Modelling of Innovation Diffusion
Directory of Open Access Journals (Sweden)
Arkadiusz Kijek
2010-01-01
Full Text Available Since the publication of the Bass model in 1969, research on the modelling of the diffusion of innovation resulted in a vast body of scientific literature consisting of articles, books, and studies of real-world applications of this model. The main objective of the diffusion model is to describe a pattern of spread of innovation among potential adopters in terms of a mathematical function of time. This paper assesses the state-of-the-art in mathematical models of innovation diffusion and procedures for estimating their parameters. Moreover, theoretical issues related to the models presented are supplemented with empirical research. The purpose of the research is to explore the extent to which the diffusion of broadband Internet users in 29 OECD countries can be adequately described by three diffusion models, i.e. the Bass model, logistic model and dynamic model. The results of this research are ambiguous and do not indicate which model best describes the diffusion pattern of broadband Internet users but in terms of the results presented, in most cases the dynamic model is inappropriate for describing the diffusion pattern. Issues related to the further development of innovation diffusion models are discussed and some recommendations are given. (original abstract
Yuvan, Steven; Bier, Martin
2018-02-01
Two decades ago Bak et al. (1997) [3] proposed a reaction-diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.
Modeling the diffusion of scientific publications
D. Fok (Dennis); Ph.H.B.F. Franses (Philip Hans)
2005-01-01
textabstractThis paper illustrates that salient features of a panel of time series of annual citations can be captured by a Bass type diffusion model. We put forward an extended version of this diffusion model, where we consider the relation between key characteristics of the diffusion process and
A model of diffuse degassing at three subduction-related volcanoes
Williams-Jones, Glyn; Stix, John; Heiligmann, Martin; Charland, Anne; Sherwood Lollar, Barbara; Arner, N.; Garzón, Gustavo V.; Barquero, Jorge; Fernandez, Erik
Radon, CO2 and δ13C in soil gas were measured at three active subduction-related stratovolcanoes (Arenal and Poás, Costa Rica; Galeras, Colombia). In general, Rn, CO2 and δ13C values are higher on the lower flanks of the volcanoes, except near fumaroles in the active craters. The upper flanks of these volcanoes have low Rn concentrations and light δ13C values. These observations suggest that diffuse degassing of magmatic gas on the upper flanks of these volcanoes is negligible and that more magmatic degassing occurs on the lower flanks where major faults and greater fracturing in the older lavas can channel magmatic gases to the surface. These results are in contrast to findings for Mount Etna where a broad halo of magmatic CO2 has been postulated to exist over much of the edifice. Differences in radon levels among the three volcanoes studied here may result from differences in age, the degree of fracturing and faulting, regional structures or the level of hydrothermal activity. Volcanoes, such as those studied here, act as plugs in the continental crust, focusing magmatic degassing towards crater fumaroles, faults and the fractured lower flanks.
On Diffusive Climatological Models.
Griffel, D. H.; Drazin, P. G.
1981-11-01
A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.
Aldarf, Mazen; Fourcade, Florence; Amrane, Abdeltif; Prigent, Yves
2006-08-01
Penicillium camembertii was cultivated on a jellified peptone-lactate based medium to simulate the composition of Camembert cheese. Diffusional limitations due to substrate consumption were not involved in the linear growth recorded during culture, while nitrogen (peptone) limitation accounted for growth cessation. Examination of gradients confirmed that medium neutralization was the consequence of lactate consumption and ammonium production. The diffusion of the lactate assimilated from the core to the rind and that of the ammonium produced from the rind to the core was described by means of a diffusion/reaction model involving a partial linking of consumption or production to growth. The model matched experimental data throughout growth.
Models of diffuse solar radiation
Energy Technology Data Exchange (ETDEWEB)
Boland, John; Ridley, Barbara [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Brown, Bruce [Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546 (Singapore)
2008-04-15
For some locations both global and diffuse solar radiation are measured. However, for many locations, only global is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from trigonometry, we need to have diffuse on the horizontal available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse radiation on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [Spencer JW. A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Sol Energy 1982; 29(1): 19-32]. Boland et al. [Modelling the diffuse fraction of global solar radiation on a horizontal surface. Environmetrics 2001; 12: 103-16] developed a validated model for Australian conditions. We detail our recent advances in developing the theoretical framework for the approach reported therein, particularly the use of the logistic function instead of piecewise linear or simple nonlinear functions. Additionally, we have also constructed a method, using quadratic programming, for identifying values that are likely to be erroneous. This allows us to eliminate outliers in diffuse radiation values, the data most prone to errors in measurement. (author)
Saxton, Michael J
2007-01-01
Modeling obstructed diffusion is essential to the understanding of diffusion-mediated processes in the crowded cellular environment. Simple Monte Carlo techniques for modeling obstructed random walks are explained and related to Brownian dynamics and more complicated Monte Carlo methods. Random number generation is reviewed in the context of random walk simulations. Programming techniques and event-driven algorithms are discussed as ways to speed simulations.
Double diffusivity model under stochastic forcing
Chattopadhyay, Amit K.; Aifantis, Elias C.
2017-05-01
The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into
Ion diffusion related to structure in molten salts
International Nuclear Information System (INIS)
Tosi, M.P.
1996-08-01
A model first developed by Zwanzig to derive transport coefficients in cold dense fluids directly from the Green-Kubo time correlation formulae allows one to relate macroscopic diffusion coefficients to the local fluid structure. Applications to various ionic diffusion processes in molten salts are reviewed. Consequences of partial structural quenching are also discussed. (author). 28 refs, 3 tabs
Measurement of relative permeability of fuel cell diffusion media
Hussaini, I.S.; Wang, C.Y.
2010-01-01
Gas diffusion layer (GDL) in PEM fuel cells plays a pivotal role in water management. Modeling of liquid water transport through the GDL relies on knowledge of relative permeability functions in the in-plane and through-plane directions
Diffusion in the special theory of relativity.
Herrmann, Joachim
2009-11-01
The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.
Parameter estimation in fractional diffusion models
Kubilius, Kęstutis; Ralchenko, Kostiantyn
2017-01-01
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides s...
He, Guangli; Zhao, Zongchang; Ming, Pingwen; Abuliti, Abudula; Yin, Caoyong
In this study, a fractal model is developed to predict the permeability and liquid water relative permeability of the GDL (TGP-H-120 carbon paper) in proton exchange membrane fuel cells (PEMFCs), based on the micrographs (by SEM, i.e. scanning electron microscope) of the TGP-H-120. Pore size distribution (PSD), maximum pore size, porosity, diameter of the carbon fiber, pore tortuosity, area dimension, hydrophilicity or hydrophobicity, the thickness of GDL and saturation are involved in this model. The model was validated by comparison between the predicted results and experimental data. The results indicate that the water relative permeability in the hydrophobicity case is much higher than in the hydrophilicity case. So, a hydrophobic carbon paper is preferred for efficient removal of liquid water from the cathode of PEMFCs.
Model of diffusers / permeators for hydrogen processing
International Nuclear Information System (INIS)
Jacobs, W. D.; Hang, T.
2008-01-01
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. (authors)
Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations
International Nuclear Information System (INIS)
Arkhincheev, V.E.
2001-04-01
To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)
Lagrangian-similarity diffusion-deposition model
International Nuclear Information System (INIS)
Horst, T.W.
1979-01-01
A Lagrangian-similarity diffusion model has been incorporated into the surface-depletion deposition model. This model predicts vertical concentration profiles far downwind of the source that agree with those of a one-dimensional gradient-transfer model
MHD diffuser model test program
Energy Technology Data Exchange (ETDEWEB)
Idzorek, J J
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment.
MHD diffuser model test program
International Nuclear Information System (INIS)
Idzorek, J.J.
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment
Experimental study of relative, turbulent diffusion
DEFF Research Database (Denmark)
Mann, J.; Ott, Søren; Andersen, J.S.
1999-01-01
The purpose is to study relative turbulent diffusion under controlled, reproducible conditions in the laboratory in order to estimate the constant C in Richardson-Obukhov's law. We get C #approx# 0.4 -- 0.6. We furthermore measure the distance-neighbourfunction, which is the probability density...... system with two computers each equipped with a frame grabber card. In the search for the best experimentalmethods we have revised the concept of local homogeneity and derived a law for the velocity--acceleration structure function. A second by-product of this effort is a relatively simple derivation...
Homogenization of neutronic diffusion models
International Nuclear Information System (INIS)
Capdebosq, Y.
1999-09-01
In order to study and simulate nuclear reactor cores, one needs to access the neutron distribution in the core. In practice, the description of this density of neutrons is given by a system of diffusion equations, coupled by non differential exchange terms. The strong heterogeneity of the medium constitutes a major obstacle to the numerical computation of this models at reasonable cost. Homogenization appears as compulsory. Heuristic methods have been developed since the origin by nuclear physicists, under a periodicity assumption on the coefficients. They consist in doing a fine computation one a single periodicity cell, to solve the system on the whole domain with homogeneous coefficients, and to reconstruct the neutron density by multiplying the solutions of the two computations. The objectives of this work are to provide mathematically rigorous basis to this factorization method, to obtain the exact formulas of the homogenized coefficients, and to start on geometries where two periodical medium are placed side by side. The first result of this thesis concerns eigenvalue problem models which are used to characterize the state of criticality of the reactor, under a symmetry assumption on the coefficients. The convergence of the homogenization process is proved, and formulas of the homogenized coefficients are given. We then show that without symmetry assumptions, a drift phenomenon appears. It is characterized by the mean of a real Bloch wave method, which gives the homogenized limit in the general case. These results for the critical problem are then adapted to the evolution model. Finally, the homogenization of the critical problem in the case of two side by side periodic medium is studied on a one dimensional on equation model. (authors)
Szardenings, Carsten; Kuhn, Jörg-Tobias; Ranger, Jochen; Holling, Heinz
2017-01-01
The respective roles of the approximate number system (ANS) and an access deficit (AD) in developmental dyscalculia (DD) are not well-known. Most studies rely on response times (RTs) or accuracy (error rates) separately. We analyzed the results of two samples of elementary school children in symbolic magnitude comparison (MC) and non-symbolic MC using a diffusion model. This approach uses the joint distribution of both RTs and accuracy in order to synthesize measures closer to ability and response caution or response conservatism. The latter can be understood in the context of the speed-accuracy tradeoff: It expresses how much a subject trades in speed for improved accuracy. We found significant effects of DD on both ability (negative) and response caution (positive) in MC tasks and a negative interaction of DD with symbolic task material on ability. These results support that DD subjects suffer from both an impaired ANS and an AD and in particular support that slower RTs of children with DD are indeed related to impaired processing of numerical information. An interaction effect of symbolic task material and DD (low mathematical ability) on response caution could not be refuted. However, in a sample more representative of the general population we found a negative association of mathematical ability and response caution in symbolic but not in non-symbolic task material. The observed differences in response behavior highlight the importance of accounting for response caution in the analysis of MC tasks. The results as a whole present a good example of the benefits of a diffusion model analysis.
Directory of Open Access Journals (Sweden)
Carsten Szardenings
2018-01-01
Full Text Available The respective roles of the approximate number system (ANS and an access deficit (AD in developmental dyscalculia (DD are not well-known. Most studies rely on response times (RTs or accuracy (error rates separately. We analyzed the results of two samples of elementary school children in symbolic magnitude comparison (MC and non-symbolic MC using a diffusion model. This approach uses the joint distribution of both RTs and accuracy in order to synthesize measures closer to ability and response caution or response conservatism. The latter can be understood in the context of the speed-accuracy tradeoff: It expresses how much a subject trades in speed for improved accuracy. We found significant effects of DD on both ability (negative and response caution (positive in MC tasks and a negative interaction of DD with symbolic task material on ability. These results support that DD subjects suffer from both an impaired ANS and an AD and in particular support that slower RTs of children with DD are indeed related to impaired processing of numerical information. An interaction effect of symbolic task material and DD (low mathematical ability on response caution could not be refuted. However, in a sample more representative of the general population we found a negative association of mathematical ability and response caution in symbolic but not in non-symbolic task material. The observed differences in response behavior highlight the importance of accounting for response caution in the analysis of MC tasks. The results as a whole present a good example of the benefits of a diffusion model analysis.
Diffusion in condensed matter methods, materials, models
Kärger, Jörg
2005-01-01
Diffusion as the process of particle transport due to stochastic movement is a phenomenon of crucial relevance for a large variety of processes and materials. This comprehensive, handbook- style survey of diffusion in condensed matter gives detailed insight into diffusion as the process of particle transport due to stochastic movement. Leading experts in the field describe in 23 chapters the different aspects of diffusion, covering microscopic and macroscopic experimental techniques and exemplary results for various classes of solids, liquids and interfaces as well as several theoretical concepts and models. Students and scientists in physics, chemistry, materials science, and biology will benefit from this detailed compilation.
A simplified model exploration research of new anisotropic diffuse radiation model
International Nuclear Information System (INIS)
Yao, Wanxiang; Li, Zhengrong; Wang, Xiao; Zhao, Qun; Zhang, Zhigang; Lin, Lin
2016-01-01
Graphical abstract: The specific process of measured diffuse radiation data. - Highlights: • Simplified diffuse radiation model is extremely important for solar radiation simulation and energy simulation. • A new simplified anisotropic diffuse radiation model (NSADR model) is proposed. • The accuracy of existing models and NSADR model is compared based on the measured values. • The accuracy of the NSADR model is higher than that of the existing models, and suitable for calculating diffuse radiation. - Abstract: More accurate new anisotropic diffuse radiation model (NADR model) has been proposed, but the parameters and calculation process of NADR model used in the process are complex. So it is difficult to widely used in the simulation software and engineering calculation. Based on analysis of the diffuse radiation model and measured diffuse radiation data, this paper put forward three hypotheses: (1) diffuse radiation from sky horizontal region is concentrated in a very thin layer which is close to the line source; (2) diffuse radiation from circumsolar region is concentrated in the point of the sun; (3) diffuse radiation from orthogonal region is concentrated in the point located at 90 degree angles with the Sun. Based on these hypotheses, NADR model is simplified to a new simplified anisotropic diffuse radiation model (NSADR model). Then the accuracy of NADR model and its simplified model (NSADR model) are compared with existing models based on the measured values, and the result shows that Perez model and its simplified model are relatively accurate among existing models. However, the accuracy of these two models is lower than the NADR model and NSADR model due to neglect the influence of the orthogonal diffuse radiation. The accuracy of the NSADR model is higher than that of the existing models, meanwhile, another advantage is that the NSADR model simplifies the process of solution parameters and calculation. Therefore it is more suitable for
Are relative depletions altered inside diffuse clouds?
International Nuclear Information System (INIS)
Joseph, C.L.
1988-01-01
The data of Jenkins, Savage, and Spitzer (1986) were used to analyze interstellar abundances and depletions of Fe, P, Mg, and Mn toward 37 stars, spanning nearly 1.0 (dex) in mean line-of-sight depletion. It was found that the depletions of these elements are linearly correlated and do not show evidence of differences in the rates of depletion or sputtering from one element to another. For a given level of overall depletion, the sightline-to-sightline rms variance in the depletion for each of these elements was less than 0.16 (dex), which is significantly smaller than is the element-to-element variance. The results suggest that, for most diffuse lines of sight, the relative abundances of these elements are set early in the lifetime of the grains and are not altered significantly thereafter. 53 references
Symmetries and modelling functions for diffusion processes
International Nuclear Information System (INIS)
Nikitin, A G; Spichak, S V; Vedula, Yu S; Naumovets, A G
2009-01-01
A constructive approach to the theory of diffusion processes is proposed, which is based on application of both symmetry analysis and the method of modelling functions. An algorithm for construction of the modelling functions is suggested. This algorithm is based on the error function expansion (ERFEX) of experimental concentration profiles. The high-accuracy analytical description of the profiles provided by ERFEX approximation allows a convenient extraction of the concentration dependence of diffusivity from experimental data and prediction of the diffusion process. Our analysis is exemplified by its employment in experimental results obtained for surface diffusion of lithium on the molybdenum (1 1 2) surface precovered with dysprosium. The ERFEX approximation can be directly extended to many other diffusion systems.
A tracer diffusion model derived from microstructure
International Nuclear Information System (INIS)
Lehikoinen, Jarmo; Muurinen, Arto; Olin, Markus
2012-01-01
Document available in extended abstract form only. Full text of publication follows: Numerous attempts have been made to explain the tracer diffusion of various solutes in compacted clays. These attempts have commonly suffered from an inability to describe the diffusion of uncharged and charged solutes with a single unified model. Here, an internally consistent approach to describing the diffusion of solutes in a heterogeneous porous medium, such as compacted bentonite, in terms of its microstructure is presented. The microstructure is taken to be represented by a succession of unit cells, which consist of two consecutive regions (Do, 1996). In the first region, the diffusion is viewed to occur in two parallel paths: one through microcrystalline units (micropores) and the other through meso-pores between the microcrystalline units. Solutes exiting these two paths are then joined together to continue diffusing through the second, disordered, region, connecting the two adjacent microcrystalline units. Adsorption (incl. co-ion exclusion) is thought to occur in the micropores, whereas meso-pores and the disordered region accommodate free species alone. Co-ions are also assumed to experience transfer resistance into and out of the micropores, which is characterized in the model by a transmission coefficient. Although the model is not new per se, its application to compacted clays has never been attempted before. It is shown that in the limit of strong adsorption, the effective diffusivity is limited from above only by the microstructural parameters of the model porous medium. As intuitive and logical as this result may appear, it has not been proven before. In the limit of vanishing disordered region, the effective diffusivity is no longer explicitly constrained by any of the model parameters. The tortuosity of the diffusion path, i.e. the quotient of the actual diffusion path length in the porous-medium coordinates and the characteristic length of the laboratory frame
Asbestos-related diffuse pleural thickening.
Fujimoto, Nobukazu; Kato, Katsuya; Usami, Ikuji; Sakai, Fumikazu; Tokuyama, Takeshi; Hayashi, Seiji; Miyamoto, Kenji; Kishimoto, Takumi
2014-01-01
The clinical features of asbestos-related diffuse pleural thickening (DPT) remain unclear. To clarify the association between radiological findings of DPT and respiratory function. Medical data from patients with asbestos-related DPT were collected, including their history of occupational or neighborhood asbestos exposure, initial symptoms, modified Medical Research Council dyspnea grade, smoking history, radiological findings, and respiratory function test results. There were 106 DPT patients between 2005 and 2010 [i.e. 103 men (97.2%) and 3 women (2.8%)]. The median age at diagnosis was 69 years (range 46-88). Patient occupations related to asbestos exposure included: asbestos product manufacturing (n = 17); the shipbuilding industry (n = 14); the construction industry (n = 13); heat insulation work (n = 12); plumbing, asbestos spraying, and electrical work (n = 7 each), and transportation and demolition work (n = 4 each). The median duration of asbestos exposure was 25 years (range 2-54), and the median latency period before the onset of DPT was 46 years (range 25-66). Involvement of the costophrenic angle (CPA) was also negatively correlated with the percent vital capacity (%VC; r = -0.448, p < 0.01). Pleural thickness and the craniocaudal and horizontal extension of pleural thickening, as determined by chest computed tomography (CT), were also negatively correlated with %VC (r = -0.226, p < 0.05; r = -0.409, p < 0.01, and r = -0.408, p < 0.01, respectively). DPT develops after a long latency period following occupational asbestos exposure and causes marked respiratory dysfunction. The extension of DPT should be evaluated by chest CT, and chest X-ray would be important for the evaluation of the involvement of the CPA.
Stochastic models for surface diffusion of molecules
Energy Technology Data Exchange (ETDEWEB)
Shea, Patrick, E-mail: patrick.shea@dal.ca; Kreuzer, Hans Jürgen [Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada)
2014-07-28
We derive a stochastic model for the surface diffusion of molecules, starting from the classical equations of motion for an N-atom molecule on a surface. The equation of motion becomes a generalized Langevin equation for the center of mass of the molecule, with a non-Markovian friction kernel. In the Markov approximation, a standard Langevin equation is recovered, and the effect of the molecular vibrations on the diffusion is seen to lead to an increase in the friction for center of mass motion. This effective friction has a simple form that depends on the curvature of the lowest energy diffusion path in the 3N-dimensional coordinate space. We also find that so long as the intramolecular forces are sufficiently strong, memory effects are usually not significant and the Markov approximation can be employed, resulting in a simple one-dimensional model that can account for the effect of the dynamics of the molecular vibrations on the diffusive motion.
Reflector modelization for neutronic diffusion and parameters identification
International Nuclear Information System (INIS)
Argaud, J.P.
1993-04-01
Physical parameters of neutronic diffusion equations can be adjusted to decrease calculations-measurements errors. The reflector being always difficult to modelize, we choose to elaborate a new reflector model and to use the parameters of this model as adjustment coefficients in the identification procedure. Using theoretical results, and also the physical behaviour of neutronic flux solutions, the reflector model consists then in its replacement by boundary conditions for the diffusion equations on the core only. This theoretical result of non-local operator relations leads then to some discrete approximations by taking into account the multiscaled behaviour, on the core-reflector interface, of neutronic diffusion solutions. The resulting model of this approach is then compared with previous reflector modelizations, and first results indicate that this new model gives the same representation of reflector for the core than previous. (author). 12 refs
Agent-based modelling of cholera diffusion
Augustijn-Beckers, Petronella; Doldersum, Tom; Useya, Juliana; Augustijn, Dionysius C.M.
2016-01-01
This paper introduces a spatially explicit agent-based simulation model for micro-scale cholera diffusion. The model simulates both an environmental reservoir of naturally occurring V.cholerae bacteria and hyperinfectious V. cholerae. Objective of the research is to test if runoff from open refuse
Stochastic diffusion models for substitutable technological innovations
Wang, L.; Hu, B.; Yu, X.
2004-01-01
Based on the analysis of firms' stochastic adoption behaviour, this paper first points out the necessity to build more practical stochastic models. And then, stochastic evolutionary models are built for substitutable innovation diffusion system. Finally, through the computer simulation of the
Bag model with diffuse surface
International Nuclear Information System (INIS)
Phatak, S.C.
1986-01-01
The constraint of a sharp bag boundary in the bag model is relaxed in the present work. This has been achieved by replacing the square-well potential of the bag model by a smooth scalar potential and introducing a term similar to the bag pressure term. The constraint of the conservation of the energy-momentum tensor is used to obtain an expression for the added bag pressure term. The model is then used to determine the static properties of the nucleon. The calculation shows that the rms charge radius and the nucleon magnetic moment are larger than the corresponding bag model values. Also, the axial vector coupling constant and the πNN coupling constant are in better agreement with the experimental values
Multiphase Microfluidics The Diffuse Interface Model
2012-01-01
Multiphase flows are typically described assuming that the different phases are separated by a sharp interface, with appropriate boundary conditions. This approach breaks down whenever the lengthscale of the phenomenon that is being studied is comparable with the real interface thickness, as it happens, for example, in the coalescence and breakup of bubbles and drops, the wetting and dewetting of solid surfaces and, in general, im micro-devices. The diffuse interface model resolves these probems by assuming that all quantities can vary continuously, so that interfaces have a non-zero thickness, i.e. they are "diffuse". The contributions in this book review the theory and describe some relevant applications of the diffuse interface model for one-component, two-phase fluids and for liquid binary mixtures, to model multiphase flows in confined geometries.
Measurement of relative permeability of fuel cell diffusion media
Hussaini, I.S.
2010-06-01
Gas diffusion layer (GDL) in PEM fuel cells plays a pivotal role in water management. Modeling of liquid water transport through the GDL relies on knowledge of relative permeability functions in the in-plane and through-plane directions. In the present work, air and water relative permeabilities are experimentally determined as functions of saturation for typical GDL materials such as Toray-060, -090, -120 carbon paper and E-Tek carbon cloth materials in their plain, untreated forms. Saturation is measured using an ex situ gravimetric method. Absolute and relative permeability functions in the two directions of interest are presented and new correlations for in-plane relative permeability of water and air are established. © 2010 Elsevier B.V. All rights reserved.
