M. D.
2016-01-12
In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb3Sn superconductors. In the first part, the governing equations for the bulk diffusion and interphase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether it ismore » the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that “frozen” bulk diffusion leads to unique composition characteristics that the bulk composition of a compound layer remains unchanged after its initial formation instead of varying with the diffusion reaction system; here the model is modified for the case of grain boundary diffusion. Lastly, we apply this model to the Nb3Sn superconductors and propose approaches to control their compositions.« less
Effective diffusivity in the middle atmosphere based on general circulation model winds
NASA Astrophysics Data System (ADS)
Kostrykin, S. V.; Schmitz, G.
2006-01-01
The mixing of a passive tracer in the stratosphere and lower mesosphere is studied on the basis of the effective diffusivity, which is obtained in the framework of the tracer-based coordinate system. This characteristic is proportional to the average diffusion flux over Lagrangian contours and inversely proportional to the mean tracer gradient. The tracer distribution used in the calculation of the effective diffusivity is obtained after integration of the advection-diffusion equation using general circulation model winds and a new numerical advection scheme with small numerical diffusivity. Using some theoretical and experimental arguments, it is shown that the interpretation of the seasonal variability of the effective diffusivity field cannot be done on the basis of the momentary wind field alone, but some flow history should be taken into account. The climatology of the effective diffusivity for different months is presented up to the lower mesosphere and compared with previous studies. In the stratosphere some new features of the effective diffusivity distribution are obtained. For example, there is a local maximum of the effective diffusivity at midlatitudes of the Northern Hemisphere of the summer middle stratosphere. The effective diffusivity fields in the lower mesosphere show a strong increase of the mean effective diffusivity from the upper stratosphere to the lower mesosphere and the existence of a complex latitudinal structure of the effective diffusivity at mesospheric heights. In the lower mesosphere there is a marked interannual variability during the Southern Hemisphere easterly wind development. A possible explanation for the obtained structure is discussed on the basis of in situ Rossby wave generation and Rossby-wave-breaking effects.
Measuring and modeling diffuse scattering in protein X-ray crystallography
Van Benschoten, Andrew H.; Liu, Lin; Gonzalez, Ana; Brewster, Aaron S.; Sauter, Nicholas K.; Fraser, James S.; Wall, Michael E.
2016-03-28
X-ray diffraction has the potential to provide rich information about the structural dynamics of macromolecules. To realize this potential, both Bragg scattering, which is currently used to derive macromolecular structures, and diffuse scattering, which reports on correlations in charge density variations, must be measured. Until now, measurement of diffuse scattering from protein crystals has been scarce because of the extra effort of collecting diffuse data. Here, we present 3D measurements of diffuse intensity collected from crystals of the enzymes cyclophilin A and trypsin. The measurements were obtained from the same X-ray diffraction images as the Bragg data, using best practices for standard data collection. To model the underlying dynamics in a practical way that could be used during structure refinement, we tested translation–libration–screw (TLS), liquid-like motions (LLM), and coarse-grained normal-modes (NM) models of protein motions. The LLM model provides a global picture of motions and was refined against the diffuse data, whereas the TLS and NM models provide more detailed and distinct descriptions of atom displacements, and only used information from the Bragg data. Whereas different TLS groupings yielded similar Bragg intensities, they yielded different diffuse intensities, none of which agreed well with the data. In contrast, both the LLM and NM models agreed substantially with the diffuse data. In conclusion, these results demonstrate a realistic path to increase the number of diffuse datasets available to the wider biosciences community and indicate that dynamics-inspired NM structural models can simultaneously agree with both Bragg and diffuse scattering.
Measuring and modeling diffuse scattering in protein X-ray crystallography
Van Benschoten, Andrew H.; Liu, Lin; Gonzalez, Ana; ...
2016-03-28
X-ray diffraction has the potential to provide rich information about the structural dynamics of macromolecules. To realize this potential, both Bragg scattering, which is currently used to derive macromolecular structures, and diffuse scattering, which reports on correlations in charge density variations, must be measured. Until now, measurement of diffuse scattering from protein crystals has been scarce because of the extra effort of collecting diffuse data. Here, we present 3D measurements of diffuse intensity collected from crystals of the enzymes cyclophilin A and trypsin. The measurements were obtained from the same X-ray diffraction images as the Bragg data, using best practicesmore » for standard data collection. To model the underlying dynamics in a practical way that could be used during structure refinement, we tested translation–libration–screw (TLS), liquid-like motions (LLM), and coarse-grained normal-modes (NM) models of protein motions. The LLM model provides a global picture of motions and was refined against the diffuse data, whereas the TLS and NM models provide more detailed and distinct descriptions of atom displacements, and only used information from the Bragg data. Whereas different TLS groupings yielded similar Bragg intensities, they yielded different diffuse intensities, none of which agreed well with the data. In contrast, both the LLM and NM models agreed substantially with the diffuse data. In conclusion, these results demonstrate a realistic path to increase the number of diffuse datasets available to the wider biosciences community and indicate that dynamics-inspired NM structural models can simultaneously agree with both Bragg and diffuse scattering.« less
Wang, Zhiwu; Hamilton-Brehm, Scott; Lochner, Adriane; Elkins, James G; Morrell-Falvey, Jennifer L
2011-01-01
Abstract: The morphological and structural properties of microbial biofilms are influenced by internal substrate diffusion and utilization processes. In the case of microbial hydrolysis of plant cell walls, only thin and uniform biofilm structures are typically formed by cellulolytic microorganisms. In this study, we develop a hydrolysate diffusion and utilization model system to examine factors influencing cellulolytic biofilm formation. Model simulations using Caldicellulosiruptor obsidiansis as a representative organism, reveal that the growth of the cellulolytic biofilm is limited by hydrolysate utilization but not diffusion. As a consequence, the cellulolytic biofilm has a uniform growth rate, and there is a hydrolysate surplus that diffuses through the cellulolytic biofilm into the bulk solution where it is consumed by planktonic cells. Predictions based on the model were tested in a cellulose fermentation study and the results are consistent with the model and previously reported experimental data. The factors determining the rate-limiting step of biofilm growth are also analyzed.
A Functional Model for Teaching Osmosis-Diffusion to Biology Students
ERIC Educational Resources Information Center
Olsen, Richard W.; Petry, Douglas E.
1976-01-01
Described is a maternal-fetal model, operated by the student, to teach osmosis-diffusion to biology students. Included are materials needed, assembly instructions, and student operating procedures. (SL)
Woo, Jiyoung; Chen, Hsinchun
2016-01-01
As social media has become more prevalent, its influence on business, politics, and society has become significant. Due to easy access and interaction between large numbers of users, information diffuses in an epidemic style on the web. Understanding the mechanisms of information diffusion through these new publication methods is important for political and marketing purposes. Among social media, web forums, where people in online communities disseminate and receive information, provide a good environment for examining information diffusion. In this paper, we model topic diffusion in web forums using the epidemiology model, the susceptible-infected-recovered (SIR) model, frequently used in previous research to analyze both disease outbreaks and knowledge diffusion. The model was evaluated on a large longitudinal dataset from the web forum of a major retail company and from a general political discussion forum. The fitting results showed that the SIR model is a plausible model to describe the diffusion process of a topic. This research shows that epidemic models can expand their application areas to topic discussion on the web, particularly social media such as web forums.
A novel tensor distribution model for the diffusion-weighted MR signal✩
Jian, Bing; Vemuri, Baba C.; Özarslan, Evren; Carney, Paul R.; Mareci, Thomas H.
2008-01-01
Diffusion MRI is a non-invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo. The directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications. In this paper, we present a novel statistical model for diffusion-weighted MR signal attenuation which postulates that the water molecule diffusion can be characterized by a continuous mixture of diffusion tensors. An interesting observation is that this continuous mixture and the MR signal attenuation are related through the Laplace transform of a probability distribution over symmetric positive definite matrices. We then show that when the mixing distribution is a Wishart distribution, the resulting closed form of the Laplace transform leads to a Rigaut-type asymptotic fractal expression, which has been phenomenologically used in the past to explain the MR signal decay but never with a rigorous mathematical justification until now. Our model not only includes the traditional diffusion tensor model as a special instance in the limiting case, but also can be adjusted to describe complex tissue structure involving multiple fiber populations. Using this new model in conjunction with a spherical deconvolution approach, we present an efficient scheme for estimating the water molecule displacement probability functions on a voxel-by-voxel basis. Experimental results on both simulations and real data are presented to demonstrate the robustness and accuracy of the proposed algorithms. PMID:17570683
Application of a diffusion-desorption rate equation model in astrochemistry.
He, Jiao; Vidali, Gianfranco
2014-01-01
Desorption and diffusion are two of the most important processes on interstellar grain surfaces; knowledge of them is critical for the understanding of chemical reaction networks in the interstellar medium (ISM). However, a lack of information on desorption and diffusion is preventing further progress in astrochemistry. To obtain desorption energy distributions of molecules from the surfaces of ISM-related materials, one usually carries out adsorption-desorption temperature programmed desorption (TPD) experiments, and uses rate equation models to extract desorption energy distributions. However, the often-used rate equation models fail to adequately take into account diffusion processes and thus are only valid in situations where adsorption is strongly localized. As adsorption-desorption experiments show that adsorbate molecules tend to occupy deep adsorption sites before occupying shallow ones, a diffusion process must be involved. Thus, it is necessary to include a diffusion term in the model that takes into account the morphology of the surface as obtained from analyses of TPD experiments. We take the experimental data of CO desorption from the MgO(100) surface and of D2 desorption from amorphous solid water ice as examples to show how a diffusion-desorption rate equation model explains the redistribution of adsorbate molecules among different adsorption sites. We extract distributions of desorption energies and diffusion energy barriers from TPD profiles. These examples are contrasted with a system where adsorption is strongly localized--HD from an amorphous silicate surface. Suggestions for experimental investigations are provided.
Wang, T K; Wan, M Y; Ko, F H; Tseng, C L
2001-05-01
The radioactive tracer technique was applied to investigate the out-diffusion of the transition metals (Cu, Fe and Co) from deep ultraviolet (DUV) photoresist into underlying substrate. Two important process parameters, viz., baking temperatures and substrate types (i.e., bare silicon, polysilicon, silicon oxide and silicon nitride), were evaluated. Results indicate that the out-diffusion of Co is insignificant, irrespective of the substrate type and baking temperature. The out-diffusion of Cu is significant for substrates of bare silicon and polysilicon but not for silicon oxide and nitride; for Fe, the story is reversed. The substrate type appears to strongly affect the diffusion, while the baking temperature does not. Also, the effect of solvent evaporation was found to play an important role in impurity diffusion. Using the method of numerical analysis, a diffusion profile was depicted in this work to describe the out-diffusion of metallic impurities from photoresist layer under various baking conditions. In addition, the effectiveness of various wet-cleaning recipes in removing metallic impurities such as Cu, Fe and Co was also studied using the radioactive tracer technique. Among the six cleaning solutions studied, SC2 and SPM are the most effective in impurity removal. An out-diffusion cleaning model was first proposed to describe the cleaning process. A new cleaning coefficient, h(T), was suggested to explain the cleaning effect. The cleaning model could explain the tracer results.
Modelling oxygen self-diffusion in UO_{2} under pressure
Cooper, Michael William D.; Grimes, R. W.; Fitzpatrick, M. E.; Chroneos, A.
2015-10-22
Access to values for oxygen self-diffusion over a range of temperatures and pressures in UO_{2} is important to nuclear fuel applications. Here, elastic and expansivity data are used in the framework of a thermodynamic model, the cBΩ model, to derive the oxygen self-diffusion coefficient in UO_{2} over a range of pressures (0–10 GPa) and temperatures (300–1900 K). Furthermore, the significant reduction in oxygen self-diffusion as a function of increasing hydrostatic pressure, and the associated increase in activation energy, is identified.
Delay-induced Turing-like waves for one-species reaction-diffusion model on a network
NASA Astrophysics Data System (ADS)
Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio
2015-09-01
A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.
Efficient simulation of diffusion-based choice RT models on CPU and GPU.
Verdonck, Stijn; Meers, Kristof; Tuerlinckx, Francis
2016-03-01
In this paper, we present software for the efficient simulation of a broad class of linear and nonlinear diffusion models for choice RT, using either CPU or graphical processing unit (GPU) technology. The software is readily accessible from the popular scripting languages MATLAB and R (both 64-bit). The speed obtained on a single high-end GPU is comparable to that of a small CPU cluster, bringing standard statistical inference of complex diffusion models to the desktop platform.
Sigalotti, Leonardo Di G; Troconis, Jorge; Sira, Eloy; Peña-Polo, Franklin; Klapp, Jaime
2014-07-01
We study numerically liquid-vapor phase separation in two-dimensional, nonisothermal, van der Waals (vdW) liquid drops using the method of smoothed particle hydrodynamics (SPH). In contrast to previous SPH simulations of drop formation, our approach is fully adaptive and follows the diffuse-interface model for a single-component fluid, where a reversible, capillary (Korteweg) force is added to the equations of motion to model the rapid but smooth transition of physical quantities through the interface separating the bulk phases. Surface tension arises naturally from the cohesive part of the vdW equation of state and the capillary forces. The drop models all start from a square-shaped liquid and spinodal decomposition is investigated for a range of initial densities and temperatures. The simulations predict the formation of stable, subcritical liquid drops with a vapor atmosphere, with the densities and temperatures of coexisting liquid and vapor in the vdW phase diagram closely matching the binodal curve. We find that the values of surface tension, as determined from the Young-Laplace equation, are in good agreement with the results of independent numerical simulations and experimental data. The models also predict the increase of the vapor pressure with temperature and the fitting to the numerical data reproduces very well the Clausius-Clapeyron relation, thus allowing for the calculation of the vaporization pressure for this vdW fluid.
Shaviv, Avi; Raban, Smadar; Zaidel, Elina
2003-05-15
A comprehensive model describing the complex and "non-Fickian" (mathematically nonlinear) nature of the release from single granules of membrane coated, controlled release fertilizers (CRFs) is proposed consisting of three stages: i. a lag period during which water penetrates the coating of the granule dissolving part of the solid fertilizer in it ii. a period of linear release during which water penetration into and release out occur concomitantly while the total volume of the granules remains practically constant; and iii. a period of "decaying release", starting as the concentration inside the granule starts to decrease. A mathematical model was developed based on vapor and nutrient diffusion equations. The model predicts the release stages in terms of measurable geometrical and chemophysical parameters such as the following: the product of granule radius and coating thickness, water and solute permeability, saturation concentration of the fertilizer, and its density. The model successfully predicts the complex and "sigmoidal" pattern of release that is essential for matching plant temporal demand to ensure high agronomic and environmental effectiveness. It also lends itself to more complex statistical formulations which account for the large variability within large populations of coated CRFs and can serve for further improving CRF production and performance.
Marchal, D; Boireau, W; Laval, J M; Moiroux, J; Bourdillon, C
1998-01-01
The long-range diffusion coefficients of isoprenoid quinones in a model of lipid bilayer were determined by a method avoiding fluorescent probe labeling of the molecules. The quinone electron carriers were incorporated in supported dimyristoylphosphatidylcholine layers at physiological molar fractions (<3 mol%). The elaborate bilayer template contained a built-in gold electrode at which the redox molecules solubilized in the bilayer were reduced or oxidized. The lateral diffusion coefficient of a natural quinone like UQ10 or PQ9 was 2.0 +/- 0.4 x 10(-8) cm2 s(-1) at 30 degrees C, two to three times smaller than the diffusion coefficient of a lipid analog in the same artificial bilayer. The lateral mobilities of the oxidized or reduced forms could be determined separately and were found to be identical in the 4-13 pH range. For a series of isoprenoid quinones, UQ2 or PQ2 to UQ10, the diffusion coefficient exhibited a marked dependence on the length of the isoprenoid chain. The data fit very well the quantitative behavior predicted by a continuum fluid model in which the isoprenoid chains are taken as rigid particles moving in the less viscous part of the bilayer and rubbing against the more viscous layers of lipid heads. The present study supports the concept of a homogeneous pool of quinone located in the less viscous region of the bilayer. PMID:9545054
Improved Modeling of In Vivo Kinetics of Slowly Diffusing Radiotracers for Tumor Imaging
Wilks, Moses Q.; Knowles, Scott M.; Wu, Anna M.; Huang, Sung-Cheng
2015-01-01
Large-molecule tracers, such as labeled antibodies, have shown success in immuno-PET for imaging of specific cell surface biomarkers. However, previous work has shown that localization of such tracers shows high levels of heterogeneity in target tissues, due to both the slow diffusion and the high affinity of these compounds. In this work, we investigate the effects of subvoxel spatial heterogeneity on measured time–activity curves in PET imaging and the effects of ignoring diffusion limitation on parameter estimates from kinetic modeling. Methods Partial differential equations (PDE) were built to model a radially symmetric reaction-diffusion equation describing the activity of immuno-PET tracers. The effects of slower diffusion on measured time–activity curves and parameter estimates were measured in silico, and a modified Levenberg–Marquardt algorithm with Bayesian priors was developed to accurately estimate parameters from diffusion-limited data. This algorithm was applied to immuno-PET data of mice implanted with prostate stem cell antigen–overexpressing tumors and injected with 124I-labeled A11 anti–prostate stem cell antigen minibody. Results Slow diffusion of tracers in linear binding models resulted in heterogeneous localization in silico but no measurable differences in time–activity curves. For more realistic saturable binding models, measured time–activity curves were strongly dependent on diffusion rates of the tracers. Fitting diffusion-limited data with regular compartmental models led to parameter estimate bias in an excess of 1,000% of true values, while the new model and fitting protocol could accurately measure kinetics in silico. In vivo imaging data were also fit well by the new PDE model, with estimates of the dissociation constant (Kd) and receptor density close to in vitro measurements and with order of magnitude differences from a regular compartmental model ignoring tracer diffusion limitation. Conclusion Heterogeneous
NASA Astrophysics Data System (ADS)
Zhu, Haochen; Ghoufi, Aziz; Szymczyk, Anthony; Balannec, Béatrice; Morineau, Denis
2012-06-01
We report the self-diffusion coefficients and hindrance factor for the diffusion of ions into cylindrical hydrophilic silica nanopores (hydrated silica) determined from molecular dynamics (MD) simulations. We make a comparison with the hindered diffusion coefficients used in continuum-based models of nanofiltration (NF). Hindrance factors for diffusion estimated from the macroscopic hydrodynamic theory were found to be in fair quantitative agreement with MD simulations for a protonated pore, but they strongly overestimate diffusion inside a deprotonated pore.
Diffusion parameters of indium for silicon process modeling
NASA Astrophysics Data System (ADS)
Kizilyalli, I. C.; Rich, T. L.; Stevie, F. A.; Rafferty, C. S.
1996-11-01
The diffusion parameters of indium in silicon are investigated. Systematic diffusion experiments in dry oxidizing ambients at temperatures ranging from 800 to 1050 °C are conducted using silicon wafers implanted with indium. Secondary-ion-mass spectrometry (SIMS) is used to analyze the dopant distribution before and after heat treatment. The oxidation-enhanced diffusion parameter [R. B. Fair, in Semiconductor Materials and Process Technology Handbook, edited by G. E. McGuire (Noyes, Park Ridge, NJ, 1988); A. M. R. Lin, D. A. Antoniadis, and R. W. Dutton, J. Electrochem. Soc. Solid-State Sci. Technol. 128, 1131 (1981); D. A. Antoniadis and I. Moskowitz, J. Appl. Phys. 53, 9214 (1982)] and the segregation coefficient at the Si/SiO2 interface [R. B. Fair and J. C. C. Tsai, J. Electrochem. Soc. Solid-State Sci. Technol. 125, 2050 (1978)] (ratio of indium concentration in silicon to that in silicon dioxide) are extracted as a function of temperature using SIMS depth profiles and the silicon process simulator PROPHET [M. Pinto, D. M. Boulin, C. S. Rafferty, R. K. Smith, W. M. Coughran, I. C. Kizilyalli, and M. J. Thoma, in IEDM Technical Digest, 1992, p. 923]. It is observed that the segregation coefficient of indium at the Si/SiO2 interface is mIn≪1, similar to boron; however, unlike boron, the segregation coefficient of indium at the Si/SiO2 interface decreases with increasing temperature. Extraction results are summarized in analytical forms suitable for incorporation into other silicon process simulators. Finally, the validity of the extracted parameters is verified by comparing the simulated and measured SIMS profiles for an indium implanted buried-channel p-channel metal-oxide-semiconductor field-effect-transistor [I. C. Kizilyalli, F. A. Stevie, and J. D. Bude, IEEE Electron Device Lett. (1996)] process that involves a gate oxidation and various other thermal processes.
Microstructural models for diffusion MRI in breast cancer and surrounding stroma: an ex vivo study
Siow, Bernard; Panagiotaki, Eleftheria; Hipwell, John H.; Mertzanidou, Thomy; Owen, Julie; Gazinska, Patrycja; Pinder, Sarah E.; Alexander, Daniel C.; Hawkes, David J.
2016-01-01
The diffusion signal in breast tissue has primarily been modelled using apparent diffusion coefficient (ADC), intravoxel incoherent motion (IVIM) and diffusion tensor (DT) models, which may be too simplistic to describe the underlying tissue microstructure. Formalin‐fixed breast cancer samples were scanned using a wide range of gradient strengths, durations, separations and orientations. A variety of one‐ and two‐compartment models were tested to determine which best described the data. Models with restricted diffusion components and anisotropy were selected in most cancerous regions and there were no regions in which conventional ADC or DT models were selected. Maps of ADC generally related to cellularity on histology, but maps of parameters from more complex models suggest that both overall cell volume fraction and individual cell size can contribute to the diffusion signal, affecting the specificity of ADC to the tissue microstructure. The areas of coherence in diffusion anisotropy images were small, approximately 1 mm, but the orientation corresponded to stromal orientation patterns on histology. PMID:28000292
A diffuse plate boundary model for Indian Ocean tectonics
NASA Technical Reports Server (NTRS)
Wiens, D. A.; Demets, C.; Gordon, R. G.; Stein, S.; Argus, D.
1985-01-01
It is suggested that motion along the virtually aseismic Owen fracture zone is negligible, so that Arabia and India are contained within a single Indo-Arabian plate divided from the Australian plate by a diffuse boundary. The boundary is a zone of concentrated seismicity and deformation commonly characterized as 'intraplate'. The rotation vector of Australia relative to Indo-Arabia is consistent with the seismologically observed 2 cm/yr of left-lateral strike-slip along the Ninetyeast Ridge, north-south compression in the Central Indian Ocean, and the north-south extension near Chagos.
12 CFR Appendix A to Part 213 - Model Forms
Code of Federal Regulations, 2010 CFR
2010-01-01
... 12 Banks and Banking 2 2010-01-01 2010-01-01 false Model Forms A Appendix A to Part 213 Banks and Banking FEDERAL RESERVE SYSTEM BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM CONSUMER LEASING (REGULATION M) Pt. 213, App. A Appendix A to Part 213—Model Forms A-1Model Open-End or Finance Vehicle Lease Disclosures A-2Model Closed-End or...
Integrating O/S models during conceptual design, part 2
NASA Technical Reports Server (NTRS)
Ebeling, Charles E.
1994-01-01
This report documents the procedures for utilizing and maintaining the Reliability & Maintainability Model (RAM) developed by the University of Dayton for the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) under NASA research grant NAG-1-1327. The purpose of the grant is to provide support to NASA in establishing operational and support parameters and costs of proposed space systems. As part of this research objective, the model described here was developed. Additional documentation concerning the development of this model may be found in Part 1 of this report. This is the 2nd part of a 3 part technical report.