Discrete random walk models for space-time fractional diffusion
International Nuclear Information System (INIS)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-01-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α is part of (0,2] and skewness θ (moduleθ≤{α,2-α}), and the first-order time derivative with a Caputo derivative of order β is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation
Fractional diffusion models of nonlocal transport
International Nuclear Information System (INIS)
Castillo-Negrete, D. del
2006-01-01
A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ∼L α , of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments
Technological diffusion in the Ramsey model
Czech Academy of Sciences Publication Activity Database
Duczynski, Petr
2002-01-01
Roč. 1, č. 3 (2002), s. 243-250 ISSN 1607-0704 Institutional research plan: CEZ:AV0Z7085904 Keywords : neoclassical growth model * technological diffusion Subject RIV: AH - Economics http://www.ijbe.org/table%20of%20content/pdf/vol1-3/06.pdf
Bremmer, Rolf H; van Gemert, Martin J C; Faber, Dirk J; van Leeuwen, Ton G; Aalders, Maurice C G
2013-08-01
Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 mm-1 at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys.19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime
International Nuclear Information System (INIS)
Tamura, Junji; Kido, Hiroko; Hato, Shinji; Homma, Toshimitsu
2009-03-01
Straight-line or segmented plume models as atmospheric diffusion models are commonly used in probabilistic accident consequence assessment (PCA) codes due to cost and time savings. The PCA code, OSCAAR developed by Japan Atomic Energy Research Institute (Present; Japan Atomic Energy Agency) uses the variable puff trajectory model to calculate atmospheric transport and dispersion of released radionuclides. In order to investigate uncertainties involved with the structure of the atmospheric dispersion/deposition model in OSCAAR, we have introduced the more sophisticated computer codes that included regional meteorological models RAMS and atmospheric transport model HYPACT, which were developed by Colorado State University, and comparative analyses between OSCAAR and RAMS/HYPACT have been performed. In this study, model verification of OSCAAR and RAMS/HYPACT was conducted using data of long term atmospheric diffusion experiments, which were carried out in Tokai-mura, Ibaraki-ken. The predictions by models and the results of the atmospheric diffusion experiments indicated relatively good agreements. And it was shown that model performance of OSCAAR was the same degree as it of RAMS/HYPACT. (author)
Modeling of Reaction Processes Controlled by Diffusion
International Nuclear Information System (INIS)
Revelli, Jorge
2003-01-01
Stochastic modeling is quite powerful in science and technology.The technics derived from this process have been used with great success in laser theory, biological systems and chemical reactions.Besides, they provide a theoretical framework for the analysis of experimental results on the field of particle's diffusion in ordered and disordered materials.In this work we analyze transport processes in one-dimensional fluctuating media, which are media that change their state in time.This fact induces changes in the movements of the particles giving rise to different phenomena and dynamics that will be described and analyzed in this work.We present some random walk models to describe these fluctuating media.These models include state transitions governed by different dynamical processes.We also analyze the trapping problem in a lattice by means of a simple model which predicts a resonance-like phenomenon.Also we study effective diffusion processes over surfaces due to random walks in the bulk.We consider different boundary conditions and transitions movements.We derive expressions that describe diffusion behaviors constrained to bulk restrictions and the dynamic of the particles.Finally it is important to mention that the theoretical results obtained from the models proposed in this work are compared with Monte Carlo simulations.We find, in general, excellent agreements between the theory and the simulations
Diffuse solar radiation estimation models for Turkey's big cities
International Nuclear Information System (INIS)
Ulgen, Koray; Hepbasli, Arif
2009-01-01
A reasonably accurate knowledge of the availability of the solar resource at any place is required by solar engineers, architects, agriculturists, and hydrologists in many applications of solar energy such as solar furnaces, concentrating collectors, and interior illumination of buildings. For this purpose, in the past, various empirical models (or correlations) have been developed in order to estimate the solar radiation around the world. This study deals with diffuse solar radiation estimation models along with statistical test methods used to statistically evaluate their performance. Models used to predict monthly average daily values of diffuse solar radiation are classified in four groups as follows: (i) From the diffuse fraction or cloudness index, function of the clearness index, (ii) From the diffuse fraction or cloudness index, function of the relative sunshine duration or sunshine fraction, (iii) From the diffuse coefficient, function of the clearness index, and (iv) From the diffuse coefficient, function of the relative sunshine duration or sunshine fraction. Empirical correlations are also developed to establish a relationship between the monthly average daily diffuse fraction or cloudness index (K d ) and monthly average daily diffuse coefficient (K dd ) with the monthly average daily clearness index (K T ) and monthly average daily sunshine fraction (S/S o ) for the three big cities by population in Turkey (Istanbul, Ankara and Izmir). Although the global solar radiation on a horizontal surface and sunshine duration has been measured by the Turkish State Meteorological Service (STMS) over all country since 1964, the diffuse solar radiation has not been measured. The eight new models for estimating the monthly average daily diffuse solar radiation on a horizontal surface in three big cites are validated, and thus, the most accurate model is selected for guiding future projects. The new models are then compared with the 32 models available in the
Modelling Nanoparticle Diffusion into Cancer Tumors
Podduturi, Vishwa Priya; Derosa, Pedro
2011-03-01
Cancer is one of the major, potentially deadly diseases and has been for years. Non-specific delivery of the drug can damage healthy tissue seriously affecting in many cases the patient's living condition. Nanoparticles are being used for a targeted drug delivery thereby reducing the dose. In addition, metallic nanoparticles are being used in thermal treatment of cancer cells where nanoparticles help concentrate heat in the tumor and away from living tissue. We proposed a model that combines random walk with diffusion principles. The particle drift velocity is taken from the Hagen-Poiseuille equation and the velocity profile of the particle at the pores in the capillary wall is obtained using the Coventorware software. Pressure gradient and concentration gradient through the capillary wall are considered. Simulations are performed in Matlab using the Monte Carlo technique. Number of particles leaving the blood vessel through a pore is obtained as a function of blood pressure, the osmotic pressure, temperature, particle concentration, blood vessel radius, and pore size, and the relative effect of each of the parameters is discussed.
Modeling the reemergence of information diffusion in social network
Yang, Dingda; Liao, Xiangwen; Shen, Huawei; Cheng, Xueqi; Chen, Guolong
2018-01-01
Information diffusion in networks is an important research topic in various fields. Existing studies either focus on modeling the process of information diffusion, e.g., independent cascade model and linear threshold model, or investigate information diffusion in networks with certain structural characteristics such as scale-free networks and small world networks. However, there are still several phenomena that have not been captured by existing information diffusion models. One of the prominent phenomena is the reemergence of information diffusion, i.e., a piece of information reemerges after the completion of its initial diffusion process. In this paper, we propose an optimized information diffusion model by introducing a new informed state into traditional susceptible-infected-removed model. We verify the proposed model via simulations in real-world social networks, and the results indicate that the model can reproduce the reemergence of information during the diffusion process.
Diffusion in energy materials: Governing dynamics from atomistic modelling
Parfitt, D.; Kordatos, A.; Filippatos, P. P.; Chroneos, A.
2017-09-01
Understanding diffusion in energy materials is critical to optimising the performance of solid oxide fuel cells (SOFCs) and batteries both of which are of great technological interest as they offer high efficiency for cleaner energy conversion and storage. In the present review, we highlight the insights offered by atomistic modelling of the ionic diffusion mechanisms in SOFCs and batteries and how the growing predictive capability of high-throughput modelling, together with our new ability to control compositions and microstructures, will produce advanced materials that are designed rather than chosen for a given application. The first part of the review focuses on the oxygen diffusion mechanisms in cathode and electrolyte materials for SOFCs and in particular, doped ceria and perovskite-related phases with anisotropic structures. The second part focuses on disordered oxides and two-dimensional materials as these are very promising systems for battery applications.
Anomalous diffusion in a symbolic model
International Nuclear Information System (INIS)
Ribeiro, H V; Lenzi, E K; Mendes, R S; Santoro, P A
2011-01-01
In this work, we investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following the power-law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach reveals a rich diffusive scenario characterized by non-Gaussian distribution and, depending on the power-law exponent or the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare the analytic results with the numerical data, thereby finding good agreement. Because of its simplicity and flexibility, this model can be a candidate for describing real systems governed by power-law probability densities.
Diffuse interface methods for multiphase flow modeling
International Nuclear Information System (INIS)
Jamet, D.
2004-01-01
Full text of publication follows:Nuclear reactor safety programs need to get a better description of some stages of identified incident or accident scenarios. For some of them, such as the reflooding of the core or the dryout of fuel rods, the heat, momentum and mass transfers taking place at the scale of droplets or bubbles are part of the key physical phenomena for which a better description is needed. Experiments are difficult to perform at these very small scales and direct numerical simulations is viewed as a promising way to give new insight into these complex two-phase flows. This type of simulations requires numerical methods that are accurate, efficient and easy to run in three space dimensions and on parallel computers. Despite many years of development, direct numerical simulation of two-phase flows is still very challenging, mostly because it requires solving moving boundary problems. To avoid this major difficulty, a new class of numerical methods is arising, called diffuse interface methods. These methods are based on physical theories dating back to van der Waals and mostly used in materials science. In these methods, interfaces separating two phases are modeled as continuous transitions zones instead of surfaces of discontinuity. Since all the physical variables encounter possibly strong but nevertheless always continuous variations across the interfacial zones, these methods virtually eliminate the difficult moving boundary problem. We show that these methods lead to a single-phase like system of equations, which makes it easier to code in 3D and to make parallel compared to more classical methods. The first method presented is dedicated to liquid-vapor flows with phase-change. It is based on the van der Waals' theory of capillarity. This method has been used to study nucleate boiling of a pure fluid and of dilute binary mixtures. We discuss the importance of the choice and the meaning of the order parameter, i.e. a scalar which discriminates one
A diffuse radar scattering model from Martian surface rocks
Calvin, W. M.; Jakosky, B. M.; Christensen, P. R.
1987-01-01
Remote sensing of Mars has been done with a variety of instrumentation at various wavelengths. Many of these data sets can be reconciled with a surface model of bonded fines (or duricrust) which varies widely across the surface and a surface rock distribution which varies less so. A surface rock distribution map from -60 to +60 deg latitude has been generated by Christensen. Our objective is to model the diffuse component of radar reflection based on this surface distribution of rocks. The diffuse, rather than specular, scattering is modeled because the diffuse component arises due to scattering from rocks with sizes on the order of the wavelength of the radar beam. Scattering for radio waves of 12.5 cm is then indicative of the meter scale and smaller structure of the surface. The specular term is indicative of large scale surface undulations and should not be causally related to other surface physical properties. A simplified model of diffuse scattering is described along with two rock distribution models. The results of applying the models to a planet of uniform fractional rock coverage with values ranging from 5 to 20% are discussed.
Radiosity diffusion model in 3D
Riley, Jason D.; Arridge, Simon R.; Chrysanthou, Yiorgos; Dehghani, Hamid; Hillman, Elizabeth M. C.; Schweiger, Martin
2001-11-01
We present the Radiosity-Diffusion model in three dimensions(3D), as an extension to previous work in 2D. It is a method for handling non-scattering spaces in optically participating media. We present the extension of the model to 3D including an extension to the model to cope with increased complexity of the 3D domain. We show that in 3D more careful consideration must be given to the issues of meshing and visibility to model the transport of light within reasonable computational bounds. We demonstrate the model to be comparable to Monte-Carlo simulations for selected geometries, and show preliminary results of comparisons to measured time-resolved data acquired on resin phantoms.
Recent advances in modelling diffuse radiation
Energy Technology Data Exchange (ETDEWEB)
Boland, John; Ridley, Barbara [Centre for Industrial and Applied Mathematics, Univ. of South Australia, Mawson Lakes, SA (Australia)
2008-07-01
Boland et al (2001) developed a validated model for Australian conditions, using a logistic function instead of piecewise linear or simple nonlinear functions. Recently, Jacovides et al (2006) have verified that this model performs well for locations in Cyprus. Their analysis includes using moving average techniques to demonstrate the form of the relationship, which corresponds well to a logistic relationship. We have made significant advances in both the intuitive and theoretical justification of the use of the logistic function. In the theoretical development of the model utilising advanced non-parametric statistical methods. We have also constructed a method of identifying values that are likely to be erroneous. Using quadratic programming, we can eliminate outliers in diffuse radiation values, the data most prone to errors in measurement. Additionally, this is a first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors (see Boland and Ridley 2007). Our more recent investigations focus on examining the effects of adding additional explanatory variables to enhance the predictability of the model. Examples for Australian and other locations will be presented. (orig.)
Diffusion processes and related topics in biology
Ricciardi, Luigi M
1977-01-01
These notes are based on a one-quarter course given at the Department of Biophysics and Theoretical Biology of the University of Chicago in 1916. The course was directed to graduate students in the Division of Biological Sciences with interests in population biology and neurobiology. Only a slight acquaintance with probability and differential equations is required of the reader. Exercises are interwoven with the text to encourage the reader to play a more active role and thus facilitate his digestion of the material. One aim of these notes is to provide a heuristic approach, using as little mathematics as possible, to certain aspects of the theory of stochastic processes that are being increasingly employed in some of the population biol ogy and neurobiology literature. While the subject may be classical, the nov elty here lies in the approach and point of view, particularly in the applica tions such as the approach to the neuronal firing problem and its related dif fusion approximations. It is a ple...
Reaction-diffusion pulses: a combustion model
International Nuclear Information System (INIS)
Campos, Daniel; Llebot, Josep Enric; Fort, Joaquim
2004-01-01
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations
Reaction-diffusion pulses: a combustion model
Energy Technology Data Exchange (ETDEWEB)
Campos, Daniel [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Llebot, Josep Enric [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Fort, Joaquim [Dept. de FIsica, Univ. de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)
2004-07-02
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations.
International Nuclear Information System (INIS)
Premuda, F.
1983-01-01
Two lines in improved neutron diffusion theory extending the efficiency of finite-difference diffusion codes to the field of optically small systems, are here reviewed. The firs involves the nodal solution for tensorial diffusion equation in slab geometry and tensorial formulation in parallelepiped and cylindrical gemometry; the dependence of critical eigenvalue from small slab thicknesses is also analitically investigated and finally a regularized tensorial diffusion equation is derived for slab. The other line refer to diffusion models formally unchanged with respect to the classical one, but where new size-dependent RTGB definitions for diffusion parameters are adopted, requiring that they allow to reproduce, in diffusion approach, the terms of neutron transport global balance; the trascendental equation for the buckling, arising in slab, sphere and parallelepiped geometry from the above requirement, are reported and the sizedependence of the new diffusion coefficient and extrapolated end point is investigated
Stochastic Modelling of the Diffusion Coefficient for Concrete
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
In the paper, a new stochastic modelling of the diffusion coefficient D is presented. The modelling is based on physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficients D is strongly dependent on the w/c ratio and the temperature....
Verifying reciprocal relations for experimental diffusion coefficients in multicomponent mixtures
DEFF Research Database (Denmark)
Medvedev, Oleg; Shapiro, Alexander
2003-01-01
The goal of the present study is to verify the agreement of the available data on diffusion in ternary mixtures with the theoretical requirement of linear non-equilibrium thermodynamics consisting in symmetry of the matrix of the phenomenological coefficients. A common set of measured diffusion...... coefficients for a three-component mixture consists of four Fickian diffusion coefficients, each being reported separately. However, the Onsager theory predicts the existence of only three independent coefficients, as one of them disappears due to the symmetry requirement. Re-calculation of the Fickian...... extended sets of experimental data and reliable thermodynamic models were available. The sensitivity of the symmetry property to different thermodynamic parameters of the models was also checked. (C) 2003 Elsevier Science B.V. All rights reserved....
Diffusion-based recommendation with trust relations on tripartite graphs
Wang, Ximeng; Liu, Yun; Zhang, Guangquan; Xiong, Fei; Lu, Jie
2017-08-01
The diffusion-based recommendation approach is a vital branch in recommender systems, which successfully applies physical dynamics to make recommendations for users on bipartite or tripartite graphs. Trust links indicate users’ social relations and can provide the benefit of reducing data sparsity. However, traditional diffusion-based algorithms only consider rating links when making recommendations. In this paper, the complementarity of users’ implicit and explicit trust is exploited, and a novel resource-allocation strategy is proposed, which integrates these two kinds of trust relations on tripartite graphs. Through empirical studies on three benchmark datasets, our proposed method obtains better performance than most of the benchmark algorithms in terms of accuracy, diversity and novelty. According to the experimental results, our method is an effective and reasonable way to integrate additional features into the diffusion-based recommendation approach.
Recommendation based on trust diffusion model.
Yuan, Jinfeng; Li, Li
2014-01-01
Recommender system is emerging as a powerful and popular tool for online information relevant to a given user. The traditional recommendation system suffers from the cold start problem and the data sparsity problem. Many methods have been proposed to solve these problems, but few can achieve satisfactory efficiency. In this paper, we present a method which combines the trust diffusion (DiffTrust) algorithm and the probabilistic matrix factorization (PMF). DiffTrust is first used to study the possible diffusions of trust between various users. It is able to make use of the implicit relationship of the trust network, thus alleviating the data sparsity problem. The probabilistic matrix factorization (PMF) is then employed to combine the users' tastes with their trusted friends' interests. We evaluate the algorithm on Flixster, Moviedata, and Epinions datasets, respectively. The experimental results show that the recommendation based on our proposed DiffTrust + PMF model achieves high performance in terms of the root mean square error (RMSE), Recall, and F Measure.
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO; HITTMEIR, SABINE; JÜ NGEL, ANSGAR
2012-01-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy
A spatial structural derivative model for ultraslow diffusion
Directory of Open Access Journals (Sweden)
Xu Wei
2017-01-01
Full Text Available This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function ex is selected as the structural function to construct the local structural derivative diffusion equation model. The analytical solution of the diffusion equation is a form of Biexponential distribution. Its corresponding mean squared displacement is numerically calculated, and increases more slowly than the logarithmic function of time. The local structural derivative diffusion equation with the structural function ex in space is an alternative physical and mathematical modeling model to characterize a kind of ultraslow diffusion.
Observational Constraints for Modeling Diffuse Molecular Clouds
Federman, S. R.
2014-02-01
Ground-based and space-borne observations of diffuse molecular clouds suggest a number of areas where further improvements to modeling efforts is warranted. I will highlight those that have the widest applicability. The range in CO fractionation caused by selective isotope photodissociation, in particular the large 12C16O/13C16O ratios observed toward stars in Ophiuchus, is not reproduced well by current models. Our ongoing laboratory measurements of oscillator strengths and predissociation rates for Rydberg transitions in CO isotopologues may help clarify the situtation. The CH+ abundance continues to draw attention. Small scale structure seen toward ζ Per may provide additional constraints on the possible synthesis routes. The connection between results from optical transitions and those from radio and sub-millimeter wave transitions requires further effort. A study of OH+ and OH toward background stars reveals that these species favor different environments. This brings to focus the need to model each cloud along the line of sight separately, and to allow the physical conditions to vary within an individual cloud, in order to gain further insight into the chemistry. Now that an extensive set of data on molecular excitation is available, the models should seek to reproduce these data to place further constraints on the modeling results.
Modeling dendrite density from magnetic resonance diffusion measurements
DEFF Research Database (Denmark)
Jespersen, Sune Nørhøj; Kroenke, CD; Østergaard, Leif
2007-01-01
in this model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (DL) and perpendicular (DT) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.......e., in extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides......Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal...
Robust and fast nonlinear optimization of diffusion MRI microstructure models.
Harms, R L; Fritz, F J; Tobisch, A; Goebel, R; Roebroeck, A
2017-07-15
Advances in biophysical multi-compartment modeling for diffusion MRI (dMRI) have gained popularity because of greater specificity than DTI in relating the dMRI signal to underlying cellular microstructure. A large range of these diffusion microstructure models have been developed and each of the popular models comes with its own, often different, optimization algorithm, noise model and initialization strategy to estimate its parameter maps. Since data fit, accuracy and precision is hard to verify, this creates additional challenges to comparability and generalization of results from diffusion microstructure models. In addition, non-linear optimization is computationally expensive leading to very long run times, which can be prohibitive in large group or population studies. In this technical note we investigate the performance of several optimization algorithms and initialization strategies over a few of the most popular diffusion microstructure models, including NODDI and CHARMED. We evaluate whether a single well performing optimization approach exists that could be applied to many models and would equate both run time and fit aspects. All models, algorithms and strategies were implemented on the Graphics Processing Unit (GPU) to remove run time constraints, with which we achieve whole brain dataset fits in seconds to minutes. We then evaluated fit, accuracy, precision and run time for different models of differing complexity against three common optimization algorithms and three parameter initialization strategies. Variability of the achieved quality of fit in actual data was evaluated on ten subjects of each of two population studies with a different acquisition protocol. We find that optimization algorithms and multi-step optimization approaches have a considerable influence on performance and stability over subjects and over acquisition protocols. The gradient-free Powell conjugate-direction algorithm was found to outperform other common algorithms in terms of
International Nuclear Information System (INIS)
Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-01-01
Highlights: • Fractal theory is introduced into the prediction of VOC diffusion coefficient. • MSFC model of the diffusion coefficient is developed for porous building materials. • The MSFC model contains detailed pore structure parameters. • The accuracy of the MSFC model is verified by independent experiments. - Abstract: 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.
A new model of anomalous phosphorus diffusion in silicon
International Nuclear Information System (INIS)
Budil, M.; Poetzl, H.; Stingeder, G.; Grasserbauer, M.
1989-01-01
A model is presented to describe the 'kink and tail' diffusion of phosphorus. The diffusion behaviour of phosphorus is expplained by the motion of phosphorus-interstitial and phosphorus-vacancy pairs in different charge states. The model yields the enhancement of diffusion in the tail region depending on surface concentration. Furthermore it yields the same selfdiffusion coefficient for interstitials as the gold diffusion experiments. A transformation of the diffusion equation was found to reduce the number of simulation equations. (author) 7 refs., 5 figs
International Nuclear Information System (INIS)
Kubaschewski, O.
1983-01-01
The diffusion rate values of titanium, its compounds and alloys are summarized and tabulated. The individual chemical diffusion coefficients and self-diffusion coefficients of certain isotopes are given. Experimental methods are listed which were used for the determination of diffusion coefficients. Some values have been taken over from other studies. Also given are graphs showing the temperature dependences of diffusion and changes in the diffusion coefficient with concentration changes
Structured inverse modeling in parabolic diffusion processess
Schulz, Volker; Siebenborn, Martin; Welker, Kathrin
2014-01-01
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A novel shape gradient is derived in parabolic processes. Furthermore quasi-Newton techniques are used in order to accelerate shape gradient based iterations in shape space. Numerical investigations support the theoretical results.
Matrix diffusion model. In situ tests using natural analogues
Energy Technology Data Exchange (ETDEWEB)
Rasilainen, K. [VTT Energy, Espoo (Finland)
1997-11-01
Matrix diffusion is an important retarding and dispersing mechanism for substances carried by groundwater in fractured bedrock. Natural analogues provide, unlike laboratory or field experiments, a possibility to test the model of matrix diffusion in situ over long periods of time. This thesis documents quantitative model tests against in situ observations, done to support modelling of matrix diffusion in performance assessments of nuclear waste repositories. 98 refs. The thesis includes also eight previous publications by author.
Matrix diffusion model. In situ tests using natural analogues
International Nuclear Information System (INIS)
Rasilainen, K.
1997-11-01
Matrix diffusion is an important retarding and dispersing mechanism for substances carried by groundwater in fractured bedrock. Natural analogues provide, unlike laboratory or field experiments, a possibility to test the model of matrix diffusion in situ over long periods of time. This thesis documents quantitative model tests against in situ observations, done to support modelling of matrix diffusion in performance assessments of nuclear waste repositories
The EZ diffusion model provides a powerful test of simple empirical effects.
van Ravenzwaaij, Don; Donkin, Chris; Vandekerckhove, Joachim
2017-04-01
Over the last four decades, sequential accumulation models for choice response times have spread through cognitive psychology like wildfire. The most popular style of accumulator model is the diffusion model (Ratcliff Psychological Review, 85, 59-108, 1978), which has been shown to account for data from a wide range of paradigms, including perceptual discrimination, letter identification, lexical decision, recognition memory, and signal detection. Since its original inception, the model has become increasingly complex in order to account for subtle, but reliable, data patterns. The additional complexity of the diffusion model renders it a tool that is only for experts. In response, Wagenmakers et al. (Psychonomic Bulletin & Review, 14, 3-22, 2007) proposed that researchers could use a more basic version of the diffusion model, the EZ diffusion. Here, we simulate experimental effects on data generated from the full diffusion model and compare the power of the full diffusion model and EZ diffusion to detect those effects. We show that the EZ diffusion model, by virtue of its relative simplicity, will be sometimes better able to detect experimental effects than the data-generating full diffusion model.
Modelling Bourdieu: An extension of the Axelrod cultural diffusion model
Trigg, Andrew B.; Bertie, Andrew J.; Himmelweit, Susan F.
2008-01-01
The contribution to the social theory of consumption of the late Pierre Bourdieu has been widely recognized, but not fully absorbed by the economics discipline. To address this lacuna, an agent-based model of Bourdieu's social theory is developed by extending Axelrod's cultural diffusion model. Bourdieu's theory is decomposed into two components: a capital effect on social interaction and an innovation effect. Whereas simulations of the capital effect are found to have a key role in the repro...
Turbulent diffusion modelling for windflow and dispersion analysis
International Nuclear Information System (INIS)
Bartzis, J.G.
1988-01-01
The need for simple but reliable models for turbulent diffusion for windflow and atmospheric dispersion analysis is a necessity today if one takes into consideration the relatively high demand in computer time and costs for such an analysis, arising mainly from the often large solution domains needed, the terrain complexity and the transient nature of the phenomena. In the accident consequence assessment often there is a need for a relatively large number of cases to be analysed increasing further the computer time and costs. Within the framework of searching for relatively simple and universal eddy viscosity/diffusivity models, a new three dimensional non isotropic model is proposed applicable to any domain complexity and any atmospheric stability conditions. The model utilizes the transport equation for turbulent kinetic energy but introduces a new approach in effective length scale estimation based on the flow global characteristics and local atmospheric stability. The model is discussed in detail and predictions are given for flow field and boundary layer thickness. The results are compared with experimental data with satisfactory results
International Nuclear Information System (INIS)
Montoto, M.; Rodriguez Rey, A.; Ruiz de Argandona, V.G.; Calleja, L.; Menendez, B.
1992-01-01
The possibility that radionuclide retardation by rock matrix diffusion will be limited in granitic rocks by geological factors is studied, as well as the possibility that diffusion will be confined to a narrow zone from water-conducting fractures. Petrophysical measurements, uranium series and geochemical analyses in the rock adjacent to fractures, have been performed to establish the extent of fracture-related microstructural changes that might influence the potential for diffusion and whether or not there is any record of diffusion of uranium, its daughters, or other elements. The results obtained from El Berrocal (Spain), Stripa (Sweden) and White-shell (Canada) granites, suggest that: (a) there is a zone adjacent to the fractures (generally less than 100 mm) where microstructural changes and enhanced uranium mobility exist; (b) the evidence for diffusion having taken place in the rock is confined largely to this zone. So, it appears that diffusivity determinations on rock collected away from the influence of fractures will not give representative data for diffusion modelling, in addition to the effect of distressing after removing rocks from depth. It is suggested that diffusion will be of limited effectiveness as a retardation mechanism in many granitic rocks, particularly in water movement confined to narrow channels where access by nuclides to the fracture walls is restricted. 51 refs., 56 figs., 9 tabs., 9 appendices
Study of a diffusion flamelet model, with preferential diffusion effects included
Delhaye, S.; Somers, L.M.T.; Bongers, H.; Oijen, van J.A.; Goey, de L.P.H.; Dias, V.
2005-01-01
The non-premixed flamelet model of Peters [1] (model1), which does not include preferential diffusion effects is investigated. Two similar models are presented, but without the assumption of unity Lewis numbers. One of these models was derived by Peters & Pitsch [2] (model2), while the other one was
Diffusion coefficient adaptive correction in Lagrangian puff model
International Nuclear Information System (INIS)
Tan Wenji; Wang Dezhong; Ma Yuanwei; Ji Zhilong
2014-01-01
Lagrangian puff model is widely used in the decision support system for nuclear emergency management. The diffusion coefficient is one of the key parameters impacting puff model. An adaptive method was proposed in this paper, which could correct the diffusion coefficient in Lagrangian puff model, and it aimed to improve the accuracy of calculating the nuclide concentration distribution. This method used detected concentration data, meteorological data and source release data to estimate the actual diffusion coefficient with least square method. The diffusion coefficient adaptive correction method was evaluated by Kincaid data in MVK, and was compared with traditional Pasquill-Gifford (P-G) diffusion scheme method. The results indicate that this diffusion coefficient adaptive correction method can improve the accuracy of Lagrangian puff model. (authors)
Carbon diffusion behavior in molybdenum at relatively low temperatures
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Hiraoka, Yutaka, E-mail: hiraoka@dap.ous.ac.j [Department of Applied Physics, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005 (Japan); Imamura, Kyosuke [Graduate School of Science, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005 (Japan); Kadokura, Takanori; Yamamoto, Yoshiharu [Materials Research Department, A.L.M.T. Corp., 2 Iwasekoshi-machi, Toyama 931-8543 (Japan)
2010-01-07
Purpose of this study is to investigate the carbon diffusion behavior in pure molybdenum at relatively low temperatures by means of fracture surface observation. Carbon addition was performed at a temperature of 1273-1373 K with the heating time being changed. Fracture surface of the specimen after carbon addition was examined using SEM and the carbon diffusion distance was estimated from the change of fracture mode as a function of the distance from the surface. Results are summarized as follows. First, the carbon diffusion distance increased approximately linearly with the increase of heating time from 1.2 to 10.8 ks. This relationship does not agree with that obtained at much higher temperatures. From Arrhenius plots of the slope of the straight line and the temperature, activation energy was calculated (155 kJ/mol). Secondly, the carbon diffusion distance estimated in this study was generally larger than that simulated using the data of Rudman, particularly at a longer heating time.
Diffusion models in metamorphic thermo chronology: philosophy and methods
International Nuclear Information System (INIS)
Munha, Jose Manuel; Tassinari, Colombo Celso Gaeta
1999-01-01
Understanding kinetics of diffusion is of major importance to the interpretation of isotopic ages in metamorphic rocks. This paper provides a review of concepts and methodologies involved on the various diffusion models that can be applied to radiogenic systems in cooling rocks. The central concept of closure temperature is critically discussed and quantitative estimates for the various diffusion models are evaluated, in order to illustrate the controlling factors and the limits of their practical application. (author)
Computing diffusivities from particle models out of equilibrium
Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia
2018-04-01
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.
Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong
2016-12-09
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 (R 2 = 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.
Modelling Ni diffusion in bentonite using different sorption models
International Nuclear Information System (INIS)
Pfingsten, W.; Baeyens, B.; Bradbury, M.
2010-01-01
(II) retardation on the Fe(II) concentration level in the bentonite pore water and the related Fe(II) sorption on exchange and surface complexation sites. The Ni(II) retardation is lower for higher Fe(II) concentrations. Generally, assuming that the Fe(II) background concentration in the bentonite is determined by saturation with siderite, Fe(II) competition reduces the Ni retardation by an order of magnitude compared to the case without competition. Since the Fe(II) concentration in the near-field of a high-level radioactive waste repository may change with time due to canister corrosion processes and mineral precipitation/dissolution reactions, the diffusion of Ni(II), and more generally also metals which are chemically similar (valence state, hydrolysis behaviour) e.g. Co, Zn, Mn.. should be modelled using mechanistic sorption models taking into account competitive sorption processes, i.e. using a more detailed reactive transport approach to describe radionuclide transport within the bentonite correctly. (authors)
A variable-order fractal derivative model for anomalous diffusion
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Liu Xiaoting
2017-01-01
Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
A consistent transported PDF model for treating differential molecular diffusion
Wang, Haifeng; Zhang, Pei
2016-11-01
Differential molecular diffusion is a fundamentally significant phenomenon in all multi-component turbulent reacting or non-reacting flows caused by the different rates of molecular diffusion of energy and species concentrations. In the transported probability density function (PDF) method, the differential molecular diffusion can be treated by using a mean drift model developed by McDermott and Pope. This model correctly accounts for the differential molecular diffusion in the scalar mean transport and yields a correct DNS limit of the scalar variance production. The model, however, misses the molecular diffusion term in the scalar variance transport equation, which yields an inconsistent prediction of the scalar variance in the transported PDF method. In this work, a new model is introduced to remedy this problem that can yield a consistent scalar variance prediction. The model formulation along with its numerical implementation is discussed, and the model validation is conducted in a turbulent mixing layer problem.
Diffuse radiation models and monthly-average, daily, diffuse data for a wide latitude range
International Nuclear Information System (INIS)
Gopinathan, K.K.; Soler, A.
1995-01-01
Several years of measured data on global and diffuse radiation and sunshine duration for 40 widely spread locations in the latitude range 36° S to 60° N are used to develop and test models for estimating monthly-mean, daily, diffuse radiation on horizontal surfaces. Applicability of the clearness-index (K) and sunshine fraction (SSO) models for diffuse estimation and the effect of combining several variables into a single multilinear equation are tested. Correlations connecting the diffuse to global fraction (HdH) with K and SSO predict Hd values more accurately than their separate use. Among clearness-index and sunshine-fraction models, SSO models are found to have better accuracy if correlations are developed for wide latitude ranges. By including a term for declinations in the correlation, the accuracy of the estimated data can be marginally improved. The addition of latitude to the equation does not help to improve the accuracy further. (author)
International Nuclear Information System (INIS)
Cardon, Clement
2016-01-01
This Ph.D. topic is focused on the modelling of stratification kinetics for an oxide-metal corium pool (U-O-Zr-steel system) in terms of multicomponent and multiphase diffusion. This work is part of a larger research effort for the development of a detailed corium pool modelling based on a CFD approach for thermal hydraulics. The overall goal is to improve the understanding of the involved phenomena and obtain closure laws for integral macroscopic models. The phase-field method coupled with an energy functional using the CALPHAD method appears to be relevant for this purpose. In a first part, we have developed a diffuse interface model in order to describe the diffusion process in the U-O system. This model has been coupled with a CALPHAD thermodynamic database and its parameterization has been developed with, in particular, an up-scaling procedure related to the interface thickness. Then, within the framework of a modelling for the U-O-Zr ternary system, we have proposed a generalization of the diffuse interface model through an assumption of local equilibrium for redox mechanisms. A particular attention was paid to the model analysis by 1D numerical simulations with a special focus on the steady state composition profiles. Finally we have applied this model to the U-O-Zr-Fe system. For that purpose, we have considered a configuration close to small-scale experimental tests of oxide-metal corium pool stratification. (author) [fr
Performance modeling of parallel algorithms for solving neutron diffusion problems
International Nuclear Information System (INIS)
Azmy, Y.Y.; Kirk, B.L.
1995-01-01
Neutron diffusion calculations are the most common computational methods used in the design, analysis, and operation of nuclear reactors and related activities. Here, mathematical performance models are developed for the parallel algorithm used to solve the neutron diffusion equation on message passing and shared memory multiprocessors represented by the Intel iPSC/860 and the Sequent Balance 8000, respectively. The performance models are validated through several test problems, and these models are used to estimate the performance of each of the two considered architectures in situations typical of practical applications, such as fine meshes and a large number of participating processors. While message passing computers are capable of producing speedup, the parallel efficiency deteriorates rapidly as the number of processors increases. Furthermore, the speedup fails to improve appreciably for massively parallel computers so that only small- to medium-sized message passing multiprocessors offer a reasonable platform for this algorithm. In contrast, the performance model for the shared memory architecture predicts very high efficiency over a wide range of number of processors reasonable for this architecture. Furthermore, the model efficiency of the Sequent remains superior to that of the hypercube if its model parameters are adjusted to make its processors as fast as those of the iPSC/860. It is concluded that shared memory computers are better suited for this parallel algorithm than message passing computers
Individual differences in emotion word processing: A diffusion model analysis.
Mueller, Christina J; Kuchinke, Lars
2016-06-01
The exploratory study investigated individual differences in implicit processing of emotional words in a lexical decision task. A processing advantage for positive words was observed, and differences between happy and fear-related words in response times were predicted by individual differences in specific variables of emotion processing: Whereas more pronounced goal-directed behavior was related to a specific slowdown in processing of fear-related words, the rate of spontaneous eye blinks (indexing brain dopamine levels) was associated with a processing advantage of happy words. Estimating diffusion model parameters revealed that the drift rate (rate of information accumulation) captures unique variance of processing differences between happy and fear-related words, with highest drift rates observed for happy words. Overall emotion recognition ability predicted individual differences in drift rates between happy and fear-related words. The findings emphasize that a significant amount of variance in emotion processing is explained by individual differences in behavioral data.
Diffusion through Pig Gastric Mucin: Effect of Relative Humidity.
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Anna Runnsjö
Full Text Available Mucus covers the epithelium found in all intestinal tracts, where it serves as an important protecting barrier, and pharmaceutical drugs administrated by the oral, rectal, vaginal, ocular, or nasal route need to penetrate the mucus in order to reach their targets. Furthermore, the diffusion in mucus as well as the viscosity of mucus in the eyes, nose and throat can change depending on the relative humidity of the surrounding air. In this study we have investigated how diffusion through gels of mucin, the main protein in mucus, is affected by changes in ambient relative humidity (i.e. water activity. Already a small decrease in water activity was found to give rise to a significant decrease in penetration rate through the mucin gel of the antibacterial drug metronidazole. We also show that a decrease in water activity leads to decreased diffusion rate in the mucin gel for the fluorophore fluorescein. This study shows that it is possible to alter transport rates of molecules through mucus by changing the water activity in the gel. It furthermore illustrates the importance of considering effects of the water activity in the mucosa during development of potential pharmaceuticals.
Asymptotic solutions of diffusion models for risk reserves
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S. Shao
2003-01-01
Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.
Energy Technology Data Exchange (ETDEWEB)
Telfeyan, Katherine Christina [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ware, Stuart Douglas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Reimus, Paul William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Birdsell, Kay Hanson [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-11-06
Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.
Telfeyan, Katherine; Ware, S. Doug; Reimus, Paul W.; Birdsell, Kay H.
2018-02-01
Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.
Lévy flight with absorption: A model for diffusing diffusivity with long tails
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., ∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., πe(D ) ˜e-D /D0 . In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., πe(D ) ˜D-1 -α with 0 <α <1 . We find that in the short time limit, the width of displacement distribution is proportional to √{T }, implying that the diffusion is Fickian. But for long times, the width is proportional to T1 /2 α which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2 α which preserves its shape at all times.
Fractional diffusion models of transport in magnetically confined plasmas
International Nuclear Information System (INIS)
Castillo-Negrete, D. del; Carreras, B. A.; Lynch, V. E.
2005-01-01
Experimental and theoretical evidence suggests that transport in magnetically confined fusion plasmas deviates from the standard diffusion paradigm. Some examples include the confinement time scaling in L-mode plasmas, rapid pulse propagation phenomena, and inward transport in off-axis fueling experiments. The limitations of the diffusion paradigm can be traced back to the restrictive assumptions in which it is based. In particular, Fick's law, one of the cornerstones of diffusive transport, assumes that the fluxes only depend on local quantities, i. e. the spatial gradient of the field (s). another key issue is the Markovian assumption that neglects memory effects. Also, at a microscopic level, standard diffusion assumes and underlying Gaussian, uncorrelated stochastic process (i. e. a Brownian random walk) with well defined characteristic spatio-temporal scales. Motivated by the need to develop models of non-diffusive transport, we discuss here a class of transport models base on the use of fractional derivative operators. The models incorporates in a unified way non-Fickian transport, non-Markovian processes or memory effects, and non-diffusive scaling. At a microscopic level, the models describe an underlying stochastic process without characteristic spatio-temporal scales that generalizes the Brownian random walk. As a concrete case study to motivate and test the model, we consider transport of tracers in three-dimensional, pressure-gradient-driven turbulence. We show that in this system transport is non-diffusive and cannot be described in the context of the standard diffusion parading. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit super-diffusive scaling. there is quantitative agreement between the turbulence transport calculations and the proposed fractional diffusion model. In particular, the model
Diffusion of hydrous species in model basaltic melt
Zhang, Li; Guo, Xuan; Wang, Qinxia; Ding, Jiale; Ni, Huaiwei
2017-10-01
Water diffusion in Fe-free model basaltic melt with up to 2 wt% H2O was investigated at 1658-1846 K and 1 GPa in piston-cylinder apparatus using both hydration and diffusion couple techniques. Diffusion profiles measured by FTIR are consistent with a model in which both molecular H2O (H2Om) and hydroxyl (OH) contribute to water diffusion. OH diffusivity is roughly 13% of H2Om diffusivity, showing little dependence on temperature or water concentration. Water diffusion is dominated by the motion of OH until total H2O (H2Ot) concentration reaches 1 wt%. The dependence of apparent H2Ot diffusivity on H2Ot concentration appears to be overestimated by a previous study on MORB melt, but H2Ot diffusivity at 1 wt% H2Ot in basaltic melt is still greater than those in rhyolitic to andesitic melts. The appreciable contribution of OH to water diffusion in basaltic melt can be explained by enhanced mobility of OH, probably associated with the development of free hydroxyl bonded with network-modifying cations, as well as higher OH concentration. Calculation based on the Nernst-Einstein equation demonstrates that OH may serve as an effective charge carrier in hydrous basaltic melt, which could partly account for the previously observed strong influence of water on electrical conductivity of basaltic melt.
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.
A discrete model to study reaction-diffusion-mechanics systems.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available 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.
Lanzafame, S; Giannelli, M; Garaci, F; Floris, R; Duggento, A; Guerrisi, M; Toschi, N
2016-05-01
An increasing number of studies have aimed to compare diffusion tensor imaging (DTI)-related parameters [e.g., mean diffusivity (MD), fractional anisotropy (FA), radial diffusivity (RD), and axial diffusivity (AD)] to complementary new indexes [e.g., mean kurtosis (MK)/radial kurtosis (RK)/axial kurtosis (AK)] derived through diffusion kurtosis imaging (DKI) in terms of their discriminative potential about tissue disease-related microstructural alterations. Given that the DTI and DKI models provide conceptually and quantitatively different estimates of the diffusion tensor, which can also depend on fitting routine, the aim of this study was to investigate model- and algorithm-dependent differences in MD/FA/RD/AD and anisotropy mode (MO) estimates in diffusion-weighted imaging of human brain white matter. The authors employed (a) data collected from 33 healthy subjects (20-59 yr, F: 15, M: 18) within the Human Connectome Project (HCP) on a customized 3 T scanner, and (b) data from 34 healthy subjects (26-61 yr, F: 5, M: 29) acquired on a clinical 3 T scanner. The DTI model was fitted to b-value =0 and b-value =1000 s/mm(2) data while the DKI model was fitted to data comprising b-value =0, 1000 and 3000/2500 s/mm(2) [for dataset (a)/(b), respectively] through nonlinear and weighted linear least squares algorithms. In addition to MK/RK/AK maps, MD/FA/MO/RD/AD maps were estimated from both models and both algorithms. Using tract-based spatial statistics, the authors tested the null hypothesis of zero difference between the two MD/FA/MO/RD/AD estimates in brain white matter for both datasets and both algorithms. DKI-derived MD/FA/RD/AD and MO estimates were significantly higher and lower, respectively, than corresponding DTI-derived estimates. All voxelwise differences extended over most of the white matter skeleton. Fractional differences between the two estimates [(DKI - DTI)/DTI] of most invariants were seen to vary with the invariant value itself as well as with MK
Quantum-corrected drift-diffusion models for transport in semiconductor devices
International Nuclear Information System (INIS)
De Falco, Carlo; Gatti, Emilio; Lacaita, Andrea L.; Sacco, Riccardo
2005-01-01
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
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. Copyright © 2015 Elsevier B.V. All rights reserved.
Simple Brownian diffusion an introduction to the standard theoretical models
Gillespie, Daniel T
2013-01-01
Brownian diffusion, the motion of large molecules in a sea of very many much smaller molecules, is topical because it is one of the ways in which biologically important molecules move about inside living cells. This book presents the mathematical physics that underlies the four simplest models of Brownian diffusion.
Wind Power in Europe. A Simultaneous Innovation-Diffusion Model
International Nuclear Information System (INIS)
Soederholm, P.; Klaassen, G.
2007-01-01
The purpose of this paper is to provide a quantitative analysis of innovation and diffusion in the European wind power sector. We derive a simultaneous model of wind power innovation and diffusion, which combines a rational choice model of technological diffusion and a learning curve model of dynamic cost reductions. These models are estimated using pooled annual time series data for four European countries (Denmark, Germany, Spain and the United Kingdom) over the time period 1986-2000. The empirical results indicate that reductions in investment costs have been important determinants of increased diffusion of wind power, and these cost reductions can in turn be explained by learning activities and public R and D support. Feed-in tariffs also play an important role in the innovation and diffusion processes. The higher the feed-in price the higher, ceteris paribus, the rate of diffusion, and we present some preliminary empirical support for the notion that the impact on diffusion of a marginal increase in the feed-in tariff will differ depending on the support system used. High feed-in tariffs, though, also have a negative effect on cost reductions as they induce wind generators to choose high-cost sites and provide fewer incentives for cost cuts. This illustrates the importance of designing an efficient wind energy support system, which not only promotes diffusion but also provides continuous incentives for cost-reducing innovations
Technology diffusion of energy-related products in residential markets
Energy Technology Data Exchange (ETDEWEB)
Davis, L.J.; Bruneau, C.L.
1987-05-01
Acceptance of energy-related technologies by end residential consumers, manufacturers of energy-related products, and other influential intermediate markets such as builders will influence the potential for market penetration of innovative energy-related technologies developed by the Department of Energy, Office of Building and Community Systems (OBCS). In this report, Pacific Northwest Laboratory reviewed the available information on technology adoption, diffusion, and decision-making processes to provide OBCS with a background and understanding of the type of research that has previously been conducted on this topic. Insight was gained as to the potential decision-making criteria and motivating factors that influence the decision-maker(s) selection of new technologies, and some of the barriers to technology adoption faced by potential markets for OBCS technologies.
Modelling of diffuse solar fraction with multiple predictors
Energy Technology Data Exchange (ETDEWEB)
Ridley, Barbara; Boland, John [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Lauret, Philippe [Laboratoire de Physique du Batiment et des Systemes, University of La Reunion, Reunion (France)
2010-02-15
For some locations both global and diffuse solar radiation are measured. However, for many locations, only global radiation is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from direct on some other plane using trigonometry, we need to have diffuse radiation on the horizontal plane available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia. Boland et al. developed a validated model for Australian conditions. Boland et al. detailed our recent advances in developing the theoretical framework for the use of the logistic function instead of piecewise linear or simple nonlinear functions and was the first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors. We have developed a multiple predictor model, which is much simpler than previous models, and uses hourly clearness index, daily clearness index, solar altitude, apparent solar time and a measure of persistence of global radiation level as predictors. This model performs marginally better than currently used models for locations in the Northern Hemisphere and substantially better for Southern Hemisphere locations. We suggest it can be used as a universal model. (author)
International Nuclear Information System (INIS)
Yuan Youhong; Liu Jianbin; Xiao Enhua; He Zhong; Ma Cong; Xiang Jun; Jin Ke; Chen Wenjian; Xiao Jiehua
2007-01-01
Objective: To investigate the correlation between the apparent diffusion coefficient (ADC) values and the expression of proliferating cell nuclear antigen (PCNA), Bax, non-metastasis 23(nm23) and E-cadherin (E-cad) genes in rabbit models of liver VX 2 tumor before and after chemoembolization. Methods: Forty rabbit models of liver VX 2 tumor were divided into four groups with 10 rabbits in each group. The first group was the control group which didn't undergo chemoembolization. The second, third and fourth groups underwent chemoembolization, and diffusion weighted imaging (DWI) was performed at 16 h, 32 h and 48 h after chemoembolization respectively. The pathological and immunohistological examinations were carried out right after DWI. The sampling areas included the normal liver parenchyma around the tumor, the outer- layer area, the peripheral area, and the central area. The expression indices of PCNA, Bax, nm23, E-cad in all the samples were recorded and their correlation with corresponding ADC value were analyzed. Results: (1) PCNA expression indices in the outer layer area, the peripheral area and central area of VX 2 tumors(65.1%, 74.7%, and 59.0% respectively) were higher than that in the area of normal parenchyma around tumor (8.3%) (X 2 =19.08, P 2 tumors (nm 23: 1.7%, 0.4% , and 6.2% respectively; Bax: 2. 0%, 1.2% , and 2. 2% respectively; E-cad:6.2%, 2.0%, and 1.6% respectively) were lower than that in the area of normal parenchyma around tumor (nm23 16.5%; Bax 40.0%; E-cad 78.0%. χ 2 =12.86, 20.17, and 22.20 respectively; P 2 tumor periphery were 83.0%, 92.6% and 85.7% in 16 h group, 32 h group and 48 h group respectively after chemoembolization and those of nm23 expression indices were 2.3%, 7.4%, 4.2% and those of Bax expression index were 0.8%, 0.5%, 0.9% and those of E-cad expression indices were 2.8%, 1.0%, 1.1%. The PCNA and nm23 expression in the area of VX 2 tumor periphery increased at the beginning and then decreased (χ 2 =14.37, 8.94; P 2
What Can the Diffusion Model Tell Us About Prospective Memory?
Horn, Sebastian S.; Bayen, Ute J.; Smith, Rebekah E.
2011-01-01
Cognitive process models, such as Ratcliff’s (1978) diffusion model, are useful tools for examining cost- or interference effects in event-based prospective memory (PM). The diffusion model includes several parameters that provide insight into how and why ongoing-task performance may be affected by a PM task and is ideally suited to analyze performance because both reaction time and accuracy are taken into account. Separate analyses of these measures can easily yield misleading interpretations in cases of speed-accuracy tradeoffs. The diffusion model allows us to measure possible criterion shifts and is thus an important methodological improvement over standard analyses. Performance in an ongoing lexical decision task (Smith, 2003) was analyzed with the diffusion model. The results suggest that criterion shifts play an important role when a PM task is added, but do not fully explain the cost effect on RT. PMID:21443332
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO
2012-12-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.
Pricing Participating Products under a Generalized Jump-Diffusion Model
Directory of Open Access Journals (Sweden)
Tak Kuen Siu
2008-01-01
Full Text Available We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regime-switching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experiments are conducted to illustrate the practical implementation of the model and to highlight some features that can be obtained from our model.
WWER radial reflector modeling by diffusion codes
International Nuclear Information System (INIS)
Petkov, P. T.; Mittag, S.
2005-01-01
The two commonly used approaches to describe the WWER radial reflectors in diffusion codes, by albedo on the core-reflector boundary and by a ring of diffusive assembly size nodes, are discussed. The advantages and disadvantages of the first approach are presented first, then the Koebke's equivalence theory is outlined and its implementation for the WWER radial reflectors is discussed. Results for the WWER-1000 reactor are presented. Then the boundary conditions on the outer reflector boundary are discussed. The possibility to divide the library into fuel assembly and reflector parts and to generate each library by a separate code package is discussed. Finally, the homogenization errors for rodded assemblies are presented and discussed (Author)
Directory of Open Access Journals (Sweden)
Juan Wang
2017-11-01
Full Text Available Understanding diffusion of intrinsically disordered proteins (IDPs under crowded environments is of ubiquitous importance to modelling related dynamics in biological systems. In the present work, we proposed a theoretical framework to study the diffusion behavior of IDPs in polymer solutions. IDP is modeled as an ensemble of particles with a wide range of gyration radius subject to Flory-Fisk distribution, where the collapse effect which leads to the shrink of IDP due to polymer crowding is included. The diffusion coefficient of IDP is calculated as the average, denoted by 〈D〉, over the values of the particle samples. By properly incorporating the scaling relations for diffusion coefficient of nanoparticle (NP in polymer solutions, we are able to evaluate 〈D〉 straightforwardly and reveal the disorder and collapse effects on IDP’s diffusion in an explicit manner. Particular attentions are paid on comparison between the diffusion coefficient of an IDP and that of a NP. Results demonstrate that both disorder and collapse can enhance IDP diffusion rate. Our analysis shows that the crossover behavior reported by experiments can be actually a general phenomenon, namely, while a NP with smaller size than that of an IDP diffuses faster in simple solutions, the IDP may become the faster one under crowded conditions. We apply our theory to analyze the diffusion of several types of IDP in a few different polymer solutions. Good agreements between the theoretical results and the experimental data are obtained.
Dynamic Diffusion Estimation in Exponential Family Models
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Sečkárová, Vladimíra
2013-01-01
Roč. 20, č. 11 (2013), s. 1114-1117 ISSN 1070-9908 R&D Projects: GA MŠk 7D12004; GA ČR GA13-13502S Keywords : diffusion estimation * distributed estimation * paremeter estimation Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.639, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/dedecius-0396518.pdf
Atomistic models of Cu diffusion in CuInSe2 under variations in composition
Sommer, David E.; Dunham, Scott T.
2018-03-01
We construct an analytic model for the composition dependence of the vacancy-mediated Cu diffusion coefficient in undoped CuInSe2 using parameters from density functional theory. The applicability of this model is supported numerically with kinetic lattice Monte Carlo and Onsager transport tensors. We discuss how this model relates to experimental measurements of Cu diffusion, arguing that our results can account for significant contributions to the bulk diffusion of Cu tracers in non-stoichiometric CuInSe2.
Age-related distribution of vertebral bone-marrow diffusivity
Energy Technology Data Exchange (ETDEWEB)
Herrmann, Jochen, E-mail: j.herrmann@uke.de [Department of Diagnostic and Interventional Radiology, Martinistraße 52, D-20246 Hamburg (Germany); Department of Pediatric Radiology, Martinistraße 52, D-20246 Hamburg (Germany); Krstin, Nina, E-mail: ninakrstin@web.de [Department of Diagnostic and Interventional Radiology, Martinistraße 52, D-20246 Hamburg (Germany); Schoennagel, Bjoern P., E-mail: b.schoennagel@uke.de [Department of Diagnostic and Interventional Radiology, Martinistraße 52, D-20246 Hamburg (Germany); Sornsakrin, Marjike, E-mail: m.sornsakrin@uke.de [Department of Pediatrics, University Medical Center Hamburg-Eppendorf, Martinistraße 52, D-20246 Hamburg (Germany); Derlin, Thorsten, E-mail: t.derlin@uke.de [Department of Diagnostic and Interventional Radiology, Martinistraße 52, D-20246 Hamburg (Germany); Busch, Jasmin D., E-mail: jd.busch@uke.de [Department of Diagnostic and Interventional Radiology, Martinistraße 52, D-20246 Hamburg (Germany); Petersen, Kay Uwe, E-mail: Kay.Petersen@med.uni-tuebingen.de [Department of Psychiatry, University Clinic Tübingen, Calwerstraße 14 Tübingen 72076 (Germany); Graessner, Joachim, E-mail: joachim.graessner@siemens.com [Siemens AG Healthcare, Lindenplatz 2, 20099 Hamburg (Germany); Adam, Gerhard, E-mail: g.adam@uke.de [Department of Diagnostic and Interventional Radiology, Martinistraße 52, D-20246 Hamburg (Germany); Habermann, Christian R., E-mail: c.habermann@uke.de [Department of Diagnostic and Interventional Radiology, Martinistraße 52, D-20246 Hamburg (Germany)
2012-12-15
Purpose: To determine age-related diffusivity changes of the lumbar bone marrow by measurement of apparent diffusion coefficient (ADC) values. Materials and methods: The local ethics committee approved this study and written informed consent was obtained. The study group comprised 88 individuals including 75 healthy volunteers and 13 patients (48 female, 40 male; mean age 36 years, range 0–84 years). The pediatric cases were recruited from patients. Echo-planar diffusion weighted imaging (DWI) was performed with b-values of 50, 400 and 800 s/mm{sup 2}. ADC-values were calculated and measured in the 1st and 2nd vertebral body of the lumbar spine. Correlation between age and ADC-values was analyzed with Spearman's rho test. Results: The ADC values of the vertebral bone marrow of the lumbar spine showed a significant negative correlation with age (rho = −0.398, p = 0.001). The mean ADC values (×10{sup −3} mm{sup 2}/s) in the age groups 0–29 years (mean age 18.0 years, n = 42) and 30–88 years (mean age 51.6 years, n = 46) were 0.54 ± 0.07 and 0.47 ± 0.08, respectively (p < 0.001, T-test). No significant differences were found between children and young adults. Conclusion: Bone marrow ADC values of the lumbar spine show a linear decrease with growing age and thereby reflect the gradual changes of cell composition occurring during marrow conversion.