Sun, Jia; Zhang, Xiao-Peng; Li, Xiao-Ting; Tang, Lei; Cui, Yong; Zhang, Xiao-Yan; Sun, Ying-Shi
2014-01-01
In vivo imaging studies in animal models are hindered by variables that contribute to poor image quality and measurement reliability. As such we sought to improve the diffusion coefficient (ADC) of an orthotopic mouse model of gastric cancer in diffusion-weighted images (DWI) using alginate moulding and Ultrasonic coupling medium. BGC-823 human gastric cancer cells were subcutaneously injected into the abdomen of nude mice and 1 mm3 primary tumour was orthotopically transplanted. Alginate and coupling medium were applied to the mice and MRI (T2 and DWI) was performed for 6 weeks. Regions of interest (ROI) were drawn and liver and tumour ADC were evaluated. Using alginate moulding, the mean quality total score of DW imaging was 8.53; however, in control animals this value was 5.20 (p < 0.001). The coefficient of variation of ADC of liver in experimental and control groups were 0.071 and 0.270 (p < 0.001), respectively, suggesting this method may be helpful for DWI studies of important human diseases such as gastric cancer. PMID:25123166
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.
Bellassai, Debora; Spinazzola, Antonio; Silvestri, Stefano
2015-01-01
In absence of results of environmental monitoring to proceed with the assessment of occupational exposure, it was developed a model that retraces the one of Pasquill and Gifford, currently used for the estimation of concentrations of pollutants at certain distances from the source in outdoor environment. Purpose of the study is the quantitative estimate of the diffusion of airborne asbestos fibers in function of the distance from the source in an factory where railway carriages were produced during the period when asbestos was sprayed as insulator of the body. The treatment was carried out in a large shed without separation from other operations. The application of the model, given the characteristics of the emitting source, has allowed us to estimate the diffusion of particles inside the shed with an expected decrease in concentration inversely proportional to the distance from the source. By appropriate calculations the concentration by weight has been converted into number offibers by volume, the unit of measure currently used for the definition of asbestos pollution.
Nilsson, Markus; van Westen, Danielle; Ståhlberg, Freddy; Sundgren, Pia C; Lätt, Jimmy
2013-08-01
Biophysical models that describe the outcome of white matter diffusion MRI experiments have various degrees of complexity. While the simplest models assume equal-sized and parallel axons, more elaborate ones may include distributions of axon diameters and axonal orientation dispersions. These microstructural features can be inferred from diffusion-weighted signal attenuation curves by solving an inverse problem, validated in several Monte Carlo simulation studies. Model development has been paralleled by microscopy studies of the microstructure of excised and fixed nerves, confirming that axon diameter estimates from diffusion measurements agree with those from microscopy. However, results obtained in vivo are less conclusive. For example, the amount of slowly diffusing water is lower than expected, and the diffusion-encoded signal is apparently insensitive to diffusion time variations, contrary to what may be expected. Recent understandings of the resolution limit in diffusion MRI, the rate of water exchange, and the presence of microscopic axonal undulation and axonal orientation dispersions may, however, explain such apparent contradictions. Knowledge of the effects of biophysical mechanisms on water diffusion in tissue can be used to predict the outcome of diffusion tensor imaging (DTI) and of diffusion kurtosis imaging (DKI) studies. Alterations of DTI or DKI parameters found in studies of pathologies such as ischemic stroke can thus be compared with those predicted by modelling. Observations in agreement with the predictions strengthen the credibility of biophysical models; those in disagreement could provide clues of how to improve them. DKI is particularly suited for this purpose; it is performed using higher b-values than DTI, and thus carries more information about the tissue microstructure. The purpose of this review is to provide an update on the current understanding of how various properties of the tissue microstructure and the rate of water exchange
NASA Astrophysics Data System (ADS)
Paparella, F.; Oliveri, F.
2009-04-01
The interplay of advection, reaction and diffusion terms in ADR equations is a rather difficult one to be modeled numerically. The kind of spurious oscillations that is usually harmless for non-reacting scalars is often amplified without bounds by reaction terms. Furthermore, in most biogeochimical applications, such as mesoscale or global-scale plankton modeling, the diffusive fluxes may be smaller than the numerical ones. Inspired by the particle-mesh methods used by cosmologists, we propose to discretize on a grid only the diffusive term of the equation, and solve the advection-reaction terms as ordinary differential equations along the characteristic lines. Diffusion happens by letting the concentration field carried by each particle to relax towards the diffusive field known on the grid, without redistributing the particles. This method, in the limit of vanishing diffusivity and for a fixed mesh size, recovers the advection-reaction solution with no numerical diffusion. We show some example numerical solutions of the ADR equations stemming from a simple predator-prey model.
Comparison and analysis of theoretical models for diffusion-controlled dissolution.
Wang, Yanxing; Abrahamsson, Bertil; Lindfors, Lennart; Brasseur, James G
2012-05-07
Dissolution models require, at their core, an accurate diffusion model. The accuracy of the model for diffusion-dominated dissolution is particularly important with the trend toward micro- and nanoscale drug particles. Often such models are based on the concept of a "diffusion layer." Here a framework is developed for diffusion-dominated dissolution models, and we discuss the inadequacy of classical models that are based on an unphysical constant diffusion layer thickness assumption, or do not correctly modify dissolution rate due to "confinement effects": (1) the increase in bulk concentration from confinement of the dissolution process, (2) the modification of the flux model (the Sherwood number) by confinement. We derive the exact mathematical solution for a spherical particle in a confined fluid with impermeable boundaries. Using this solution, we analyze the accuracy of a time-dependent "infinite domain model" (IDM) and "quasi steady-state model" (QSM), both formally derived for infinite domains but which can be applied in approximate fashion to confined dissolution with proper adjustment of a concentration parameter. We show that dissolution rate is sensitive to the degree of confinement or, equivalently, to the total concentration C(tot). The most practical model, the QSM, is shown to be very accurate for most applications and, consequently, can be used with confidence in design-level dissolution models so long as confinement is accurately treated. The QSM predicts the ratio of diffusion layer thickness to particle radius (the Sherwood number) as a constant plus a correction that depends on the degree of confinement. The QSM also predicts that the time required for complete saturation or dissolution in diffusion-controlled dissolution experiments is singular (i.e., infinite) when total concentration equals the solubility. Using the QSM, we show that measured differences in dissolution rate in a diffusion-controlled dissolution experiment are a result of
The Diffuse Galactic Gamma-Ray Emission Model for GLAST LAT
Porter, T.A.; Digel, S.W.; Grenier, I.A.; Moskalenko, I.V.; Strong, A.W.; /Garching, Max Planck Inst., MPE
2007-06-13
Diffuse emission from the Milky Way dominates the gamma-ray sky. About 80% of the high-energy luminosity of the Milky Way comes from processes in the interstellar medium. The Galactic diffuse emission traces interactions of energetic particles, primarily protons and electrons, with the interstellar gas and radiation field, thus delivering information about cosmic-ray spectra and interstellar mass in distant locations. Additionally, the Galactic diffuse emission is the celestial foreground for the study of gamma-ray point sources and the extragalactic diffuse gamma-ray emission. We will report on the latest developments in the modeling of the Galactic diffuse emission, which will be used for the Gamma Ray Large Area Space Telescope (GLAST) investigations.
Quasilinear model for energetic particle diffusion in radial and velocity space
Waltz, R. E.; Staebler, G. M.; Bass, E. M.
2013-04-15
A quasilinear model for passive energetic particle (EP) turbulent diffusion in radial and velocity space is fitted and tested against nonlinear gyrokinetic tokamak simulations with the GYRO code [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)]. Off diagonal elements of a symmetric positive definite 2 Multiplication-Sign 2 EP diffusion matrix account for fluxes up radial (energy) gradients driven by energy (radial) gradients of the EP velocity space distribution function. The quasilinear ratio kernel of the model is provided by a simple analytic formula for the EP radial and velocity space EP diffusivity relative to radial thermal ion energy diffusivity at each linear mode of the turbulence driven by the thermal plasma. The TGLF [G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas 14, 0055909 (2007); ibid. 15, 0055908 (2008)] tokamak transport model provides the linear mode frequency and growth rates to the kernel as well as the nonlinear spectral weight for each mode.
Convergence of the binomial tree method for Asian options in jump-diffusion models
NASA Astrophysics Data System (ADS)
Kim, Kwang Ik; Qian, Xiao-Song
2007-06-01
The binomial tree methods (BTM), first proposed by Cox, Ross and Rubinstein [J. Cox, S. Ross, M. Rubinstein, Option pricing: A simplified approach, J. Finan. Econ. 7 (1979) 229-264] in diffusion models and extended by Amin [K.I. Amin, Jump diffusion option valuation in discrete time, J. Finance 48 (1993) 1833-1863] to jump-diffusion models, is one of the most popular approaches to pricing options. In this paper, we present a binomial tree method for Asian options in jump-diffusion models and show its equivalence to certain explicit difference scheme. Employing numerical analysis and the notion of viscosity solution, we prove the uniform convergence of the binomial tree method for European-style and American-style Asian options.
Analytic model for the runaway distribution function in the presence of spatial diffusion
Catto, P.J. Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 ); Myra, J.R. ); Wootton, A.J. )
1994-03-01
A steady-state kinetic model for runaway electrons in the presence of radial diffusion in a stochastic magnetic field is adopted and solved for a constant magnetic diffusivity. The model is constructed to recover the correct runaway production rate in the absence of spatial diffusion. The parallel energetic electron distribution function [ital f] is found by matching the solutions from three regions in parallel velocity space and is employed to form moments of [ital f]. Upper and lower bounds on the spatial diffusion are obtained by using these moments and the model exhibits the strong sensitivity to collisionality needed to explain the difference between similar plasmas with little or no hard x-ray signal and those with significant hard x-ray signals.
Garrido-Baserba, Manel; Sobhani, Reza; Asvapathanagul, Pitiporn; McCarthy, Graham W; Olson, Betty H; Odize, Victory; Al-Omari, Ahmed; Murthy, Sudhir; Nifong, Andrea; Godwin, Johnnie; Bott, Charles B; Stenstrom, Michael K; Shaw, Andrew R; Rosso, Diego
2017-03-15
This research systematically studied the behavior of aeration diffuser efficiency over time, and its relation to the energy usage per diffuser. Twelve diffusers were selected for a one year fouling study. Comprehensive aeration efficiency projections were carried out in two WRRFs with different influent rates, and the influence of operating conditions on aeration diffusers' performance was demonstrated. This study showed that the initial energy use, during the first year of operation, of those aeration diffusers located in high rate systems (with solids retention time - SRT-less than 2 days) increased more than 20% in comparison to the conventional systems (2 > SRT). Diffusers operating for three years in conventional systems presented the same fouling characteristics as those deployed in high rate processes for less than 15 months. A new procedure was developed to accurately project energy consumption on aeration diffusers; including the impacts of operation conditions, such SRT and organic loading rate, on specific aeration diffusers materials (i.e. silicone, polyurethane, EPDM, ceramic). Furthermore, it considers the microbial colonization dynamics, which successfully correlated with the increase of energy consumption (r(2):0.82 ± 7). The presented energy model projected the energy costs and the potential savings for the diffusers after three years in operation in different operating conditions. Whereas the most efficient diffusers provided potential costs spanning from 4900 USD/Month for a small plant (20 MGD, or 74,500 m(3)/d) up to 24,500 USD/Month for a large plant (100 MGD, or 375,000 m(3)/d), other diffusers presenting less efficiency provided spans from 18,000USD/Month for a small plant to 90,000 USD/Month for large plants. The aim of this methodology is to help utilities gain more insight into process mechanisms and design better energy efficiency strategies at existing facilities to reduce energy consumption.
Comparative evaluation of two simple diffuse reflectance models for biological tissue applications.
Zonios, George; Bassukas, Ioannis; Dimou, Aikaterini
2008-09-20
We present a comparative evaluation of two simple diffuse reflectance models for biological tissue applications. One model is based on a widely accepted and used in biomedical optics implementation of diffusion theory, and the other one is based on a semiempirical approach derived from basic physical principles. We test the models on tissue phantoms and on human skin, utilizing a standard six-around-one optical fiber probe for light delivery and collection. We show that both models are suitable for use with an optical fiber probe and illustrate the potential, applicability, and validity range of the models.
Perpendicular Diffusion of Solar Energetic Particles: Model Results and Implications for Electrons
NASA Astrophysics Data System (ADS)
Strauss, R. Du Toit; Dresing, Nina; Engelbrecht, N. Eugene
2017-03-01
The processes responsible for the effective longitudinal transport of solar energetic particles (SEPs) are still not completely understood. We address this issue by simulating SEP electron propagation using a spatially 2D transport model that includes perpendicular diffusion. By implementing, as far as possible, the most reasonable estimates of the transport (diffusion) coefficients, we compare our results, in a qualitative manner, to recent observations at energies of 55–105 keV, focusing on the longitudinal distribution of the peak intensity, the maximum anisotropy, and the onset time. By using transport coefficients that are derived from first principles, we limit the number of free parameters in the model to (i) the probability of SEPs following diffusing magnetic field lines, quantified by a\\in [0,1], and (ii) the broadness of the Gaussian injection function. It is found that the model solutions are extremely sensitive to the magnitude of the perpendicular diffusion coefficient and relatively insensitive to the form of the injection function as long as a reasonable value of a = 0.2 is used. We illustrate the effects of perpendicular diffusion on the model solutions and discuss the viability of this process as a dominant mechanism by which SEPs are transported in longitude. Lastly, we try to quantity the effectiveness of perpendicular diffusion as an interplay between the magnitude of the relevant diffusion coefficient and the SEP intensity gradient driving the diffusion process. It follows that perpendicular diffusion is extremely effective early in an SEP event when large intensity gradients are present, while the effectiveness quickly decreases with time thereafter.
Modelling the effect of diffuse light on canopy photosynthesis in controlled environments
NASA Technical Reports Server (NTRS)
Cavazzoni, James; Volk, Tyler; Tubiello, Francesco; Monje, Oscar; Janes, H. W. (Principal Investigator)
2002-01-01
A layered canopy model was used to analyze the effects of diffuse light on canopy gross photosynthesis in controlled environment plant growth chambers, where, in contrast to the field, highly diffuse light can occur at high irradiance. The model suggests that high diffuse light fractions (approximately 0.7) and irradiance (1400 micromoles m-2 s-1) may enhance crop life-cycle canopy gross photosynthesis for hydroponic wheat by about 20% compared to direct light at the same irradiance. Our simulations suggest that high accuracy is not needed in specifying diffuse light fractions in chambers between approximately 0.7 and 1, because simulated photosynthesis for closed canopies plateau in this range. We also examined the effect of leaf angle distribution on canopy photosynthesis under growth chamber conditions, as these distributions determine canopy extinction coefficients for direct and diffuse light. We show that the spherical leaf angle distribution is not suitable for modeling photosynthesis of planophile canopies (e.g., soybean and peanut) in growth chambers. Also, the absorption of the light reflected from the surface below the canopy should generally be included in model simulations, as the corresponding albedo values in the photosynthetically active range may be quite high in growth chambers (e.g., approximately 0.5). In addition to the modeling implications, our results suggest that diffuse light conditions should be considered when drawing conclusions from experiments in controlled environments.
Diffusion of a Sustainable Farming Technique in Sri Lanka: An Agent-Based Modeling Approach
NASA Astrophysics Data System (ADS)
Jacobi, J. H.; Gilligan, J. M.; Carrico, A. R.; Truelove, H. B.; Hornberger, G.
2012-12-01
We live in a changing world - anthropogenic climate change is disrupting historic climate patterns and social structures are shifting as large scale population growth and massive migrations place unprecedented strain on natural and social resources. Agriculture in many countries is affected by these changes in the social and natural environments. In Sri Lanka, rice farmers in the Mahaweli River watershed have seen increases in temperature and decreases in precipitation. In addition, a government led resettlement project has altered the demographics and social practices in villages throughout the watershed. These changes have the potential to impact rice yields in a country where self-sufficiency in rice production is a point of national pride. Studies of the climate can elucidate physical effects on rice production, while research on social behaviors can illuminate the influence of community dynamics on agricultural practices. Only an integrated approach, however, can capture the combined and interactive impacts of these global changes on Sri Lankan agricultural. As part of an interdisciplinary team, we present an agent-based modeling (ABM) approach to studying the effects of physical and social changes on farmers in Sri Lanka. In our research, the diffusion of a sustainable farming technique, the system of rice intensification (SRI), throughout a farming community is modeled to identify factors that either inhibit or promote the spread of a more sustainable approach to rice farming. Inputs into the ABM are both physical and social and include temperature, precipitation, the Palmer Drought Severity Index (PDSI), community trust, and social networks. Outputs from the ABM demonstrate the importance of meteorology and social structure on the diffusion of SRI throughout a farming community.
Balcom, B J; Petersen, N O
1993-01-01
We have systematically investigated the probe size and shape dependence of lateral diffusion in model dimyristoyl phosphatidylcholine membranes. Linear hydrophobic polymers, which differ in length by an order of magnitude, were used to explore the effect on the lateral diffusion coefficient of hydrodynamic restrictions in the bilayer interior. The polymers employed are isoprenoid alcohols--citronellol, solanesol, and dolichol. Tracer lateral diffusion coefficients were measured by fluorescence photobleaching recovery. Despite the large difference in lengths, the nitrobenzoxadiazole labelled alcohols all diffuse at the rate of lipid self-diffusion (5.0 x 10(-12) m2 s-1, 29 degrees C) in the liquid crystal phase. Companion measurements in isotropic polymer solution, in gel phase lipid membranes and with nonpolar fluorescent polyaromatic hydrocarbons, show a marked dependence of the lateral diffusion coefficient on the probe molecule size. Our results in the liquid crystal phase are in accord with free area theory which asserts that lateral diffusion in the membrane is restricted by the surface-free area. Probe molecules which are significantly longer than the host phospholipid, seven times longer in the case of dolichol, are still restricted in their lateral motion by the surface properties of the bilayer in the liquid crystal phase. Fluorescence quenching experiments indicate that the nitrobenzoxadiazole label does not reside at the aqueous interface, although it must reside in close proximity according to the diffusion measurements. PMID:8218892
MO-G-BRF-07: Anomalously Fast Diffusion of Carbon Nanotubes Carriers in 3D Tissue Model
Wang, Y; Bahng, J; Kotov, N
2014-06-15
Purpose: We aim to investigate and understand diffusion process of carbon nanotubes (CNTs) and other nanoscale particles in tissue and organs. Methods: In this research, we utilized a 3D model tissue of hepatocellular carcinoma (HCC)cultured in inverted colloidal crystal (ICC) scaffolds to compare the diffusivity of CNTs with small molecules such as Rhodamine and FITC in vitro, and further investigated the transportation of CNTs with and without targeting ligand, TGFβ1. The real-time permeation profiles of CNTs in HCC tissue model with high temporal and spatial resolution was demonstrated by using standard confocal microscopy. Quantitative analysis of the diffusion process in 3D was carried out using luminescence intensity in a series of Z-stack images obtained for different time points of the diffusion process after initial addition of CNTs or small molecules to the cell culture and the image data was analyzed by software ImageJ and Mathematica. Results: CNTs display diffusion rate in model tissues substantially faster than small molecules of the similar charge such as FITC, and the diffusion rate of CNTs are significantly enhanced with targeting ligand, TGFβ1. Conclusion: In terms of the advantages of in-vitro model, we were able to have access to measuring the rate of CNT penetration at designed conditions with variable parameters. And the findings by using this model, changed our understanding about advantages of CNTs as nanoscale drug carriers and provides design principles for making new drug carriers for both treatment and diagnostics. Additionally the fast diffusion opens the discussion of the best possible drug carriers to reach deep parts of cancerous tissues, which is often a prerequisite for successful cancer treatment. This work was supported by the Center for Photonic and Multiscale Nanomaterials funded by National Science Foundation Materials Research Science and Engineering Center program DMR 1120923. The work was also partially supported by NSF
Compartment models of the diffusion MR signal in brain white matter: a taxonomy and comparison.
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.
A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks
Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan
2015-01-01
Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest. PMID:25491372
King, M.D.; Burkardt, N.; Clark, B.T.
2006-01-01
Recent literature on the diffusion of innovations concentrates either specifically on public adoption of policy, where social or environmental conditions are the dependent variables for adoption, or on private adoption of an innovation, where emphasis is placed on the characteristics of the innovation itself. This article uses both the policy diffusion literature and the diffusion of innovation literature to assess watershed management councils' decisions to adopt, or not adopt, scientific models. Watershed management councils are a relevant case study because they possess both public and private attributes. We report on a survey of councils in the United States that was conducted to determine the criteria used when selecting scientific models for studying watershed conditions. We found that specific variables from each body of literature play a role in explaining the choice to adopt scientific models by these quasi-public organizations. The diffusion of innovation literature contributes to an understanding of how organizations select models by confirming the importance of a model's ability to provide better data. Variables from the policy diffusion literature showed that watershed management councils that employ consultants are more likely to use scientific models. We found a gap between those who create scientific models and those who use these models. We recommend shrinking this gap through more communication between these actors and advancing the need for developers to provide more technical assistance.
Nowacki, P.; Samson, P.J.; Sillman, S.
1996-10-01
It is shown that Urban Airshed Model (UAM-IV) calculated air pollutant concentrations during photochemical smog episodes in Atlanta, Georgia, depend strongly on the numerical parameterization of the daytime vertical diffusivity. Results found suggest that vertical mixing is overestimated by the UAM-IV during unstable daytime conditions, as calculated vertical diffusivity values exceed measured and comparable literature values. Although deviations between measured and UAM-IV calculated air pollutant concentrations may only in part be due the UAM-IV diffusivity parameterization, results indicate the large error potential in vertical diffusivity parameterization. Easily implemented enhancements to UAM-IV algorithms are proposed, thus improving UAM-IV modeling performance during unstable stratification. 38 refs., 14 figs., 1 tab.
Development of a convective diffusion model for lead pipe rigs operating in laminar flow.
Cardew, P T
2006-06-01
As part of achieving lower lead standards water undertakers are utilising lead pipe rigs to quantify the benefit of treatment measures. A convective diffusion model is developed for lead pipe rigs operating in laminar flow, and applied to the three operating steps of flushing, sampling and stagnation. The model is used to determine the appropriate time-scales for each stage, and the sensitivity of the measure to variations in flow-rate. In contrast to rigs operating in turbulent flow the average lead observed leaving the pipe and that in the pipe, after a period of stagnation, are substantially different. Equations are derived for both, and take into account the residual distribution of lead left in the pipe after flushing. It is shown that the lead concentration observed leaving the pipe is well approximated by a single exponential term in contrast to the concentration within the pipe. Predictions are made on the residual lead concentration that can be achieved through flushing, and its dependence on flow-rate. The relevance of the laminar flow model to that in domestic lead pipes is discussed.
12 CFR Appendix A to Part 213 - Model Forms
Code of Federal Regulations, 2011 CFR
2011-01-01
... (REGULATION M) Pt. 213, App. A Appendix A to Part 213—Model Forms A-1Model Open-End or Finance Vehicle Lease Disclosures A-2Model Closed-End or Net Vehicle Lease Disclosures A-3Model Furniture Lease Disclosures...
17 CFR Appendix A to Part 160 - Model Privacy Form
Code of Federal Regulations, 2010 CFR
2010-04-01
... notice, to meet the content requirements of the privacy notice and opt-out notice set forth in §§ 160.6 and 160.7 of this part. (b) The model form is a standardized form, including page layout, content... the model form, as appropriate. 2. The Contents of the Model Privacy Form The model form consists...