Weak diffusion limits of dynamic conditional correlation models
DEFF Research Database (Denmark)
Hafner, Christian M.; Laurent, Sebastien; Violante, Francesco
The properties of dynamic conditional correlation (DCC) models are still not entirely understood. This paper fills one of the gaps by deriving weak diffusion limits of a modified version of the classical DCC model. The limiting system of stochastic differential equations is characterized...... by a diffusion matrix of reduced rank. The degeneracy is due to perfect collinearity between the innovations of the volatility and correlation dynamics. For the special case of constant conditional correlations, a non-degenerate diffusion limit can be obtained. Alternative sets of conditions are considered...
International Nuclear Information System (INIS)
Smirnova, E.S.; Chuvil'deev, V.N.
1998-01-01
The model is suggested which describes the influence of large-angle grain boundary migration on a diffusion controlled creep rate in polycrystalline materials (Coble creep). The model is based on the concept about changing the value of migrating boundary free volume when introducing dislocations distributed over the grain bulk into this boundary. Expressions are obtained to calculate the grain boundary diffusion coefficient under conditions of boundary migration and the parameter, which characterized the value of Coble creep acceleration. A comparison is made between calculated and experimental data for Cd, Co and Fe
Verification of atmospheric diffusion models with data of atmospheric diffusion experiments
International Nuclear Information System (INIS)
Hato, Shinji; Homma, Toshimitsu
2009-02-01
The atmospheric diffusion experiments were implemented by Japan Atomic Energy Research Institute (JAERI) around Mount Tsukuba in 1989 and 1990, and the tracer gas concentration were monitored. In this study, the Gauss Plume Model and RAMS/HYPACT that are meteorological forecast code and atmospheric diffusion code with detailed physical law are made a comparison between monitored concentration. In conclusion, the Gauss Plume Model is better than RAM/HYPACT even complex topography if the estimation is around tens of kilometer form release point and the change in weather is constant for short time. This reason is difference of wind between RAMS and observation. (author)
Smith, Rachel A; Kim, Youllee; Zhu, Xun; Doudou, Dimi Théodore; Sternberg, Eleanore D; Thomas, Matthew B
2018-01-01
This study documents an investigation into the adoption and diffusion of eave tubes, a novel mosquito vector control, during a large-scale scientific field trial in West Africa. The diffusion of innovations (DOI) and the integrated model of behavior (IMB) were integrated (i.e., innovation attributes with attitudes and social pressures with norms) to predict participants' (N = 329) diffusion intentions. The findings showed that positive attitudes about the innovation's attributes were a consistent positive predictor of diffusion intentions: adopting it, maintaining it, and talking with others about it. As expected by the DOI and the IMB, the social pressure created by a descriptive norm positively predicted intentions to adopt and maintain the innovation. Drawing upon sharing research, we argued that the descriptive norm may dampen future talk about the innovation, because it may no longer be seen as a novel, useful topic to discuss. As predicted, the results showed that as the descriptive norm increased, the intention to talk about the innovation decreased. These results provide broad support for integrating the DOI and the IMB to predict diffusion and for efforts to draw on other research to understand motivations for social diffusion.
Duchêne, Gaëtan; Peeters, Frank; Peeters, André; Duprez, Thierry
2017-08-01
To compare the sensitivity and early temporal changes of diffusion parameters obtained from diffusion tensor imaging (DTI), diffusional kurtosis imaging (DKI), q-space analysis (QSA) and bi-exponential modelling in hyperacute stroke patients. A single investigational acquisition allowing the four diffusion analyses was performed on seven hyperacute stroke patients with a 3T system. The percentage change between ipsi- and contralateral regions were compared at admission and 24 h later. Two out of the seven patients were imaged every 6 h during this period. Kurtoses from both DKI and QSA were the most sensitive of the tested diffusion parameters in the few hours following ischemia. An early increase-maximum-decrease pattern of evolution was highlighted during the 24-h period for all parameters proportional to diffusion coefficients. A similar pattern was observed for both kurtoses in only one of two patients. Our comparison was performed using identical diffusion encoding timings and on patients in the same stage of their condition. Although preliminary, our findings confirm those of previous studies that showed enhanced sensitivity of kurtosis. A fine time mapping of diffusion metrics in hyperacute stroke patients was presented which advocates for further investigations on larger animal or human cohorts.
Diffuse Scattering Model of Indoor Wideband Propagation
DEFF Research Database (Denmark)
Franek, Ondrej; Andersen, Jørgen Bach; Pedersen, Gert Frølund
2011-01-01
segments in total and approximately 2 min running time on average computer. Frequency independent power levels at the walls around the circumference of the room and at four receiver locations in the middle of the room are observed. It is demonstrated that after finite period of initial excitation the field...... radio coverage predictions.......This paper presents a discrete-time numerical algorithm for computing field distribution in indoor environment by diffuse scattering from walls. Calculations are performed for a rectangular room with semi-reflective walls. The walls are divided into 0.5 x 0.5 m segments, resulting in 2272 wall...
MODEL OF THE TOKAMAK EDGE DENSITY PEDESTAL INCLUDING DIFFUSIVE NEUTRALS
International Nuclear Information System (INIS)
BURRELL, K.H.
2003-01-01
OAK-B135 Several previous analytic models of the tokamak edge density pedestal have been based on diffusive transport of plasma plus free-streaming of neutrals. This latter neutral model includes only the effect of ionization and neglects charge exchange. The present work models the edge density pedestal using diffusive transport for both the plasma and the neutrals. In contrast to the free-streaming model, a diffusion model for the neutrals includes the effect of both charge exchange and ionization and is valid when charge exchange is the dominant interaction. Surprisingly, the functional forms for the electron and neutral density profiles from the present calculation are identical to the results of the previous analytic models. There are some differences in the detailed definition of various parameters in the solution. For experimentally relevant cases where ionization and charge exchange rate are comparable, both models predict approximately the same width for the edge density pedestal
Microscopic modeling of the Raman diffusion
International Nuclear Information System (INIS)
Benisti, D.; Morice, O.; Gremillet, L.; Strozzi, D.
2010-01-01
In the typical conditions of density and electronic temperature of the Laser Megajoule (LMJ), a quantitative assessment of the Raman reflectivity requires an accurate calculation of the non-linear movement of each electron submitted to the waves propagating in the plasma. The interaction of a laser beam with a plasma generates an electronic wave shifted in frequency (that can be back-scattered) and an electron plasma wave (OPE). The OPE can give to the electrons a strongly non-linear movement by trapping them in a potential well. This non-linearity of microscopic origin has an impact on the plasma electronic density. We have succeeded in computing this plasma electronic density in a very accurate way by combining the principles of a perturbative approach with those of an adiabatic theory. Results show that the Raman diffusion can grow on temperature and density ranges more important than expected. We have predicted the threshold and the behavior of the Raman diffusion above this threshold as accurately as we had done it with a Vlasov code but by being 10000 times more rapid. (A.C.)
A strongly nonlinear reaction-diffusion model for a deterministic diffusive epidemic
International Nuclear Information System (INIS)
Kirane, M.; Kouachi, S.
1992-10-01
In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the diffusivities. (author). 7 refs
DEFF Research Database (Denmark)
Beauquier, Maxime; Schürmann, Carsten
2011-01-01
In this paper, we present a model based on relations for bigraphical reactive system [Milner09]. Its defining characteristics are that validity and reaction relations are captured as traces in a multi-set rewriting system. The relational model is derived from Milner's graphical definition...
Mockler, Eva; Reaney, Simeon; Mellander, Per-Erik; Wade, Andrew; Collins, Adrian; Arheimer, Berit; Bruen, Michael
2017-04-01
The agricultural sector is the most common suspected source of nutrient pollution in Irish rivers. However, it is also often the most difficult source to characterise due to its predominantly diffuse nature. Particulate phosphorus in surface water and dissolved phosphorus in groundwater are of particular concern in Irish water bodies. Hence the further development of models and indices to assess diffuse sources of contaminants are required for use by the Irish Environmental Protection Agency (EPA) to provide support for river basin planning. Understanding connectivity in the landscape is a vital component of characterising the source-pathway-receptor relationships for water-borne contaminants, and hence is a priority in this research. The DIFFUSE Project will focus on connectivity modelling and incorporation of connectivity into sediment, nutrient and pesticide risk mapping. The Irish approach to understanding and managing natural water bodies has developed substantially in recent years assisted by outputs from multiple research projects, including modelling and analysis tools developed during the Pathways and CatchmentTools projects. These include the Pollution Impact Potential (PIP) maps, which are an example of research output that is used by the EPA to support catchment management. The PIP maps integrate an understanding of the pollution pressures and mobilisation pathways and, using the source-pathways-receptor model, provide a scientific basis for evaluation of mitigation measures. These maps indicate the potential risk posed by nitrate and phosphate from diffuse agricultural sources to surface and groundwater receptors and delineate critical source areas (CSAs) as a means of facilitating the targeting of mitigation measures. Building on this previous research, the DIFFUSE Project will develop revised and new catchment managements tools focused on connectivity, sediment, phosphorus and pesticides. The DIFFUSE project will strive to identify the state
Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.
2013-01-01
Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to
Directory of Open Access Journals (Sweden)
Claude Rodrigue Bambe Moutsinga
2018-01-01
Full Text Available Most existing multivariate models in finance are based on diffusion models. These models typically lead to the need of solving systems of Riccati differential equations. In this paper, we introduce an efficient method for solving systems of stiff Riccati differential equations. In this technique, a combination of Laplace transform and homotopy perturbation methods is considered as an algorithm to the exact solution of the nonlinear Riccati equations. The resulting technique is applied to solving stiff diffusion model problems that include interest rates models as well as two and three-factor stochastic volatility models. We show that the present approach is relatively easy, efficient and highly accurate.
Diffusion related isotopic fractionation effects with one-dimensional advective–dispersive transport
Energy Technology Data Exchange (ETDEWEB)
Xu, Bruce S. [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Lollar, Barbara Sherwood [Earth Sciences Department, University of Toronto, 22 Russell Street, Toronto, ON M5S 3B1 (Canada); Passeport, Elodie [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Chemical Engineering and Applied Chemistry Department, University of Toronto, 200 College Street, Toronto, ON M5S 3E5 (Canada); Sleep, Brent E., E-mail: sleep@ecf.utoronto.ca [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada)
2016-04-15
larger than 10, DRIF effects will likely not be observable for common groundwater contaminants. Importantly, under most field conditions, D{sub mech}/D{sub eff} ≥ 10 is usually satisfied in the longitudinal direction, suggesting that DRIF is not likely to be observable in most groundwater systems in which contaminant transport is predominantly one-dimensional. Given the importance in the MDL it is recommended that MDL should always be explicitly reported in both modeling and field studies. - Highlights: • Diffusion-related isotope fractionation (DRIF) in subsurface contaminant transport • Investigation of effect of ratio of mechanical dispersion to diffusion • No observable DRIF for mechanical dispersion to diffusion ratio above 10 • Ratio of source concentration to detection limit important • Plume lengths over which DRIF is detectable are limited.
Diffusion related isotopic fractionation effects with one-dimensional advective–dispersive transport
International Nuclear Information System (INIS)
Xu, Bruce S.; Lollar, Barbara Sherwood; Passeport, Elodie; Sleep, Brent E.
2016-01-01
effects will likely not be observable for common groundwater contaminants. Importantly, under most field conditions, D_m_e_c_h/D_e_f_f ≥ 10 is usually satisfied in the longitudinal direction, suggesting that DRIF is not likely to be observable in most groundwater systems in which contaminant transport is predominantly one-dimensional. Given the importance in the MDL it is recommended that MDL should always be explicitly reported in both modeling and field studies. - Highlights: • Diffusion-related isotope fractionation (DRIF) in subsurface contaminant transport • Investigation of effect of ratio of mechanical dispersion to diffusion • No observable DRIF for mechanical dispersion to diffusion ratio above 10 • Ratio of source concentration to detection limit important • Plume lengths over which DRIF is detectable are limited.
Flux-limited diffusion models in radiation hydrodynamics
International Nuclear Information System (INIS)
Pomraning, G.C.; Szilard, R.H.
1993-01-01
The authors discuss certain flux-limited diffusion theories which approximately describe radiative transfer in the presence of steep spatial gradients. A new formulation is presented which generalizes a flux-limited description currently in widespread use for large radiation hydrodynamic calculations. This new formation allows more than one Case discrete mode to be described by a flux-limited diffusion equation. Such behavior is not extant in existing formulations. Numerical results predicted by these flux-limited diffusion models are presented for radiation penetration into an initially cold halfspace. 37 refs., 5 figs
Convergence of surface diffusion parameters with model crystal size
Cohen, Jennifer M.; Voter, Arthur F.
1994-07-01
A study of the variation in the calculated quantities for adatom diffusion with respect to the size of the model crystal is presented. The reported quantities include surface diffusion barrier heights, pre-exponential factors, and dynamical correction factors. Embedded atom method (EAM) potentials were used throughout this effort. Both the layer size and the depth of the crystal were found to influence the values of the Arrhenius factors significantly. In particular, exchange type mechanisms required a significantly larger model than standard hopping mechanisms to determine adatom diffusion barriers of equivalent accuracy. The dynamical events that govern the corrections to transition state theory (TST) did not appear to be as sensitive to crystal depth. Suitable criteria for the convergence of the diffusion parameters with regard to the rate properties are illustrated.
Models as Relational Categories
Kokkonen, Tommi
2017-11-01
Model-based learning (MBL) has an established position within science education. It has been found to enhance conceptual understanding and provide a way for engaging students in authentic scientific activity. Despite ample research, few studies have examined the cognitive processes regarding learning scientific concepts within MBL. On the other hand, recent research within cognitive science has examined the learning of so-called relational categories. Relational categories are categories whose membership is determined on the basis of the common relational structure. In this theoretical paper, I argue that viewing models as relational categories provides a well-motivated cognitive basis for MBL. I discuss the different roles of models and modeling within MBL (using ready-made models, constructive modeling, and generative modeling) and discern the related cognitive aspects brought forward by the reinterpretation of models as relational categories. I will argue that relational knowledge is vital in learning novel models and in the transfer of learning. Moreover, relational knowledge underlies the coherent, hierarchical knowledge of experts. Lastly, I will examine how the format of external representations may affect the learning of models and the relevant relations. The nature of the learning mechanisms underlying students' mental representations of models is an interesting open question to be examined. Furthermore, the ways in which the expert-like knowledge develops and how to best support it is in need of more research. The discussion and conceptualization of models as relational categories allows discerning students' mental representations of models in terms of evolving relational structures in greater detail than previously done.
Nonequilibrium two-dimensional Ising model with stationary uphill diffusion
Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia
2018-03-01
Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.
When mechanism matters: Bayesian forecasting using models of ecological diffusion
Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.
2017-01-01
Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.
Energy Technology Data Exchange (ETDEWEB)
Capdebosq, Y
1999-09-01
In order to study and simulate nuclear reactor cores, one needs to access the neutron distribution in the core. In practice, the description of this density of neutrons is given by a system of diffusion equations, coupled by non differential exchange terms. The strong heterogeneity of the medium constitutes a major obstacle to the numerical computation of this models at reasonable cost. Homogenization appears as compulsory. Heuristic methods have been developed since the origin by nuclear physicists, under a periodicity assumption on the coefficients. They consist in doing a fine computation one a single periodicity cell, to solve the system on the whole domain with homogeneous coefficients, and to reconstruct the neutron density by multiplying the solutions of the two computations. The objectives of this work are to provide mathematically rigorous basis to this factorization method, to obtain the exact formulas of the homogenized coefficients, and to start on geometries where two periodical medium are placed side by side. The first result of this thesis concerns eigenvalue problem models which are used to characterize the state of criticality of the reactor, under a symmetry assumption on the coefficients. The convergence of the homogenization process is proved, and formulas of the homogenized coefficients are given. We then show that without symmetry assumptions, a drift phenomenon appears. It is characterized by the mean of a real Bloch wave method, which gives the homogenized limit in the general case. These results for the critical problem are then adapted to the evolution model. Finally, the homogenization of the critical problem in the case of two side by side periodic medium is studied on a one dimensional on equation model. (authors)
Statistical model of a gas diffusion electrode. III. Photomicrograph study
Energy Technology Data Exchange (ETDEWEB)
Winsel, A W
1965-12-01
A linear section through a gas diffusion electrode produces a certain distribution function of sinews with the pores. From this distribution function some qualities of the pore structure are derived, and an automatic device to determine the distribution function is described. With a statistical model of a gas diffusion electrode the behavior of a DSK electrode is discussed and compared with earlier measurements of the flow resistance of this material.
International Nuclear Information System (INIS)
Kotrappa, P.; Bhanti, D.P.; Raghunath, B.
1976-01-01
The results of a study of the diffusivity of unattached decay products of thoron with respect to air changes using a recently developed diffusion sampler are reported. The dependence of diffusivity of radon/thoron decay products on relative humidity has also been investigated by measurement of diffusion coefficients in an atmosphere where relative humidities varied from 5 to 90%. Results are shown tabulated. (U.K.)
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, D T . But some studies have suggested a possible relationship between D T and the air changes per hour (ACH) through a room. The main goal of this study was to accurately estimate D T 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 D T and ACH, providing a surrogate parameter for estimating D T in real-life settings. For the first time, a mathematical expression for the relationship between D T 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 D T 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.
Numerical modelling of random walk one-dimensional diffusion
International Nuclear Information System (INIS)
Vamos, C.; Suciu, N.; Peculea, M.
1996-01-01
The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies
Modelling and simulation of diffusive processes methods and applications
Basu, SK
2014-01-01
This book addresses the key issues in the modeling and simulation of diffusive processes from a wide spectrum of different applications across a broad range of disciplines. Features: discusses diffusion and molecular transport in living cells and suspended sediment in open channels; examines the modeling of peristaltic transport of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; reviews thermal characterization of non-homogeneous media and scale-dependent porous dispersion resulting from velocity fluctuations; describes the modeling of nitrogen fate and transport
The taste cell-related diffuse chemosensory system.
Sbarbati, A; Osculati, F
2005-03-01
Elements expressing the molecular mechanisms of gustatory transduction have been described in several organs in the digestive and respiratory apparatuses. These taste cell-related elements are isolated cells, which are not grouped in buds, and they have been interpreted as chemoreceptors. Their presence in epithelia of endodermal origin suggests the existence of a diffuse chemosensory system (DCS) sharing common signaling mechanisms with the "classic" taste organs. The elements of this taste cell-related DCS display a site-related morphologic polymorphism, and in the past they have been indicated with various names (e.g., brush, tuft, caveolated, fibrillo-vesicular or solitary chemosensory cells). It may be that the taste cell-related DCS is like an iceberg: the taste buds are probably only the most visible portion, with most of the iceberg more caudally located in the form of solitary chemosensory cells or chemosensory clusters. Comparative anatomical studies in lower vertebrates suggest that this 'submerged' portion may represent the most phylogenetically ancient component of the system, which is probably involved in defensive or digestive mechanisms. In the taste buds, the presence of several cell subtypes and of a wide range of molecular mechanisms permits precise food analysis. The larger, 'submerged' portion of the iceberg is composed of a polymorphic population of isolated elements or cell clusters in which the molecular cascade of cell signaling needs to be explored in detail. The little data we have strongly suggests a close relationship with taste cells. Morphological and biochemical considerations suggest that the DCS is a potential new drug target. Modulation of the respiratory and digestive apparatuses through substances, which act on the molecular receptors of this chemoreceptive system, could be a new frontier in drug discovery.
A model of non-Gaussian diffusion in heterogeneous media
Lanoiselée, Yann; Grebenkov, Denis S.
2018-04-01
Recent progress in single-particle tracking has shown evidence of the non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. Similar behavior has also been observed in granular materials, turbulent flows, gels and colloidal suspensions, suggesting that this is a general feature of diffusion in complex media. A possible interpretation of this phenomenon is that a tracer explores a medium with spatio-temporal fluctuations which result in local changes of diffusivity. We propose and investigate an ergodic, easily interpretable model, which implements the concept of diffusing diffusivity. Depending on the parameters, the distribution of displacements can be either flat or peaked at small displacements with an exponential tail at large displacements. We show that the distribution converges slowly to a Gaussian one. We calculate statistical properties, derive the asymptotic behavior and discuss some implications and extensions.
Modelling of monovacancy diffusion in W over wide temperature range
International Nuclear Information System (INIS)
Bukonte, L.; Ahlgren, T.; Heinola, K.
2014-01-01
The diffusion of monovacancies in tungsten is studied computationally over a wide temperature range from 1300 K until the melting point of the material. Our modelling is based on Molecular Dynamics technique and Density Functional Theory. The monovacancy migration barriers are calculated using nudged elastic band method for nearest and next-nearest neighbour monovacancy jumps. The diffusion pre-exponential factor for monovacancy diffusion is found to be two to three orders of magnitude higher than commonly used in computational studies, resulting in attempt frequency of the order 10 15 Hz. Multiple nearest neighbour jumps of monovacancy are found to play an important role in the contribution to the total diffusion coefficient, especially at temperatures above 2/3 of T m , resulting in an upward curvature of the Arrhenius diagram. The probabilities for different nearest neighbour jumps for monovacancy in W are calculated at different temperatures
The parton model for the diffusion
International Nuclear Information System (INIS)
Ducati, M.B. Gay; Machado, M.V.T.
1999-01-01
We analyze the Buchmueller-Hebecker model for diffraction processes, point out its predictions to the diffractive structure function F D(3) 2 (x IP , β,Q 2 ). The break of factorization for the F D93) 2 present in recent H1 data is well described introducing an extra soft (reggeon) contribution as an extension to the model. (author)
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 combinatorial model of malware diffusion via bluetooth connections.
Directory of Open Access Journals (Sweden)
Stefano Merler
Full Text Available 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.
Diffusion approximation for modeling of 3-D radiation distributions
International Nuclear Information System (INIS)
Zardecki, A.; Gerstl, S.A.W.; De Kinder, R.E. Jr.
1985-01-01
A three-dimensional transport code DIF3D, based on the diffusion approximation, is used to model the spatial distribution of radiation energy arising from volumetric isotropic sources. Future work will be concerned with the determination of irradiances and modeling of realistic scenarios, relevant to the battlefield conditions. 8 refs., 4 figs
Energy Technology Data Exchange (ETDEWEB)
Jakob, A
2004-07-01
In this report a comprehensive overview on the matrix diffusion of solutes in fractured crystalline rocks is presented. Some examples from observations in crystalline bedrock are used to illustrate that matrix diffusion indeed acts on various length scales. Fickian diffusion is discussed in detail followed by some considerations on rock porosity. Due to the fact that the dual-porosity medium model is a very common and versatile method for describing solute transport in fractured porous media, the transport equations and the fundamental assumptions, approximations and simplifications are discussed in detail. There is a variety of geometrical aspects, processes and events which could influence matrix diffusion. The most important of these, such as, e.g., the effect of the flow-wetted fracture surface, channelling and the limited extent of the porous rock for matrix diffusion etc., are addressed. In a further section open issues and unresolved problems related to matrix diffusion are mentioned. Since matrix diffusion is one of the key retarding processes in geosphere transport of dissolved radionuclide species, matrix diffusion was consequently taken into account in past performance assessments of radioactive waste repositories in crystalline host rocks. Some issues regarding matrix diffusion are site-specific while others are independent of the specific situation of a planned repository for radioactive wastes. Eight different performance assessments from Finland, Sweden and Switzerland were considered with the aim of finding out how matrix diffusion was addressed, and whether a consistent picture emerges regarding the varying methodology of the different radioactive waste organisations. In the final section of the report some conclusions are drawn and an outlook is given. An extensive bibliography provides the reader with the key papers and reports related to matrix diffusion. (author)
Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model
Energy Technology Data Exchange (ETDEWEB)
Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand); Fichtner, Horst; Walter, Dominik [Institut für Theoretische Physik IV, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780 Bochum (Germany)
2017-05-20
We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatment of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.
Numerical modelling of swirling diffusive flames
Directory of Open Access Journals (Sweden)
Parra-Santos Teresa
2016-01-01
Full Text Available Computational Fluid Dynamics has been used to study the mixing and combustion of two confined jets whose setup and operating conditions are those of the benchmark of Roback and Johnson. Numerical model solves 3D transient Navier Stokes for turbulent and reactive flows. Averaged velocity profiles using RNG swirl dominated k-epsilon model have been validated with experimental measurements from other sources for the non reactive case. The combustion model is Probability Density Function. Bearing in mind the annular jet has swirl number over 0.5, a vortex breakdown appears in the axis of the burner. Besides, the sudden expansion with a ratio of 2 in diameter between nozzle exits and the test chamber produces the boundary layer separation with the corresponding torus shape recirculation. Contrasting the mixing and combustion models, the last one produces the reduction of the vortex breakdown.
Diffusion theory model for optimization calculations of cold neutron sources
International Nuclear Information System (INIS)
Azmy, Y.Y.