McAuley, W J; Lad, M D; Mader, K T; Santos, P; Tetteh, J; Kazarian, S G; Hadgraft, J; Lane, M E
2010-02-01
The uptake and diffusion of solvents across polymer membranes is important in controlled drug delivery, effects on drug uptake into, for example, infusion bags and containers, as well as transport across protective clothing. Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) spectroscopy has been used to monitor the effects of different solvents on the diffusion of a model compound, 4-cyanophenol (CNP) across silicone membrane and on the equilibrium concentration of CNP obtained in the membrane following diffusion. ATR-FTIR spectroscopic imaging of membrane diffusion was used to gain an understanding of when the boundary conditions applied to Fick's second law, used to model the diffusion of permeants across the silicone membrane do not hold. The imaging experiments indicated that when the solvent was not taken up appreciably into the membrane, the presence of discrete solvent pools between the ATR crystal and the silicone membrane can affect the diffusion profile of the permeant. This effect is more significant if the permeant has a high solubility in the solvent. In contrast, solvents that are taken up into the membrane to a greater extent, or those where the solubility of the permeant in the vehicle is relatively low, were found to show a good fit to the diffusion model. As such these systems allow the ATR-FTIR spectroscopic approach to give mechanistic insight into how the particular solvents enhance permeation. The solubility of CNP in the solvent and the uptake of the solvent into the membrane were found to be important influences on the equilibrium concentration of the permeant obtained in the membrane following diffusion. In general, solvents which were taken up to a significant extent into the membrane and which caused the membrane to swell increased the diffusion coefficient of the permeant in the membrane though other factors such as solvent viscosity may also be important.
Diffusion of a collaborative care model in primary care: a longitudinal qualitative study
2013-01-01
Background Although collaborative team models (CTM) improve care processes and health outcomes, their diffusion poses challenges related to difficulties in securing their adoption by primary care clinicians (PCPs). The objectives of this study are to understand: (1) how the perceived characteristics of a CTM influenced clinicians' decision to adopt -or not- the model; and (2) the model's diffusion process. Methods We conducted a longitudinal case study based on the Diffusion of Innovations Theory. First, diffusion curves were developed for all 175 PCPs and 59 nurses practicing in one borough of Paris. Second, semi-structured interviews were conducted with a representative sample of 40 PCPs and 15 nurses to better understand the implementation dynamics. Results Diffusion curves showed that 3.5 years after the start of the implementation, 100% of nurses and over 80% of PCPs had adopted the CTM. The dynamics of the CTM's diffusion were different between the PCPs and the nurses. The slopes of the two curves are also distinctly different. Among the nurses, the critical mass of adopters was attained faster, since they adopted the CTM earlier and more quickly than the PCPs. Results of the semi-structured interviews showed that these differences in diffusion dynamics were mostly founded in differences between the PCPs' and the nurses' perceptions of the CTM's compatibility with norms, values and practices and its relative advantage (impact on patient management and work practices). Opinion leaders played a key role in the diffusion of the CTM among PCPs. Conclusion CTM diffusion is a social phenomenon that requires a major commitment by clinicians and a willingness to take risks; the role of opinion leaders is key. Paying attention to the notion of a critical mass of adopters is essential to developing implementation strategies that will accelerate the adoption process by clinicians. PMID:23289966
Wang, Jing
2013-01-11
We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. A strict single-file (no passing) constraint occurs in the diffusion within such narrow pores. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice–gas model for this reaction–diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction–diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction–diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion (SFD) in this multispecies system. Noting the shortcomings of mf-RDE and h-RDE, we then develop a generalized hydrodynamic (GH) formulation of appropriate gh-RDE which incorporates an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The gh-RDE elucidate the non-exponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth. Then an extended model of a catalytic conversion reaction within a functionalized nanoporous material is developed to assess the effect of varying the reaction product – pore interior interaction from attractive to repulsive. The analysis is performed utilizing the generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport for both irreversible and reversible reactions.
Modeling of tower relief dynamics: Part 1
Cassata, J.R.; Dasgupta, S.; Gandhi, S.L. )
1993-10-01
In an environmentally responsible, safe and health-conscious design, a relief system must contain all relieving gases or vapors. The system must include treatment of these gases or vapors in a flare, scrubber or other appropriate device prior to discharge to the atmosphere. The benefit of a dynamic simulation is most significant in designing these systems. Dynamic modeling provides accurate answers to key questions which must be addressed. It identifies the design-setting relief scenario for any possible upset such as loss of reflux, power failure, loss of cooling water, fire, etc. It accurately quantifies the maximum relief rate and time dependency of the relief rates. This permits a safe relief system design that is not overly conservative.
A novel rumor diffusion model considering the effect of truth in online social media
NASA Astrophysics Data System (ADS)
Sun, Ling; Liu, Yun; Zeng, Qing-An; Xiong, Fei
2015-12-01
In this paper, we propose a model to investigate how truth affects rumor diffusion in online social media. Our model reveals a relation between rumor and truth — namely, when a rumor is diffusing, the truth about the rumor also diffuses with it. Two patterns of the agents used to identify rumor, self-identification and passive learning are taken into account. Combining theoretical proof and simulation analysis, we find that the threshold value of rumor diffusion is negatively correlated to the connectivity between nodes in the network and the probability β of agents knowing truth. Increasing β can reduce the maximum density of the rumor spreaders and slow down the generation speed of new rumor spreaders. On the other hand, we conclude that the best rumor diffusion strategy must balance the probability of forwarding rumor and the probability of agents losing interest in the rumor. High spread rate λ of rumor would lead to a surge in truth dissemination which will greatly limit the diffusion of rumor. Furthermore, in the case of unknown λ, increasing β can effectively reduce the maximum proportion of agents who do not know the truth, but cannot narrow the rumor diffusion range in a certain interval of β.
Diffusion of Tritiated Water (HTO) Through Compacted Bentonite Clay : Mechanisms and Modeling
NASA Astrophysics Data System (ADS)
Bourg, I. C.; Bourg, A. C.; Sposito, G.
2002-12-01
Diffusion through microporous materials has long been tackled with common tools of hydrogeological investigation, adapted to materials with a larger pore size. Parameters such as the porosity, tortuosity and adsorption coefficients are still usually defined as if there were a clear boundary between the free pore water and the solid phase. We suggest that a closer look at the structure of microporous materials is necessary and can yield successful mechanistic models of diffusion. Our case study is the diffusion of tritiated water (HTO) through compacted bentonite clay. In compacted bentonite, due to the high montmorillonite content of bentonite, the pore water is in intimate contact with the surface and most of the microporous water solvates the exchangeable cations. Despite this, HTO diffusion is often used as a non-reactive tracer to probe the pore geometry of compacted clay, yielding very high tortuosity coefficients (up to 40-60, far above the expected 3 for a random array of flat pores). We describe a model that accounts for the dual porosity of compacted bentonite (interlayer and inter-aggregate pores) and the higher viscosity of water in montmorillonite interlayers. This model successfully predicts HTO diffusion through bentonites with different montmorillonite contents (from 50 to 100 %) in a wide range of bulk dry densities (up to 2.0 kg/L). The model has no adjustable parameters. This is important to the diffusion of all other species through compacted bentonite clays, because models of the diffusion of reactive species are generally built on the geometric pore properties derived from the diffusion of "non-reactive" species such as HTO.
Solution of classical evolutionary models in the limit when the diffusion approximation breaks down
NASA Astrophysics Data System (ADS)
Saakian, David B.; Hu, Chin-Kun
2016-10-01
The discrete time mathematical models of evolution (the discrete time Eigen model, the Moran model, and the Wright-Fisher model) have many applications in complex biological systems. The discrete time Eigen model rather realistically describes the serial passage experiments in biology. Nevertheless, the dynamics of the discrete time Eigen model is solved in this paper. The 90% of results in population genetics are connected with the diffusion approximation of the Wright-Fisher and Moran models. We considered the discrete time Eigen model of asexual virus evolution and the Wright-Fisher model from population genetics. We look at the logarithm of probabilities and apply the Hamilton-Jacobi equation for the models. We define exact dynamics for the population distribution for the discrete time Eigen model. For the Wright-Fisher model, we express the exact steady state solution and fixation probability via the solution of some nonlocal equation then give the series expansion of the solution via degrees of selection and mutation rates. The diffusion theories result in the zeroth order approximation in our approach. The numeric confirms that our method works in the case of strong selection, whereas the diffusion method fails there. Although the diffusion method is exact for the mean first arrival time, it provides incorrect approximation for the dynamics of the tail of distribution.
Model coupling intraparticle diffusion/sorption, nonlinear sorption, and biodegradation processes
Karapanagioti, Hrissi K.; Gossard, Chris M.; Strevett, Keith A.; Kolar, Randall L.; Sabatini, David A.
2001-01-01
Diffusion, sorption and biodegradation are key processes impacting the efficiency of natural attenuation. While each process has been studied individually, limited information exists on the kinetic coupling of these processes. In this paper, a model is presented that couples nonlinear and nonequilibrium sorption (intraparticle diffusion) with biodegradation kinetics. Initially, these processes are studied independently (i.e., intraparticle diffusion, nonlinear sorption and biodegradation), with appropriate parameters determined from these independent studies. Then, the coupled processes are studied, with an initial data set used to determine biodegradation constants that were subsequently used to successfully predict the behavior of a second data set. The validated model is then used to conduct a sensitivity analysis, which reveals conditions where biodegradation becomes desorption rate-limited. If the chemical is not pre-equilibrated with the soil prior to the onset of biodegradation, then fast sorption will reduce aqueous concentrations and thus biodegradation rates. Another sensitivity analysis demonstrates the importance of including nonlinear sorption in a coupled diffusion/sorption and biodegradation model. While predictions based on linear sorption isotherms agree well with solution concentrations, for the conditions evaluated this approach overestimates the percentage of contaminant biodegraded by as much as 50%. This research demonstrates that nonlinear sorption should be coupled with diffusion/sorption and biodegradation models in order to accurately predict bioremediation and natural attenuation processes. To our knowledge this study is unique in studying nonlinear sorption coupled with intraparticle diffusion and biodegradation kinetics with natural media.
A hybrid transport-diffusion model for radiative transfer in absorbing and scattering media
NASA Astrophysics Data System (ADS)
Roger, M.; Caliot, C.; Crouseilles, N.; Coelho, P. J.
2014-10-01
A new multi-scale hybrid transport-diffusion model for radiative transfer is proposed in order to improve the efficiency of the calculations close to the diffusive regime, in absorbing and strongly scattering media. In this model, the radiative intensity is decomposed into a macroscopic component calculated by the diffusion equation, and a mesoscopic component. The transport equation for the mesoscopic component allows to correct the estimation of the diffusion equation, and then to obtain the solution of the linear radiative transfer equation. In this work, results are presented for stationary and transient radiative transfer cases, in examples which concern solar concentrated and optical tomography applications. The Monte Carlo and the discrete-ordinate methods are used to solve the mesoscopic equation. It is shown that the multi-scale model allows to improve the efficiency of the calculations when the medium is close to the diffusive regime. The proposed model is a good alternative for radiative transfer at the intermediate regime where the macroscopic diffusion equation is not accurate enough and the radiative transfer equation requires too much computational effort.
A model for surface diffusion of trans-membrane proteins on lipid bilayers
NASA Astrophysics Data System (ADS)
Agrawal, Ashutosh; Steigmann, David J.
2011-06-01
The equilibrium theory of lipid membranes is modified to include the effects of a continuous distribution of trans-membrane proteins. These influence membrane shape and evolve in accordance with a diffusive balance law. The model is purely mechanical in the absence of the proteins. Conditions ensuring energy dissipation in the presence of diffusion are given and an example constitutive function is used to simulate the coupled inertia-less interplay between membrane shape and protein distribution. The work extends an earlier continuum theory of equilibrium configurations of composite lipid-protein membranes to accommodate surface diffusion.
Using a Quasipotential Transformation for Modeling Diffusion Media inPolymer-Electrolyte Fuel Cells
Weber, Adam Z.; Newman, John
2008-08-29
In this paper, a quasipotential approach along with conformal mapping is used to model the diffusion media of a polymer-electrolyte fuel cell. This method provides a series solution that is grid independent and only requires integration along a single boundary to solve the problem. The approach accounts for nonisothermal phenomena, two-phase flow, correct placement of the electronic potential boundary condition, and multilayer media. The method is applied to a cathode diffusion medium to explore the interplay between water and thermal management and performance, the impact of the rib-to-channel ratio, and the existence of diffusion under the rib and flooding phenomena.
Assessing cognitive processes with diffusion model analyses: a tutorial based on fast-dm-30
Voss, Andreas; Voss, Jochen; Lerche, Veronika
2015-01-01
Diffusion models can be used to infer cognitive processes involved in fast binary decision tasks. The model assumes that information is accumulated continuously until one of two thresholds is hit. In the analysis, response time distributions from numerous trials of the decision task are used to estimate a set of parameters mapping distinct cognitive processes. In recent years, diffusion model analyses have become more and more popular in different fields of psychology. This increased popularity is based on the recent development of several software solutions for the parameter estimation. Although these programs make the application of the model relatively easy, there is a shortage of knowledge about different steps of a state-of-the-art diffusion model study. In this paper, we give a concise tutorial on diffusion modeling, and we present fast-dm-30, a thoroughly revised and extended version of the fast-dm software (Voss and Voss, 2007) for diffusion model data analysis. The most important improvement of the fast-dm version is the possibility to choose between different optimization criteria (i.e., Maximum Likelihood, Chi-Square, and Kolmogorov-Smirnov), which differ in applicability for different data sets. PMID:25870575
Time-varying boundaries for diffusion models of decision making and response time
Zhang, Shunan; Lee, Michael D.; Vandekerckhove, Joachim; Maris, Gunter; Wagenmakers, Eric-Jan
2014-01-01
Diffusion models are widely-used and successful accounts of the time course of two-choice decision making. Most diffusion models assume constant boundaries, which are the threshold levels of evidence that must be sampled from a stimulus to reach a decision. We summarize theoretical results from statistics that relate distributions of decisions and response times to diffusion models with time-varying boundaries. We then develop a computational method for finding time-varying boundaries from empirical data, and apply our new method to two problems. The first problem involves finding the time-varying boundaries that make diffusion models equivalent to the alternative sequential sampling class of accumulator models. The second problem involves finding the time-varying boundaries, at the individual level, that best fit empirical data for perceptual stimuli that provide equal evidence for both decision alternatives. We discuss the theoretical and modeling implications of using time-varying boundaries in diffusion models, as well as the limitations and potential of our approach to their inference. PMID:25538642
NASA Astrophysics Data System (ADS)
Ingo, Carson; Sui, Yi; Chen, Yufen; Parrish, Todd; Webb, Andrew; Ronen, Itamar
2015-03-01
In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.
Film model approximation for particle-diffusion-controlled binary ion exchange
Carta, G.; Cincotti, A.; Cao, G.
1999-01-01
A new rate expression for particle-diffusion-controlled ion exchange, based on an equivalent pseudosteady-state film resistance model, is developed. The rate expression approximates the electric field effects on intraparticle diffusion in spherical ion-exchangers. With regard to the prediction of batch exchange and column breakthrough curves for both irreversible and reversible processes, the model captures the essential traits of the coupled diffusion phenomenon described by the Nernst-Planck equation with results of accuracy comparable to that obtained when using the linear driving force approximation for systems with constant diffusivity. Numerical results for the exchange of two counterions of equal valence are presented as application examples for different mobility ratios and selectivity coefficients.
Sershen, Cheryl L; Plimpton, Steven J; May, Elebeoba E
2014-01-01
This paper describes a method for incorporating a diffusion field modeling oxygen usage and dispersion in a multi-scale model of Mycobacterium tuberculosis (Mtb) infection mediated granuloma formation. We implemented this method over a floating-point field to model oxygen dynamics in host tissue during chronic phase response and Mtb persistence. The method avoids the requirement of satisfying the Courant-Friedrichs-Lewy (CFL) condition, which is necessary in implementing the explicit version of the finite-difference method, but imposes an impractical bound on the time step. Instead, diffusion is modeled by a matrix-based, steady state approximate solution to the diffusion equation. Presented in figure 1 is the evolution of the diffusion profiles of a containment granuloma over time.
Plimpton, Steven J.; Sershen, Cheryl L.; May, Elebeoba E.
2015-01-01
This paper describes a method for incorporating a diffusion field modeling oxygen usage and dispersion in a multi-scale model of Mycobacterium tuberculosis (Mtb) infection mediated granuloma formation. We implemented this method over a floating-point field to model oxygen dynamics in host tissue during chronic phase response and Mtb persistence. The method avoids the requirement of satisfying the Courant-Friedrichs-Lewy (CFL) condition, which is necessary in implementing the explicit version of the finite-difference method, but imposes an impractical bound on the time step. Instead, diffusion is modeled by a matrix-based, steady state approximate solution to the diffusion equation. Moreover, presented in figuremore » 1 is the evolution of the diffusion profiles of a containment granuloma over time.« less
Plimpton, Steven J.; Sershen, Cheryl L.; May, Elebeoba E.
2015-01-01
This paper describes a method for incorporating a diffusion field modeling oxygen usage and dispersion in a multi-scale model of Mycobacterium tuberculosis (Mtb) infection mediated granuloma formation. We implemented this method over a floating-point field to model oxygen dynamics in host tissue during chronic phase response and Mtb persistence. The method avoids the requirement of satisfying the Courant-Friedrichs-Lewy (CFL) condition, which is necessary in implementing the explicit version of the finite-difference method, but imposes an impractical bound on the time step. Instead, diffusion is modeled by a matrix-based, steady state approximate solution to the diffusion equation. Moreover, presented in figure 1 is the evolution of the diffusion profiles of a containment granuloma over time.
NASA Astrophysics Data System (ADS)
Ver Eecke, H. C.; Oslowski, D. M.; Butterfield, D. A.; Olson, E. J.; Lilley, M. D.; Holden, J. F.
2009-12-01
In 2008 and 2009, 534 hydrothermal fluid samples and 5 actively-venting black smoker chimneys were collected using Alvin for correlative microbiological and chemical analyses as part of the Endeavour Segment and Axial Volcano Geochemistry and Ecology Research (EAGER) program. Hyperthermophilic, autotrophic Fe(III) oxide reducers, methanogens, and sulfur-reducing heterotrophs were enriched for at 85 and 95°C using most-probable-number estimates from 28 diffuse fluid and 8 chimney samples. Heterotrophs were the most abundant of the three groups in both diffuse fluids and black-smoker chimneys. Iron reducers were more abundant than methanogens, and more abundant in sulfide-hosted vents than in basalt-hosted vents. Fluid chemistry suggests that there is net biogenic methanogenesis at the Marker 113/62 diffuse vent at Axial Volcano but nowhere else sampled. The growth of hyperthermophilic methanogens and heterotrophs was modeled in the lab using pure cultures. Methanocaldococcus jannaschii grew at 82°C in a 2-liter reactor with continuous gas flow at H2 concentrations between 20 and 225 µM with a H2 km of 100 µM. Correlating H2 end-member mixing curves from vent fluids and seawater with our laboratory modeling study suggests that H2 concentrations are limiting for Methanocaldococcus growth at most Mothra, Main Field, and High Rise vent sites at Endeavour but sufficient to support growth at some Axial Volcano vents. Therefore, hyperthermophilic methanogens may depend on H2 syntrophy at low H2 sites. Twenty-one pure hyperthermophilic heterotroph strains each grew on α-1,4 and β-1,4 linked sugars and polypeptides with concomitant H2 production. The H2 production rate (cell-1 doubling-1) for Pyrococcus furiosus at 95°C without sulfur was 29 fmol, 36 fmol, and 53 fmol for growth on α-1,4 sugars, β-1,4 sugars, and peptides, respectively. The CH4 production rate for M. jannaschii was 390 fmol cell-1 doubling-1; therefore, we estimate that it would take approximately
Parameter-free continuous drift-diffusion models of amorphous organic semiconductors.
Kordt, Pascal; Stodtmann, Sven; Badinski, Alexander; Al Helwi, Mustapha; Lennartz, Christian; Andrienko, Denis
2015-09-21
Continuous drift-diffusion models are routinely used to optimize organic semiconducting devices. Material properties are incorporated into these models via dependencies of diffusion constants, mobilities, and injection barriers on temperature, charge density, and external field. The respective expressions are often provided by the generic Gaussian disorder models, parametrized on experimental data. We show that this approach is limited by the fixed range of applicability of analytic expressions as well as approximations inherent to lattice models. To overcome these limitations we propose a scheme which first tabulates simulation results performed on small-scale off-lattice models, corrects for finite size effects, and then uses the tabulated mobility values to solve the drift-diffusion equations. The scheme is tested on DPBIC, a state of the art hole conductor for organic light emitting diodes. We find a good agreement between simulated and experimentally measured current-voltage characteristics for different film thicknesses and temperatures.
NASA Astrophysics Data System (ADS)
Winkelmann, Stefanie; Schütte, Christof
2016-12-01
Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments, and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented.
Modeling and Uncertainty Quantification of Vapor Sorption and Diffusion in Heterogeneous Polymers
Sun, Yunwei; Harley, Stephen J.; Glascoe, Elizabeth A.
2015-08-13
A high-fidelity model of kinetic and equilibrium sorption and diffusion is developed and exercised. The gas-diffusion model is coupled with a triple-sorption mechanism: Henry’s law absorption, Langmuir adsorption, and pooling or clustering of molecules at higher partial pressures. Sorption experiments are conducted and span a range of relative humidities (0-95 %) and temperatures (30-60 °C). Kinetic and equilibrium sorption properties and effective diffusivity are determined by minimizing the absolute difference between measured and modeled uptakes. Uncertainty quantification and sensitivity analysis methods are described and exercised herein to demonstrate the capability of this modeling approach. Water uptake in silica-filled and unfilled poly(dimethylsiloxane) networks is investigated; however, the model is versatile enough to be used with a wide range of materials and vapors.
Ocampo-Perez, Raul; Leyva-Ramos, Roberto; Mendoza-Barron, Jovita; Guerrero-Coronado, Rosa M
2011-12-01
The concentration decay curves for the adsorption of phenol on organobentonite were obtained in an agitated tank batch adsorber. The experimental adsorption rate data were interpreted with diffusional models as well as first-order, second-order and Langmuir kinetic models. The surface diffusion model adjusted the data quite well, revealing that the overall rate of adsorption was controlled by surface diffusion. Furthermore, the surface diffusion coefficient increased raising the mass of phenol adsorbed at equilibrium and was independent of the particle diameter in the range 0.042-0.0126 cm. It was demonstrated that the overall rate of adsorption was essentially not affected by the external mass transfer. The second-order and the Langmuir kinetic models fitted the experimental data quite well; however, the kinetic constants of both models varied without any physical meaning while increasing the particle size and the mass of phenol adsorbed at equilibrium.
A marginalized two-part model for semicontinuous data.