1987-01-01
Cold neutron sources are becoming increasingly important and common experimental facilities made available at many research reactors around the world due to the high utility of cold neutrons in scattering experiments. The authors describe a simple two-group diffusion model of an infinite slab LD 2 cold source. The simplicity of the model permits to obtain an analytical solution from which one can deduce the reason for the optimum thickness based solely on diffusion-type phenomena. Also, a second more sophisticated model is described and the results compared to a deterministic transport calculation. The good (particularly qualitative) agreement between the results suggests that diffusion theory methods can be used in parametric and optimization studies to avoid the generally more expensive transport calculations
International Nuclear Information System (INIS)
Mizia, R.E.; Clark, D.E.; Glazoff, M.V.; Lister, Tedd E.; Trowbridge, T.L.
2011-01-01
A research effort was made to evaluate the usefulness of modern thermodynamic and diffusion computational tools, Thermo-Calc(copyright) and Dictra(copyright), in optimizing the parameters for diffusion welding of Alloy 800H. This would achieve a substantial reduction in the overall number of experiments required to achieve optimal welding and post-weld heat treatment conditions. This problem is important because diffusion welded components of Alloy 800H are being evaluated for use in assembling compact, micro-channel heat exchangers that are being proposed in the design of a high temperature gas-cooled reactor by the US Department of Energy. The modeling was done in close contact with experimental work. The latter included using the Gleeble 3500 System(reg sign) for welding simulation, mechanical property measurement, and light optical and Scanning Electron Microscopy. The modeling efforts suggested a temperature of 1150 C for 1 hour with an applied pressure of 5 MPa using a 15 μm Ni foil as a joint filler to reduce chromium oxidation on the welded surfaces. Good agreement between modeled and experimentally determined concentration gradients was achieved, and model refinements to account for the complexity of actual alloy materials are suggested.
Radon diffusion through multilayer earthen covers: models and simulations
International Nuclear Information System (INIS)
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. The study has been conducted using a four-phase approach. The first phase develops the solution to the steady-state radon-diffusion equation in one-dimensieered barriers; disposal charge analysis; analysis of spent fuel policy implementation; spent f water. Field measurements and observations are reported for each site. Analytical data and field measurements are presented in tables and maps. Uranium concentrations in the sediments which were above detection limits ranged from 0.10 t 51.2 ppM. The mean of the logarithms of the uranium concentrations was 0.53. A group of high uranium concentrations occurs near the junctions of quadrangles AB, AC, BB, a 200 mK. In case 2), x-ray studies of isotopic phase separation in 3 He-- 4 He bcc solids were carried out by B. A. Fraass
The dynamics of multimodal integration: The averaging diffusion model.
Turner, Brandon M; Gao, Juan; Koenig, Scott; Palfy, Dylan; L McClelland, James
2017-12-01
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.
Diffusion of a collaborative care model in primary care: a longitudinal qualitative study
Directory of Open Access Journals (Sweden)
Vedel Isabelle
2013-01-01
Full Text Available 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.
Diffusion approximation of neuronal models revisited
Czech Academy of Sciences Publication Activity Database
Čupera, Jakub
2014-01-01
Roč. 11, č. 1 (2014), s. 11-25 ISSN 1547-1063. [International Workshop on Neural Coding (NC) /10./. Praha, 02.09.2012-07.09.2012] R&D Projects: GA ČR(CZ) GAP103/11/0282 Institutional support: RVO:67985823 Keywords : stochastic model * neuronal activity * first-passage time Subject RIV: JD - Computer Applications, Robotics Impact factor: 0.840, year: 2014
Directory of Open Access Journals (Sweden)
Olena G. Filatova
2018-04-01
Full Text Available Better insight into white matter (WM alterations after stroke onset could help to understand the underlying recovery mechanisms and improve future interventions. MR diffusion imaging enables to assess such changes. Our goal was to investigate the relation of WM diffusion characteristics derived from diffusion models of increasing complexity with the motor function of the upper limb. Moreover, we aimed to evaluate the variation of such characteristics across different WM structures of chronic stroke patients in comparison to healthy subjects. Subjects were scanned with a two b-value diffusion-weighted MRI protocol to exploit multiple diffusion models: single tensor, single tensor with isotropic compartment, bi-tensor model, bi-tensor with isotropic compartment. From each model we derived the mean tract fractional anisotropy (FA, mean (MD, radial (RD and axial (AD diffusivities outside the lesion site based on a WM tracts atlas. Asymmetry of these measures was correlated with the Fugl-Meyer upper extremity assessment (FMA score and compared between patient and control groups. Eighteen chronic stroke patients and eight age-matched healthy individuals participated in the study. Significant correlation of the outcome measures with the clinical scores of stroke recovery was found. The lowest correlation of the corticospinal tract FAasymmetry and FMA was with the single tensor model (r = −0.3, p = 0.2 whereas the other models reported results in the range of r = −0.79 ÷ −0.81 and p = 4E-5 ÷ 8E-5. The corticospinal tract and superior longitudinal fasciculus showed most alterations in our patient group relative to controls. Multiple compartment models yielded superior correlation of the diffusion measures and FMA compared to the single tensor model.
Estimation and prediction under local volatility jump-diffusion model
Kim, Namhyoung; Lee, Younhee
2018-02-01
Volatility is an important factor in operating a company and managing risk. In the portfolio optimization and risk hedging using the option, the value of the option is evaluated using the volatility model. Various attempts have been made to predict option value. Recent studies have shown that stochastic volatility models and jump-diffusion models reflect stock price movements accurately. However, these models have practical limitations. Combining them with the local volatility model, which is widely used among practitioners, may lead to better performance. In this study, we propose a more effective and efficient method of estimating option prices by combining the local volatility model with the jump-diffusion model and apply it using both artificial and actual market data to evaluate its performance. The calibration process for estimating the jump parameters and local volatility surfaces is divided into three stages. We apply the local volatility model, stochastic volatility model, and local volatility jump-diffusion model estimated by the proposed method to KOSPI 200 index option pricing. The proposed method displays good estimation and prediction performance.
Asymmetric diffusion model for oblique-incidence reflectometry
Institute of Scientific and Technical Information of China (English)
Yaqin Chen; Liji Cao; Liqun Sun
2011-01-01
A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectom-etry. By fitting to this asymmetric diffusion model, the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10% from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp') away from the incident point; particularly, μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10% accuracy. The method is verified by Monte Carlo simulations and experimentally tested on a phantom.%A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectometry.By fitting to this asymmetric diffusion model,the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10％ from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp')away from the incident point;particularly,μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10％ accuracy.The method is verified by Monte Carlo simulations and experimentally tested on a phantom.Knowledge about the optical properties,including the absorption coefficient (μa) and the reduced scattering coefficient (μ's =μs(1-g)),where μs is the scattering coefficient and g is the anisotropy factor of scattering,of biological tissues plays an important role for optical therapeutic and diagnostic techniques in medicine.
A fractional motion diffusion model for grading pediatric brain tumors.
Karaman, M Muge; Wang, He; Sui, Yi; Engelhard, Herbert H; Li, Yuhua; Zhou, Xiaohong Joe
2016-01-01
To demonstrate the feasibility of a novel fractional motion (FM) diffusion model for distinguishing low- versus high-grade pediatric brain tumors; and to investigate its possible advantage over apparent diffusion coefficient (ADC) and/or a previously reported continuous-time random-walk (CTRW) diffusion model. With approval from the institutional review board and written informed consents from the legal guardians of all participating patients, this study involved 70 children with histopathologically-proven brain tumors (30 low-grade and 40 high-grade). Multi- b -value diffusion images were acquired and analyzed using the FM, CTRW, and mono-exponential diffusion models. The FM parameters, D fm , φ , ψ (non-Gaussian diffusion statistical measures), and the CTRW parameters, D m , α , β (non-Gaussian temporal and spatial diffusion heterogeneity measures) were compared between the low- and high-grade tumor groups by using a Mann-Whitney-Wilcoxon U test. The performance of the FM model for differentiating between low- and high-grade tumors was evaluated and compared with that of the CTRW and the mono-exponential models using a receiver operating characteristic (ROC) analysis. The FM parameters were significantly lower ( p < 0.0001) in the high-grade ( D fm : 0.81 ± 0.26, φ : 1.40 ± 0.10, ψ : 0.42 ± 0.11) than in the low-grade ( D fm : 1.52 ± 0.52, φ : 1.64 ± 0.13, ψ : 0.67 ± 0.13) tumor groups. The ROC analysis showed that the FM parameters offered better specificity (88% versus 73%), sensitivity (90% versus 82%), accuracy (88% versus 78%), and area under the curve (AUC, 93% versus 80%) in discriminating tumor malignancy compared to the conventional ADC. The performance of the FM model was similar to that of the CTRW model. Similar to the CTRW model, the FM model can improve differentiation between low- and high-grade pediatric brain tumors over ADC.
Scale-invariant Green-Kubo relation for time-averaged diffusivity
Meyer, Philipp; Barkai, Eli; Kantz, Holger
2017-12-01
In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function. The time-averaged mean-squared displacement is given by 〈δ2¯〉 ˜2 DνtβΔν -β , where t is the total measurement time and Δ is the lag time. Here ν is the anomalous diffusion exponent obtained from ensemble-averaged measurements 〈x2〉 ˜tν , while β ≥-1 marks the growth or decline of the kinetic energy 〈v2〉 ˜tβ . Thus, we establish a connection between exponents that can be read off the asymptotic properties of the velocity correlation function and similarly for the transport constant Dν. We demonstrate our results with nonstationary scale-invariant stochastic and deterministic models, thereby highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average. If the averaged kinetic energy is finite, β =0 , the time scaling of 〈δ2¯〉 and 〈x2〉 are identical; however, the time-averaged transport coefficient Dν is not identical to the corresponding ensemble-averaged diffusion constant.
Evaluation of the Thermodynamic Models for the Thermal Diffusion Factor
DEFF Research Database (Denmark)
Gonzalez-Bagnoli, Mariana G.; Shapiro, Alexander; Stenby, Erling Halfdan
2003-01-01
Over the years, several thermodynamic models for the thermal diffusion factors for binary mixtures have been proposed. The goal of this paper is to test some of these models in combination with different equations of state. We tested the following models: those proposed by Rutherford and Drickamer...... we applied different thermodynamic models, such as the Soave-Redlich-Kwong and the Peng-Robinson equations of state. The necessity to try different thermo-dynamic models is caused by the high sensitivity of the thermal diffusion factors to the values of the partial molar properties. Two different...... corrections for the determination of the partial molar volumes have been implemented; the Peneloux correction and the correction based on the principle of corresponding states....
A novel rumor diffusion model considering the effect of truth in online social media
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 model of delayed hydride cracking in zirconium alloys
Shmakov, AA; Kalin, BA; Matvienko, YG; Singh, RN; De, PK
2004-01-01
We develop a method for the evaluation of the rate of delayed hydride cracking in zirconium alloys. The model is based on the stationary solution of the phenomenological diffusion equation and the detailed analysis of the distribution of hydrostatic stresses in the plane of a sharp tensile crack.
Three dimensional simulated modelling of diffusion capacitance of ...
African Journals Online (AJOL)
A three dimensional (3-D) simulated modelling was developed to analyse the excess minority carrier density in the base of a polycrystalline bifacial silicon solar cell. The concept of junction recombination velocity was ado-pted to quantify carrier flow through the junction, and to examine the solar cell diffusion capacitance for ...
Analytically solvable models of reaction-diffusion systems
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)
2004-05-01
We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.
An improved analytical model of diffusion through the RIST target
Bennett, J R J
2003-01-01
The diffusion and effusion through the RIST target is calculated using a more realistic model than previously. Extremely good fits to the data are obtained and new values of the time constants of effusion through the target and the ioniser are found.
Modeling intragranular diffusion in low-connectivity granular media
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.
Modeling the oxygen diffusion of nanocomposite-based food packaging films.
Bhunia, Kanishka; Dhawan, Sumeet; Sablani, Shyam S
2012-07-01
Polymer-layered silicate nanocomposites have been shown to improve the gas barrier properties of food packaging polymers. This study developed a computer simulation model using the commercial software, COMSOL Multiphysics to analyze changes in oxygen barrier properties in terms of relative diffusivity, as influenced by configuration and structural parameters that include volume fraction (φ), aspect ratio (α), intercalation width (W), and orientation angle (θ) of nanoparticles. The simulation was performed at different φ (1%, 3%, 5%, and 7%), α (50, 100, 500, and 1000), and W (1, 3, 5, and 7 nm). The θ value was varied from 0° to 85°. Results show that diffusivity decreases with increasing volume fraction, but beyond φ = 5% and α = 500, diffusivity remained almost constant at W values of 1 and 3 nm. Higher relative diffusivity coincided with increasing W and decreasing α value for the same volume fraction of nanoparticles. Diffusivity increased as the rotational angle increased, gradually diminishing the influence of nanoparticles. Diffusivity increased drastically as θ changed from 15° to 30° (relative increment in relative diffusivity was almost 3.5 times). Nanoparticles with exfoliation configuration exhibited better oxygen barrier properties compared to intercalation. The finite element model developed in this study provides insight into oxygen barrier properties for nanocomposite with a wide range of structural parameters. This model can be used to design and manufacture an ideal nanocomposite-based food packaging film with improved gas barrier properties for industrial applications. The model will assist in designing nanocomposite polymeric structures of desired gas barrier properties for food packaging applications. In addition, this study will be helpful in formulating a combination of nanoparticle structural parameters for designing nanocomposite membranes with selective permeability for the industrial applications including membrane
Comparison Of Diffuse Solar Radiation Models Using Data For ...
African Journals Online (AJOL)
Measurements of global solar radiation and sunshine duration data during the period from 1984 to 1999 were supplied by IITA (International Institute of Tropical Agriculture) at Onne. The data were used to establish empirical relationships that would connect the daily monthly average diffuse irradiation with both relative ...
An alternative atmospheric diffusion model for control room habitability assessments
International Nuclear Information System (INIS)
Ramsdell, J.V. Jr.
1990-01-01
The US Nuclear Regulatory (NRC) staff uses procedures to evaluate control room designs for compliance with General Design Criterion 19 of the Code of Federal Regulations, Appendix A, 10 CRF Part 50. These procedures deal primarily with radiation protection. However, other hazardous materials, for example, chlorine, pose a potential threat to control room habitability. The NRC is considering changes in their current procedures to update methods and extend their applicability. Two changes to the current procedures are suggested: using a puff diffusion model to estimate concentrations at air intakes and using a new method to estimate diffusion coefficients
Turing and Non-Turing patterns in diffusive plankton model
Directory of Open Access Journals (Sweden)
N. K. Thakur
2015-03-01
Full Text Available In this paper, we investigate a Rosenzweig-McAurthur model and its variant for phytoplankton, zooplankton and fish population dynamics with Holling type II and III functional responses. We present the theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially distributed population with local diffusion. The choice of parameter values is important to study the effect of diffusion, also it depends more on the nonlinearity of the system. With the help of numerical simulations, we observe the formation of spatiotemporal patterns both inside and outside the Turing space.
On a Generalized Squared Gaussian Diffusion Model for Option Valuation
Directory of Open Access Journals (Sweden)
Edeki S.O.
2017-01-01
Full Text Available In financial mathematics, option pricing models are vital tools whose usefulness cannot be overemphasized. Modern approaches and modelling of financial derivatives are therefore required in option pricing and valuation settings. In this paper, we derive via the application of Ito lemma, a pricing model referred to as Generalized Squared Gaussian Diffusion Model (GSGDM for option pricing and valuation. Same approach can be considered via Stratonovich stochastic dynamics. We also show that the classical Black-Scholes, and the square root constant elasticity of variance models are special cases of the GSGDM. In addition, general solution of the GSGDM is obtained using modified variational iterative method (MVIM.
Macroscopic diffusion models for precipitation in crystalline gallium arsenide
Energy Technology Data Exchange (ETDEWEB)
Kimmerle, Sven-Joachim Wolfgang
2009-09-21
Based on a thermodynamically consistent model for precipitation in gallium arsenide crystals including surface tension and bulk stresses by Dreyer and Duderstadt, we propose two different mathematical models to describe the size evolution of liquid droplets in a crystalline solid. The first model treats the diffusion-controlled regime of interface motion, while the second model is concerned with the interface-controlled regime of interface motion. Our models take care of conservation of mass and substance. These models generalise the well-known Mullins- Sekerka model for Ostwald ripening. We concentrate on arsenic-rich liquid spherical droplets in a gallium arsenide crystal. Droplets can shrink or grow with time but the centres of droplets remain fixed. The liquid is assumed to be homogeneous in space. Due to different scales for typical distances between droplets and typical radii of liquid droplets we can derive formally so-called mean field models. For a model in the diffusion-controlled regime we prove this limit by homogenisation techniques under plausible assumptions. These mean field models generalise the Lifshitz-Slyozov-Wagner model, which can be derived from the Mullins-Sekerka model rigorously, and is well understood. Mean field models capture the main properties of our system and are well adapted for numerics and further analysis. We determine possible equilibria and discuss their stability. Numerical evidence suggests in which case which one of the two regimes might be appropriate to the experimental situation. (orig.)
Leaky-box approximation to the fractional diffusion model
International Nuclear Information System (INIS)
Uchaikin, V V; Sibatov, R T; Saenko, V V
2013-01-01
Two models based on fractional differential equations for galactic cosmic ray diffusion are applied to the leaky-box approximation. One of them (Lagutin-Uchaikin, 2000) assumes a finite mean free path of cosmic ray particles, another one (Lagutin-Tyumentsev, 2004) uses distribution with infinite mean distance between collision with magnetic clouds, when the trajectories have form close to ballistic. Calculations demonstrate that involving boundary conditions is incompatible with spatial distributions given by the second model.
Energy Technology Data Exchange (ETDEWEB)
Lai, Vincent; Khong, Pek Lan [University of Hong Kong, Department of Diagnostic Radiology, Li Ka Shing Faculty of Medicine, Queen Mary Hospital, Pok Fu Lam (China); Lee, Victor Ho Fun; Lam, Ka On; Sze, Henry Chun Kin [University of Hong Kong, Department of Clinical Oncology, Li Ka Shing Faculty of Medicine, Queen Mary Hospital, Pok Fu Lam (China); Chan, Queenie [Philips Healthcare, Hong Kong, Shatin, New Territories (China)
2015-06-01
To determine the utility of stretched exponential diffusion model in characterisation of the water diffusion heterogeneity in different tumour stages of nasopharyngeal carcinoma (NPC). Fifty patients with newly diagnosed NPC were prospectively recruited. Diffusion-weighted MR imaging was performed using five b values (0-2,500 s/mm{sup 2}). Respective stretched exponential parameters (DDC, distributed diffusion coefficient; and alpha (α), water heterogeneity) were calculated. Patients were stratified into low and high tumour stage groups based on the American Joint Committee on Cancer (AJCC) staging for determination of the predictive powers of DDC and α using t test and ROC curve analyses. The mean ± standard deviation values were DDC = 0.692 ± 0.199 (x 10{sup -3} mm{sup 2}/s) for low stage group vs 0.794 ± 0.253 (x 10{sup -3} mm{sup 2}/s) for high stage group; α = 0.792 ± 0.145 for low stage group vs 0.698 ± 0.155 for high stage group. α was significantly lower in the high stage group while DDC was negatively correlated. DDC and α were both reliable independent predictors (p < 0.001), with α being more powerful. Optimal cut-off values were (sensitivity, specificity, positive likelihood ratio, negative likelihood ratio) DDC = 0.692 x 10{sup -3} mm{sup 2}/s (94.4 %, 64.3 %, 2.64, 0.09), α = 0.720 (72.2 %, 100 %, -, 0.28). The heterogeneity index α is robust and can potentially help in staging and grading prediction in NPC. (orig.)
International Nuclear Information System (INIS)
Lai, Vincent; Khong, Pek Lan; Lee, Victor Ho Fun; Lam, Ka On; Sze, Henry Chun Kin; Chan, Queenie
2015-01-01
To determine the utility of stretched exponential diffusion model in characterisation of the water diffusion heterogeneity in different tumour stages of nasopharyngeal carcinoma (NPC). Fifty patients with newly diagnosed NPC were prospectively recruited. Diffusion-weighted MR imaging was performed using five b values (0-2,500 s/mm 2 ). Respective stretched exponential parameters (DDC, distributed diffusion coefficient; and alpha (α), water heterogeneity) were calculated. Patients were stratified into low and high tumour stage groups based on the American Joint Committee on Cancer (AJCC) staging for determination of the predictive powers of DDC and α using t test and ROC curve analyses. The mean ± standard deviation values were DDC = 0.692 ± 0.199 (x 10 -3 mm 2 /s) for low stage group vs 0.794 ± 0.253 (x 10 -3 mm 2 /s) for high stage group; α = 0.792 ± 0.145 for low stage group vs 0.698 ± 0.155 for high stage group. α was significantly lower in the high stage group while DDC was negatively correlated. DDC and α were both reliable independent predictors (p < 0.001), with α being more powerful. Optimal cut-off values were (sensitivity, specificity, positive likelihood ratio, negative likelihood ratio) DDC = 0.692 x 10 -3 mm 2 /s (94.4 %, 64.3 %, 2.64, 0.09), α = 0.720 (72.2 %, 100 %, -, 0.28). The heterogeneity index α is robust and can potentially help in staging and grading prediction in NPC. (orig.)
Diffusion in higher dimensional SYK model with complex fermions
Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong
2018-01-01
We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.
Fractional Heat Conduction Models and Thermal Diffusivity Determination
Directory of Open Access Journals (Sweden)
Monika Žecová
2015-01-01
Full Text Available The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.
A Diffusion Model for Two-sided Service Systems
Homma, Koichi; Yano, Koujin; Funabashi, Motohisa
A diffusion model is proposed for two-sided service systems. ‘Two-sided’ refers to the existence of an economic network effect between two different and interrelated groups, e.g., card holders and merchants in an electronic money service. The service benefit for a member of one side depends on the number and quality of the members on the other side. A mathematical model by J. H. Rohlfs explains the network (or bandwagon) effect of communications services. In Rohlfs' model, only the users' group exists and the model is one-sided. This paper extends Rohlfs' model to a two-sided model. We propose, first, a micro model that explains individual behavior in regard to service subscription of both sides and a computational method that drives the proposed model. Second, we develop macro models with two diffusion-rate variables by simplifying the micro model. As a case study, we apply the models to an electronic money service and discuss the simulation results and actual statistics.
Characterization and modeling of thermal diffusion and aggregation in nanofluids.
Energy Technology Data Exchange (ETDEWEB)
Gharagozloo, Patricia E.; Goodson, Kenneth E. (Stanford University, Stanford, CA)
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.
Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage
Allen, Rebecca
2015-04-01
ABSTRACT Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage Rebecca Allen Geological CO2 storage is an engineering feat that has been undertaken around the world for more than two decades, thus accurate modeling of flow and transport behavior is of practical importance. Diffusive and convective transport are relevant processes for buoyancy-driven convection of CO2 into underlying fluid, a scenario that has received the attention of numerous modeling studies. While most studies focus on Darcy-scale modeling of this scenario, relatively little work exists at the pore-scale. In this work, properties evaluated at the pore-scale are used to investigate the transport behavior modeled at the Darcy-scale. We compute permeability and two different forms of tortuosity, namely hydraulic and diffusive. By generating various pore ge- ometries, we find hydraulic and diffusive tortuosity can be quantitatively different in the same pore geometry by up to a factor of ten. As such, we emphasize that these tortuosities should not be used interchangeably. We find pore geometries that are characterized by anisotropic permeability can also exhibit anisotropic diffusive tortuosity. This finding has important implications for buoyancy-driven convection modeling; when representing the geological formation with an anisotropic permeabil- ity, it is more realistic to also account for an anisotropic diffusivity. By implementing a non-dimensional model that includes both a vertically and horizontally orientated 5 Rayleigh number, we interpret our findings according to the combined effect of the anisotropy from permeability and diffusive tortuosity. In particular, we observe the Rayleigh ratio may either dampen or enhance the diffusing front, and our simulation data is used to express the time of convective onset as a function of the Rayleigh ratio. Also, we implement a lattice Boltzmann model for thermal convective flows, which we treat as an analog for
International Nuclear Information System (INIS)
Savoye, S.; Beaucaire, C.; Grenut, B.; Fayette, A.
2015-01-01
Highlights: • HTO and 85 Sr diffusion is studied in clayrocks under increasing ionic strengths. • Sr diffusive flux is 5 times higher than HTO under standard porewater ionic strength. • Sr diffusive flux is reduced when the porewater ionic strength increases. • The Sr diffusive evolution is qualitatively reproduced by a surface diffusion model. - Abstract: Diffusion of cations in clayrocks is widely investigated, because deep clay-rich formations are currently considered as one of the potential host rocks for radioactive waste repositories. However, several authors have already reported that sorbing cations seem to diffuse at rates larger than those predicted by a simple pore diffusion model from their sorption coefficients and from the diffusive flux of non-sorbing water tracers. This process has been attributed to the migration of cations within the electrical double layer, next to the mineral surfaces, called the surface diffusion phenomenon. The aim of this work was to verify whether this “enhanced” cation diffusion compared to neutral species was observed for strontium and, if so, to what extent this effect might vary with the salinity of the synthetic solutions. These questions were addressed by performing batch sorption, through-diffusion and out-diffusion experiments on rock samples from the Callovo-Oxfordian claystone formation (France). The results showed that there was a good agreement of the distribution ratios (R D ) determined on crushed and intact rocks by batch and through-diffusion methods with a R D decrease related to the increase of the sodium concentration, a sorption competitor. Such a trend was also well reproduced by means of a geochemical modeling based on the multi-site ion exchange (MSIE) theory. Moreover, the “enhanced” diffusion for strontium was clearly observed in this study: the Sr diffusive flux was almost five times higher than that for HTO in the cell with the lowest ionic strength, and diminished to less than 1
Diffusion models for corona formation in metagabbros from the Western Grenville Province, Canada
Grant, Shona M.
1988-01-01
Metagabbro bodies in SW Grenville Province display a variety of disequilibrium corona textures between spinel-clouded plagioclase and primary olivine or opaque oxide. Textural evidence favours a single-stage, subsolidus origin for the olivine coronas and diffusive mass transfer is believed to have been the rate-controlling process. Irreversible thermodynamics have been used to model two different garnet symplectite-bearing corona sequences in terms of steady state diffusion. In the models the flux of each component is related to the chemical potential gradients of all diffusing species by the Onsager or L-coefficients for diffusion. These coefficients are analogous to experimentally determined diffusion coefficients ( d), but relate the flux of components to chemical potential rather than concentration gradients. The major constraint on the relative values of Onsager coefficients comes from the observed mole fraction, X, of garnet in the symplectites; in (amph-gt) symplectites X {Gt/Sym}˜0.80, compared with ˜0.75 in (cpx-gt) symplectites. Several models using simple oxide components, and two different modifications of the reactant plagioclase composition, give the following qualitative results: the very low mobility of aluminium appears to control the rate of corona formation. Mg and Fe have similar mobility, and Mg can be up to 6 8 times more mobile than sodium. Determination of calcium mobility is problematical because of a proposed interaction with cross-coefficient terms reflecting “uphill” Ca-diffusion, i.e., calcium diffusing up its own chemical potential gradient. If these terms are not introduced, it is difficult to generate the required proportions of garnet in the symplectite. However, at moderate values of the cross-coefficient ratios, Mg can be up to 4 6 times more mobile than calcium ( L MgMg/LCaCaCaCa/LAlAl>3).