Smith, Valerie A; Preisser, John S; Neelon, Brian; Maciejewski, Matthew L
2014-12-10
In health services research, it is common to encounter semicontinuous data characterized by a point mass at zero followed by a right-skewed continuous distribution with positive support. Examples include health expenditures, in which the zeros represent a subpopulation of patients who do not use health services, while the continuous distribution describes the level of expenditures among health services users. Semicontinuous data are typically analyzed using two-part mixture models that separately model the probability of health services use and the distribution of positive expenditures among users. However, because the second part conditions on a non-zero response, conventional two-part models do not provide a marginal interpretation of covariate effects on the overall population of health service users and non-users, even though this is often of greatest interest to investigators. Here, we propose a marginalized two-part model that yields more interpretable effect estimates in two-part models by parameterizing the model in terms of the marginal mean. This model maintains many of the important features of conventional two-part models, such as capturing zero-inflation and skewness, but allows investigators to examine covariate effects on the overall marginal mean, a target of primary interest in many applications. Using a simulation study, we examine properties of the maximum likelihood estimates from this model. We illustrate the approach by evaluating the effect of a behavioral weight loss intervention on health-care expenditures in the Veterans Affairs health-care system.
Combustor diffuser interaction program
NASA Technical Reports Server (NTRS)
Srinivasan, Ram; Thorp, Daniel
1986-01-01
Advances in gas turbine engine performance are achieved by using compressor systems with high stage loading and low part count, which result in high exit Mach numbers. The diffuser and combustor systems in such engines should be optimized to reduce system pressure loss and to maximize the engine thrust-to-weight ratio and minimize length. The state-of-the-art combustor-diffuser systems do not meet these requirements. Detailed understanding of the combustor-diffuser flow field interaction is required for designing advanced gas turbine engines. An experimental study of the combustor-diffuser interaction (CDI) is being conducted to obtain data for the evaluation and improvement of analytical models applicable to a wide variety of diffuser designs. The CDI program consists of four technical phases: Literature Search; Baseline Configuration; Parametric Configurations; and Performance Configurations. Phase 2 of the program is in progress.
NASA Astrophysics Data System (ADS)
Yuste, S. B.; Abad, E.; Baumgaertner, A.
2016-07-01
We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ ,P (ℓ ) ˜ℓ-(1 +α ) (α >0 ). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.
2015-01-01
proposed. 3.1. Sequential Diffusion Filter ( SDF ). The sequential diffu- sion filter ( SDF ) scheme is similar to the S3DVar method derived by Xie et al...17]. The SDF scheme uses a sequence of 3DVars to obtain the final estimation to retrieve information from all wavelengths from long- to shortwaves...in turn. The matrix is modeled by applying the diffusion filter sequentially in and direction, respectively. SDF begins its sequence with a
Yuste, S B; Abad, E; Baumgaertner, A
2016-07-01
We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ,P(ℓ)∼ℓ^{-(1+α)} (α>0). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.
Testing and modeling of diffusion bonded prototype optical windows under ITER conditions
Jacobs, M.; Van Oost, G.; Degrieck, J.; De Baere, I.; Gusarov, A.; Gubbels, F.; Massaut, V.
2011-07-01
Glass-metal joints are a part of ITER optical diagnostics windows. These joints must be leak tight for the safety (presence of tritium in ITER) and to preserve the vacuum. They must also withstand the ITER environment: temperatures up to 220 deg.C and fast neutron fluxes of {approx}3.10{sup 9} n/cm{sup 2}.s. At the moment, little information is available about glass-metal joints suitable for ITER. Therefore, we performed mechanical and thermal tests on some prototypes of an aluminium diffusion bonded optical window. Finite element modeling with Abaqus code was used to understand the experimental results. The prototypes were helium leaking probably due to very tiny cracks in the interaction layer between the steel and the aluminium. However, they were all able to withstand a thermal cycling test up to 200 deg. C; no damage could be seen after the tests by visual inspection. The prototypes successfully passed push-out test with a 500 N load. During the destructive push-out tests the prototypes broke at a 6-12 kN load between the aluminium layer and the steel or the glass, depending on the surface quality of the glass. The microanalysis of the joints has also been performed. The finite element modeling of the push-out tests is in a reasonable agreement with the experiments. According to the model, the highest thermal stress is created in the aluminium layer. Thus, the aluminium joint seems to be the weakest part of the prototypes. If this layer is improved, it will probably make the prototype helium leak tight and as such, a good ITER window candidate. (authors)
Hierarchical Diffusion Models for Two-Choice Response Times
ERIC Educational Resources Information Center
Vandekerckhove, Joachim; Tuerlinckx, Francis; Lee, Michael D.
2011-01-01
Two-choice response times are a common type of data, and much research has been devoted to the development of process models for such data. However, the practical application of these models is notoriously complicated, and flexible methods are largely nonexistent. We combine a popular model for choice response times--the Wiener diffusion…
NASA Astrophysics Data System (ADS)
Porth, O.; Vorster, M. J.; Lyutikov, M.; Engelbrecht, N. E.
2016-08-01
We study the transport of high-energy particles in pulsar wind nebulae (PWN) using three-dimensional magnetohydrodynamic (MHD) and test-particle simulations, as well as a Fokker-Planck particle transport model. The latter includes radiative and adiabatic losses, diffusion, and advection on the background flow of the simulated MHD nebula. By combining the models, the spatial evolution of flux and photon index of the X-ray synchrotron emission is modelled for the three nebulae G21.5-0.9, the inner regions of Vela, and 3C 58, thereby allowing us to derive governing parameters: the magnetic field strength, average flow velocity, and spatial diffusion coefficient. For comparison, the nebulae are also modelled with the semi-analytic Kennel & Coroniti model but the Porth et al. model generally yields better fits to the observational data. We find that high velocity fluctuations in the turbulent nebula (downstream of the termination shock) give rise to efficient diffusive transport of particles, with average Péclet number close to unity, indicating that both advection and diffusion play an important role in particle transport. We find that the diffusive transport coefficient of the order of ˜ 2 × 1027(Ls/0.42 Ly) cm2 s- 1 (Ls is the size of the termination shock) is independent of energy up to extreme particle Lorentz factors of γp ˜ 1010.
Ocean Turbulence I: One-Point Closure Model Momentum and Heat Vertical Diffusivities
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Howard, A.; Cheng, Y.; Dubovikov, M. S.
1999-01-01
Since the early forties, one-point turbulence closure models have been the canonical tools used to describe turbulent flows in many fields. In geophysics, Mellor and Yamada applied such models using the 1980 state-of-the art. Since then, no improvements were introduced to alleviate two major difficulties: 1) closure of the pressure correlations, which affects the correct determination of the critical Richardson number Ri(sub cr) above which turbulent mixing is no longer possible and 2) the need to express the non-local third-order moments (TOM) in terms of lower order moments rather than via the down-gradient approximation as done thus far, since the latter seriously underestimates the TOMs. Since 1) and 2) are still being dealt with adjustable parameters which weaken the credibility of the models, alternative models, not based on turbulence modeling, have been suggested. The aim of this paper is to show that new information, partly derived from the newest 2-point closure model discussed, can be used to solve these shortcomings. The new one-point closure model, which in its simplest form is algebraic and thus simple to implement, is first shown to reproduce a variety of data. Then, it is used in a Ocean-General Circulation Model (O-GCM) where it reproduces well a large variety of ocean data. While phenomenological models are specifically tuned to ocean turbulence, the present model is not. It is first tested against laboratory data on stably stratified flows and then used in an O-GCM. It is more general, more predictive and more resilient, e.g., it can incorporate phenomena like wave-breaking at the surface, salinity diffusivity, non-locality, etc. One important feature that naturally comes out of the new model is that the predicted Richardson critical value Ri(sub cr) is Ri (sub cr approx. = 1) in agreement with both Large Eddy Simulations (LES) and empirical evidence while all previous models predicted Ri (sub cr approx. = 0.2) which led to a considerable
McMillan, S.A.; Werth, C.J.
1999-07-01
A new model was developed to determine if reduced uptake rates observed during isotope exchange experiments could plausibly be attributed to sterically hindered counter-diffusion in one-dimensional micropores. During exchange experiments, hydrogenated trichloroethylene ({sup 1}HTCE) was displaced with deuterated TCE (DTCE) in the slow-desorbing sites of a silica gel, a groundwater sediment, and a clay and silt fraction. To describe this process, the model accounts for co- and counter-diffusion of TCE isotopes in one-dimensional micropores, where each micropore type is defined by a single codiffusion rate constant and a single counter-diffusion rate constant. For silica gel, isotope exchange was simulated in a single micropore type. For geosorbents, isotope exchange was simulated in a distribution of micropore types characterized by a {gamma} distribution of diffusion rate constants. Simulation results indicate that (1) the proposed model accounts for the mechanisms controlling isotope exchange in the silica gel and the groundwater sediment and (2) the rate of counter-diffusion is up to 6 times slower than the rate of codiffusion. This suggests that steric hindrance between counter-diffusing sorbates can significantly affect mass transfer and, consequently, the transport of chemical mixtures in the subsurface.
Analysis of key parameters in a diffusion type beach profile evolution model
NASA Astrophysics Data System (ADS)
Karunarathna, Harshinie; Horrillo-Caraballo, Jose M.; Spivack, Mark; Reeve, Dominic E.
2011-02-01
Diffusion type formulations are commonly used in beach profile evolution models. The practical idea behind that is to map the behaviour of the beach profile onto a simple mathematical model that exhibits the same behaviour under defined operating conditions. The success of this approach is based on the accurate determination of key parameters in the diffusion model that govern its behaviour, using observed beach behaviour in the field. In order to determine these parameters, i.e. diffusion coefficient and a time and space varying source function, we used observations of historic beach profiles at Milford-on-Sea beach in Christchurch Bay, Dorset, United Kingdom. The relationship between the diffusion coefficient and Dean's equilibrium profile was investigated, leading to a new interpretation of the diffusion coefficient in terms of the sediment characteristics. The analysis also shows the significance of the diffusion process in the medium to long term evolution of the beach profile. A canonical correlation analysis (CCA) was undertaken in order to identify patterns of behaviour between wave conditions and source terms, and the possible correlations between them. The analysis provides strong evidence of a useful link between the source term in the simple dynamical equation and the distribution of wave steepness.
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Dubovikov, M. S.; Howard, A.; Cheng, Y.
1999-01-01
In papers 1 and 2 we have presented the results of the most updated 1-point closure model for the turbulent vertical diffusivities of momentum, heat and salt, K(sub m,h,s). In this paper, we derive the analytic expressions for K(sub m,h,s) using a new 2-point closure model that has recently been developed and successfully tested against some approx. 80 turbulence statistics for different flows. The new model has no free parameters. The expressions for K(sub m, h. s) are analytical functions of two stability parameters: the Turner number R(sub rho) (salinity gradient/temperature gradient) and the Richardson number R(sub i) (temperature gradient/shear). The turbulent kinetic energy K and its rate of dissipation may be taken local or non-local (K-epsilon model). Contrary to all previous models that to describe turbulent mixing below the mixed layer (ML) have adopted three adjustable "background diffusivities" for momentum. heat and salt, we propose a model that avoids such adjustable diffusivities. We assume that below the ML, K(sub m,h,s) have the same functional dependence on R(sub i) and R(sub rho) derived from the turbulence model. However, in order to compute R(sub i) below the ML, we use data of vertical shear due to wave-breaking measured by Gargett et al. (1981). The procedure frees the model from adjustable background diffusivities and indeed we use the same model throughout the entire vertical extent of the ocean. Using the new K(sub m,h, s), we run an O-GCM and present a variety of results that we compare with Levitus and the KPP model. Since the traditional 1-point (used in papers 1 and 2) and the new 2-point closure models used here represent different modeling philosophies and procedures, testing them in an O-GCM is indispensable. The basic motivation is to show that the new 2-point closure model gives results that are overall superior to the 1-point closure in spite of the fact that the latter rely on several adjustable parameters while the new 2-point
Numerical study of a macroscopic finite pulse model of the diffusion MRI signal.
Li, Jing-Rebecca; Nguyen, Hang Tuan; Nguyen, Dang Van; Haddar, Houssem; Coatléven, Julien; Le Bihan, Denis
2014-11-01
Diffusion magnetic resonance imaging (dMRI) is an imaging modality that probes the diffusion characteristics of a sample via the application of magnetic field gradient pulses. The dMRI signal from a heterogeneous sample includes the contribution of the water proton magnetization from all spatial positions in a voxel. If the voxel can be spatially divided into different Gaussian diffusion compartments with inter-compartment exchange governed by linear kinetics, then the dMRI signal can be approximated using the macroscopic Karger model, which is a system of coupled ordinary differential equations (ODEs), under the assumption that the duration of the diffusion-encoding gradient pulses is short compared to the diffusion time (the narrow pulse assumption). Recently, a new macroscopic model of the dMRI signal, without the narrow pulse restriction, was derived from the Bloch-Torrey partial differential equation (PDE) using periodic homogenization techniques. When restricted to narrow pulses, this new homogenized model has the same form as the Karger model. We conduct a numerical study of the new homogenized model for voxels that are made up of periodic copies of a representative volume that contains spherical and cylindrical cells of various sizes and orientations and show that the signal predicted by the new model approaches the reference signal obtained by solving the full Bloch-Torrey PDE in O(ε(2)), where ε is the ratio between the size of the representative volume and a measure of the diffusion length. When the narrow gradient pulse assumption is not satisfied, the new homogenized model offers a much better approximation of the full PDE signal than the Karger model. Finally, preliminary results of applying the new model to a voxel that is not made up of periodic copies of a representative volume are shown and discussed.
A novel approach to modelling water transport and drug diffusion through the stratum corneum
2010-01-01
Background The potential of using skin as an alternative path for systemically administering active drugs has attracted considerable interest, since the creation of novel drugs capable of diffusing through the skin would provide a great step towards easily applicable -and more humane- therapeutic solutions. However, for drugs to be able to diffuse, they necessarily have to cross a permeability barrier: the stratum corneum (SC), the uppermost set of skin layers. The precise mechanism by which drugs penetrate the skin is generally thought to be diffusion of molecules through this set of layers following a "tortuous pathway" around corneocytes, i.e. impermeable dead cells. Results In this work, we simulate water transport and drug diffusion using a three-dimensional porous media model. Our numerical simulations show that diffusion takes place through the SC regardless of the direction and magnitude of the fluid pressure gradient, while the magnitude of the concentrations calculated are consistent with experimental studies. Conclusions Our results support the possibility for designing arbitrary drugs capable of diffusing through the skin, the time-delivery of which is solely restricted by their diffusion and solubility properties. PMID:20716360
Modelling and simulating reaction-diffusion systems using coloured Petri nets.
Liu, Fei; Blätke, Mary-Ann; Heiner, Monika; Yang, Ming
2014-10-01
Reaction-diffusion systems often play an important role in systems biology when developmental processes are involved. Traditional methods of modelling and simulating such systems require substantial prior knowledge of mathematics and/or simulation algorithms. Such skills may impose a challenge for biologists, when they are not equally well-trained in mathematics and computer science. Coloured Petri nets as a high-level and graphical language offer an attractive alternative, which is easily approachable. In this paper, we investigate a coloured Petri net framework integrating deterministic, stochastic and hybrid modelling formalisms and corresponding simulation algorithms for the modelling and simulation of reaction-diffusion processes that may be closely coupled with signalling pathways, metabolic reactions and/or gene expression. Such systems often manifest multiscaleness in time, space and/or concentration. We introduce our approach by means of some basic diffusion scenarios, and test it against an established case study, the Brusselator model.
Anomalous diffusion for bed load transport with a physically-based model
NASA Astrophysics Data System (ADS)
Fan, N.; Singh, A.; Foufoula-Georgiou, E.; Wu, B.
2013-12-01
Diffusion of bed load particles shows both normal and anomalous behavior for different spatial-temporal scales. Understanding and quantifying these different types of diffusion is important not only for the development of theoretical models of particle transport but also for practical purposes, e.g., river management. Here we extend a recently proposed physically-based model of particle transport by Fan et al. [2013] to further develop an Episodic Langevin equation (ELE) for individual particle motion which reproduces the episodic movement (start and stop) of sediment particles. Using the proposed ELE we simulate particle movements for a large number of uniform size particles, incorporating different probability distribution functions (PDFs) of particle waiting time. For exponential PDFs of waiting times, particles reveal ballistic motion in short time scales and turn to normal diffusion at long time scales. The PDF of simulated particle travel distances also shows a change in its shape from exponential to Gamma to Gaussian with a change in timescale implying different diffusion scaling regimes. For power-law PDF (with power - μ) of waiting times, the asymptotic behavior of particles at long time scales reveals both super-diffusion and sub-diffusion, however, only very heavy tailed waiting times (i.e. 1.0 < μ < 1.5) could result in sub-diffusion. We suggest that the contrast between our results and previous studies (for e.g., studies based on fractional advection-diffusion models of thin/heavy tailed particle hops and waiting times) results could be due the assumption in those studies that the hops are achieved instantaneously, but in reality, particles achieve their hops within finite times (as we simulate here) instead of instantaneously, even if the hop times are much shorter than waiting times. In summary, this study stresses on the need to rethink the alternative models to the previous models, such as, fractional advection-diffusion equations, for studying
Modeling convective core overshoot and diffusion in Procyon constrained by asteroseismic data
Guenther, D. B.; Gruberbauer, M.; Demarque, P.
2014-06-01
We compare evolved stellar models, which match Procyon's mass and position in the HR diagram, to current ground-based asteroseismic observations. Diffusion of helium and metals along with two conventional core overshoot descriptions and the Kuhfuss nonlocal theory of convection are considered. We establish that one of the two published asteroseismic data reductions for Procyon, which mainly differ in their identification of even versus odd l values, is a significantly more probable and self-consistent match to our models than the other. The most probable models according to our Bayesian analysis have evolved to just short of turnoff, still retaining a hydrogen convective core. Our most probable models include Y and Z diffusion and have conventional core overshoot between 0.9 and 1.5 pressure scale heights, which increases the outer radius of the convective core by between 36% and 43%, respectively. We discuss the significance of this comparatively higher than expected core overshoot amount in terms of internal mixing during evolution. The parameters of our most probable models are similar regardless of whether adiabatic or nonadiabatic model p-mode frequencies are compared to the observations, although, the Bayesian probabilities are greater when the nonadiabatic model frequencies are used. All the most probable models (with or without core overshoot, adiabatic or nonadiabatic model frequencies, diffusion or no diffusion, including priors for the observed HRD location and mass or not) have masses that are within 1σ of the observed mass 1.497 ± 0.037 M {sub ☉}.
Empirical models relating viscosity and tracer diffusion in magmatic silicate melts
NASA Astrophysics Data System (ADS)
Mungall, James E.
2002-01-01
The Adam-Gibbs equations describing relaxation in silicate melts are applied to diffusion of trace components of multicomponent liquids. The Adam-Gibbs theory is used as a starting point to derive an explicit relation between viscosity and diffusion including non-Arrhenian temperature dependence. The general form of the equation is Diη = Aiexp{Δ( scEi)/ TSc}, where D is diffusivity, η is melt viscosity, T is absolute temperature, Δ( scEi) is the difference between the products of activation energies and local configurational entropies for viscous and diffusive relaxation, Ai is a constant that depends on the characteristics of the diffusing solute particles, and Sc is configurational entropy of the melt. The general equation will be impractical for most predictive purposes due to the paucity of configurational entropy data for silicate melts. Under most magmatic conditions the proposed non-Arrhenian behaviour can be neglected, allowing the general equation to be simplified to a generalized form of the Eyring equation to describe diffusion of solutes that interact weakly with the melt structure: Diη/ T = Qiexp{Δ Ei/ RT}, where Qi and Δ Ei depend on the characteristics of the solute and the melt structure. If the diffusing solute interacts strongly with the melt structure or is a network-forming cation itself, then Δ Ei = 0, and the relation between viscosity and diffusion has the functional form of the classic Eyring and Stokes-Einstein equations; Diη/ T = Qi. If the diffusing solute can make diffusive jumps without requiring cooperative rearrangement of the melt structure, the diffusivity is entirely decoupled from melt viscosity and should be Arrhenian, i.e., Di = Qiexp{ Bi/ T}. A dataset of 594 published diffusivities in melts ranging from the system CAS through diopside, basalt, andesite, anhydrous rhyolite, hydrous rhyolite, and peralkaline rhyolite to albite, orthoclase, and jadeite is compared with the model equations. Alkali diffusion is completely
Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption
Chirkunov, Yu. A.
2015-10-15
We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential
Forecasting turbulent modes with nonparametric diffusion models: Learning from noisy data
NASA Astrophysics Data System (ADS)
Berry, Tyrus; Harlim, John
2016-04-01
In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the availability of a noise-free training data set observing the full state space of the dynamics, in real applications we often have only partial observations which are corrupted by noise. To alleviate these practical issues, following the theory of embedology, the diffusion model is built using the delay-embedding coordinates of the data. We show that this delay embedding biases the geometry of the data in a way which extracts the most stable component of the dynamics and reduces the influence of independent additive observation noise. The resulting diffusion forecast model approximates the semigroup solutions of the generator of the underlying dynamics in the limit of large data and when the observation noise vanishes. As in any standard forecasting problem, the forecasting skill depends crucially on the accuracy of the initial conditions. We introduce a novel Bayesian method for filtering the discrete-time noisy observations which works with the diffusion forecast to determine the forecast initial densities. Numerically, we compare this nonparametric approach with standard stochastic parametric models on a wide-range of well-studied turbulent modes, including the Lorenz-96 model in weakly chaotic to fully turbulent regimes and the barotropic modes of a quasi-geostrophic model with baroclinic instabilities. We show that when the only available data is the low-dimensional set of noisy modes that are being modeled, the diffusion forecast is indeed competitive to the perfect model.
12 CFR Appendix A to Part 233 - Model Notice
Code of Federal Regulations, 2010 CFR
2010-01-01
... FUNDING OF UNLAWFUL INTERNET GAMBLING (REGULATION GG) Part 233, App. A Appendix A to Part 233—Model Notice Re: U.S. Unlawful Internet Gambling Enforcement Act Notice Dear : On , U.S. government officials informed us that your institution processed payments through our facilities for Internet...
12 CFR Appendix A to Part 233 - Model Notice
Code of Federal Regulations, 2011 CFR
2011-01-01
... FUNDING OF UNLAWFUL INTERNET GAMBLING (REGULATION GG) Part 233, App. A Appendix A to Part 233—Model Notice Re: U.S. Unlawful Internet Gambling Enforcement Act Notice Dear : On , U.S. government officials informed us that your institution processed payments through our facilities for Internet...
Tariné Gombkŏtö, Z; Molnár, J; Farkasné Gunics, G; Regdon, G; Selmeczi, B
1992-11-01
After the physical parameters had been determined, the in vitro drug liberation from vaginal suppositories containing 100 mg of antibacterial agent (sulphadimine, chloramphenicol, gentamicin-sulphate) was studied by membrane diffusion and microbiological methods. Among the vehicles available in Hungary the hydrophylic Massa macrogoli was found to be the best for this purpose. Among the lipophilic bases the in vitro drug liberation of the French Suppocire NA product was significantly better (p < 0.05) compared to the other lipophilic bases. This vehicle is recommended by the authors for the topical treatment of vaginitis, as these suppositories have the further advantage that they can easily be produced on a magistral, galenical or industrial scale as well. In the first part of the publication the formulation and some important physical parameters of lipophilic and hydrophilic antibacterial suppositories for vaginal use were described. In the present paper the drug liberation ability of the compositions with proper physical parameters was studied. The published results were obtained from measurements performed 1 week after formulation.
Radiation transport phenomena and modeling. Part A: Codes; Part B: Applications with examples
Lorence, L.J. Jr.; Beutler, D.E.
1997-09-01
This report contains the notes from the second session of the 1997 IEEE Nuclear and Space Radiation Effects Conference Short Course on Applying Computer Simulation Tools to Radiation Effects Problems. Part A discusses the physical phenomena modeled in radiation transport codes and various types of algorithmic implementations. Part B gives examples of how these codes can be used to design experiments whose results can be easily analyzed and describes how to calculate quantities of interest for electronic devices.