Nonequilibrium relation between potential and stationary distribution for driven diffusion
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel; Shergelashvili, B.M.
2009-01-01
Roč. 80, č. 1 (2009), 011121/1-011121/10 ISSN 1539-3755 R&D Projects: GA ČR GA202/07/0404 Institutional research plan: CEZ:AV0Z10100520 Keywords : diffusion * fluctuations * inverse problems Subject RIV: BE - Theoretical Physics Impact factor: 2.400, year: 2009 http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLEEE8000080000001011121000001&idtype=cvips&gifs=Yes
Daniels, Marcus G.; Farmer, J. Doyne; Gillemot, László; Iori, Giulia; Smith, Eric
2003-03-01
We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.
International Nuclear Information System (INIS)
Tachi, Yukio; Suyama, Tadahiro; Ochs, Michael
2014-01-01
To predict the long-term migration of radionuclides (RNs) under variable conditions within the framework of safety analyses for geological disposal, thermodynamic sorption models are very powerful tools. The integrated sorption and diffusion (ISD) model for compacted bentonite was developed to achieve a consistent combination of clay–water interaction, sorption, and diffusion models. The basic premise considered in the ISD model was to consistently use the same simple surface model design and parameters for describing RNs sorption/diffusion as well as clay surface and porewater chemistry. A simple 1-site non-electrostatic surface complexation model in combination with a 1-site ion exchange model was selected to keep sorption model characteristics relatively robust for compacted systems. Fundamental parameters for the proposed model were evaluated from surface titration data for purified montmorillonite. The resulting basic model was then parameterized on the basis of selected published sorption data-sets for Np(V), Am(III), and U(VI) in dispersed systems, which cover a range of key geochemical conditions such as pH, ionic strength, and carbonate concentration. The sorption trends for these RNs can be quantitatively described by the model considering a full suite of surface species including hydrolytic and carbonate species. The application of these models to the description of diffusive-sorptive transport in compacted bentonites is presented in Part 2. (author)
Modeling Cryptosporidium spp. Oocyst Inactivation in Bubble-Diffuser Ozone Contactors
1998-07-01
requirements for Giardia lamblia (G. lamblia) and viruses under the Surface Water Treatment Rule (SWTR). Minimum CT requirements include relatively...parvum and C. muris ) oocysts in ozone bubble-diffuser contactors. The model is calibrated with semi-batch kinetic data, verified with pilot-scale
Bos, Charles S.
2008-01-01
When analysing the volatility related to high frequency financial data, mostly non-parametric approaches based on realised or bipower variation are applied. This article instead starts from a continuous time diffusion model and derives a parametric analog at high frequency for it, allowing
Modeling information diffusion in time-varying community networks
Cui, Xuelian; Zhao, Narisa
2017-12-01
Social networks are rarely static, and they typically have time-varying network topologies. A great number of studies have modeled temporal networks and explored social contagion processes within these models; however, few of these studies have considered community structure variations. In this paper, we present a study of how the time-varying property of a modular structure influences the information dissemination. First, we propose a continuous-time Markov model of information diffusion where two parameters, mobility rate and community attractiveness, are introduced to address the time-varying nature of the community structure. The basic reproduction number is derived, and the accuracy of this model is evaluated by comparing the simulation and theoretical results. Furthermore, numerical results illustrate that generally both the mobility rate and community attractiveness significantly promote the information diffusion process, especially in the initial outbreak stage. Moreover, the strength of this promotion effect is much stronger when the modularity is higher. Counterintuitively, it is found that when all communities have the same attractiveness, social mobility no longer accelerates the diffusion process. In addition, we show that the local spreading in the advantage group has been greatly enhanced due to the agglomeration effect caused by the social mobility and community attractiveness difference, which thus increases the global spreading.
An innovation diffusion model for new mobile technologies acceptance
Directory of Open Access Journals (Sweden)
Barkoczia Nadi
2017-01-01
Full Text Available This paper aims to approach the diffusion model developed in 1960 by Frank Bass has been utilized to study the distribution of different types of new products and services. The Bass Model helps by describing the process in which new products are adopted in a market. This model is a useful tool for predicting the first purchase of an innovative product for which there are competing alternatives on the market. It also provides the innovator with information regarding the size of customers and the adoption time for the product. The second part of the paper is dedicated to a monographic study of specific conceptual correlations between the diffusion of technology and marketing management that emphasizes technological uncertainty and market uncertainty as major risks to innovative projects. In the final section, the results of empirical research conducted in Baia-Mare, Romania will be presented in a way that uses diffusion Bass model to estimate the adoption period for new mobile technologies.
Social influence and perceptual decision making: a diffusion model analysis.
Germar, Markus; Schlemmer, Alexander; Krug, Kristine; Voss, Andreas; Mojzisch, Andreas
2014-02-01
Classic studies on social influence used simple perceptual decision-making tasks to examine how the opinions of others change individuals' judgments. Since then, one of the most fundamental questions in social psychology has been whether social influence can alter basic perceptual processes. To address this issue, we used a diffusion model analysis. Diffusion models provide a stochastic approach for separating the cognitive processes underlying speeded binary decisions. Following this approach, our study is the first to disentangle whether social influence on decision making is due to altering the uptake of available sensory information or due to shifting the decision criteria. In two experiments, we found consistent evidence for the idea that social influence alters the uptake of available sensory evidence. By contrast, participants did not adjust their decision criteria.
Modeling and Analysis of New Products Diffusion on Heterogeneous Networks
Directory of Open Access Journals (Sweden)
Shuping Li
2014-01-01
Full Text Available We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.
Modelling and control of a diffusion/LPCVD furnace
Dewaard, H.; Dekoning, W. L.
1988-12-01
Heat transfer inside a cylindrical resistance diffusion/Low Pressure Chemical Vapor Deposition (LPCVD) furnace is studied with the aim of developing an improved temperature controller. A model of the thermal behavior is derived, which covers the important class of furnaces equipped with semitransparent quartz process tubes. The model takes into account the thermal behavior of the thermocouples. Currently used temperature controllers are shown to be highly inefficient for very large scale integration applications. Based on the model an alternative temperature controller of the LQG (linear quadratic Gaussian) type is proposed which features direct wafer temperature control. Some simulation results are given.
Statistical models of a gas diffusion electrode: II. Current resistent
Energy Technology Data Exchange (ETDEWEB)
Proksch, D B; Winsel, O W
1965-07-01
The authors describe an apparatus for measuring the flow resistance of gas diffusion electrodes which is a mechanical analog of the Wheatstone bridge for measuring electric resistance. The flow resistance of a circular DSK electrode sheet, consisting of two covering layers and a working layer between them, was measured as a function of the gas pressure. While the pressure first was increased and then decreased, a hysteresis occurred, which is discussed and explained by a statistical model of a porous electrode.
Analysis of a diffuse interface model of multispecies tumor growth
Czech Academy of Sciences Publication Activity Database
Dai, M.; Feireisl, Eduard; Rocca, E.; Schimperna, G.; Schonbek, M.E.
2017-01-01
Roč. 30, č. 4 (2017), s. 1639-1658 ISSN 0951-7715 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Cahn-Hilliard equation * Darcy law * diffuse interface model Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/article/10.1088/1361-6544/aa6063/meta
Diffusion properties of a guiding center plasma in a model electrostatic turbulence
International Nuclear Information System (INIS)
Pettini, M.; Vulpiani, A.; Misguich, J.H.; Balescu, R.; De Leener, M.; Orban, J.
1986-01-01
Numerical simulations have been performed to calculate the diffusion coefficient of several hundreds of charged particles across a strong magnetic field B, due to a known spectrum of electrostatic fluctuations. The results have been compared with the turbulent diffusion theory proposed by Misguich et al. The equation of motion is solved with a model electrostatic potential. This potential is also the Hamiltonian of this chaotic non-autonomous system: positive Lyapunov exponents are found in qualitative agreement with theoretical predictions. The absolute diffusion coefficients found in two different models exhibit a transition between two scaling regions: a classical scaling at low amplitudes (D ∼ E 2 /B 2 ), and a Bohm scaling at higher amplitudes (D ∼ E/B), in agreement with the predictions for these models. The value of the diffusion coefficient obtained in the isotropic model shows a satisfactory agreement with the theory. The study of the relative diffusion of initially close particles yields a clear quantitative confirmation of the clump effect and of the validity of the theoretical treatment of such nonlinearities. (26 fig, 20 refs)
An epidemic model of rumor diffusion in online social networks
Cheng, Jun-Jun; Liu, Yun; Shen, Bo; Yuan, Wei-Guo
2013-01-01
So far, in some standard rumor spreading models, the transition probability from ignorants to spreaders is always treated as a constant. However, from a practical perspective, the case that individual whether or not be infected by the neighbor spreader greatly depends on the trustiness of ties between them. In order to solve this problem, we introduce a stochastic epidemic model of the rumor diffusion, in which the infectious probability is defined as a function of the strength of ties. Moreover, we investigate numerically the behavior of the model on a real scale-free social site with the exponent γ = 2.2. We verify that the strength of ties plays a critical role in the rumor diffusion process. Specially, selecting weak ties preferentially cannot make rumor spread faster and wider, but the efficiency of diffusion will be greatly affected after removing them. Another significant finding is that the maximum number of spreaders max( S) is very sensitive to the immune probability μ and the decay probability v. We show that a smaller μ or v leads to a larger spreading of the rumor, and their relationships can be described as the function ln(max( S)) = Av + B, in which the intercept B and the slope A can be fitted perfectly as power-law functions of μ. Our findings may offer some useful insights, helping guide the application in practice and reduce the damage brought by the rumor.
A model for diffuse and global irradiation on horizontal surface
International Nuclear Information System (INIS)
Jain, P.C.
1984-01-01
The intensity of the direct radiation and the diffuse radiation at any time on a horizontal surface are each expressed as fractions of the intensity of the extraterrestrial radiation. Using these and assuming a random distribution of the bright sunshine hours and not too wide variations in the values of the transmission coefficients, a number of relations for estimating the global and the diffuse irradiation are derived. Two of the relations derived are already known empirically. The formulation lends more confidence in the use of the already empirically known relations providing them a theoretical basis, and affords more flexibility to the estimation techniques by supplying new equations. The study identifies three independent basic parameters and the constants appearing in the various equations as simple functions of these three basic parameters. Experimental data for the diffuse irradiation, the global irradiation and the bright sunshine duration for Macerata (Italy), Salisbury and Bulawayo (Zimbabwe) is found to show good correlation for the linear equations, and the nature and the interrelationships of the constants are found to be as predicted by the theory
THE LOS ALAMOS NATIONAL LABORATORY ATMOSPHERIC TRANSPORT AND DIFFUSION MODELS
Energy Technology Data Exchange (ETDEWEB)
M. WILLIAMS [and others
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.
Yearly, seasonal and monthly daily average diffuse sky radiation models
International Nuclear Information System (INIS)
Kassem, A.S.; Mujahid, A.M.; Turner, D.W.
1993-01-01
A daily average diffuse sky radiation regression model based on daily global radiation was developed utilizing two year data taken near Blytheville, Arkansas (Lat. =35.9 0 N, Long. = 89.9 0 W), U.S.A. The model has a determination coefficient of 0.91 and 0.092 standard error of estimate. The data were also analyzed for a seasonal dependence and four seasonal average daily models were developed for the spring, summer, fall and winter seasons. The coefficient of determination is 0.93, 0.81, 0.94 and 0.93, whereas the standard error of estimate is 0.08, 0.102, 0.042 and 0.075 for spring, summer, fall and winter, respectively. A monthly average daily diffuse sky radiation model was also developed. The coefficient of determination is 0.92 and the standard error of estimate is 0.083. A seasonal monthly average model was also developed which has 0.91 coefficient of determination and 0.085 standard error of estimate. The developed monthly daily average and daily models compare well with a selected number of previously developed models. (author). 11 ref., figs., tabs
Diffusion Forecasting Model with Basis Functions from QR-Decomposition
Harlim, John; Yang, Haizhao
2017-12-01
The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to Itô diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the Fokker-Planck equation with a discrete representation of the shift (Koopman) operator on a set of basis functions generated via the diffusion maps algorithm. While the choice of these basis functions is provably optimal under appropriate conditions, computing these basis functions is quite expensive since it requires the eigendecomposition of an N× N diffusion matrix, where N denotes the data size and could be very large. For large-scale forecasting problems, only a few leading eigenvectors are computationally achievable. To overcome this computational bottleneck, a new set of basis functions constructed by orthonormalizing selected columns of the diffusion matrix and its leading eigenvectors is proposed. This computation can be carried out efficiently via the unpivoted Householder QR factorization. The efficiency and effectiveness of the proposed algorithm will be shown in both deterministically chaotic and stochastic dynamical systems; in the former case, the superiority of the proposed basis functions over purely eigenvectors is significant, while in the latter case forecasting accuracy is improved relative to using a purely small number of eigenvectors. Supporting arguments will be provided on three- and six-dimensional chaotic ODEs, a three-dimensional SDE that mimics turbulent systems, and also on the two spatial modes associated with the boreal winter Madden-Julian Oscillation obtained from applying the Nonlinear Laplacian Spectral Analysis on the measured Outgoing Longwave Radiation.
Computing diffuse fraction of global horizontal solar radiation: A model comparison.
Dervishi, Sokol; Mahdavi, Ardeshir
2012-06-01
For simulation-based prediction of buildings' energy use or expected gains from building-integrated solar energy systems, information on both direct and diffuse component of solar radiation is necessary. Available measured data are, however, typically restricted to global horizontal irradiance. There have been thus many efforts in the past to develop algorithms for the derivation of the diffuse fraction of solar irradiance. In this context, the present paper compares eight models for estimating diffuse fraction of irradiance based on a database of measured irradiance from Vienna, Austria. These models generally involve mathematical formulations with multiple coefficients whose values are typically valid for a specific location. Subsequent to a first comparison of these eight models, three better performing models were selected for a more detailed analysis. Thereby, the coefficients of the models were modified to account for Vienna data. The results suggest that some models can provide relatively reliable estimations of the diffuse fractions of the global irradiance. The calibration procedure could only slightly improve the models' performance.
Diffusion Modeling: A Study of the Diffusion of “Jatropha Curcas ...
African Journals Online (AJOL)
Consequently, the study recommended the use of diffusion networks which integrate interpersonal networks, and multimedia strategies for the effective diffusion of innovation such as Jacodiesel in Adamawa State and other parts of the country. Keywords: Sustainability, Diffusion, Innovation, Communicative Influence, ...
Discriminative Relational Topic Models.
Chen, Ning; Zhu, Jun; Xia, Fei; Zhang, Bo
2015-05-01
Relational topic models (RTMs) provide a probabilistic generative process to describe both the link structure and document contents for document networks, and they have shown promise on predicting network structures and discovering latent topic representations. However, existing RTMs have limitations in both the restricted model expressiveness and incapability of dealing with imbalanced network data. To expand the scope and improve the inference accuracy of RTMs, this paper presents three extensions: 1) unlike the common link likelihood with a diagonal weight matrix that allows the-same-topic interactions only, we generalize it to use a full weight matrix that captures all pairwise topic interactions and is applicable to asymmetric networks; 2) instead of doing standard Bayesian inference, we perform regularized Bayesian inference (RegBayes) with a regularization parameter to deal with the imbalanced link structure issue in real networks and improve the discriminative ability of learned latent representations; and 3) instead of doing variational approximation with strict mean-field assumptions, we present collapsed Gibbs sampling algorithms for the generalized relational topic models by exploring data augmentation without making restricting assumptions. Under the generic RegBayes framework, we carefully investigate two popular discriminative loss functions, namely, the logistic log-loss and the max-margin hinge loss. Experimental results on several real network datasets demonstrate the significance of these extensions on improving prediction performance.
Gavrilin, A V
2001-01-01
Low temperature composite superconductors stabilized with extra large cross-section pure aluminum are currently in use for the Large Helical Device in Japan, modern big detectors such as ATLAS at CERN, and other large magnets. In these types of magnet systems, the rated average current density is not high and the peak field in a region of interest is about 2-4 T. Aluminum stabilized superconductors result in high stability margins and relatively long quench times. Appropriate quench analyses, both for longitudinal and transverse propagation, have to take into account a rather slow diffusion of current from the superconductor into the thick aluminum stabilizer. An exact approach to modeling of the current diffusion would be based on directly solving the Maxwell's equations in parallel with thermal diffusion and conduction relations. However, from a practical point of view, such an approach should be extremely time consuming due to obvious restrictions of computation capacity. At the same time, there exist cert...
Numerical computation of the linear stability of the diffusion model for crystal growth simulation
Energy Technology Data Exchange (ETDEWEB)
Yang, C.; Sorensen, D.C. [Rice Univ., Houston, TX (United States); Meiron, D.I.; Wedeman, B. [California Institute of Technology, Pasadena, CA (United States)
1996-12-31
We consider a computational scheme for determining the linear stability of a diffusion model arising from the simulation of crystal growth. The process of a needle crystal solidifying into some undercooled liquid can be described by the dual diffusion equations with appropriate initial and boundary conditions. Here U{sub t} and U{sub a} denote the temperature of the liquid and solid respectively, and {alpha} represents the thermal diffusivity. At the solid-liquid interface, the motion of the interface denoted by r and the temperature field are related by the conservation relation where n is the unit outward pointing normal to the interface. A basic stationary solution to this free boundary problem can be obtained by writing the equations of motion in a moving frame and transforming the problem to parabolic coordinates. This is known as the Ivantsov parabola solution. Linear stability theory applied to this stationary solution gives rise to an eigenvalue problem of the form.
Thermodynamic modelling of fast dopant diffusion in Si
Saltas, V.; Chroneos, A.; Vallianatos, F.
2018-04-01
In the present study, nickel and copper fast diffusion in silicon is investigated in the framework of the cBΩ thermodynamic model, which connects point defect parameters with the bulk elastic and expansion properties. All the calculated point defect thermodynamic properties (activation Gibbs free energy, activation enthalpy, activation entropy, and activation volume) exhibit temperature dependence due to the non-linear anharmonic behavior of the isothermal bulk modulus of Si. Calculated activation enthalpies (0.15-0.16 eV for Ni and 0.17-0.19 eV for Cu) are in agreement with the reported experimental results. Small values of calculated activation volumes for both dopants (˜4% of the mean atomic volume) are consistent with the interstitial diffusion of Ni and Cu in Si.
Parker, L. N.; Zank, G. P.
2013-12-01
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 (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).
International Nuclear Information System (INIS)
Olague, N.E.; Price, L.L.
1991-01-01
The greater confinement disposal (GCD) project is an ongoing project examining the disposal of orphan wastes in Area 5 of the Nevada Test Site. One of the major tasks for the project is performance assessment. With regard to performance assessment, a preliminary conceptual model for ground-water flow and radionuclide transport to the accessible environment at the GCD facilities has been developed. One of the transport pathways that has been postulated is diffusion of radionuclides in the liquid phase upward to the land surface. This pathway is not usually considered in a performance assessment, but is included in the GCD conceptual model because of relatively low recharge estimates at the GCD site and the proximity of the waste to the land surface. These low recharge estimates indicate that convective flow downward to the water table may be negligible; thus, diffusion upward to the land surface may then become important. As part of a preliminary performance assessment which considered a basecase scenario and a climate-change scenario, a first approximation for modeling the liquid-diffusion pathway was formulated. The model includes an analytical solution that incorporates both diffusion and radioactivity decay. Overall, these results indicate that, despite the configuration of the GCD facilities that establishes the need for considering the liquid-diffusion pathway, the GCD disposal concept appears to be a technically feasible method for disposing of orphan wastes. Future analyses will consist of investigating the underlying assumptions of the liquid-diffusion model, refining the model is necessary, and reducing uncertainty in the input parameters. 11 refs., 6 figs
Continuum modelling of silicon diffusion in indium gallium arsenide
Aldridge, Henry Lee, Jr.
A possible method to overcome the physical limitations experienced by continued transistor scaling and continue improvements in performance and power consumption is integration of III-V semiconductors as alternative channel materials for logic devices. Indium Gallium Arsenide (InGaAs) is such a material from the III-V semiconductor family, which exhibit superior electron mobilities and injection velocities than that of silicon. In order for InGaAs integration to be realized, contact resistances must be minimized through maximizing activation of dopants in this material. Additionally, redistribution of dopants during processing must be clearly understood and ultimately controlled at the nanometer-scale. In this work, the activation and diffusion behavior of silicon, a prominent n-type dopant in InGaAs, has been characterized and subsequently modelled using the Florida Object Oriented Process and Device Simulator (FLOOPS). In contrast to previous reports, silicon exhibits non-negligible diffusion in InGaAs, even for smaller thermal budget rapid thermal anneals (RTAs). Its diffusion is heavily concentration-dependent, with broadening "shoulder-like" profiles when doping levels exceed 1-3x1019cm -3, for both ion-implanted and Molecular Beam Epitaxy (MBE)-grown cases. Likewise a max net-activation value of ˜1.7x1019cm -3 is consistently reached with enough thermal processing, regardless of doping method. In line with experimental results and several ab-initio calculation results, rapid concentration-dependent diffusion of Si in InGaAs and the upper limits of its activation is believed to be governed by cation vacancies that serve as compensating defects in heavily n-type regions of InGaAs. These results are ultimately in line with an amphoteric defect model, where the activation limits of dopants are an intrinsic limitation of the material, rather than governed by individual dopant species or their methods of incorporation. As a result a Fermi level dependent point
Relation between physicomechanical properties and diffusion phenomena in composite materials
International Nuclear Information System (INIS)
Nicaise, E.
1984-06-01
One of the procedures for storing low and medium activity nuclear waste consists of coating the contaminated material in a thermosetting resin. The drums thus constitued are stored in concreted underground trenches, then covered with cement, bitumen or clayey soil. Although the risk of water circulation is low, this element represents on the one hand the major cause of natural deterioration of the polymer, and on the other hand the most likely vehicle for conveying the radioactive ions confined in the drums. It is for this reason that the study of the behaviour of polyester or epoxide-based macromolecular materials with regard to water constitutes the first stage of this work. The second part of the thesis is directed towards the study of compound materials. Indeed, the charges are represented in the first case by the nuclear waste itself; in the second case, they are introduced into the polymer beforehand, on the one hand to reduce costs, and on the other hand to give the mixture suitable mechanical and rheological properties. In this study, three types of mineral charge are added in an epoxide resin: glass balls surface-treated or not, and sand. Various techniques are implemented in order to assess and characterize the interfacial adhesion, in the different systems. The strongest polymer-charge bonds are sought in order to resist natural deterioration. Finally, the object of the confinement process, is to avoid dispersion of low and medium activity substances ( 137 Cs, 90 Sr, 60 Co, 106 Ru..) in the environment. The final stage of this work therefore consists in assessing the barrier qualities of pure or charged polymers with regard to radioactive ion diffusion. We will show in particular that the use of fine resin membranes enables the diffusion coefficient of the 137 Cs to be calculated [fr
Diffusion of innovations in Axelrod’s model
Tilles, Paulo F. C.; Fontanari, José F.
2015-11-01
Axelrod's model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e., individuals become more similar when they interact) and homophily (i.e., individuals interact preferentially with similar others). The strength of these social influences are controlled by two parameters: $F$, the number of features that characterizes the cultures and $q$, the common number of states each feature can assume. Here we assume that the innovation is a new state of a cultural feature of a single individual -- the innovator -- and study how the innovation spreads through the networks among the individuals. For infinite regular lattices in one (1D) and two dimensions (2D), we find that initially the successful innovation spreads linearly with the time $t$, but in the long-time limit it spreads diffusively ($\\sim t^{1/2}$) in 1D and sub-diffusively ($\\sim t/\\ln t$) in 2D. For finite lattices, the growth curves for the number of adopters are typically concave functions of $t$. For random graphs with a finite number of nodes $N$, we argue that the classical S-shaped growth curves result from a trade-off between the average connectivity $K$ of the graph and the per feature diversity $q$. A large $q$ is needed to reduce the pace of the initial spreading of the innovation and thus delimit the early-adopters stage, whereas a large $K$ is necessary to ensure the onset of the take-off stage at which the number of adopters grows superlinearly with $t$. In an infinite random graph we find that the number of adopters of a successful innovation scales with $t^\\gamma$ with $\\gamma =1$ for $K> 2$ and $1/2 < \\gamma < 1$ for $K=2$. We suggest that the exponent $\\gamma$ may be a useful index to characterize the process of diffusion of successful innovations in diverse scenarios.
A kinetic theory of diffusion in general relativity with cosmological scalar field
International Nuclear Information System (INIS)
Calogero, Simone
2011-01-01
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It is shown that the energy-momentum tensor for this matter model is not divergence-free, which makes it inconsistent to couple the Fokker-Planck equation to the Einstein equations. This problem can be solved by postulating the existence of additional matter fields in spacetime or by modifying the Einstein equations. The case of a cosmological scalar field term added to the left hand side of the Einstein equations is studied in some details. For the simplest cosmological model, namely the flat Robertson-Walker spacetime, it is shown that, depending on the initial value of the cosmological scalar field, which can be identified with the present observed value of the cosmological constant, either unlimited expansion or the formation of a singularity in finite time will occur in the future. Future collapse into a singularity also takes place for a suitable small but positive present value of the cosmological constant, in contrast to the standard diffusion-free scenario
A current induced diffusion model of gas sputtering
International Nuclear Information System (INIS)
Hotston, E.S.