Validation of fast diffusion kurtosis MRI for imaging acute ischemia in a rodent model of stroke
Sun, Phillip Zhe; Wang, Yu; Mandeville, Emiri; Chan, Suk-Tak; Lo, Eng H; Ji, Xunming
2014-01-01
Diffusion-weighted imaging (DWI) captures ischemic tissue that is likely to infarct, and has become one of the most widely used acute stroke imaging techniques. Diffusion kurtosis imaging (DKI) has lately been postulated as a complementary MRI method to stratify the heterogeneously damaged DWI lesion. However, the conventional DKI acquisition time is relatively long, limiting its use in the acute stroke setting. Recently, Hansen et al. proposed a fast kurtosis mapping method and demonstrated it in fixed brains and control subjects. The fast DKI approach provides mean diffusion and kurtosis measurements under substantially reduced scan time, making it amenable to acute stroke imaging. Because it is not practical to obtain and compare different means of DKI to test whether the fast DKI method can reliably detect diffusion and kurtosis lesions in acute stroke patients, our study investigated its diagnostic value using an animal model of acute stroke, a critical step before fast DKI acquisition can be routinely applied in the acute stroke setting. We found significant correlation, per voxel, between the diffusion and kurtosis coefficients measured using the fast and conventional DKI protocols. In acute stroke rats, both DKI methods yielded diffusion and kurtosis lesions that were in good agreement. Importantly, substantial kurtosis/diffusion lesion mismatch was observed using the conventional (26±13%, P<0.01) and fast DKI methods (23±8%, P<0.01). In addition, regression analysis showed that the kurtosis/diffusion lesion mismatch obtained using conventional and fast DKI methods were substantially correlated (R2=0.57, P=0.02). Our results confirmed that the recently proposed fast DKI method is capable of capturing heterogeneous diffusion and kurtosis lesions in acute ischemic stroke, and thus is suitable for translational applications in the acute stroke clinical setting. PMID:25208309
Validation of fast diffusion kurtosis MRI for imaging acute ischemia in a rodent model of stroke.
Sun, Phillip Zhe; Wang, Yu; Mandeville, Emiri; Chan, Suk-Tak; Lo, Eng H; Ji, Xunming
2014-11-01
Diffusion-weighted imaging (DWI) captures ischemic tissue that is likely to infarct, and has become one of the most widely used acute stroke imaging techniques. Diffusion kurtosis imaging (DKI) has lately been postulated as a complementary MRI method to stratify the heterogeneously damaged DWI lesion. However, the conventional DKI acquisition time is relatively long, limiting its use in the acute stroke setting. Recently, a fast kurtosis mapping method has been demonstrated in fixed brains and control subjects. The fast DKI approach provides mean diffusion and kurtosis measurements under substantially reduced scan time, making it amenable to acute stroke imaging. Because it is not practical to obtain and compare different means of DKI to test whether the fast DKI method can reliably detect diffusion and kurtosis lesions in acute stroke patients, our study investigated its diagnostic value using an animal model of acute stroke, a critical step before fast DKI acquisition can be routinely applied in the acute stroke setting. We found significant correlation, per voxel, between the diffusion and kurtosis coefficients measured using the fast and conventional DKI protocols. In acute stroke rats, the two DKI methods yielded diffusion and kurtosis lesions that were in good agreement. Importantly, substantial kurtosis-diffusion lesion mismatch was observed using the conventional (26 ± 13%, P < 0.01) and fast DKI methods (23 ± 8%, P < 0.01). In addition, regression analysis showed that the kurtosis-diffusion lesion mismatches obtained using conventional and fast DKI methods were substantially correlated (R(2) = 0.57, P = 0.02). Our results confirmed that the recently proposed fast DKI method is capable of capturing heterogeneous diffusion and kurtosis lesions in acute ischemic stroke, and thus is suitable for translational applications in the acute stroke clinical setting.
NASA Astrophysics Data System (ADS)
Akimoto, Takuma; Yamamoto, Eiji
2016-12-01
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of single-particle-tracking measurements. Irreproducibility of time-averaged observables has been theoretically studied in the context of weak ergodicity breaking in stochastic processes. Here, we provide rigorous descriptions of equilibrium and non-equilibrium diffusion processes for the annealed transit time model, which is a heterogeneous diffusion model in living cells. We give analytical solutions for the mean square displacement (MSD) and the relative standard deviation of the time-averaged MSD for equilibrium and non-equilibrium situations. We find that the time-averaged MSD grows linearly with time and that the time-averaged diffusion coefficients are intrinsically random (irreproducible) even in the long-time measurements in non-equilibrium situations. Furthermore, the distribution of the time-averaged diffusion coefficients converges to a universal distribution in the sense that it does not depend on initial conditions. Our findings pave the way for a theoretical understanding of distributional behavior of the time-averaged diffusion coefficients in disordered systems.
Rare events and their impact on velocity diffusion in a stochastic Fermi-Ulam model.
Karlis, A K; Diakonos, F K; Constantoudis, V; Schmelcher, P
2008-10-01
A simplified version of the stochastic Fermi-Ulam model is investigated in order to elucidate the effect of a class of rare low-velocity events on the velocity diffusion process and consequently Fermi acceleration. The relative fraction of these events, for sufficiently large times, decreases monotonically with increasing variance of the magnitude of the particle velocity. However, a treatment of the diffusion problem which totally neglects these events, gives rise to a glaring inconsistency associated with the mean value of the magnitude of the velocity in the ensemble. We propose a general scheme for treating the diffusion process in velocity space, which succeeds in capturing the effect of the low-velocity events on the diffusion, providing a consistent description of the acceleration process. The present study exemplifies the influence of low-probability events on the transport properties of time-dependent billiards.
Volume concentration and size dependence of diffuse reflectance in a fractal soft tissue model.
Sharma, S K; Banerjee, Srilekha
2005-06-01
Employing a fractal model for the particle size distribution, we examine the possibility of relating the size/volume concentration changes in the tissue to its diffuse reflectance. It is noted that for the practically interesting range of fractal dimension values alpha, the curves depicting the variation of diffuse reflectance (the ratio of diffuse reflectance at two suitably chosen source detector separations) with alpha at fixed volume concentration Tv, are single valued. The same is true if alpha is fixed and Tv is varied. This crucial observation shows that it should be possible to identify changes in the size/volume concentration of the tissue from the diffuse reflectance measurement at two source detector separations when either alpha or Tv is a priori known. Similar results have been obtained for ratio of fluence measured at two suitably chosen depths within the tissue.
Fractional motion model for characterization of anomalous diffusion from NMR signals.
Fan, Yang; Gao, Jia-Hong
2015-07-01
Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.
Fractional motion model for characterization of anomalous diffusion from NMR signals
NASA Astrophysics Data System (ADS)
Fan, Yang; Gao, Jia-Hong
2015-07-01
Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.
Proposing an Educational Scaling-and-Diffusion Model for Inquiry-Based Learning Designs
ERIC Educational Resources Information Center
Hung, David; Lee, Shu-Shing
2015-01-01
Education cannot adopt the linear model of scaling used by the medical sciences. "Gold standards" cannot be replicated without considering process-in-learning, diversity, and student-variedness in classrooms. This article proposes a nuanced model of educational scaling-and-diffusion, describing the scaling (top-down supports) and…
A time-periodic reaction-diffusion epidemic model with infection period
NASA Astrophysics Data System (ADS)
Zhang, Liang; Wang, Zhi-Cheng
2016-10-01
In this paper, we propose a time-periodic and diffusive SIR epidemic model with constant infection period. By introducing the basic reproduction number R_0 via a next generation operator for this model, we show that the disease goes extinction if R_0 < 1; while the disease is uniformly persistent if R_0 > 1.
NASA Astrophysics Data System (ADS)
Wang, Mingxin; Pang, Peter Y. H.; Chen, Wenyan
2008-10-01
This paper studies positive steady-state solutions of the diffusive Holling-Tanner prey-predator model in heterogeneous environments subject to the homogeneous Neumann boundary condition. In particular, it investigates the appearance of sharp spatial patterns arising from degeneracies of the model.
Barbante, Paolo; Frezzotti, Aldo; Gibelli, Livio
2014-12-09
The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviations of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.
A ranking of diffusion MRI compartment models with in vivo human brain data
Ferizi, Uran; Schneider, Torben; Panagiotaki, Eleftheria; Nedjati-Gilani, Gemma; Zhang, Hui; Wheeler-Kingshott, Claudia A M; Alexander, Daniel C
2014-01-01
Purpose Diffusion magnetic resonance imaging (MRI) microstructure imaging provides a unique noninvasive probe into tissue microstructure. The technique relies on biophysically motivated mathematical models, relating microscopic tissue features to the magnetic resonance (MR) signal. This work aims to determine which compartment models of diffusion MRI are best at describing measurements from in vivo human brain white matter. Methods Recent work shows that three compartment models, designed to capture intra-axonal, extracellular, and isotropically restricted diffusion, best explain multi-b-value data sets from fixed rat corpus callosum. We extend this investigation to in vivo by using a live human subject on a clinical scanner. The analysis compares models of one, two, and three compartments and ranks their ability to explain the measured data. We enhance the original methodology to further evaluate the stability of the ranking. Results As with fixed tissue, three compartment models explain the data best. However, a clearer hierarchical structure and simpler models emerge. We also find that splitting the scanning into shorter sessions has little effect on the ranking of models, and that the results are broadly reproducible across sessions. Conclusion Three compartments are required to explain diffusion MR measurements from in vivo corpus callosum, which informs the choice of model for microstructure imaging applications in the brain. Magn Reson Med 72:1785–1792, 2014. © 2013 The authors. Magnetic Resonance in Medicine Published by Wiley Periodicals, Inc. on behalf of International Society of Medicine in Resonance. PMID:24347370
Jump diffusion models and the evolution of financial prices
NASA Astrophysics Data System (ADS)
Figueiredo, Annibal; de Castro, Marcio T.; da Silva, Sergio; Gleria, Iram
2011-08-01
We analyze a stochastic model to describe the evolution of financial prices. We consider the stochastic term as a sum of the Wiener noise and a jump process. We point to the effects of the jumps on the return time evolution, a central concern of the econophysics literature. The presence of jumps suggests that the process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. We then extend the De Finetti functions to a generalized nonlinear model and show the model to be capable of explaining return behavior.
Mathematical model of diffusion-limited evolution of multiple gas bubbles in tissue
NASA Technical Reports Server (NTRS)
Srinivasan, R. Srini; Gerth, Wayne A.; Powell, Michael R.
2003-01-01
Models of gas bubble dynamics employed in probabilistic analyses of decompression sickness incidence in man must be theoretically consistent and simple, if they are to yield useful results without requiring excessive computations. They are generally formulated in terms of ordinary differential equations that describe diffusion-limited gas exchange between a gas bubble and the extravascular tissue surrounding it. In our previous model (Ann. Biomed. Eng. 30: 232-246, 2002), we showed that with appropriate representation of sink pressures to account for gas loss or gain due to heterogeneous blood perfusion in the unstirred diffusion region around the bubble, diffusion-limited bubble growth in a tissue of finite volume can be simulated without postulating a boundary layer across which gas flux is discontinuous. However, interactions between two or more bubbles caused by competition for available gas cannot be considered in this model, because the diffusion region has a fixed volume with zero gas flux at its outer boundary. The present work extends the previous model to accommodate interactions among multiple bubbles by allowing the diffusion region volume of each bubble to vary during bubble evolution. For given decompression and tissue volume, bubble growth is sustained only if the bubble number density is below a certain maximum.
Hydrogen diffusion into the subsurfaces of model metal catalysts from first principles.
Shen, Xiangjian; Li, Yuanjie; Liu, Xianglin; Zhang, Dandan; Gao, Jian; Liang, Tianshui
2017-02-01
Diffusion pathways of atomic hydrogen on model catalyst surfaces and into subsurfaces are of great significance in the exploration of novel catalytic hydrogenation in heterogeneous catalysis. We present in detail the diffusion pathways of hydrogen on seven different open and closed model catalyst surfaces from first principles calculations. Seven transition metal catalysts with thirteen different crystal surfaces, i.e., Co(001), Ni(100) and Ni(111), Pd(100) and (111), Pt(100) and (111), Cu(100) and (111), Ag(100) and (111) and Au(100) and (111), are taken into account. Thirteen corresponding potential energy surfaces (PESs) are constructed for modelling hydrogen diffusion on these model catalyst surfaces and into the subsurfaces by interpolating ab initio density functional theory energy points (∼2000 for each surface). The minimum energy diffusion pathways for hydrogen on the surfaces and into the subsurfaces are globally searched for based on PESs using a mesh method, and are in excellent agreement with those calculated from the nudged elastic band method. Furthermore, the important substrate relaxation effect can decrease the diffusion barriers for hydrogen into catalyst subsurfaces. The high reactivity of subsurface reactants mainly comes from the residual energy of subsurface hydrogen emerging from the subsurface onto the surface.
Effects of spatial diffusion on nonequilibrium steady states in a model for prebiotic evolution
NASA Astrophysics Data System (ADS)
Intoy, B. F.; Wynveen, A.; Halley, J. W.
2016-10-01
Effects of spatial diffusion in a Kauffman-like model for prebiotic evolution previously studied in a "well-mixed" limit are reported. The previous model was parametrized by a parameter p defined as the probability that a possible reaction in a network of reactions characterizing the artificial chemistry actually appears in the chemical network. In the model reported here, we numerically study a grid of such well-mixed reactors on a two-dimensional spatial lattice in which the model chemical constituents can hop between neighboring reactors at a rate controlled by a second parameter η . We report the frequency of appearance of three distinct types of nonequilibrium steady states, characterized as "diffusively alive locally dead" (DALD), "diffusively dead locally alive" (DDLA) and "diffusively alive locally alive" (DALA). The types are defined according to whether they are chemically equilibrated at each site, diffusively equilibrated between sites, or neither, respectively. With our parametrization of the definitions of these nonequilibrium states, many of the DALA states are growing rapidly in population due to the explosive population growth of a few sites, while their entropy remains well below its equilibrium value. Sharp temporal transitions occur as exploding sites appear. DALD states occur less commonly than the other types and also usually harbor a few explosively growing sites but transitions are less sharp than in DALA systems.
Payvandi, S; Daly, K R; Zygalakis, K C; Roose, T
2014-11-01
Plants rely on the conducting vessels of the phloem to transport the products of photosynthesis from the leaves to the roots, or to any other organs, for growth, metabolism, and storage. Transport within the phloem is due to an osmotically-generated pressure gradient and is hence inherently nonlinear. Since convection dominates over diffusion in the main bulk flow, the effects of diffusive transport have generally been neglected by previous authors. However, diffusion is important due to boundary layers that form at the ends of the phloem, and at the leaf-stem and stem-root boundaries. We present a mathematical model of transport which includes the effects of diffusion. We solve the system analytically in the limit of high Münch number which corresponds to osmotic equilibrium and numerically for all parameter values. We find that the bulk solution is dependent on the diffusion-dominated boundary layers. Hence, even for large Péclet number, it is not always correct to neglect diffusion. We consider the cases of passive and active sugar loading and unloading. We show that for active unloading, the solutions diverge with increasing Péclet. For passive unloading, the convergence of the solutions is dependent on the magnitude of loading. Diffusion also permits the modelling of an axial efflux of sugar in the root zone which may be important for the growing root tip and for promoting symbiotic biological interactions in the soil. Therefore, diffusion is an essential mechanism for transport in the phloem and must be included to accurately predict flow.
Stability and Hopf bifurcation for a prey-predator model with prey-stage structure and diffusion.
Wang, Mingxin
2008-04-01
In this paper, we first propose a prey-predator model with prey-stage structure and diffusion. Then we discuss the following three problems: (1) stability of non-negative constant steady states for the reduced ODE system and the corresponding reaction diffusion system with homogeneous Neumann boundary conditions; (2) Hopf bifurcation for the ODE system; (3) Hopf bifurcation created by diffusion.
Analysis of the absorptive behavior of photopolymer materials. Part I. Theoretical modeling
NASA Astrophysics Data System (ADS)
Li, Haoyu; Qi, Yue; Guo, Jinxin; Sheridan, John T.
2015-01-01
Photopolymers have received a great deal of attention due to their broad range of applications. The variation of their absorptive behavior during exposure is pivotal to the study of such materials. A model combining the associated electromagnetics and photochemical kinetics is presented to describe these absorptive processes. Such a model is critical in describing both self-modulations during holographic recording and also self-focusing effects. To describe the photophysical and photochemical changes taking place, a modulated equivalent electrical conductivity is introduced. Temporal variations of the concentrations of dye, monomer, and polymer are then predicted using the modified nonlocal photopolymerization driven diffusion model. The numerical convergence of the model is examined. Comparisons between the predictions of the model and experimental results, for both acrylamide/polyvinyl alcohol and Phenanthrenequinone doped poly(methyl methacrylate) photopolymer materials, are presented and analyzed in Part II of this paper.
NASA Astrophysics Data System (ADS)
Fazeli, Mohammadreza
In this thesis, pore network modeling was used to study how the microstructure of the polymer electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL) influences multiphase transport within the composite layer. An equivalent pore network of a GDL was used to study the effects of GDL/catalyst layer condensation points and contact quality on the spatial distribution of liquid water in the GDL. Next, pore networks extracted from synchrotron-based micro-computed tomography images of compressed GDLs were employed to simulate liquid water transport in GDL materials over a range of compression pressures, and favorable GDL compression values for preferred liquid water distributions were found for two commercially available GDL materials. Finally, a technique was developed for calculating the oxygen diffusivity in carbon paper substrates with a microporous layer (MPL) coating through pore network modeling. A hybrid network was incorporated into the pore network model, and effective diffusivity predictions of MPL coated GDL materials were obtained.
Dermic diffusion and stratum corneum: a state of the art review of mathematical models.
Couto, Ana; Fernandes, Rúben; Cordeiro, M Natália S; Reis, Sara S; Ribeiro, Rogério T; Pessoa, Ana M
2014-03-10
Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives.
Integrating O/S models during conceptual design, part 1
NASA Technical Reports Server (NTRS)
Ebeling, Charles E.
1994-01-01
The University of Dayton is pleased to submit this report to the National Aeronautics and Space Administration (NASA), Langley Research Center, which integrates a set of models for determining operational capabilities and support requirements during the conceptual design of proposed space systems. This research provides for the integration of the reliability and maintainability (R&M) model, both new and existing simulation models, and existing operations and support (O&S) costing equations in arriving at a complete analysis methodology. Details concerning the R&M model and the O&S costing model may be found in previous reports accomplished under this grant (NASA Research Grant NAG1-1327). In the process of developing this comprehensive analysis approach, significant enhancements were made to the R&M model, updates to the O&S costing model were accomplished, and a new simulation model developed. This is the 1st part of a 3 part technical report.
NASA Astrophysics Data System (ADS)
Hund, S. J.; Antaki, J. F.
2009-10-01
Transport phenomena of platelets and white blood cells (WBCs) are fundamental to the processes of vascular disease and thrombosis. Unfortunately, the dilute volume occupied by these cells is not amenable to fluid-continuum modeling, and yet the cell count is large enough that modeling each individual cell is impractical for most applications. The most feasible option is to treat them as dilute species governed by convection and diffusion; however, this is further complicated by the role of the red blood cell (RBC) phase on the transport of these cells. We therefore propose an extended convection-diffusion (ECD) model based on the diffusive balance of a fictitious field potential, Ψ, that accounts for the gradients of both the dilute phase and the local hematocrit. The ECD model was applied to the flow of blood in a tube and between parallel plates in which a profile for the RBC concentration field was imposed and the resulting platelet concentration field predicted. Compared to prevailing enhanced-diffusion models that dispersed the platelet concentration field, the ECD model was able to simulate a near-wall platelet excess, as observed experimentally. The extension of the ECD model depends only on the ability to prescribe the hematocrit distribution, and therefore may be applied to a wide variety of geometries to investigate platelet-mediated vascular disease and device-related thrombosis.
Modeling photovoltaic diffusion: an analysis of geospatial datasets
NASA Astrophysics Data System (ADS)
Davidson, Carolyn; Drury, Easan; Lopez, Anthony; Elmore, Ryan; Margolis, Robert
2014-07-01
This study combines address-level residential photovoltaic (PV) adoption trends in California with several types of geospatial information—population demographics, housing characteristics, foreclosure rates, solar irradiance, vehicle ownership preferences, and others—to identify which subsets of geospatial information are the best predictors of historical PV adoption. Number of rooms, heating source and house age were key variables that had not been previously explored in the literature, but are consistent with the expected profile of a PV adopter. The strong relationship provided by foreclosure indicators and mortgage status have less of an intuitive connection to PV adoption, but may be highly correlated with characteristics inherent in PV adopters. Next, we explore how these predictive factors and model performance varies between different Investor Owned Utility (IOU) regions in California, and at different spatial scales. Results suggest that models trained with small subsets of geospatial information (five to eight variables) may provide similar explanatory power as models using hundreds of geospatial variables. Further, the predictive performance of models generally decreases at higher resolution, i.e., below ZIP code level since several geospatial variables with coarse native resolution become less useful for representing high resolution variations in PV adoption trends. However, for California we find that model performance improves if parameters are trained at the regional IOU level rather than the state-wide level. We also find that models trained within one IOU region are generally representative for other IOU regions in CA, suggesting that a model trained with data from one state may be applicable in another state.
Navarro, Juan M; Escolano, José; Cobos, Maximo; López, José J
2013-03-01
The diffusion equation model was used for room acoustic simulations to predict the sound pressure level and the reverberation time. The technical literature states that the diffusion equation method accurately models the late portion of the room impulse response if the energy is sufficiently scattered. This work provides conclusions on the validity of the diffusion equation model for rooms with homogeneous dimensions in relation to the scattering coefficients of the boundaries. A systematic evaluation was conducted out to determine the ranges of the absorption and scattering coefficient values that result in low noticeable differences between the predictions from a geometrical acoustic model and those from the diffusion equation model.
Modelling of phosphorus inputs to rivers from diffuse and point sources.
Bowes, Michael J; Smith, Jim T; Jarvie, Helen P; Neal, Colin
2008-06-01
The difference in timing of point and diffuse phosphorus (P) delivery to a river produces clear differences in the P concentration-flow relationship. Point inputs decrease in concentration with increasing river flow, due to dilution of a relatively constant input, whereas diffuse (non-point) load usually increases with river flow. This study developed a simple model, based on this fundamental difference, which allowed point and diffuse inputs to be quantified by modelling their contribution to river P concentration as a power-law function of flow. The relationships between total phosphorus (TP) concentration and river flow were investigated for three contrasting UK river catchments; the Swale (Yorkshire), the Frome (Dorset) and the Avon (Warwickshire). A load apportionment model was fitted to this empirical data to give estimates of point and diffuse load inputs at each monitoring site, at high temporal resolution. The model produced TP source apportionments that were similar to those derived from an export coefficient approach. For many diffuse-dominated sites within this study (with up to 75% of the annual TP load derived from diffuse sources), the model showed that reductions of point inputs would be most effective in order to reduce eutrophication risk, due to point source dominance during the plant and algae growing period. This modelling approach should provide simple, robust and rapid TP source apportionment from most concentration-flow datasets. It does not require GIS, information on land use, catchment size, population or livestock density, and could provide a valuable and versatile tool to catchment managers for determining suitable river mitigation options.
Spectral diffusion in a fluctuating charge model of water
NASA Astrophysics Data System (ADS)
Corcelli, S. A.; Lawrence, C. P.; Asbury, J. B.; Steinel, T.; Fayer, M. D.; Skinner, J. L.
2004-11-01
We apply the combined electronic structure/molecular dynamics approach of Corcelli, Lawrence, and Skinner [J. Chem. Phys. 120, 8107 (2004)] to the fluctuating charge (SPC-FQ) model of liquid water developed by Rick, Stuart, and Berne [J. Chem. Phys. 101, 6141 (1994)]. For HOD in H2O the time scale for the long-time decay of the OD stretch frequency time-correlation function, which corresponds to the time scale for hydrogen-bond rearrangement in the liquid, is about 1.5 ps. This result is significantly longer than the 0.9 ps decay previously calculated for the nonpolarizable SPC/E water model. Our results for the SPC-FQ model are in better agreement with recent vibrational echo experiments.
Hasnain, Sabeeha; McClendon, Christopher L.; Hsu, Monica T.; Jacobson, Matthew P.; Bandyopadhyay, Pradipta
2014-01-01
A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI. PMID:25180859
Turing patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme
NASA Astrophysics Data System (ADS)
Li, Shanbing; Wu, Jianhua; Dong, Yaying
2015-09-01
In this paper, we consider a reaction-diffusion model with Degn-Harrison reaction scheme. Some fundamental analytic properties of nonconstant positive solutions are first investigated. We next study the stability of constant steady-state solution to both ODE and PDE models. Our result also indicates that if either the size of the reactor or the effective diffusion rate is large enough, then the system does not admit nonconstant positive solutions. Finally, we establish the global structure of steady-state bifurcations from simple eigenvalues by bifurcation theory and the local structure of the steady-state bifurcations from double eigenvalues by the techniques of space decomposition and implicit function theorem.
Parameters estimation using the first passage times method in a jump-diffusion model
NASA Astrophysics Data System (ADS)
Khaldi, K.; Meddahi, S.
2016-06-01
The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time (FPT method) generalized for all passage times (GPT method), in order to estimate the parameters of stochastic Jump-Diffusion process. (2) it compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the GPT method and those obtained by the moments method and the FPT method applied to the Merton Jump-Diffusion (MJD) model.
Normal diffusion in crystal structures and higher-dimensional billiard models with gaps.
Sanders, David P
2008-12-01
We show, both heuristically and numerically, that three-dimensional periodic Lorentz gases-clouds of particles scattering off crystalline arrays of hard spheres-often exhibit normal diffusion, even when there are gaps through which particles can travel without ever colliding-i.e., when the system has an infinite horizon. This is the case provided that these gaps are not "too large," as measured by their dimension. The results are illustrated with simulations of a simple three-dimensional model having different types of diffusive regime and are then extended to higher-dimensional billiard models, which include hard-sphere fluids.
Lumb, Matthew P.; Steiner, Myles A.; Geisz, John F.; Walters, Robert J.
2014-11-21
The analytical drift-diffusion formalism is able to accurately simulate a wide range of solar cell architectures and was recently extended to include those with back surface reflectors. However, as solar cells approach the limits of material quality, photon recycling effects become increasingly important in predicting the behavior of these cells. In particular, the minority carrier diffusion length is significantly affected by the photon recycling, with consequences for the solar cell performance. In this paper, we outline an approach to account for photon recycling in the analytical Hovel model and compare analytical model predictions to GaAs-based experimental devices operating close to the fundamental efficiency limit.
Boundary-reaction-diffusion model for oscillatory zoning in binary crystals grown from solution.
Kalischewski, Felix; Lubashevsky, Ihor; Heuer, Andreas
2007-02-01
Oscillatory Zoning (OZ) is a phenomenon exhibited by many geologically formed crystals. It is characterized by quasiperiodic oscillations in the composition of a solid solution, caused by self-organization. We present a model for OZ. The growth mechanism applied includes species diffusion through the solution bulk, particle adsorption, surface diffusion, and subsequently desorption or incorporation into the crystal. This mechanism, in particular, can provide the synchronization effects necessary to reproduce the layered structure of experimentally obtained crystals, lacking in other models. We conduct a linear stability analysis combined with numerical simulations. Our results reproduce the experimental findings with respect to the patterns formed and a critical supersaturation necessary for OZ to occur.
NASA Technical Reports Server (NTRS)
Dumbauld, R. K.; Bjorklund, J. R.; Bowers, J. F.
1973-01-01
The NASA/MSFC multilayer diffusion models are discribed which are used in applying meteorological information to the estimation of toxic fuel hazards resulting from the launch of rocket vehicle and from accidental cold spills and leaks of toxic fuels. Background information, definitions of terms, description of the multilayer concept are presented along with formulas for determining the buoyant rise of hot exhaust clouds or plumes from conflagrations, and descriptions of the multilayer diffusion models. A brief description of the computer program is given, and sample problems and their solutions are included. Derivations of the cloud rise formulas, users instructions, and computer program output lists are also included.
Yao, Yi; Berkowitz, Max L. E-mail: ykanai@unc.edu; Kanai, Yosuke E-mail: ykanai@unc.edu
2015-12-28
The translational diffusivity of water in solutions of alkali halide salts depends on the identity of ions, exhibiting dramatically different behavior even in solutions of similar salts of NaCl and KCl. The water diffusion coefficient decreases as the salt concentration increases in NaCl. Yet, in KCl solution, it slightly increases and remains above bulk value as salt concentration increases. Previous classical molecular dynamics simulations have failed to describe this important behavior even when polarizable models were used. Here, we show that inclusion of dynamical charge transfer among water molecules produces results in a quantitative agreement with experiments. Our results indicate that the concentration-dependent diffusivity reflects the importance of many-body effects among the water molecules in aqueous ionic solutions. Comparison with quantum mechanical calculations shows that a heterogeneous and extended distribution of charges on water molecules around the ions due to ion-water and also water-water charge transfer plays a very important role in controlling water diffusivity. Explicit inclusion of the charge transfer allows us to model accurately the difference in the concentration-dependent water diffusivity between Na{sup +} and K{sup +} ions in simulations, and it is likely to impact modeling of a wide range of systems for medical and technological applications.
Physical integrated diffusion-oxidation model for implanted nitrogen in silicon
NASA Astrophysics Data System (ADS)
Adam, Lahir Shaik; Law, Mark E.; Dokumaci, Omer; Hegde, Suri
2002-02-01
Scaling the gate oxide thickness is one of many process development challenges facing device engineers today. Nitrogen implantation has been used to control gate oxide thickness. By varying the dose of the nitrogen implant, process engineers can have multiple gate oxide thicknesses in the same process. Although it has been observed that nitrogen retards gate oxidation kinetics, the physics of how this occurs is not yet well understood. Since the retardation in oxide growth is due to the diffusion of nitrogen and its subsequent incorporation at the silicon/silicon oxide interface, the study of the diffusion behavior of nitrogen in silicon becomes important. Further, it is also necessary to study how this diffusion behavior impacts oxide growth. Models have been developed to explore these issues. The diffusion model is based on ab initio results and is compared to experimental results at two temperatures. The oxide reduction model is based on the diffusion of nitrogen to the surface. The surface nitrogen is coupled to the surface reaction rate of silicon and oxygen to moderate oxide growth.
NASA Technical Reports Server (NTRS)
Parker, L. Neergaard; Zank, G. P.
2013-01-01
Successful forecasting of energetic particle events in space weather models require algorithms for correctly predicting the spectrum of ions accelerated from a background population of charged particles. We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box. We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (E(sub max)) appropriate for quasi-parallel and quasi-perpendicular shocks and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).
NASA Astrophysics Data System (ADS)
Yao, Yi; Berkowitz, Max L.; Kanai, Yosuke
2015-12-01
The translational diffusivity of water in solutions of alkali halide salts depends on the identity of ions, exhibiting dramatically different behavior even in solutions of similar salts of NaCl and KCl. The water diffusion coefficient decreases as the salt concentration increases in NaCl. Yet, in KCl solution, it slightly increases and remains above bulk value as salt concentration increases. Previous classical molecular dynamics simulations have failed to describe this important behavior even when polarizable models were used. Here, we show that inclusion of dynamical charge transfer among water molecules produces results in a quantitative agreement with experiments. Our results indicate that the concentration-dependent diffusivity reflects the importance of many-body effects among the water molecules in aqueous ionic solutions. Comparison with quantum mechanical calculations shows that a heterogeneous and extended distribution of charges on water molecules around the ions due to ion-water and also water-water charge transfer plays a very important role in controlling water diffusivity. Explicit inclusion of the charge transfer allows us to model accurately the difference in the concentration-dependent water diffusivity between Na+ and K+ ions in simulations, and it is likely to impact modeling of a wide range of systems for medical and technological applications.
Yao, Yi; Berkowitz, Max L; Kanai, Yosuke
2015-12-28
The translational diffusivity of water in solutions of alkali halide salts depends on the identity of ions, exhibiting dramatically different behavior even in solutions of similar salts of NaCl and KCl. The water diffusion coefficient decreases as the salt concentration increases in NaCl. Yet, in KCl solution, it slightly increases and remains above bulk value as salt concentration increases. Previous classical molecular dynamics simulations have failed to describe this important behavior even when polarizable models were used. Here, we show that inclusion of dynamical charge transfer among water molecules produces results in a quantitative agreement with experiments. Our results indicate that the concentration-dependent diffusivity reflects the importance of many-body effects among the water molecules in aqueous ionic solutions. Comparison with quantum mechanical calculations shows that a heterogeneous and extended distribution of charges on water molecules around the ions due to ion-water and also water-water charge transfer plays a very important role in controlling water diffusivity. Explicit inclusion of the charge transfer allows us to model accurately the difference in the concentration-dependent water diffusivity between Na(+) and K(+) ions in simulations, and it is likely to impact modeling of a wide range of systems for medical and technological applications.
Diffusion of active particles with stochastic torques modeled as α-stable noise
NASA Astrophysics Data System (ADS)
Nötel, Jörg; Sokolov, Igor M.; Schimansky-Geier, Lutz
2017-01-01
We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular velocity is generated by a constant torque and random fluctuations described as a Lévy-stable noise. Two situations are investigated. First, we study white Lévy noise where the constant speed and the angular noise generate a persistent motion characterized by the persistence time {τ }D. At this time scale the crossover from ballistic to normal diffusive behavior is observed. The corresponding diffusion coefficient can be obtained analytically for the whole class of symmetric α-stable noises. As typical for models with noise-driven angular dynamics, the diffusion coefficient depends non-monotonously on the angular noise intensity. As second example, we study angular noise as described by an Ornstein-Uhlenbeck process with correlation time {τ }c driven by the Cauchy white noise. We discuss the asymptotic diffusive properties of this model and obtain the same analytical expression for the diffusion coefficient as in the first case which is thus independent on {τ }c. Remarkably, for {τ }c\\gt {τ }D the crossover from a non-Gaussian to a Gaussian distribution of displacements takes place at a time {τ }G which can be considerably larger than the persistence time {τ }D.
DIFMOD2: A NEXT GENERATION DIFFUSE LAYER MODEL
Jenne (1998) suggested that the majority of uncertainty in our current ability to model the environmental partitioning behavior of ionic species on natural surfaces resulted from uncertainties in our understanding of surface acidity behavior. Traditional 2-pK Grahame-Gouy-Chapma...
NASA Technical Reports Server (NTRS)
Hood, L. L.
1983-01-01
A modeling analysis is carried out of six experimental phase space density profiles for nearly equatorially mirroring protons using methods based on the approach of Thomsen et al. (1977). The form of the time-averaged radial diffusion coefficient D(L) that gives an optimal fit to the experimental profiles is determined under the assumption that simple satellite plus Ring E absorption of inwardly diffusing particles and steady-state radial diffusion are the dominant physical processes affecting the proton data in the L range that is modeled. An extension of the single-satellite model employed by Thomsen et al. to a model that includes multisatellite and ring absorption is described, and the procedures adopted for estimating characteristic satellite and ring absorption times are defined. The results obtained in applying three representative solid-body absorption models to evaluate D(L) in the range where L is between 4 and 16 are reported, and a study is made of the sensitivity of the preferred amplitude and L dependence for D(L) to the assumed model parameters. The inferred form of D(L) is then compared with that which would be predicted if various proposed physical mechanisms for driving magnetospheric radial diffusion are operative at Saturn.
Data assimilation experiments using the diffusive back and forth nudging for the NEMO ocean model
NASA Astrophysics Data System (ADS)
Ruggiero, G. A.; Ourmières, Y.; Cosme, E.; Blum, J.; Auroux, D.; Verron, J.
2014-07-01
The Diffusive Back and Forth Nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known Nudging method. It consists in a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore in the DBFN, the Nudging asymptotic behavior is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modeled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article the DBFN approximations and their consequences on the data assimilation system set-up are analyzed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence.
2013-01-01
Background Diffusion is a key component of many biological processes such as chemotaxis, developmental differentiation and tissue morphogenesis. Since recently, the spatial gradients caused by diffusion can be assessed in-vitro and in-vivo using microscopy based imaging techniques. The resulting time-series of two dimensional, high-resolutions images in combination with mechanistic models enable the quantitative analysis of the underlying mechanisms. However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters. Methods We introduce a likelihood function for image-based measurements with log-normal distributed noise. Based upon this likelihood function we formulate the maximum likelihood estimation problem, which is solved using PDE-constrained optimization methods. To assess the uncertainty and practical identifiability of the parameters we introduce profile likelihoods for diffusion processes. Results and conclusion As proof of concept, we model certain aspects of the guidance of dendritic cells towards lymphatic vessels, an example for haptotaxis. Using a realistic set of artificial measurement data, we estimate the five kinetic parameters of this model and compute profile likelihoods. Our novel approach for the estimation of model parameters from image data as well as the proposed identifiability analysis approach is widely applicable to diffusion processes. The profile likelihood based method provides more rigorous uncertainty bounds in contrast to local approximation methods. PMID:24267545
An analytical model for estimating water exchange rate in white matter using diffusion MRI.
Davoodi-Bojd, Esmaeil; Chopp, Michael; Soltanian-Zadeh, Hamid; Wang, Shiyang; Ding, Guangliang; Jiang, Quan
2014-01-01
Substantial effort is being expended on using micro-structural modeling of the white matter, with the goal of relating diffusion weighted magnetic resonance imaging (DWMRI) to the underlying structure of the tissue, such as axonal density. However, one of the important parameters affecting diffusion is the water exchange rate between the intra- and extra-axonal space, which has not been fully investigated and is a crucial marker of brain injury such as multiple sclerosis (MS), stroke, and traumatic brain injury (TBI). To our knowledge, there is no diffusion analytical model which includes the Water eXchange Rate (WXR) without the requirement of short gradient pulse (SGP) approximation. We therefore propose a new analytical model by deriving the diffusion signal for a permeable cylinder, assuming a clinically feasible pulse gradient spin echo (PGSE) sequence. Simulations based on Markov Random Walk confirm that the exchange parameter included in our model has a linear correlation (R2>0.88) with the actual WXR. Moreover, increasing WXR causes the estimated values of diameter and volume fraction of the cylinders to increase and decrease, respectively, which is consistent with our findings from histology measurements in tissues near TBI regions. This model was also applied to the diffusion signal acquired from ex vivo brains of 14 male (10 TBI and 4 normal) rats using hybrid diffusion imaging. The estimated values of axon diameter and axonal volume fraction are in agreement with their corresponding histological measurements in normal brains, with 0.96 intra-class correlation coefficient value resulting from consistency analysis. Moreover, a significant increase (p = 0.001) in WXR and diameter and decrease in axonal volume fraction in the TBI boundary were detected in the TBI rats compared with the normal rats.
Kekenes-Huskey, Peter M; Eun, Changsun; McCammon, J A
2015-09-07
Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion "barriers" arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to "compartments" of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways.
NASA Astrophysics Data System (ADS)
Kekenes-Huskey, Peter M.; Eun, Changsun; McCammon, J. A.
2015-09-01
Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion "barriers" arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to "compartments" of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways.
2011-10-01
Design and Implementation of a Numerical Technique to Inform Anisotropic Hyperelastic Finite Element Models using Diffusion-Weighted Imaging by...Implementation of a Numerical Technique to Inform Anisotropic Hyperelastic Finite Element Models using Diffusion-Weighted Imaging Reuben H. Kraft and Amy M. Dagro...Implementation of a Numerical Technique to Inform Anisotropic Hyperelastic Finite Element Models using Diffusion-Weighted Imaging AH80Reuben H. Kraft and
Fluid particle diffusion in a semidilute suspension of model micro-organisms.
Ishikawa, Takuji; Locsei, J T; Pedley, T J
2010-08-01
We calculate non-Brownian fluid particle diffusion in a semidilute suspension of swimming micro-organisms. Each micro-organism is modeled as a spherical squirmer, and their motions in an infinite suspension otherwise at rest are computed by the Stokesian-dynamics method. In calculating the fluid particle motions, we propose a numerical method based on a combination of the boundary element technique and Stokesian dynamics. We present details of the numerical method and examine its accuracy. The limitation of semidiluteness is required to ensure accuracy of the fluid particle velocity calculation. In the case of a suspension of non-bottom-heavy squirmers the spreading of fluid particles becomes diffusive in a shorter time than that of the squirmers, and the diffusivity of fluid particles is smaller than that of squirmers. It is confirmed that the probability density distribution of fluid particles also shows diffusive properties. The effect of tracer particle size is investigated by inserting some inert spheres of the same radius as the squirmers, instead of fluid particles, into the suspension. The diffusivity for inert spheres is not less than one tenth of that for fluid particles, even though the particle size is totally different. Scaling analysis indicates that the diffusivity of fluid particles and inert spheres becomes proportional to the volume fraction of squirmers in the semidilute regime provided that there is no more than a small recirculation region around a squirmer, which is confirmed numerically. In the case of a suspension of bottom-heavy squirmers, horizontal diffusivity decreases considerably even with small values of the bottom heaviness, which indicates the importance of bottom heaviness in the diffusion phenomena. We believe that these fundamental findings will enhance our understanding of the basic mechanics of a suspension of swimming micro-organisms.
Fluid particle diffusion in a semidilute suspension of model micro-organisms
NASA Astrophysics Data System (ADS)
Ishikawa, Takuji; Locsei, J. T.; Pedley, T. J.
2010-08-01
We calculate non-Brownian fluid particle diffusion in a semidilute suspension of swimming micro-organisms. Each micro-organism is modeled as a spherical squirmer, and their motions in an infinite suspension otherwise at rest are computed by the Stokesian-dynamics method. In calculating the fluid particle motions, we propose a numerical method based on a combination of the boundary element technique and Stokesian dynamics. We present details of the numerical method and examine its accuracy. The limitation of semidiluteness is required to ensure accuracy of the fluid particle velocity calculation. In the case of a suspension of non-bottom-heavy squirmers the spreading of fluid particles becomes diffusive in a shorter time than that of the squirmers, and the diffusivity of fluid particles is smaller than that of squirmers. It is confirmed that the probability density distribution of fluid particles also shows diffusive properties. The effect of tracer particle size is investigated by inserting some inert spheres of the same radius as the squirmers, instead of fluid particles, into the suspension. The diffusivity for inert spheres is not less than one tenth of that for fluid particles, even though the particle size is totally different. Scaling analysis indicates that the diffusivity of fluid particles and inert spheres becomes proportional to the volume fraction of squirmers in the semidilute regime provided that there is no more than a small recirculation region around a squirmer, which is confirmed numerically. In the case of a suspension of bottom-heavy squirmers, horizontal diffusivity decreases considerably even with small values of the bottom heaviness, which indicates the importance of bottom heaviness in the diffusion phenomena. We believe that these fundamental findings will enhance our understanding of the basic mechanics of a suspension of swimming micro-organisms.
Reaction-diffusion model for the growth of avascular tumor
NASA Astrophysics Data System (ADS)
Ferreira, S. C.; Martins, M. L.; Vilela, M. J.
2002-02-01
A nutrient-limited model for avascular cancer growth including cell proliferation, motility, and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the simulated tumors incorporate a spatial structure composed of a central necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferating cells in agreement with biological data. Finally, our results indicate that the competition for nutrients among normal and cancer cells may be a determining factor in generating papillary tumor morphology.
Minimal model for short-time diffusion in periodic potentials.
Emary, Clive; Gernert, Robert; Klapp, Sabine H L
2012-12-01
We investigate the dynamics of a single, overdamped colloidal particle, which is driven by a constant force through a one-dimensional periodic potential. We focus on systems with large barrier heights where the lowest-order cumulants of the density field, that is, average position and the mean-squared displacement, show nontrivial (nondiffusive) short-time behavior characterized by the appearance of plateaus. We demonstrate that this "cage-like" dynamics can be well described by a discretized master equation model involving two states (related to two positions) within each potential valley. Nontrivial predictions of our approach include analytic expressions for the plateau heights and an estimate of the "de-caging time" obtained from the study of deviations from Gaussian behavior. The simplicity of our approach means that it offers a minimal model to describe the short-time behavior of systems with hindered dynamics.
Climate change alters diffusion of forest pest: A model study
NASA Astrophysics Data System (ADS)
Jo, Woo Seong; Kim, Hwang-Yong; Kim, Beom Jun
2017-01-01
Population dynamics with spatial information is applied to understand the spread of pests. We introduce a model describing how pests spread in discrete space. The number of pest descendants at each site is controlled by local information such as temperature, precipitation, and the density of pine trees. Our simulation leads to a pest spreading pattern comparable to the real data for pine needle gall midge in the past. We also simulate the model in two different climate conditions based on two different representative concentration pathways scenarios for the future. We observe that after an initial stage of a slow spread of pests, a sudden change in the spreading speed occurs, which is soon followed by a large-scale outbreak. We found that a future climate change causes the outbreak point to occur earlier and that the detailed spatio-temporal pattern of the spread depends on the source position from which the initial pest infection starts.
A fractional diffusion equation model for cancer tumor
NASA Astrophysics Data System (ADS)
Iyiola, Olaniyi Samuel; Zaman, F. D.
2014-10-01
In this article, we consider cancer tumor models and investigate the need for fractional order derivative as compared to the classical first order derivative in time. Three different cases of the net killing rate are taken into account including the case where net killing rate of the cancer cells is dependent on the concentration of the cells. At first, we use a relatively new analytical technique called q-Homotopy Analysis Method on the resulting time-fractional partial differential equations to obtain analytical solution in form of convergent series with easily computable components. Our numerical analysis enables us to give some recommendations on the appropriate order (fractional) of derivative in time to be used in modeling cancer tumor.