1980-01-01
A model is proposed to explain the experimental results on deuteron trapping in stainless steel targets at low temperatures carried out at Garching and Culham. The model proposes that the ions are trapped in two kinds of sites: Deep sites with high activation energy and shallow sites of low activation energy. Trapped deuterons reach the surface of the target by being expelled from shallow sites by the action of the ion beam and migrate to nearby sites in a random way, thus moving by a bombardment induced diffusion. Ions diffusing to the target surface and being released are said to be sputtered from the target. It has been necessary to assume numerical values for sizes of some of the processes which occur. With a suitable choice of values the model successfully predicts the numbers of deuterons trapped per unit area of the target, the obserbed density profile of the trapped ions and the threshold at which sputtering starts. The model also successfully describes the replacement of the trapped deuterons by protons, when the deuteron beam is replaced by a proton beam. The collision cross-section for beam ions and ions trapped in shallow sites is too large, 4 x 10 -13 cm 2 , for a binary collision and it is tentatively suggested that the ions in the shallow sites may be in small voids in the target which may be connected with blister formation. Comparison of the present model with one being developed to describe the trapping of deuterons in carbon suggests that it may be possible to describe all gas sputtering experiments in terms of diffusion processes. (orig.)
International Nuclear Information System (INIS)
Marinak, M.
1990-02-01
The problem of deducing χ 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. χ 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 χ e is a local value, not an average value of the radial χ e profile. 7 refs., 6 figs., 1 tab
Mathematical modelling of pasta dough dynamic viscosity, thermal conductivity and diffusivity
Directory of Open Access Journals (Sweden)
Andrei Ionuţ SIMION
2015-08-01
Full Text Available This work aimed to study the mathematical variation of three main thermodynamic properties (dynamic viscosity, thermal conductivity and thermal diffusivity of pasta dough obtained by mixing wheat semolina and water with dough humidity and deformation speed (for dynamic viscosity, respectively with dough humidity and temperature (for thermal diffusivity and conductivity. The realized regression analysis of existing graphical data led to the development of mathematical models with a high degree of accuracy. The employed statistical tests (least squares, relative error and analysis of variance revealed that the obtained equations are able to describe and predict the tendency of the dough thermodynamic properties.
The Water-Induced Linear Reduction Gas Diffusivity Model Extended to Three Pore Regions
DEFF Research Database (Denmark)
Chamindu, T. K. K. Deepagoda; de Jonge, Lis Wollesen; Kawamoto, Ken
2015-01-01
. Characterization of soil functional pore structure is an essential prerequisite to understand key gas transport processes in variably saturated soils in relation to soil ecosystems, climate, and environmental services. In this study, the water-induced linear reduction (WLR) soil gas diffusivity model originally...... gas diffusivity from moist to dry conditions across differently structured porous media, including narrow soil size fractions, perforated plastic blocks, fractured limestone, peaty soils, aggregated volcanic ash soils, and particulate substrates for Earth- or space-based applications. The new Cip...
Sooting Characteristics and Modeling in Counterflow Diffusion Flames
Wang, Yu
2013-11-01
Soot formation is one of the most complex phenomena in combustion science and an understanding of the underlying physico-chemical mechanisms is important. This work adopted both experimental and numerical approaches to study soot formation in laminar counterfl ow diffusion flames. As polycyclic aromatic hydrocarbons (PAHs) are the precursors of soot particles, a detailed gas-phase chemical mechanism describing PAH growth upto coronene for fuels with 1 to 4 carbon atoms was validated against laminar premixed and counter- flow diffusion fl ames. Built upon this gas-phase mechanism, a soot model was then developed to describe soot inception and surface growth. This soot model was sub- sequently used to study fuel mixing effect on soot formation in counterfl ow diffusion flames. Simulation results showed that compared to the baseline case of the ethylene flame, the doping of 5% (by volume) propane or ethane in ethylene tends to increase the soot volume fraction and number density while keeping the average soot size almost unchanged. These results are in agreement with experimental observations. Laser light extinction/scattering as well as laser induced fluorescence techniques were used to study the effect of strain rate on soot and PAH formation in counterfl ow diffusion ames. The results showed that as strain rate increased both soot volume fraction and PAH concentrations decreased. The concentrations of larger PAH were more sensitive to strain rate compared to smaller ones. The effect of CO2 addition on soot formation was also studied using similar experimental techniques. Soot loading was reduced with CO2 dilution. Subsequent numerical modeling studies were able to reproduce the experimental trend. In addition, the chemical effect of CO2 addition was analyzed using numerical data. Critical conditions for the onset of soot were systematically studied in counterfl ow diffusion ames for various gaseous hydrocarbon fuels and at different strain rates. A sooting
International Nuclear Information System (INIS)
Villamaina, D; Puglisi, A; Vulpiani, A
2008-01-01
We study a gas of hard rods on a ring, driven by an external thermostat, with either elastic or inelastic collisions, which exhibits sub-diffusive behavior, 2 > ∼ t 1/2 . We show the validity of the usual fluctuation–dissipation (FD) relation, i.e. the proportionality between the response function and the correlation function, when the gas is elastic or diluted. In contrast, in strongly inelastic or dense cases, when the tracer velocity is no longer independent of the other degrees of freedom, the Einstein formula fails and must be replaced by a more general FD relation. (letter)
Continuous-time random-walk model for anomalous diffusion in expanding media
Le Vot, F.; Abad, E.; Yuste, S. B.
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
Continuous-time random-walk model for anomalous diffusion in expanding media.
Le Vot, F; Abad, E; Yuste, S B
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
Application of the evolution theory in modelling of innovation diffusion
Directory of Open Access Journals (Sweden)
Krstić Milan
2016-01-01
Full Text Available The theory of evolution has found numerous analogies and applications in other scientific disciplines apart from biology. In that sense, today the so-called 'memetic-evolution' has been widely accepted. Memes represent a complex adaptable system, where one 'meme' represents an evolutional cultural element, i.e. the smallest unit of information which can be identified and used in order to explain the evolution process. Among others, the field of innovations has proved itself to be a suitable area where the theory of evolution can also be successfully applied. In this work the authors have started from the assumption that it is also possible to apply the theory of evolution in the modelling of the process of innovation diffusion. Based on the conducted theoretical research, the authors conclude that the process of innovation diffusion in the interpretation of a 'meme' is actually the process of imitation of the 'meme' of innovation. Since during the process of their replication certain 'memes' show a bigger success compared to others, that eventually leads to their natural selection. For the survival of innovation 'memes', their manifestations are of key importance in the sense of their longevity, fruitfulness and faithful replicating. The results of the conducted research have categorically confirmed the assumption of the possibility of application of the evolution theory with the innovation diffusion with the help of innovation 'memes', which opens up the perspectives for some new researches on the subject.
Different approach to the modeling of nonfree particle diffusion
Buhl, Niels
2018-03-01
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore networks to general geometric domains can be considered and that the (free random walk) central limit theorem can be generalized to cover also the nonfree case. The latter gives rise to a continuum-limit description of the diffusive motion where the effect of partially absorbing barriers is accounted for in a natural and non-Markovian way that, in contrast to the traditional approach, quantifies the absorptivity of a barrier in terms of a dimensionless parameter in the range 0 to 1. The generalized theorem gives two general analytic expressions for the continuum-limit propagator: an infinite sum of Gaussians and an infinite sum of plane waves. These expressions entail the known method-of-images and Laplace eigenfunction expansions as special cases and show how the presence of partially absorbing barriers can lead to phenomena such as line splitting and band gap formation in the plane wave wave-number spectrum.
On diffusion processes with variable drift rates as models for decision making during learning
International Nuclear Information System (INIS)
Eckhoff, P; Holmes, P; Law, C; Connolly, P M; Gold, J I
2008-01-01
We investigate Ornstein-Uhlenbeck and diffusion processes with variable drift rates as models of evidence accumulation in a visual discrimination task. We derive power-law and exponential drift-rate models and characterize how parameters of these models affect the psychometric function describing performance accuracy as a function of stimulus strength and viewing time. We fit the models to psychophysical data from monkeys learning the task to identify parameters that best capture performance as it improves with training. The most informative parameter was the overall drift rate describing the signal-to-noise ratio of the sensory evidence used to form the decision, which increased steadily with training. In contrast, secondary parameters describing the time course of the drift during motion viewing did not exhibit steady trends. The results indicate that relatively simple versions of the diffusion model can fit behavior over the course of training, thereby giving a quantitative account of learning effects on the underlying decision process
Dense-gas dispersion advection-diffusion model
International Nuclear Information System (INIS)
Ermak, D.L.
1992-07-01
A dense-gas version of the ADPIC particle-in-cell, advection- diffusion model was developed to simulate the atmospheric dispersion of denser-than-air releases. In developing the model, it was assumed that the dense-gas effects could be described in terms of the vertically-averaged thermodynamic properties and the local height of the cloud. The dense-gas effects were treated as a perturbation to the ambient thermodynamic properties (density and temperature), ground level heat flux, turbulence level (diffusivity), and windfield (gravity flow) within the local region of the dense-gas cloud. These perturbations were calculated from conservation of energy and conservation of momentum principles along with the ideal gas law equation of state for a mixture of gases. ADPIC, which is generally run in conjunction with a mass-conserving wind flow model to provide the advection field, contains all the dense-gas modifications within it. This feature provides the versatility of coupling the new dense-gas ADPIC with alternative wind flow models. The new dense-gas ADPIC has been used to simulate the atmospheric dispersion of ground-level, colder-than-ambient, denser-than-air releases and has compared favorably with the results of field-scale experiments
Diffusion and reaction within porous packing media: a phenomenological model.
Jones, W L; Dockery, J D; Vogel, C R; Sturman, P J
1993-04-25
A phenomenological model has been developed to describe biomass distribution and substrate depletion in porous diatomaceous earth (DE) pellets colonized by Pseudomonas aeruginosa. The essential features of the model are diffusion, attachment and detachment to/from pore walls of the biomass, diffusion of substrate within the pellet, and external mass transfer of both substrate and biomass in the bulk fluid of a packed bed containing the pellets. A bench-scale reactor filled with DE pellets was inoculated with P. aeruginosa and operated in plug flow without recycle using a feed containing glucose as the limiting nutrient. Steady-state effluent glucose concentrations were measured at various residence times, and biomass distribution within the pellet was measured at the lowest residence time. In the model, microorganism/substrate kinetics and mass transfer characteristics were predicted from the literature. Only the attachment and detachment parameters were treated as unknowns, and were determined by fitting biomass distribution data within the pellets to the mathematical model. The rate-limiting step in substrate conversion was determined to be internal mass transfer resistance; external mass transfer resistance and microbial kinetic limitations were found to be nearly negligible. Only the outer 5% of the pellets contributed to substrate conversion.
Modeling of 1D Anomalous Diffusion in Fractured Nanoporous Media
Directory of Open Access Journals (Sweden)
Albinali Ali
2016-07-01
Full Text Available Fractured nanoporous reservoirs include multi-scale and discontinuous fractures coupled with a complex nanoporous matrix. Such systems cannot be described by the conventional dual-porosity (or multi-porosity idealizations due to the presence of different flow mechanisms at multiple scales. More detailed modeling approaches, such as Discrete Fracture Network (DFN models, similarly suffer from the extensive data requirements dictated by the intricacy of the flow scales, which eventually deter the utility of these models. This paper discusses the utility and construction of 1D analytical and numerical anomalous diffusion models for heterogeneous, nanoporous media, which is commonly encountered in oil and gas production from tight, unconventional reservoirs with fractured horizontal wells. A fractional form of Darcy’s law, which incorporates the non-local and hereditary nature of flow, is coupled with the classical mass conservation equation to derive a fractional diffusion equation in space and time. Results show excellent agreement with established solutions under asymptotic conditions and are consistent with the physical intuitions.
Subgrid models for mass and thermal diffusion in turbulent mixing
International Nuclear Information System (INIS)
Lim, H; Yu, Y; Glimm, J; Li, X-L; Sharp, D H
2010-01-01
We propose a new method for the large eddy simulation (LES) of turbulent mixing flows. The method yields convergent probability distribution functions (PDFs) for temperature and concentration and a chemical reaction rate when applied to reshocked Richtmyer-Meshkov (RM) unstable flows. Because such a mesh convergence is an unusual and perhaps original capability for LES of RM flows, we review previous validation studies of the principal components of the algorithm. The components are (i) a front tracking code, FronTier, to control numerical mass diffusion and (ii) dynamic subgrid scale (SGS) models to compensate for unresolved scales in the LES. We also review the relevant code comparison studies. We compare our results to a simple model based on 1D diffusion, taking place in the geometry defined statistically by the interface (the 50% isoconcentration surface between the two fluids). Several conclusions important to physics could be drawn from our study. We model chemical reactions with no closure approximations beyond those in the LES of the fluid variables itself, and as with dynamic SGS models, these closures contain no adjustable parameters. The chemical reaction rate is specified by the joint PDF for temperature and concentration. We observe a bimodal distribution for the PDF and we observe significant dependence on fluid transport parameters.
Compact Models for Defect Diffusivity in Semiconductor Alloys.
Energy Technology Data Exchange (ETDEWEB)
Wright, Alan F. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Nanostructure Physics Department; Modine, Normand A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Nanostructure Physics Department; Lee, Stephen R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Advanced Materials Sciences Department; Foiles, Stephen M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Materials and Data Science Department
2017-09-01
Predicting transient effects caused by short - pulse neutron irradiation of electronic devices is an important part of Sandia's mission. For example , predicting the diffusion of radiation - induced point defects is needed with in Sandia's Qualification Alternative to the Sandia Pulsed Reactor (QASPR) pro gram since defect diffusion mediates transient gain recovery in QASPR electronic devices. Recently, the semiconductors used to fabricate radiation - hard electronic devices have begun to shift from silicon to III - V compounds such as GaAs, InAs , GaP and InP . An advantage of this shift is that it allows engineers to optimize the radiation hardness of electronic devices by using alloy s such as InGaAs and InGaP . However, the computer codes currently being used to simulate transient radiation effects in QASP R devices will need to be modified since they presume that defect properties (charge states, energy levels, and diffusivities) in these alloys do not change with time. This is not realistic since the energy and properties of a defect depend on the types of atoms near it and , therefore, on its location in the alloy. In particular, radiation - induced defects are created at nearly random locations in an alloy and the distribution of their local environments - and thus their energies and properties - evolves with time as the defects diffuse through the alloy . To incorporate these consequential effects into computer codes used to simulate transient radiation effects, we have developed procedures to accurately compute the time dependence of defect energies and properties and then formulate them within compact models that can be employed in these computer codes. In this document, we demonstrate these procedures for the case of the highly mobile P interstitial (I P ) in an InGaP alloy. Further dissemination only as authorized to U.S. Government agencies and their contractors; other requests shall be approved by the originating facility or higher DOE
Anomalous diffusion in neutral evolution of model proteins
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.
Residual sweeping errors in turbulent particle pair diffusion in a Lagrangian diffusion model.
Malik, Nadeem A
2017-01-01
Thomson, D. J. & Devenish, B. J. [J. Fluid Mech. 526, 277 (2005)] and others have suggested that sweeping effects make Lagrangian properties in Kinematic Simulations (KS), Fung et al [Fung J. C. H., Hunt J. C. R., Malik N. A. & Perkins R. J. J. Fluid Mech. 236, 281 (1992)], unreliable. However, such a conclusion can only be drawn under the assumption of locality. The major aim here is to quantify the sweeping errors in KS without assuming locality. Through a novel analysis based upon analysing pairs of particle trajectories in a frame of reference moving with the large energy containing scales of motion it is shown that the normalized integrated error [Formula: see text] in the turbulent pair diffusivity (K) due to the sweeping effect decreases with increasing pair separation (σl), such that [Formula: see text] as σl/η → ∞; and [Formula: see text] as σl/η → 0. η is the Kolmogorov turbulence microscale. There is an intermediate range of separations 1 < σl/η < ∞ in which the error [Formula: see text] remains negligible. Simulations using KS shows that in the swept frame of reference, this intermediate range is large covering almost the entire inertial subrange simulated, 1 < σl/η < 105, implying that the deviation from locality observed in KS cannot be atributed to sweeping errors. This is important for pair diffusion theory and modeling. PACS numbers: 47.27.E?, 47.27.Gs, 47.27.jv, 47.27.Ak, 47.27.tb, 47.27.eb, 47.11.-j.
The brush model - a new approach to numerical modeling of matrix diffusion in fractured clay stone
International Nuclear Information System (INIS)
Lege, T.; Shao, H.
1998-01-01
A special approach for numerical modeling of contaminant transport in fractured clay stone is presented. The rock matrix and the fractures are simulated with individual formulations for FE grids and transport, coupled into a single model. The capacity of the rock matrix to take up contaminants is taken into consideration with a discrete simulation of matrix diffusion. Thus, the natural process of retardation due to matrix diffusion can be better simulated than by a standard introduction of an empirical parameter into the transport equation. Transport in groundwater in fractured clay stone can be simulated using a model called a 'brush model'. The 'brush handle' is discretized by 2-D finite elements. Advective-dispersive transport in groundwater in the fractures is assumed. The contaminant diffuses into 1D finite elements perpendicular to the fractures, i.e., the 'bristles of the brush'. The conclusion is drawn that matrix diffusion is an important property of fractured clay stone for contaminant retardation. (author)
Bayesian uncertainty quantification in linear models for diffusion MRI.
Sjölund, Jens; Eklund, Anders; Özarslan, Evren; Herberthson, Magnus; Bånkestad, Maria; Knutsson, Hans
2018-03-29
Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification. Copyright © 2018 Elsevier Inc. All rights reserved.
A chaotic model for advertising diffusion problem with competition
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.
Memory Effects and Coverage Dependence of Surface Diffusion in a Model Adsorption System
DEFF Research Database (Denmark)
Vattulainen, Ilpo Tapio; Ying, S. C.; Ala-Nissila, T.
1999-01-01
in tracer and collective diffusion. We show that memory effects can be very pronounced deep inside the ordered phases and in regions close to first and second order phase transition boundaries. Particular attention is paid to the details of the time dependence of memory effects. The memory effect in tracer......We study the coverage dependence of surface diffusion coefficients for a strongly interacting adsorption system O/W(110) via Monte Carlo simulations of a lattice-gas model. In particular, we consider the nature and emergence of memory effects as contained in the corresponding correlation factors...... diffusion is found to decay following a power law after an initial transient period. This behavior persists until the hydrodynamic regime is reached, after which the memory effect decays exponentially. The time required to reach the hydrodynamical regime and the related exponential decay is strongly...
Energy Technology Data Exchange (ETDEWEB)
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.
Modeling the Determinants Influencing the Diffusion of Mobile Internet
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.
A diffusive ink transport model for lipid dip-pen nanolithography
Urtizberea, A.; Hirtz, M.
2015-09-01
Despite diverse applications, phospholipid membrane stacks generated by dip-pen nanolithography (DPN) still lack a thorough and systematic characterization that elucidates the whole ink transport process from writing to surface spreading, with the aim of better controlling the resulting feature size and resolution. We report a quantitative analysis and modeling of the dependence of lipid DPN features (area, height and volume) on dwell time and relative humidity. The ink flow rate increases with humidity in agreement with meniscus size growth, determining the overall feature size. The observed time dependence indicates the existence of a balance between surface spreading and the ink flow rate that promotes differences in concentration at the meniscus/substrate interface. Feature shape is controlled by the substrate surface energy. The results are analyzed within a modified model for the ink transport of diffusive inks. At any humidity the dependence of the area spread on the dwell time shows two diffusion regimes: at short dwell times growth is controlled by meniscus diffusion while at long dwell times surface diffusion governs the process. The critical point for the switch of regime depends on the humidity.Despite diverse applications, phospholipid membrane stacks generated by dip-pen nanolithography (DPN) still lack a thorough and systematic characterization that elucidates the whole ink transport process from writing to surface spreading, with the aim of better controlling the resulting feature size and resolution. We report a quantitative analysis and modeling of the dependence of lipid DPN features (area, height and volume) on dwell time and relative humidity. The ink flow rate increases with humidity in agreement with meniscus size growth, determining the overall feature size. The observed time dependence indicates the existence of a balance between surface spreading and the ink flow rate that promotes differences in concentration at the meniscus
Digital Repository Service at National Institute of Oceanography (India)
Jyothi, D.; Murty, T.V.R.; Sarma, V.V.; Rao, D.P.
conditions. As the pollutant load on the estuary increases, the. water quality may deteriorate rapidly and therefore the scientific interests are centered on the analysis of water quality. The pollutants will be subjected to a number of physical, chemical... study we have applied one-dimensional advection-diffusion model for the waters of Gauthami Godavari estuary to determine the axial diffusion coefficients and thereby to predict the impact assessment. The study area (Fig. 1) is the lower most 32 km...
Heijkenskjöld-Rentzhog, C; Nordvall, L; Janson, C; Borres, M P; Alving, K; Malinovschi, A
2014-08-01
Inflammation in the small airways might contribute to incomplete asthma disease control despite intensive treatment in some subgroups of patients. Exhaled NO (FeNO) is a marker of inflammation in asthma and the estimated NO contribution from small airways (CalvNO ) is believed to reflect distal inflammation. Recent studies recommend adjustments of CalvNO for trumpet model and axial diffusion (TMAD-adj). This study aimed to investigate the clinical correlates of CalvNO , both TMAD-adjusted and unadjusted. Asthma symptoms, asthma control, lung function, bronchial responsiveness, blood eosinophils, atopy and treatment level were assessed in 410 subjects, aged 10-35 years. Exhaled NO was measured at different flow-rates and CalvNO calculated, with TMAD-adjustment according to Condorelli. Trumpet model and axial diffusion-adjusted CalvNO was not related to daytime wheeze (P = 0.27), FEF50 (P = 0.23) or bronchial responsiveness (P = 0.52). On the other hand, unadjusted CalvNO was increased in subjects with daytime wheeze (P < 0.001), decreased FEF50 (P = 0.02) and with moderate-to-severe compared to normal bronchial responsiveness (P < 0.001). All these characteristics correlated with increased FeNO (all P < 0.05). Unadjusted CalvNO was positively related to bronchial NO flux (J'awNO ) (r = 0.22, P < 0.001) while TMAD-adjCalvNO was negatively related to J'awNO (r = -0.38, P < 0.001). Adjusted CalvNO was not associated with any asthma characteristics studied in this large asthma cohort. However, both FeNO and unadjusted CalvNO related to asthma symptoms, lung function and bronchial responsiveness. We suggest a potential overadjustment by current TMAD-corrections, validated in healthy or unobstructed asthmatics. Further studies assessing axial diffusion in asthmatics with different degrees of airway obstruction and the validity of proposed TMAD-corrections are warranted. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Introducing serendipity in a social network model of knowledge diffusion
International Nuclear Information System (INIS)
Cremonini, Marco
2016-01-01
Highlights: • Serendipity as a control mechanism for knowledge diffusion in social network. • Local communication enhanced in the periphery of a network. • Prevalence of hub nodes in the network core mitigated. • Potential disruptive effect on network formation of uncontrolled serendipity. - Abstract: In this paper, we study serendipity as a possible strategy to control the behavior of an agent-based network model of knowledge diffusion. The idea of considering serendipity in a strategic way has been first explored in Network Learning and Information Seeking studies. After presenting the major contributions of serendipity studies to digital environments, we discuss the extension to our model: Agents are enriched with random topics for establishing new communication according to different strategies. The results show how important network properties could be influenced, like reducing the prevalence of hubs in the network’s core and increasing local communication in the periphery, similar to the effects of more traditional self-organization methods. Therefore, from this initial study, when serendipity is opportunistically directed, it appears to behave as an effective and applicable approach to social network control.
Zirconium - ab initio modelling of point defects diffusion
International Nuclear Information System (INIS)
Gasca, Petrica
2010-01-01
Zirconium is the main element of the cladding found in pressurized water reactors, under an alloy form. Under irradiation, the cladding elongate significantly, phenomena attributed to the vacancy dislocation loops growth in the basal planes of the hexagonal compact structure. The understanding of the atomic scale mechanisms originating this process motivated this work. Using the ab initio atomic modeling technique we studied the structure and mobility of point defects in Zirconium. This led us to find four interstitial point defects with formation energies in an interval of 0.11 eV. The migration paths study allowed the discovery of activation energies, used as entry parameters for a kinetic Monte Carlo code. This code was developed for calculating the diffusion coefficient of the interstitial point defect. Our results suggest a migration parallel to the basal plane twice as fast as one parallel to the c direction, with an activation energy of 0.08 eV, independent of the direction. The vacancy diffusion coefficient, estimated with a two-jump model, is also anisotropic, with a faster process in the basal planes than perpendicular to them. Hydrogen influence on the vacancy dislocation loops nucleation was also studied, due to recent experimental observations of cladding growth acceleration in the presence of this element [fr
International Nuclear Information System (INIS)
Wen, Zijuan; Fu, Shengmao
2016-01-01
This paper deals with a strongly coupled reaction-diffusion system modeling a competitor-competitor-mutualist three-species model with diffusion, self-diffusion and nonlinear cross-diffusion and subject to Neumann boundary conditions. First, we establish the persistence of a corresponding reaction-diffusion system without self- and cross-diffusion. Second, the global asymptotic stability of the unique positive equilibrium for weakly coupled PDE system is established by using a comparison method. Moreover, under certain conditions about the intra- and inter-species effects, we prove that the uniform positive steady state is linearly unstable for the cross-diffusion system when one of the cross-diffusions is large enough. The results indicate that Turing instability can be driven solely from strong diffusion effect of the first species (or the second species or the third species) due to the pressure of the second species (or the first species).
Modelling thermal radiation and soot formation in buoyant diffusion flames
International Nuclear Information System (INIS)
Demarco Bull, R.A.
2012-01-01
The radiative heat transfer plays an important role in fire problems since it is the dominant mode of heat transfer between flames and surroundings. It controls the pyrolysis, and therefore the heat release rate, and the growth rate of the fire. In the present work a numerical study of buoyant diffusion flames is carried out, with the main objective of modelling the thermal radiative transfer and the soot formation/destruction processes. In a first step, different radiative property models were tested in benchmark configurations. It was found that the FSCK coupled with the Modest and Riazzi mixing scheme was the best compromise in terms of accuracy and computational requirements, and was a good candidate to be implemented in CFD codes dealing with fire problems. In a second step, a semi-empirical soot model, considering acetylene and benzene as precursor species for soot nucleation, was validated in laminar co flow diffusion flames over a wide range of hydrocarbons (C1-C3) and conditions. In addition, the optically-thin approximation was found to produce large discrepancies in the upper part of these small laminar flames. Reliable predictions of soot volume fractions require the use of an advanced radiation model. Then the FSCK and the semi-empirical soot model were applied to simulate laboratory-scale and intermediate-scale pool fires of methane and propane. Predicted flame structures as well as the radiant heat flux transferred to the surroundings were found to be in good agreement with the available experimental data. Finally, the interaction between radiation and turbulence was quantified. (author)
The development of radioactivity diffusion model in global ocean
International Nuclear Information System (INIS)
Nakano, M.; Watanabe, H.; Katagiri, H.