Evaluation of solute diffusion tortuosity factor models for variously saturated soils
NASA Astrophysics Data System (ADS)
Chou, Hsinyi; Wu, Laosheng; Zeng, Lingzao; Chang, Andrew
2012-10-01
Solute diffusion flux in soil is described by Fick's law along with a tortuosity factor to account for the tortuous and reduced diffusive pathway blocked by soil particles. Predictive models based on empirical or conceptual relationships with other more commonly measured soil attributes have been proposed to replace the time-consuming and multifarious laboratory measurements. However, these models have not been systematically tested and evaluated with soils of different textures under comparable conditions. This study determined solute diffusion coefficients and calculated tortuosity factors of a sand, a sandy clay loam, and a clay at various degrees of water saturation, and used the experimental data to test the predictive capabilities of these models. All the test models can fit the experimental data reasonably well as evidenced by low root mean square errors (RMSEs). When the proposed (fixed) parameter values were used, the widely accepted Millington and Quirk tortuosity model resulted in highest RMSEs for all three test soils. In terms of model efficiency as described by Akaike weight, however, the tortuosity factors of the sand and sandy clay loam soils are best represented by a quadratic function of volumetric soil water content (with the largest Akaike weights), while the combined parallel-series conceptual model assuming different configurations of film and pore water is the best for the clay soil. The Olesen power function tortuosity model has the second largest Akaike weights for the sand and sandy clay loam soils, while the So and Nye linear model has the second largest Akaike weight for the clay soil. The two-region linear model of log (tortuosity factor) versus soil water content uses a similar framework to the conceptual model, and it can satisfactorily fit to the experimental data well (low RMSEs), but with low Akaike weights due to the large number of parameters in the model. Adaption of the findings from this study may substantially improve solute
Intergenerational Educational Encounters: Part 2--Counseling Implications of the Model
ERIC Educational Resources Information Center
Gamliel, Tova; Reichental, Yael; Eyal, Nitza
2007-01-01
This second paper commences where Part 1 concluded in volume 33, number 1, 2006. The paper describes the relations reflected in the Model-of-Knowledge between all partners of the intergenerational encounters at school--children, old adults, and teachers. The Model-of-Knowledge represents a relatively balanced approach toward the generations'…
GALEN's model of parts and wholes: experience and comparisons.
Rogers, J.; Rector, A.
2000-01-01
Part-whole relations play a critical role in the OpenGALEN Common Reference Model. We describe how particular characteristics of the underlying formalism have influenced GALEN's view on partonomy, and in more detail discuss how specific modelling issues have driven development of an extended set of partitive semantic links. PMID:11079977
A Computational Model of Cell Migration in Response to Biochemical Diffusion
Dexter, Nicholas C; Kruse, Kara L; Nutaro, James J; Ward, Richard C
2009-01-01
The Computational Sciences and Engineering Division of the Oak Ridge National Laboratory is partnering with the University of Tennessee Graduate School of Medicine to design a computational model describing various factors related to the development of intimal hyperplasia (IH) in response to arterial injury. This research focuses on modeling the chemotactic and haptotactic processes that stimulate vascular smooth muscle cell migration into the intima. A hybrid discrete-continuous mathematical model of cell migration in response to biochemical diffusion was developed in C++. Chemoattractant diffusion is modeled as a continuous partial differential equation, whereas migration of the cells is modeled as a series of discrete events. Results obtained from the discrete state model for cell migration agree with those obtained from Boyden chamber experiments.
Improved lattice Boltzmann model for multi-component diffusion flow with large pressure difference
NASA Astrophysics Data System (ADS)
Liu, Fu-Min; Wang, An-Lin; Qiu, Ruo-Fan; Jiang, Tao
2016-05-01
The pseudopotential lattice Boltzmann model has been widely used to solve multi-phase and multi-component flow problems. However, original pseudopotential model cannot be used in simulating diffusion flow with large pressure difference because of its limitation. In this paper, we incorporate pseudopotential model with a new form of effective mass to solve this problem based on the relationship between pressure difference and effective mass. The improved model is verified through Laplace’s law and binary immiscible Poiseuille flow. By simulating pipeline binary diffusion flow and two-inlet binary cavity jet flow, we show that the improved model can achieve larger pressure difference than pseudopotential model with traditional effective mass forms.
Gonzalez, Juan Eugenio Iglesias; Thompson, Paul M.; Zhao, Aishan; Tu, Zhuowen
2011-01-01
Purpose: This work describes a spatially variant mixture model constrained by a Markov random field to model high angular resolution diffusion imaging (HARDI) data. Mixture models suit HARDI well because the attenuation by diffusion is inherently a mixture. The goal is to create a general model that can be used in different applications. This study focuses on image denoising and segmentation (primarily the former). Methods: HARDI signal attenuation data are used to train a Gaussian mixture model in which the mean vectors and covariance matrices are assumed to be independent of spatial locations, whereas the mixture weights are allowed to vary at different lattice positions. Spatial smoothness of the data is ensured by imposing a Markov random field prior on the mixture weights. The model is trained in an unsupervised fashion using the expectation maximization algorithm. The number of mixture components is determined using the minimum message length criterion from information theory. Once the model has been trained, it can be fitted to a noisy diffusion MRI volume by maximizing the posterior probability of the underlying noiseless data in a Bayesian framework, recovering a denoised version of the image. Moreover, the fitted probability maps of the mixture components can be used as features for posterior image segmentation. Results: The model-based denoising algorithm proposed here was compared on real data with three other approaches that are commonly used in the literature: Gaussian filtering, anisotropic diffusion, and Rician-adapted nonlocal means. The comparison shows that, at low signal-to-noise ratio, when these methods falter, our algorithm considerably outperforms them. When tractography is performed on the model-fitted data rather than on the noisy measurements, the quality of the output improves substantially. Finally, ventricle and caudate nucleus segmentation experiments also show the potential usefulness of the mixture probability maps for
Application of ab-initio calculations to modeling of nanoscale diffusion and activation in silicon
NASA Astrophysics Data System (ADS)
Diebel, Milan
As ULSI devices enter the nanoscale, ultra-shallow and highly electrically active junctions become necessary. New materials and 3D device structures as well as new process technologies are under exploration to meet the requirements of future devices. A detailed understanding of the atomistic mechanisms of point-defect/dopant interactions which govern diffusion and activation behavior is required to overcome the challenges in building these devices. This dissertation describes how ab-initio calculations can be used to develop physical models of diffusion and activation in silicon. A hierarchy of approaches (ab-initio, kinetic lattice Monte Carlo, continuum) is used to bridge the gaps in time scale and system size between atomistic calculations and nanoscale devices. This modeling approach is demonstrated by investigating two very different challenges in process technology: F co-implantation and stress effects on dopant diffusion/activation. In the first application, ab-initio calculations are used to understand anomalous F diffusion behavior. A set of strongly bound fluorine vacancy complexes (FnVm ) were found. The decoration of vacancies/dangling silicon bonds by fluorine leads to fluorine accumulating in vacancy rich regions, which explains the fluorine redistribution behavior reported experimentally. The revealed interactions of F with point-defects explain the benefits of F co-implantation for B and P activation and diffusion. Based on the insight gained, a simplified F diffusion model at the continuum level (50--100 nm scale) is extracted that accounts for co-implantation effects on B and P for various implant energies and doses. The second application addresses the effect of stress on point-defect/dopant equilibrium concentration, diffusion, and activation. A methodology is developed to extract detailed stress effects from ab-initio calculations. The approach is used to extract induced strains and elasticity tensors for various defects and impurities in order
Ion diffusion coefficients model and molar conductivities of ionic salts in aprotic solvents.
Garrido, Leoncio; Mejía, Alberto; García, Nuria; Tiemblo, Pilar; Guzmán, Julio
2015-02-19
In the study of the electric properties of electrolytes, the determination of the diffusion coefficients of the species that intervene in the charge transport process is of great importance, particularly that of the free ions (D(+) and D(-)), the only species that contribute to the conductivity. In this work we propose a model that allows, with reasonable assumptions, determination of D(+) and D(-), and the degree of dissociation of the salt, α, at different concentrations, using the diffusion coefficients experimentally obtained with NMR. Also, it is shown that the NMR data suffice to estimate the conductivity of the electrolytes. The model was checked by means of experimental results of conductivity and NMR diffusion coefficients obtained with solutions of lithium triflate in ethylene and propylene carbonates, as well as with other results taken from the literature.
DePalma, Glen; Turnidge, John; Craig, Bruce A
2017-02-01
The determination of diffusion test breakpoints has become a challenging issue due to the increasing resistance of microorganisms to antibiotics. Currently, the most commonly-used method for determining these breakpoints is the modified error-rate bounded method. Its use has remained widespread despite the introduction of several model-based methods that have been shown superior in terms of precision and accuracy. However, the computational complexities associated with these new approaches has been a significant barrier for clinicians. To remedy this, we developed and examine the utility of a free online software package designed for the determination of diffusion test breakpoints: dBETS (diffusion Breakpoint Estimation Testing Software). This software package allows clinicians to easily analyze data from susceptibility experiments through visualization, error-rate bounded, and model-based approaches. We analyze four publicly available data sets from the Clinical and Laboratory Standards Institute using dBETS.
A radially resolved kinetic model for nonlocal electron ripple diffusion losses in tokamaks
NASA Astrophysics Data System (ADS)
Robertson, Scott
2006-09-01
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 electrons 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)].
The development and preliminary application of an invariant coupled diffusion and chemistry model
NASA Technical Reports Server (NTRS)
Hilst, G. R.; Donaldson, C. DUP.; Teske, M.; Contiliano, R.; Freiberg, J.
1973-01-01
In many real-world pollution chemical reaction problems, the rate of reaction problems, the rate of reaction may be greatly affected by unmixedness. An approximate closure scheme for a chemical kinetic submodel which conforms to the principles of invariant modeling and which accounts for the effects of inhomogeneous mixing over a wide range of conditions has been developed. This submodel has been coupled successfully with invariant turbulence and diffusion models, permitting calculation of two-dimensional diffusion of two reacting (isothermally) chemical species. The initial calculations indicate the ozone reactions in the wake of stratospheric aircraft will be substantially affected by the rate of diffusion of ozone into the wake, and in the early wake, by unmixedness.
Kojic, M.; Milosevic, M.; Kojic, N.; Kim, K.; Ferrari, M.; Ziemys, A.
2014-01-01
Mass transport by diffusion within composite materials may depend not only on internal microstructural geometry, but also on the chemical interactions between the transported substance and the material of the microstructure. Retrospectively, there is a gap in methods and theory to connect material microstructure properties with macroscale continuum diffusion characteristics. Here we present a new hierarchical multiscale model for diffusion within composite materials that couples material microstructural geometry and interactions between diffusing particles and the material matrix. This model, which bridges molecular dynamics (MD) and the finite element (FE) method, is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. The procedure is general and robust for evaluating constitutive material parameters of the continuum model. These parameters include the traditional bulk diffusion coefficients and, additionally, the distances from the solid surface accounting for surface interaction effects. We implemented our models to glucose diffusion through the following two geometrical/material configurations: tightly packed silica nanospheres, and a complex fibrous structure surrounding nanospheres. Then, rhodamine 6G diffusion analysis through an aga-rose gel network was performed, followed by a model validation using our experimental results. The microstructural model, numerical homogenization and continuum model offer a new platform for modeling and predicting mass diffusion through complex biological environment and within composite materials that are used in a wide range of applications, like drug delivery and nanoporous catalysts. PMID:24578582
2010-05-01
to Professor Chris Arney and LTC Donovan Phillips for providing valuable feedback on this project. vii MODELING OF DIFFUSION THROUGH A...only does the study of networks afford the U.S. Army greater information sharing abilities, it could also give a better understanding of enemy...These models are named for the conditions by which a node changes state. The first model gives each node its own threshold which must be reached before
User's guide to the MESOI diffusion model and to the utility programs UPDATE and LOGRVU
Athey, G.F.; Allwine, K.J.; Ramsdell, J.V.
1981-11-01
MESOI is an interactive, Lagrangian puff trajectory diffusion model. The model is documented separately (Ramsdell and Athey, 1981); this report is intended to provide MESOI users with the information needed to successfully conduct model simulations. The user is also provided with guidance in the use of the data file maintenance and review programs; UPDATE and LOGRVU. Complete examples are given for the operaton of all three programs and an appendix documents UPDATE and LOGRVU.
Thieulot, Cedric; Janssen, L P B M; Español, Pep
2005-07-01
A previously formulated smoothed particle hydrodynamics model for a phase separating mixture is tested for the case when viscous processes are negligible and only mass and energy diffusive processes take place. We restrict ourselves to the case of a binary mixture that can exhibit liquid-liquid phase separation. The thermodynamic consistency of the model is assessed and the potential of the model to study complex pattern formation in the presence of various thermal boundaries is illustrated.
Meeting Review: Diffuse X-Ray Scattering to Model Protein Motions
Wall, Michael E.; Adams, Paul D.; Fraser, James S.; Sautter, Nicholas K.
2014-01-01
Problems in biology increasingly need models of protein flexibility to understand and control protein function. At the same time, as they improve, crystallographic methods are marching closer to the limits of what can be learned from Bragg data in isolation. It is thus inevitable that mainstream protein crystallography will turn to diffuse scattering to model protein motions and improve crystallographic models. The time is ripe to make it happen. PMID:24507780
Spatially explicit control of invasive species using a reaction-diffusion model
Bonneau, Mathieu; Johnson, Fred A.; Romagosa, Christina M.
2016-01-01
Invasive species, which can be responsible for severe economic and environmental damages, must often be managed over a wide area with limited resources, and the optimal allocation of effort in space and time can be challenging. If the spatial range of the invasive species is large, control actions might be applied only on some parcels of land, for example because of property type, accessibility, or limited human resources. Selecting the locations for control is critical and can significantly impact management efficiency. To help make decisions concerning the spatial allocation of control actions, we propose a simulation based approach, where the spatial distribution of the invader is approximated by a reaction–diffusion model. We extend the classic Fisher equation to incorporate the effect of control both in the diffusion and local growth of the invader. The modified reaction–diffusion model that we propose accounts for the effect of control, not only on the controlled locations, but on neighboring locations, which are based on the theoretical speed of the invasion front. Based on simulated examples, we show the superiority of our model compared to the state-of-the-art approach. We illustrate the use of this model for the management of Burmese pythons in the Everglades (Florida, USA). Thanks to the generality of the modified reaction–diffusion model, this framework is potentially suitable for a wide class of management problems and provides a tool for managers to predict the effects of different management strategies.
3D choroid neovascularization growth prediction based on reaction-diffusion model
NASA Astrophysics Data System (ADS)
Zhu, Shuxia; Chen, Xinjian; Shi, Fei; Xiang, Dehui; Zhu, Weifang; Chen, Haoyu
2016-03-01
Choroid neovascularization (CNV) is a kind of pathology from the choroid and CNV-related disease is one important cause of vision loss. It is desirable to predict the CNV growth rate so that appropriate treatment can be planned. In this paper, we seek to find a method to predict the growth of CNV based on 3D longitudinal Optical Coherence Tomography (OCT) images. A reaction-diffusion model is proposed for prediction. The method consists of four phases: pre-processing, meshing, CNV growth modeling and prediction. We not only apply the reaction-diffusion model to the disease region, but also take the surrounding tissues into consideration including outer retinal layer, inner retinal layer and choroid layer. The diffusion in these tissues is considered as isotropic. The finite-element-method (FEM) is used to solve the partial differential equations (PDE) in the diffusion model. The curve of CNV growth with treatment are fitted and then we can predict the CNV status in a future time point. The preliminary results demonstrated that our proposed method is accurate and the validity and feasibility of our model is obvious.
Physical modelling and adaptive predictive control of diffusion/LPCVD reactors
NASA Astrophysics Data System (ADS)
Dewaard, H.
1992-12-01
The aim of this study is to design a temperature controller for batch electric diffusion/low pressure chemical vapor deposition (LPCVD) furnaces, that complies with the increasingly more stringent requirements of VLSI processing. A mathematical model has been developed for batch electric diffusion/LPCVD reactors that are currently used in the semiconductor industry for the fabrication of micro-electronic devices. The model has been formulated in terms of partial integro-differential equations, which are derived from the basic energy conservation law of physics. The model takes into account the effects of radiation and conduction. Chapter 2 gives a detailed description of the furnace system and provides some insight into the processes that take place. In chapter 3, the model of the diffusion/LPPCVD furnace is derived. Chapter 4 deals with the design of a temperature control system for the diffusion/LPCVD reactor, that makes use of the model as developed in chapter 3. Chapter 5 gives the results of the control designs, both of simulation and of application on a real furnace. Results of the linear quadratic Gaussian controller, the (non-adaptive) reduced order controller, and the adaptive predictive controller are presented. Finally, in chapter 6, some conclusions are drawn and suggestions for further research are given.
An Application of Epidemiological Modeling to Information Diffusion
NASA Astrophysics Data System (ADS)
McCormack, Robert; Salter, William
Messages often spread within a population through unofficial - particularly web-based - media. Such ideas have been termed "memes." To impede the flow of terrorist messages and to promote counter messages within a population, intelligence analysts must understand how messages spread. We used statistical language processing technologies to operationalize "memes" as latent topics in electronic text and applied epidemiological techniques to describe and analyze patterns of message propagation. We developed our methods and applied them to English-language newspapers and blogs in the Arab world. We found that a relatively simple epidemiological model can reproduce some dynamics of observed empirical relationships.
Multi-view and 3D deformable part models.
Pepik, Bojan; Stark, Michael; Gehler, Peter; Schiele, Bernt
2015-11-01
As objects are inherently 3D, they have been modeled in 3D in the early days of computer vision. Due to the ambiguities arising from mapping 2D features to 3D models, 3D object representations have been neglected and 2D feature-based models are the predominant paradigm in object detection nowadays. While such models have achieved outstanding bounding box detection performance, they come with limited expressiveness, as they are clearly limited in their capability of reasoning about 3D shape or viewpoints. In this work, we bring the worlds of 3D and 2D object representations closer, by building an object detector which leverages the expressive power of 3D object representations while at the same time can be robustly matched to image evidence. To that end, we gradually extend the successful deformable part model [1] to include viewpoint information and part-level 3D geometry information, resulting in several different models with different level of expressiveness. We end up with a 3D object model, consisting of multiple object parts represented in 3D and a continuous appearance model. We experimentally verify that our models, while providing richer object hypotheses than the 2D object models, provide consistently better joint object localization and viewpoint estimation than the state-of-the-art multi-view and 3D object detectors on various benchmarks (KITTI [2] , 3D object classes [3] , Pascal3D+ [4] , Pascal VOC 2007 [5] , EPFL multi-view cars[6] ).
Approximation of epidemic models by diffusion processes and their statistical inference.
Guy, Romain; Larédo, Catherine; Vergu, Elisabeta
2015-02-01
Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an
Modeling diffusion of electrical appliances in the residential sector
McNeil, Michael A.; Letschert, Virginie E.
2009-11-22
This paper presents a methodology for modeling residential appliance uptake as a function of root macroeconomic drivers. The analysis concentrates on four major energy end uses in the residential sector: refrigerators, washing machines, televisions and air conditioners. The model employs linear regression analysis to parameterize appliance ownership in terms of household income, urbanization and electrification rates according to a standard binary choice (logistic) function. The underlying household appliance ownership data are gathered from a variety of sources including energy consumption and more general standard of living surveys. These data span a wide range of countries, including many developing countries for which appliance ownership is currently low, but likely to grow significantly over the next decades as a result of economic development. The result is a 'global' parameterization of appliance ownership rates as a function of widely available macroeconomic variables for the four appliances studied, which provides a reliable basis for interpolation where data are not available, and forecasting of ownership rates on a global scale. The main value of this method is to form the foundation of bottom-up energy demand forecasts, project energy-related greenhouse gas emissions, and allow for the construction of detailed emissions mitigation scenarios.
Developing a laser shockwave model for characterizing diffusion bonded interfaces
Lacy, Jeffrey M. Smith, James A. Rabin, Barry H.
2015-03-31
The US National Nuclear Security Agency has a Global Threat Reduction Initiative (GTRI) with the goal of reducing the worldwide use of high-enriched uranium (HEU). A salient component of that initiative is the conversion of research reactors from HEU to low enriched uranium (LEU) fuels. An innovative fuel is being developed to replace HEU in high-power research reactors. The new LEU fuel is a monolithic fuel made from a U-Mo alloy foil encapsulated in Al-6061 cladding. In order to support the fuel qualification process, the Laser Shockwave Technique (LST) is being developed to characterize the clad-clad and fuel-clad interface strengths in fresh and irradiated fuel plates. LST is a non-contact method that uses lasers for the generation and detection of large amplitude acoustic waves to characterize interfaces in nuclear fuel plates. However, because the deposition of laser energy into the containment layer on a specimen's surface is intractably complex, the shock wave energy is inferred from the surface velocity measured on the backside of the fuel plate and the depth of the impression left on the surface by the high pressure plasma pulse created by the shock laser. To help quantify the stresses generated at the interfaces, a finite element method (FEM) model is being utilized. This paper will report on initial efforts to develop and validate the model by comparing numerical and experimental results for back surface velocities and front surface depressions in a single aluminum plate representative of the fuel cladding.
Geometrical measurement of cardiac wavelength in reaction-diffusion models
NASA Astrophysics Data System (ADS)
Dupraz, Marie; Jacquemet, Vincent
2014-09-01
The dynamics of reentrant arrhythmias often consists in multiple wavelets propagating throughout an excitable medium. An arrhythmia can be sustained only if these reentrant waves have a sufficiently short wavelength defined as the distance traveled by the excitation wave during its refractory period. In a uniform medium, wavelength may be estimated as the product of propagation velocity and refractory period (electrophysiological wavelength). In order to accurately measure wavelength in more general substrates relevant to atrial arrhythmias (heterogeneous and anisotropic), we developed a mathematical framework to define geometrical wavelength at each time instant based on the length of streamlines following the propagation velocity field within refractory regions. Two computational methods were implemented: a Lagrangian approach in which a set of streamlines were integrated, and an Eulerian approach in which wavelength was the solution of a partial differential equation. These methods were compared in 1D/2D tissues and in a model of the left atrium. An advantage of geometrical definition of wavelength is that the wavelength of a wavelet can be tracked over time with high temporal resolution and smaller temporal variability in an anisotropic and heterogeneous medium. The results showed that the average electrophysiological wavelength was consistent with geometrical measurements of wavelength. Wavelets were however often shorter than the electrophysiological wavelength due to interactions with boundaries and other wavelets. These tools may help to assess more accurately the relation between substrate properties and wavelet dynamics in computer models.
Developing a laser shockwave model for characterizing diffusion bonded interfaces
NASA Astrophysics Data System (ADS)
Lacy, Jeffrey M.; Smith, James A.; Rabin, Barry H.
2015-03-01
The US National Nuclear Security Agency has a Global Threat Reduction Initiative (GTRI) with the goal of reducing the worldwide use of high-enriched uranium (HEU). A salient component of that initiative is the conversion of research reactors from HEU to low enriched uranium (LEU) fuels. An innovative fuel is being developed to replace HEU in high-power research reactors. The new LEU fuel is a monolithic fuel made from a U-Mo alloy foil encapsulated in Al-6061 cladding. In order to support the fuel qualification process, the Laser Shockwave Technique (LST) is being developed to characterize the clad-clad and fuel-clad interface strengths in fresh and irradiated fuel plates. LST is a non-contact method that uses lasers for the generation and detection of large amplitude acoustic waves to characterize interfaces in nuclear fuel plates. However, because the deposition of laser energy into the containment layer on a specimen's surface is intractably complex, the shock wave energy is inferred from the surface velocity measured on the backside of the fuel plate and the depth of the impression left on the surface by the high pressure plasma pulse created by the shock laser. To help quantify the stresses generated at the interfaces, a finite element method (FEM) model is being utilized. This paper will report on initial efforts to develop and validate the model by comparing numerical and experimental results for back surface velocities and front surface depressions in a single aluminum plate representative of the fuel cladding.
Diffuse-Interface Modelling of Flow in Porous Media
NASA Astrophysics Data System (ADS)
Addy, Doug; Pradas, Marc; Schmuck, Marcus; Kalliadasis, Serafim
2016-11-01
Multiphase flows are ubiquitous in a wide spectrum of scientific and engineering applications, and their computational modelling often poses many challenges associated with the presence of free boundaries and interfaces. Interfacial flows in porous media encounter additional challenges and complexities due to their inherently multiscale behaviour. Here we investigate the dynamics of interfaces in porous media using an effective convective Cahn-Hilliard (CH) equation recently developed in from a Stokes-CH equation for microscopic heterogeneous domains by means of a homogenization methodology, where the microscopic details are taken into account as effective tensor coefficients which are given by a Poisson equation. The equations are decoupled under appropriate assumptions and solved in series using a classic finite-element formulation with the open-source software FEniCS. We investigate the effects of different microscopic geometries, including periodic and non-periodic, at the bulk fluid flow, and find that our model is able to describe the effective macroscopic behaviour without the need to resolve the microscopic details.
NASA Astrophysics Data System (ADS)
Li, Z.; Hudson, M. K.; Chen, Y.
2013-12-01
The outer boundary energetic electron flux is used as a driver in radial diffusion calculations, and its precise determination is critical to the solution. A new model was proposed recently based on THEMIS measurements to express the boundary flux as three fit functions of solar wind parameters in a response window, that depend on energy and which solar parameter is used: speed, density, or both (Shin and Lee, 2013). The Dartmouth radial diffusion model has been run using LANL geosynchronous satellite measurements as the outer boundary for a one-month interval in July to August 2004 and the calculated phase space density (PSD) is compared with GPS measurements at the GPS orbit (L=4.16), at magnetic equatorial plane crossings, as a test of the model. We also used the outer boundary generated from the Shin and Lee model and examined this boundary condition by computing the error relative to the simulation using a LANL geosynchronous spacecraft data-driven outer boundary. The calculation shows that there is overestimation and underestimation at different times, however the new boundary condition can be used to drive the radial diffusion model generally, producing the phase space density increase and dropout during a storm with a relatively small error. Having this new method based on a solar wind parametrized data set, we can run the radial diffusion model for storms when particle measurements are not available at the outer boundary. We chose the Whole Heliosphere Interval (WHI) as an example and compared the result with MHD/test-particle simulations (Hudson et al., 2012), obtaining much better agreement with PSD based on GPS measurements at L=4.16 using the diffusion model, which incorporates atmospheric losses.
Kleinle, J; Vogt, K; Lüscher, H R; Müller, L; Senn, W; Wyler, K; Streit, J
1996-01-01
A three-dimensional model for release and diffusion of glutamate in the synaptic cleft was developed and solved analytically. The model consists of a source function describing transmitter release from the vesicle and a diffusion function describing the spread of transmitter in the cleft. Concentration profiles of transmitter at the postsynaptic side were calculated for different transmitter concentrations in a vesicle, release scenarios, and diffusion coefficients. From the concentration profiles the receptor occupancy could be determined using alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor kinetics. It turned out that saturation of receptors and sufficiently fast currents could only be obtained if the diffusion coefficient was one order of magnitude lower than generally assumed, and if the postsynaptic receptors formed clusters with a diameter of roughly 100 nm directly opposite the release sites. Under these circumstances the gradient of the transmitter concentration at the postsynaptic membrane outside the receptor clusters was steep, with minimal cross-talk among neighboring receptor clusters. These findings suggest that for each release site a corresponding receptor aggregate exists, subdividing an individual synapse into independent functional subunits without the need for specific lateral diffusion barriers. Images FIGURE 1 PMID:8913582
NASA Technical Reports Server (NTRS)
Parker, Linda Neergaard; Zank, Gary P.
2013-01-01
We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).
Parallel acceleration of diffuse scattering model for indoor radio prediction by CUDA
NASA Astrophysics Data System (ADS)
Meng, Xiao; Guo, Li-xin; Tao, Wei
2013-10-01
Radio wave propagation prediction is very important for the design of the mobile communication network. The raytracing algorithm is a commonly used computational method for site-specific prediction of the radio channel characteristics of wireless communication systems. However, it does not consider the diffuse scattering. Therefore, an indoor diffuse scattering model which based on diffuse scattering theory and FDTD is established. The diffuse scattering of indoor walls and ceiling and floor is calculated at a series of discrete time instance in this method. In recent years, the compute unified device architecture (CUDA) of NVIDIA takes advantage of the GPU for parallel computing, and greatly improve the speed of computation. Because there is a large number of data to deal with, in order to reduce the computation time, a GPU-based diffuse scattering model for indoor radio prediction is introduced in this paper, which fully utilizes the parallel processing capabilities of CUDA to further improve the computational efficiency. It can be found that good acceleration effect has been achieved.
Rai, Varun
2016-08-15
This project sought to enable electric utilities in Texas to accelerate diffusion of residential solar photovoltaic (PV) by systematically identifying and targeting existing barriers to PV adoption. A core goal of the project was to develop an integrated research framework that combines survey research, econometric modeling, financial modeling, and implementation and evaluation of pilot projects to study the PV diffusion system. This project considered PV diffusion as an emergent system, with attention to the interactions between the constituent parts of the PV socio-technical system including: economics of individual decision-making; peer and social influences; behavioral responses; and information and transaction costs. We also conducted two pilot projects, which have yielded new insights into behavioral and informational aspects of PV adoption. Finally, this project has produced robust and generalizable results that will provide deeper insights into the technology-diffusion process that will be applicable for the design of utility programs for other technologies such as home-energy management systems and plug-in electric vehicles. When we started this project in 2013 there was little systematic research on characterizing the decision-making process of households interested in adopting PV. This project was designed to fill that research gap by analyzing the PV adoption process from the consumers' decision-making perspective and with the objective to systematically identifying and addressing the barriers that consumers face in the adoption of PV. The two key components of that decision-making process are consumers' evaluation of: (i) uncertainties and non-monetary costs associated with the technology and (ii) the direct monetary cost-benefit. This project used an integrated approach to study both the non-monetary and the monetary components of the consumer decision-making process.
Verdecchia, Kyle; Diop, Mamadou; Morrison, Laura B.; Lee, Ting-Yim; St. Lawrence, Keith
2015-01-01
Diffuse correlation spectroscopy (DCS) is a non-invasive optical technique capable of monitoring tissue perfusion. The normalized temporal intensity autocorrelation function generated by DCS is typically characterized by assuming that the movement of erythrocytes can be modeled as a Brownian diffusion-like process instead of by the expected random flow model. Recently, a hybrid model, referred to as the hydrodynamic diffusion model, was proposed, which combines the random and Brownian flow models. The purpose of this study was to investigate the best model to describe autocorrelation functions acquired directly on the brain in order to avoid confounding effects of extracerebral tissues. Data were acquired from 11 pigs during normocapnia and hypocapnia, and flow changes were verified by computed tomography perfusion (CTP). The hydrodynamic diffusion model was found to provide the best fit to the autocorrelation functions; however, no significant difference for relative flow changes measured by the Brownian and hydrodynamic diffusion models was observed. PMID:26600995
Simulation of evaporation of a sessile drop using a diffuse interface model
NASA Astrophysics Data System (ADS)
Sefiane, Khellil; Ding, Hang; Sahu, Kirti; Matar, Omar
2008-11-01
We consider here the evaporation dynamics of a Newtonian liquid sessile drop using an improved diffuse interface model. The governing equations for the drop and surrounding vapour are both solved, and separated by the order parameter (i.e. volume fraction), based on the previous work of Ding et al. JCP 2007. The diffuse interface model has been shown to be successful in modelling the moving contact line problems (Jacqmin 2000; Ding and Spelt 2007, 2008). Here, a pinned contact line of the drop is assumed. The evaporative mass flux at the liquid-vapour interface is a function of local temperature constitutively and treated as a source term in the interface evolution equation, i.e. Cahn-Hilliard equation. The model is validated by comparing its predictions with data available in the literature. The evaporative dynamics are illustrated in terms of drop snapshots, and a quantitative comparison with the results using a free surface model are made.
An evaluation of the role of eddy diffusion in stratospheric interactive two-dimensional models
NASA Technical Reports Server (NTRS)
Schneider, Hans R.; Ko, Malcolm K. W.; Sze, Nien Dak; Shi, Guang-Yu; Wang, Wei-Chyung
1989-01-01
An interactive two-dimensional model of the stratosphere, consisting of a primitive equation dynamics module, a simplified HO(x) ozone model, and a full radiative transfer scheme, is used to study the effect of eddy diffusion in the model. Consideration is given to the effects of nonlocal forcing from dissipation in the model troposphere and frictional drag at mesospheric levels, mechanical damping in the stratosphere itself, and potential vorticity flux due to large scale waves. It is found that the ozone distributions generated with the model are very sensitive to the choice of values for the friction and the eddy diffusion coefficients. It is shown that reasonable latitudinal gradients of ozone may be obtained by using small values for the mechanical damping for the mid- and high-latitude stratopsphere.
Steady-state solutions of a diffusive energy-balance climate model and their stability
NASA Technical Reports Server (NTRS)
Ghil, M.
1975-01-01
A diffusive energy-balance climate model, governed by a nonlinear parabolic partial differential equation, was studied. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. Models similar to the main one are considered, and the number of their steady states was determined. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The stability under small perturbations of the main model's climates was investigated. A stability criterion is derived, and its application shows that the present climate and the deep freeze are stable, whereas the model's glacial is unstable. The dependence was examined of the number of steady states and of their stability on the average solar radiation.
NASA Technical Reports Server (NTRS)
Brodnick, Jacob; Richardson, Brian; Ramachandran, Narayanan
2015-01-01
The Low Profile Diffuser (LPD) project originated as an award from the Marshall Space Flight Center (MSFC) Advanced Development (ADO) office to the Main Propulsion Systems Branch (ER22). The task was created to develop and test an LPD concept that could produce comparable performance to a larger, traditionally designed, ullage gas diffuser while occupying a smaller volume envelope. Historically, ullage gas diffusers have been large, bulky devices that occupy a significant portion of the propellant tank, decreasing the tank volume available for propellant. Ullage pressurization of spacecraft propellant tanks is required to prevent boil-off of cryogenic propellants and to provide a positive pressure for propellant extraction. To achieve this, ullage gas diffusers must slow hot, high-pressure gas entering a propellant tank from supersonic speeds to only a few meters per second. Decreasing the incoming gas velocity is typically accomplished through expansion to larger areas within the diffuser which has traditionally led to large diffuser lengths. The Fluid Dynamics Branch (ER42) developed and applied advanced Computational Fluid Dynamics (CFD) analysis methods in order to mature the LPD design from and initial concept to an optimized test prototype and to provide extremely accurate pre-test predictions of diffuser performance. Additionally, the diffuser concept for the Core Stage of the Space Launch System (SLS) was analyzed in a short amount of time to guide test data collection efforts of the qualification of the device. CFD analysis of the SLS diffuser design provided new insights into the functioning of the device and was qualitatively validated against hot wire anemometry of the exterior flow field. Rigorous data analysis of the measurements was performed on static and dynamic pressure data, data from two microphones, accelerometers and hot wire anemometry with automated traverse. Feasibility of the LPD concept and validation of the computational model were
Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model
NASA Astrophysics Data System (ADS)
Ruggiero, G. A.; Ourmières, Y.; Cosme, E.; Blum, J.; Auroux, D.; Verron, J.
2015-04-01
The diffusive back-and-forth nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known nudging method. It consists of a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore, in the DBFN, the nudging asymptotic behaviour is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability, the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modelled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article, the DBFN approximations and their consequences for the data assimilation system set-up are analysed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence. The conducted sensitivity tests show that the 4Dvar profits of long assimilation windows to propagate surface information downwards, and that for the DBFN, it is worth using short assimilation windows to reduce the impact of diffusion-induced errors. Moreover, the DBFN is less sensitive to the first guess than the 4Dvar.
Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models
NASA Astrophysics Data System (ADS)
Giese, Wolfgang; Eigel, Martin; Westerheide, Sebastian; Engwer, Christian; Klipp, Edda
2015-12-01
In silico experiments bear the potential for further understanding of biological transport processes by allowing a systematic modification of any spatial property and providing immediate simulation results. Cell polarization and spatial reorganization of membrane proteins are fundamental for cell division, chemotaxis and morphogenesis. We chose the yeast Saccharomyces cerevisiae as an exemplary model system which entails the shuttling of small Rho GTPases such as Cdc42 and Rho, between an active membrane-bound form and an inactive cytosolic form. We used partial differential equations to describe the membrane-cytosol shuttling of proteins. In this study, a consistent extension of a class of 1D reaction-diffusion systems into higher space dimensions is suggested. The membrane is modeled as a thin layer to allow for lateral diffusion and the cytosol is modeled as an enclosed volume. Two well-known polarization mechanisms were considered. One shows the classical Turing-instability patterns, the other exhibits wave-pinning dynamics. For both models, we investigated how cell shape and diffusion barriers like septin structures or bud scars influence the formation of signaling molecule clusters and subsequent polarization. An extensive set of in silico experiments with different modeling hypotheses illustrated the dependence of cell polarization models on local membrane curvature, cell size and inhomogeneities on the membrane and in the cytosol. In particular, the results of our computer simulations suggested that for both mechanisms, local diffusion barriers on the membrane facilitate Rho GTPase aggregation, while diffusion barriers in the cytosol and cell protrusions limit spontaneous molecule aggregations of active Rho GTPase locally.
Robust multi-component modeling of diffusion tensor magnetic resonance imaging data
NASA Astrophysics Data System (ADS)
Kadah, Yasser M.; Ma, Xiangyang; LaConte, Stephen; Yassine, Inas; Hu, Xiaoping
2005-04-01
In conventional diffusion tensor imaging (DTI) based on magnetic resonance data, each voxel is assumed to contain a single component having diffusion properties that can be fully represented by a single tensor. In spite of its apparent lack of generality, this assumption has been widely used in clinical and research purpose. This resulted in situations where correct interpretation of data was hampered by mixing of components and/or tractography. Even though this assumption can be valid in some cases, the general case involves mixing of components resulting in significant deviation from the single tensor model. Hence, a strategy that allows the decomposition of data based on a mixture model has the potential of enhancing the diagnostic value of DTI. This work aims at developing a stable solution for the most general problem of multi-component modeling of diffusion tensor imaging data. This model does not include any assumptions about the nature or volume ratio of any of the components and utilizes a projection pursuit based strategy whereby a combination of exhaustive search and least-squares estimation is used to estimate 1D projections of the solution. Then, such solutions are combined to compute the multidimensional components in a fast and robust manner. The new method is demonstrated by both computer simulations and real diffusion-weighted data. The preliminary results indicate the success of the new method and its potential to enhance the interpretation of DTI data sets.
Coarse-grained model of water diffusion and proton conductivity in hydrated polyelectrolyte membrane
NASA Astrophysics Data System (ADS)
Lee, Ming-Tsung; Vishnyakov, Aleksey; Neimark, Alexander V.
2016-01-01
Using dissipative particle dynamics (DPD), we simulate nanoscale segregation, water diffusion, and proton conductivity in hydrated sulfonated polystyrene (sPS). We employ a novel model [Lee et al. J. Chem. Theory Comput. 11(9), 4395-4403 (2015)] that incorporates protonation/deprotonation equilibria into DPD simulations. The polymer and water are modeled by coarse-grained beads interacting via short-range soft repulsion and smeared charge electrostatic potentials. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with the base beads representing water and sulfonate anions. Morse bond formation and breakup artificially mimics the Grotthuss mechanism of proton hopping between the bases. The DPD model is parameterized by matching the proton mobility in bulk water, dissociation constant of benzenesulfonic acid, and liquid-liquid equilibrium of water-ethylbenzene solutions. The DPD simulations semi-quantitatively predict nanoscale segregation in the hydrated sPS into hydrophobic and hydrophilic subphases, water self-diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from isolated water clusters to a 3D network. The analysis of hydrophilic subphase connectivity and water diffusion demonstrates the importance of the dynamic percolation effect of formation and breakup of temporary junctions between water clusters. The proposed DPD model qualitatively predicts the ratio of proton to water self-diffusion and its dependence on the hydration level that is in reasonable agreement with experiments.
Specifying Theories of Developmental Dyslexia: A Diffusion Model Analysis of Word Recognition
ERIC Educational Resources Information Center
Zeguers, Maaike H. T.; Snellings, Patrick; Tijms, Jurgen; Weeda, Wouter D.; Tamboer, Peter; Bexkens, Anika; Huizenga, Hilde M.
2011-01-01
The nature of word recognition difficulties in developmental dyslexia is still a topic of controversy. We investigated the contribution of phonological processing deficits and uncertainty to the word recognition difficulties of dyslexic children by mathematical diffusion modeling of visual and auditory lexical decision data. The first study showed…
Mathematical model of diffusion-limited gas bubble dynamics in unstirred tissue with finite volume
NASA Technical Reports Server (NTRS)
Srinivasan, R. Srini; Gerth, Wayne A.; Powell, Michael R.
2002-01-01
Models of gas bubble dynamics for studying decompression sickness have been developed by considering the bubble to be immersed in an extravascular tissue with diffusion-limited gas exchange between the bubble and the surrounding unstirred tissue. In previous versions of this two-region model, the tissue volume must be theoretically infinite, which renders the model inapplicable to analysis of bubble growth in a finite-sized tissue. We herein present a new two-region model that is applicable to problems involving finite tissue volumes. By introducing radial deviations to gas tension in the diffusion region surrounding the bubble, the concentration gradient can be zero at a finite distance from the bubble, thus limiting the tissue volume that participates in bubble-tissue gas exchange. It is shown that these deviations account for the effects of heterogeneous perfusion on gas bubble dynamics, and are required for the tissue volume to be finite. The bubble growth results from a difference between the bubble gas pressure and an average gas tension in the surrounding diffusion region that explicitly depends on gas uptake and release by the bubble. For any given decompression, the diffusion region volume must stay above a certain minimum in order to sustain bubble growth.
Coarse-grained model of water diffusion and proton conductivity in hydrated polyelectrolyte membrane
Lee, Ming-Tsung; Vishnyakov, Aleksey; Neimark, Alexander V.
2016-01-07
Using dissipative particle dynamics (DPD), we simulate nanoscale segregation, water diffusion, and proton conductivity in hydrated sulfonated polystyrene (sPS). We employ a novel model [Lee et al. J. Chem. Theory Comput. 11(9), 4395-4403 (2015)] that incorporates protonation/deprotonation equilibria into DPD simulations. The polymer and water are modeled by coarse-grained beads interacting via short-range soft repulsion and smeared charge electrostatic potentials. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with the base beads representing water and sulfonate anions. Morse bond formation and breakup artificially mimics the Grotthuss mechanism of proton hopping between the bases. The DPD model is parameterized by matching the proton mobility in bulk water, dissociation constant of benzenesulfonic acid, and liquid-liquid equilibrium of water-ethylbenzene solutions. The DPD simulations semi-quantitatively predict nanoscale segregation in the hydrated sPS into hydrophobic and hydrophilic subphases, water self-diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from isolated water clusters to a 3D network. The analysis of hydrophilic subphase connectivity and water diffusion demonstrates the importance of the dynamic percolation effect of formation and breakup of temporary junctions between water clusters. The proposed DPD model qualitatively predicts the ratio of proton to water self-diffusion and its dependence on the hydration level that is in reasonable agreement with experiments.
ERIC Educational Resources Information Center
Schriewer, Jurgen
2009-01-01
This article is about the so-called Bologna process and the historically unprecedented diffusion of an abstract model for the restructuring and harmonization of higher education studies and degrees across Europe it has fuelled. This process is interpreted here as a particular example of much larger processes of world-level interconnection and…
ERIC Educational Resources Information Center
Ratcliff, Roger; Love, Jessica; Thompson, Clarissa A.; Opfer, John E.
2012-01-01
Children (n = 130; M[subscript age] = 8.51-15.68 years) and college-aged adults (n = 72; M[subscript age] = 20.50 years) completed numerosity discrimination and lexical decision tasks. Children produced longer response times (RTs) than adults. R. Ratcliff's (1978) diffusion model, which divides processing into components (e.g., quality of…
Nonlinear models for the adoption and diffusion of innovations for industrial energy conservation.
Jacobsen, Joseph J; Guastello, Stephen J
2007-10-01
Four different theoretical models for explaining the diffusion of innovation were compared for 13 energy-related innovations--the Theory of Planned Behavior, the S-curve for Diffusion of Innovations, the power law distribution, and the cusp catastrophe. The substantive concern was to explore the roles of facilitative and obstructive factors in diffusing industrial and commercial innovations. Participants were 102 industrial plant and facilities managers from sites that were among the top users of electrical energy and natural gas in the United States. They completed a survey that contained measurements of positive attitudes toward innovation, organizational resistance to innovation, and the extent to which they had investigated or adopted each of the target innovations. Seven of the 13 innovations exhibited strong cusp catastrophe models (via nonlinear regression, average R2 = .91) compared to linear alternative models (average R2 = .31) for those innovations; the S-curve for diffusion was regarded as a simplified version of the cusp. One innovation was characterized best by a power law distribution (R2 = .94), and the remaining five were characterized best by a linear model that was based on the Theory of Planned Behavior (R2 = .41). Different underlying dynamics for the various innovations were implied by these results.
Weber, Adam
2010-03-05
A macroscopic-modeling methodology to account for the chemical and structural properties of fuel-cell diffusion media is developed. A previous model is updated to include for the first time the use of experimentally measured capillary pressure -- saturation relationships through the introduction of a Gaussian contact-angle distribution into the property equations. The updated model is used to simulate various limiting-case scenarios of water and gas transport in fuel-cell diffusion media. Analysis of these results demonstrate that interfacial conditions are more important than bulk transport in these layers, where the associated mass-transfer resistance is the result of higher capillary pressures at the boundaries and the steepness of the capillary pressure -- saturation relationship. The model is also used to examine the impact of a microporous layer, showing that it dominates the response of the overall diffusion medium. In addition, its primary mass-transfer-related effect is suggested to be limiting the water-injection sites into the more porous gas-diffusion layer.
Although detailed thermodynamic analyses of the 2-pK diffuse layer surface complexation model generally specify bound site activity coefficients for the purpose of accounting for those non-ideal excess free energies contributing to bound site electrochemical potentials, in applic...
Uncovering Implicit Assumptions: A Large-Scale Study on Students' Mental Models of Diffusion
ERIC Educational Resources Information Center
Stains, Marilyne; Sevian, Hannah
2015-01-01
Students' mental models of diffusion in a gas phase solution were studied through the use of the Structure and Motion of Matter (SAMM) survey. This survey permits identification of categories of ways students think about the structure of the gaseous solute and solvent, the origin of motion of gas particles, and trajectories of solute particles in…
NASA Astrophysics Data System (ADS)
Tereshchenko, S. A.; Dolgushin, S. A.; Titenok, S. A.
2013-10-01
In the present work the absorption and reduced scattering coefficients of the homogeneous scattering medium are determined using three various types of the diffusion model (classical, refined and extrapolated) in the case of the scattering slab geometry. The expression for the refined diffusion model in this case was derived for the first time. These coefficients are determined from experimental temporal distributions of transmitted photons at different slab thickness (from 10 mm to 110 mm) with fitting procedure. The specific dependencies of the scattering and absorption coefficients on the slab thickness were obtained for each of the examined models, although it is physically impossible for the same substance. This effect is caused by the fact that the significant features of the scattering indicatrix are lost when the diffusion approximation has been applied to the time-dependent radiation transport equation. This explanation was confirmed by Monte Carlo simulation, where the similar dependencies were obtained. There are presented several remarks regarding the experimental measurements when diffusion models are used.
A Model for Determining Information Diffusion in a Family Planning Program
ERIC Educational Resources Information Center
Jackson, Audrey R.
1972-01-01
Knowledge of the existence of birth control clinics is seen as a function of proximity to clinics, friendliness of neighborhood, and propensity to discuss birth control with neighbors. A conceptual model is developed to illustrate variables contributing to the diffusion of birth control information in a public health family planning program.…