2000-01-01
The radioactivity diffusion model in global ocean has been developing in order to assess the long-term behavior of radioactive materials for discharge from nuclear facility. The model system consists of two parts. One is to calculate current velocity; and the other is for particle chasing. Both systems are executed by Macintosh personal computer. A lot of techniques to estimate ocean current velocity were investigated in geophysical field. The robust diagnosis model advocated by Sarmiento and Bryan was applied to build the numerical calculation system for getting the current velocity field in global scale. The latitudinal and longitudinal lattices were 2 degrees each and the number of vertical layer was 15. The movement of radioactive materials by current and diffusion were calculated using the particle chasing system. The above-mentioned current velocity field and the initial particle positions at will were read by the system. The movement of a particle was calculated using the interpolated current data step by step. The diffusion of a particle was calculated by random walk method. The model was verified by using the fallout data from atmospheric nuclear test. Yearly and latitudinal fallout data was adopted from UNSCEAR1977. The calculation result was compared with the observation data that includes total amount and vertical profile of Cs-137 and Pu-239,240 in the North Pacific Ocean. The result of the verification was agreed with the following general knowledge. Though the fallout amount between 40N and 50N was the biggest in the world, the amount in the seawater between 40N and 50N was smaller than that in south of 40N because of horizontal transportation, which carried water from north to south. As for vertical profile, Cs-137 could be accurately calculated except the surface layer. However the observation peak of Pu-239,240 existed deeper than the calculation peak. This model could calculate the vertical profile of Cs-137 because most of Cs exists as dissolved
Pre-Clinical Models of Diffuse Intrinsic Pontine Glioma
Directory of Open Access Journals (Sweden)
Oren J Becher
2015-07-01
Full Text Available Diffuse Intrinsic Pontine Glioma (DIPG is a rare and incurable brain tumor that arises in the brainstem of children predominantly between the ages of six and eight. Its intricate morphology and involvement of normal pons tissue precludes surgical resection, and the standard of care today remains fractionated radiation alone. In the past 30 years, there have been no significant advances made in the treatment of DIPG. This is largely because we lack good models of DIPG and therefore have little biological basis for treatment. In recent years however, due to increased biopsy and acquisition of autopsy specimens, research is beginning to unravel the genetic and epigenetic drivers of DIPG. Insight gleaned from these studies has led to improvements in approaches to both model these tumors in the lab, as well as to potentially treat them in the clinic. This review will detail the initial strides towards modeling DIPG in animals, which included allograft and xenograft rodent models using non-DIPG glioma cells. Important advances in the field came with the development of in vitro cell and in vivo xenograft models derived directly from autopsy material of DIPG patients or from human embryonic stem cells. Lastly, we will summarize the progress made in the development of genetically engineered mouse models of DIPG. Cooperation of studies incorporating all of these modeling systems to both investigate the unique mechanisms of gliomagenesis in the brainstem and to test potential novel therapeutic agents in a preclinical setting will result in improvement in treatments for DIPG patients.
A Jump Diffusion Model for Volatility and Duration
DEFF Research Database (Denmark)
Wei, Wei; Pelletier, Denis
by the market microstructure theory. Traditional measures of volatility do not utilize durations. I adopt a jump diffusion process to model the persistence of intraday volatility and conditional duration, and their interdependence. The jump component is disentangled from the continuous part of the price......, volatility and conditional duration process. I develop a MCMC algorithm for the inference of irregularly spaced multivariate process with jumps. The algorithm provides smoothed estimates of the latent variables such as spot volatility, jump times and jump sizes. I apply this model to IBM data and I find...... meaningful relationship between volatility and conditional duration. Also, jumps play an important role in the total variation, but the jump variation is smaller than traditional measures that use returns sampled at lower frequency....
A self-consistent spin-diffusion model for micromagnetics
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Manchon, Aurelien; Praetorius, Dirk; Suess, Dieter
2016-01-01
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 self-consistent spin-diffusion model for micromagnetics
Abert, Claas
2016-12-17
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.
Decomposition in aluminium alloys: diffuse scattering and crystal modelling
International Nuclear Information System (INIS)
Aslam-Malik, A.
1995-01-01
In the present study the microstructure of metastable precipitates in Al-Ag and Al-Cu, so called pre-precipitates or Guinier-Preston (GP) zones, was investigated. In both systems important aspects of the microstructure are still controversially discussed. In Al-Ag two forms of GP zones are suggested; depending on the aging temperatures above or below about 443 K, ε- or η-zones should evolve. Differences between these two types of zones may be due to differences in internal order and/or composition. In Al-Cu the characterization of GP I zones is difficult because of the strong atomic displacements around the zones. The proper separation of short-range order and displacement scattering within a diffuse scattering experiment is still under discussion. The technique used to determine the short-range order in both alloys was diffuse scattering with neutrons and X-rays. To separate short-range order and displacement scattering, the methods of Georgopoulos-Cohen (X-ray scattering) and Borie-Sparks (neutron scattering) were used. Of main importance is the optimization of the scattering contrast and thus the scattering contribution due to short-range order. Short-range order scattering is rationalized in terms of pair correlations. Crystals may subsequently be modelled to visualize the microstructure. The Al-Ag system was investigated by diffuse X-ray wide-angle scattering and small-angle neutron scattering. The small-angle neutron scattering measurement was necessary since the GP zones in Al-Ag are almost spherical and the main scattering contribution is found close to the origin of reciprocal space. The small-angle scattering is not that important in the case of Al-Cu because the main scattering extends along (100) owing to the planar character of the GP I zones on (100) lattice planes. (author) 24 figs., 10 tabs., refs
Modeling Periodic Impulsive Effects on Online TV Series Diffusion.
Fu, Peihua; Zhu, Anding; Fang, Qiwen; Wang, Xi
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. 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. 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. 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. The buzz in public social communities
Modeling Periodic Impulsive Effects on Online TV Series Diffusion.
Directory of Open Access Journals (Sweden)
Peihua Fu
Full Text Available 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.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.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.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. The buzz in public
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
Relating R and D and investment policies to CCS market diffusion through two-factor learning
International Nuclear Information System (INIS)
Lohwasser, Richard; Madlener, Reinhard
2013-01-01
Carbon capture and storage (CCS) has the potential to play a major role in the stabilization of anthropogenic greenhouse gases. To develop the capture technology from its current demonstration phase towards commercial maturity, significant funding is directed to CCS, such as the EU’s €4.5 bn NER300 fund. However, we know little about how this funding relates to market diffusion of CCS. This paper addresses that question. We initially review past learning effects from both capacity installations and R and D efforts for a similar technology using the concept of two-factor learning. We apply the obtained learning-by-doing and learning-by-searching rates to CCS in the electricity market model HECTOR, which simulates 19 European countries hourly until 2040, to understand the impact of learning and associated policies on CCS market diffusion. We evaluate the effectiveness of policies addressing learning-by-doing and learning-by-searching by relating the policy budget to the realized CCS capacity and find that, at lower policy cost, both methods are about equally effective. At higher spending levels, policies promoting learning-by-doing are more effective. Overall, policy effectiveness increases in low CO 2 price scenarios, but the CO 2 price still remains the key prerequisite for the economic competitiveness, even with major policy support. - Highlights: ► Identified two-factor learning rates for CCS through empirical data from flue gas desulphurization. ► Evaluated effectiveness of CCS stimulation policies addressing learning-by-doing and learning-by-researching. ► Both policy types are about equally effective with small policy budgets. ► Policies addressing learning-by-doing, e.g., subsidies to CCS projects, are more effective with large policy budgets. ► Analysis deployed HECTOR power market model that simulates 19 European countries on hourly granularity until 2040.
Mezzasalma, Stefano A
2007-03-15
The theoretical basis of a recent theory of Brownian relativity for polymer solutions is deepened and reexamined. After the problem of relative diffusion in polymer solutions is addressed, its two postulates are formulated in all generality. The former builds a statistical equivalence between (uncorrelated) timelike and shapelike reference frames, that is, among dynamical trajectories of liquid molecules and static configurations of polymer chains. The latter defines the "diffusive horizon" as the invariant quantity to work with in the special version of the theory. Particularly, the concept of universality in polymer physics corresponds in Brownian relativity to that of covariance in the Einstein formulation. Here, a "universal" law consists of a privileged observation, performed from the laboratory rest frame and agreeing with any diffusive reference system. From the joint lack of covariance and simultaneity implied by the Brownian Lorentz-Poincaré transforms, a relative uncertainty arises, in a certain analogy with quantum mechanics. It is driven by the difference between local diffusion coefficients in the liquid solution. The same transformation class can be used to infer Fick's second law of diffusion, playing here the role of a gauge invariance preserving covariance of the spacetime increments. An overall, noteworthy conclusion emerging from this view concerns the statistics of (i) static macromolecular configurations and (ii) the motion of liquid molecules, which would be much more related than expected.
Modelling of diffusion from equilibrium diffraction fluctuations in ordered phases
International Nuclear Information System (INIS)
Arapaki, E.; Argyrakis, P.; Tringides, M.C.
2008-01-01
Measurements of the collective diffusion coefficient D c at equilibrium are difficult because they are based on monitoring low amplitude concentration fluctuations generated spontaneously, that are difficult to measure experimentally. A new experimental method has been recently used to measure time-dependent correlation functions from the diffraction intensity fluctuations and was applied to measure thermal step fluctuations. The method has not been applied yet to measure superstructure intensity fluctuations in surface overlayers and to extract D c . With Monte Carlo simulations we study equilibrium fluctuations in Ising lattice gas models with nearest neighbor attractive and repulsive interactions. The extracted diffusion coefficients are compared to the ones obtained from equilibrium methods. The new results are in good agreement with the results from the other methods, i.e., D c decreases monotonically with coverage Θ for attractive interactions and increases monotonically with Θ for repulsive interactions. Even the absolute value of D c agrees well with the results obtained with the probe area method. These results confirm that this diffraction based method is a novel, reliable way to measure D c especially within the ordered region of the phase diagram when the superstructure spot has large intensity
Modeling of interstitial diffusion of ion-implanted boron
International Nuclear Information System (INIS)
Velichko, O.I.; Knyazheva, N.V.
2009-01-01
A model of the interstitial diffusion of ion-implanted boron during rapid thermal annealing of silicon layers previously amorphized by implantation of germanium has been proposed. It is supposed that the boron interstitials are created continuously during annealing due to generation, dissolution, or rearrangement of the clusters of impurity atoms which are formed in the ion-implanted layers with impurity concentration above the solubility limit. The local elastic stresses arising due to the difference of boron atomic radius and atomic radius of silicon also contribute to the generation of boron interstitials. A simulation of boron redistribution during thermal annealing for 60 s at a temperature of 850 C has been carried out. The calculated profile agrees well with the experimental data. A number of the parameters of interstitial diffusion have been derived. In particular, the average migration length of nonequilibrium boron interstitials is equal to 12 nm. It was also obtained that approximately 1.94% of boron atoms were converted to the interstitial sites, participated in the fast interstitial migration, and then became immobile again transferring into a substitutional position or forming the electrically inactive complexes with crystal lattice defects. (authors)
Analytical model of diffuse reflectance spectrum of skin tissue
Energy Technology Data Exchange (ETDEWEB)
Lisenko, S A; Kugeiko, M M; Firago, V A [Belarusian State University, Minsk (Belarus); Sobchuk, A N [B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk (Belarus)
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)
Study of superionic conductors dynamics by continued diffusion model
International Nuclear Information System (INIS)
Bennai, M.
1993-12-01
The superionic conductors form a special category of solids characterized by their remarkable transport properties and are in general, Simplified as being constituted by the superposition of two inter penetrable crystal lattices. The ions of the first one form a rigid structure through which the other ions of opposite charge diffuse in quasi-liquid way. Basing on experimental and theoretical arguments, it was proved necessary to adopt a model of N-body continued diffusion which the basic theory is that of brownian movement. This thesis deals with the study of the dynamic structure factor S (q,w) and its line half width by the method of development in continued fractions issued from the Mori theory. With regard to the analytical difficulty met at the time of the static correlations functions calculation, the homogeneous approximation was applied and the notion of effective strength was introduced. So, it was obtained general relationships which give the static correlation functions, only in term of the static structure factor of liquids and effective potential. 98 refs.; 22 figs. (F.M.)
Postural control model interpretation of stabilogram diffusion analysis
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.
Directory of Open Access Journals (Sweden)
Fatma E. El-Khouly
2017-10-01
Full Text Available Despite decades of clinical trials for diffuse intrinsic pontine glioma (DIPG, patient survival does not exceed 10% at two years post-diagnosis. Lack of benefit from systemic chemotherapy may be attributed to an intact bloodbrain barrier (BBB. We aim to develop a theoretical model including relevant physicochemical properties in order to review whether applied chemotherapeutics are suitable for passive diffusion through an intact BBB or whether local administration via convection-enhanced delivery (CED may increase their therapeutic potential. Physicochemical properties (lipophilicity, molecular weight, and charge in physiological environment of anticancer drugs historically and currently administered to DIPG patients, that affect passive diffusion over the BBB, were included in the model. Subsequently, the likelihood of BBB passage of these drugs was ascertained, as well as their potential for intratumoral administration via CED. As only non-molecularly charged, lipophilic, and relatively small sized drugs are likely to passively diffuse through the BBB, out of 51 drugs modeled, only 8 (15%—carmustine, lomustine, erlotinib, vismodegib, lenalomide, thalidomide, vorinostat, and mebendazole—are theoretically qualified for systemic administration in DIPG. Local administration via CED might create more therapeutic options, excluding only positively charged drugs and drugs that are either prodrugs and/or only available as oral formulation. A wide variety of drugs have been administered systemically to DIPG patients. Our model shows that only few are likely to penetrate the BBB via passive diffusion, which may partly explain the lack of efficacy. Drug distribution via CED is less dependent on physicochemical properties and may increase the therapeutic options for DIPG.
Banerjee, Puja; Yashonath, Subramanian; Bagchi, Biman
2017-04-01
While most of the existing theoretical and simulation studies have focused on simple, spherical, halide and alkali ions, many chemically, biologically, and industrially relevant electrolytes involve complex non-spherical polyatomic ions like nitrate, chlorate, and sulfate to name only a few. Interestingly, some polyatomic ions in spite of being larger in size show anomalously high diffusivity and therefore cause a breakdown of the venerable Stokes-Einstein (S-E) relation between the size and diffusivity. Here we report a detailed analysis of the dynamics of anions in aqueous potassium nitrate (KNO3) and aqueous potassium acetate (CH3COOK) solutions. The two ions, nitrate (-NO3) and acetate (CH3-CO2 ), with their similar size show a large difference in diffusivity values. We present evidence that the translational motion of these polyatomic ions is coupled to the rotational motion of the ion. We show that unlike the acetate ion, nitrate ion with a symmetric charge distribution among all periphery oxygen atoms shows a faster rotational motion with large amplitude rotational jumps which enhances its translational motion due to translational-rotational coupling. By creating a family of modified-charge model systems, we have analysed the rotational motion of asymmetric polyatomic ions and the contribution of it to the translational motion. These model systems help clarifying and establishing the relative contribution of rotational motion in enhancing the diffusivity of the nitrate ion over the value predicted by the S-E relation and also over the other polyatomic ions having asymmetric charge distribution like the acetate ion. In the latter case, reduced rotational motion results in lower diffusivity values than those with symmetric charge distribution. We propose translational-rotational coupling as a general mechanism of the breakdown of the S-E relation in the case of polyatomic ions.
A diffusive ink transport model for lipid dip-pen nanolithography.
Urtizberea, A; Hirtz, M
2015-10-14
Despite diverse applications, phospholipid membrane stacks generated by dip-pen nanolithography (DPN) still lack a thorough and systematic characterization that elucidates the whole ink transport process from writing to surface spreading, with the aim of better controlling the resulting feature size and resolution. We report a quantitative analysis and modeling of the dependence of lipid DPN features (area, height and volume) on dwell time and relative humidity. The ink flow rate increases with humidity in agreement with meniscus size growth, determining the overall feature size. The observed time dependence indicates the existence of a balance between surface spreading and the ink flow rate that promotes differences in concentration at the meniscus/substrate interface. Feature shape is controlled by the substrate surface energy. The results are analyzed within a modified model for the ink transport of diffusive inks. At any humidity the dependence of the area spread on the dwell time shows two diffusion regimes: at short dwell times growth is controlled by meniscus diffusion while at long dwell times surface diffusion governs the process. The critical point for the switch of regime depends on the humidity.
The drift diffusion model as the choice rule in reinforcement learning.
Pedersen, Mads Lund; Frank, Michael J; Biele, Guido
2017-08-01
Current reinforcement-learning models often assume simplified decision processes that do not fully reflect the dynamic complexities of choice processes. Conversely, sequential-sampling models of decision making account for both choice accuracy and response time, but assume that decisions are based on static decision values. To combine these two computational models of decision making and learning, we implemented reinforcement-learning models in which the drift diffusion model describes the choice process, thereby capturing both within- and across-trial dynamics. To exemplify the utility of this approach, we quantitatively fit data from a common reinforcement-learning paradigm using hierarchical Bayesian parameter estimation, and compared model variants to determine whether they could capture the effects of stimulant medication in adult patients with attention-deficit hyperactivity disorder (ADHD). The model with the best relative fit provided a good description of the learning process, choices, and response times. A parameter recovery experiment showed that the hierarchical Bayesian modeling approach enabled accurate estimation of the model parameters. The model approach described here, using simultaneous estimation of reinforcement-learning and drift diffusion model parameters, shows promise for revealing new insights into the cognitive and neural mechanisms of learning and decision making, as well as the alteration of such processes in clinical groups.
Relative distance between tracers as a measure of diffusivity within moving aggregates
Pönisch, Wolfram; Zaburdaev, Vasily
2018-02-01
Tracking of particles, be it a passive tracer or an actively moving bacterium in the growing bacterial colony, is a powerful technique to probe the physical properties of the environment of the particles. One of the most common measures of particle motion driven by fluctuations and random forces is its diffusivity, which is routinely obtained by measuring the mean squared displacement of the particles. However, often the tracer particles may be moving in a domain or an aggregate which itself experiences some regular or random motion and thus masks the diffusivity of tracers. Here we provide a method for assessing the diffusivity of tracer particles within mobile aggregates by measuring the so-called mean squared relative distance (MSRD) between two tracers. We provide analytical expressions for both the ensemble and time averaged MSRD allowing for direct identification of diffusivities from experimental data.
Reaction-diffusion modeling of hydrogen in beryllium
Energy Technology Data Exchange (ETDEWEB)
Wensing, Mirko; Matveev, Dmitry; Linsmeier, Christian [Forschungszentrum Juelich GmbH, Institut fuer Energie- und Klimaforschung - Plasmaphysik (Germany)
2016-07-01
Beryllium will be used as first-wall material for the future fusion reactor ITER as well as in the breeding blanket of DEMO. In both cases it is important to understand the mechanisms of hydrogen retention in beryllium. In earlier experiments with beryllium low-energy binding states of hydrogen were observed by thermal desorption spectroscopy (TDS) which are not yet well understood. Two candidates for these states are considered: beryllium-hydride phases within the bulk and surface effects. The retention of deuterium in beryllium is studied by a reaction rate approach using a coupled reaction diffusion system (CRDS)-model relying on ab initio data from density functional theory calculations (DFT). In this contribution we try to assess the influence of surface recombination.
Semenycheva, Alexandra V.; Chuvil'deev, Vladimir N.; Nokhrin, Aleksey V.
2018-05-01
The paper offers a model describing the process of grain boundary self-diffusion in metals with phase transitions in the solid state. The model is based on ideas and approaches found in the theory of non-equilibrium grain boundaries. The range of application of basic relations contained in this theory is shown to expand, as they can be used to calculate the parameters of grain boundary self-diffusion in high-temperature and low-temperature phases of metals with a phase transition. The model constructed is used to calculate grain boundary self-diffusion activation energy in titanium and zirconium and an explanation is provided as to their abnormally low values in the low-temperature phase. The values of grain boundary self-diffusion activation energy are in good agreement with the experiment.
Diffusive Phenomena and the Austenite/Martensite Relative Stability in Cu-Based Shape-Memory Alloys
Pelegrina, J. L.; Yawny, A.; Sade, M.
2018-02-01
The main characteristic of martensitic phase transitions is the coordinate movement of the atoms which takes place athermally, without the contribution of diffusion during its occurrence. However, the impacts of diffusive phenomena on the relative stability between the phases involved and, consequently, on the associated transformation temperatures and functional properties can be significant. This is particularly evident in the case of Cu-based shape-memory alloys where atomic diffusion in both austenite and martensite metastable phases might occur even at room-temperature levels, giving rise to a variety of intensively studied phenomena. In the present study, the progresses made in the understanding of three selected diffusion-related effects of importance in Cu-Zn-Al and Cu-Al-Be alloys are reviewed. They are the after-quench retained disorder in the austenitic structure and its subsequent reordering, the stabilization of the martensite, and the effect of applied stress on the austenitic order. It is shown how the experimental results obtained from tests performed on single crystal material can be rationalized under the shed of a model developed to evaluate the variation of the relative stability between the phases in terms of atom pairs interchanges.
Modeling of immision from power plants using stream-diffusion model
International Nuclear Information System (INIS)
Kanevce, Lj.; Kanevce, G.; Markoski, A.
1996-01-01
Analyses of simple empirical and integral immision models, comparing with complex three dimensional differential models is given. Complex differential models needs huge computer power, so they can't be useful for practical engineering calculations. In this paper immision modeling, using stream-diffusion approach is presented. Process of dispersion is divided into two parts. First part is called stream part, it's near the source of the pollutants, and it's presented with defected turbulent jet in wind field. This part finished when the velocity of stream (jet) becomes equal with wind speed. Boundary conditions in the end of the first part, are initial for the second, called diffusion part, which is modeling with tri dimensional diffusion equation. Gradient of temperature, wind speed profile and coefficient of diffusion in this model must not be constants, they can change with the height. Presented model is much simpler than the complete meteorological differential models which calculates whole fields of meteorological parameters. Also, it is more complex and gives more valuable results for dispersion of pollutants from widely used integral and empirical models
Modelling water fluxes for the analysis of diffuse pollution at the river basin scale
Wit, de M.; Meinardi, C.R.; Wendland, F.; Kunkel, R.
2000-01-01
Diffuse pollution is a significant and sometimes even major component of surface water pollution. Diffuse inputs of pollutants to the surface water are related to runoff of precipitation. This means that the analysis of diffuse pollutant fluxes from the land surface to the surface water requires an
Ranger, Jochen; Kuhn, Jörg-Tobias; Szardenings, Carsten
2017-05-01
Cognitive psychometric models embed cognitive process models into a latent trait framework in order to allow for individual differences. Due to their close relationship to the response process the models allow for profound conclusions about the test takers. However, before such a model can be used its fit has to be checked carefully. In this manuscript we give an overview over existing tests of model fit and show their relation to the generalized moment test of Newey (Econometrica, 53, 1985, 1047) and Tauchen (J. Econometrics, 30, 1985, 415). We also present a new test, the Hausman test of misspecification (Hausman, Econometrica, 46, 1978, 1251). The Hausman test consists of a comparison of two estimates of the same item parameters which should be similar if the model holds. The performance of the Hausman test is evaluated in a simulation study. In this study we illustrate its application to two popular models in cognitive psychometrics, the Q-diffusion model and the D-diffusion model (van der Maas, Molenaar, Maris, Kievit, & Boorsboom, Psychol Rev., 118, 2011, 339; Molenaar, Tuerlinckx, & van der Maas, J. Stat. Softw., 66, 2015, 1). We also compare the performance of the test to four alternative tests of model fit, namely the M 2 test (Molenaar et al., J. Stat. Softw., 66, 2015, 1), the moment test (Ranger et al., Br. J. Math. Stat. Psychol., 2016) and the test for binned time (Ranger & Kuhn, Psychol. Test. Asess. , 56, 2014b, 370). The simulation study indicates that the Hausman test is superior to the latter tests. The test closely adheres to the nominal Type I error rate and has higher power in most simulation conditions. © 2017 The British Psychological Society.
Modelling thermal radiation in buoyant turbulent diffusion flames
Consalvi, J. L.; Demarco, R.; Fuentes, A.
2012-10-01
This work focuses on the numerical modelling of radiative heat transfer in laboratory-scale buoyant turbulent diffusion flames. Spectral gas and soot radiation is modelled by using the Full-Spectrum Correlated-k (FSCK) method. Turbulence-Radiation Interactions (TRI) are taken into account by considering the Optically-Thin Fluctuation Approximation (OTFA), the resulting time-averaged Radiative Transfer Equation (RTE) being solved by the Finite Volume Method (FVM). Emission TRIs and the mean absorption coefficient are then closed by using a presumed probability density function (pdf) of the mixture fraction. The mean gas flow field is modelled by the Favre-averaged Navier-Stokes (FANS) equation set closed by a buoyancy-modified k-ɛ model with algebraic stress/flux models (ASM/AFM), the Steady Laminar Flamelet (SLF) model coupled with a presumed pdf approach to account for Turbulence-Chemistry Interactions, and an acetylene-based semi-empirical two-equation soot model. Two sets of experimental pool fire data are used for validation: propane pool fires 0.3 m in diameter with Heat Release Rates (HRR) of 15, 22 and 37 kW and methane pool fires 0.38 m in diameter with HRRs of 34 and 176 kW. Predicted flame structures, radiant fractions, and radiative heat fluxes on surrounding surfaces are found in satisfactory agreement with available experimental data across all the flames. In addition further computations indicate that, for the present flames, the gray approximation can be applied for soot with a minor influence on the results, resulting in a substantial gain in Computer Processing Unit (CPU) time when the FSCK is used to treat gas radiation.
International Nuclear Information System (INIS)
Sada, Koichi; Michioka, Takenobu; Ichikawa, Yoichi; Komiyama, Sumito
2009-01-01
A numerical simulation method has been developed to predict atmospheric flow and stack gas diffusion, considering the buildings and complex terrain located near and relatively far from a stack, respectively. The turbulence closure technique was used for flow calculation, some calculation grids on the ground near a stack were treated as buildings, and stack gas diffusion was predicted using the Lagrangian particle model. The calculated flow and stack gas diffusion results were compared with those obtained by wind tunnel experiments under actual terrain containing buildings. Effective stack height was estimated by comparing the surface concentration along the plume axis with those under a flat-plate condition, and it was apparent that the effective stack heights estimated by calculations were almost the same as those obtained by the wind tunnel experiment. Then, the effective dose and relative concentration of stack gas were calculated using the effective stack heights obtained by a numerical model. Almost the same effective dose and relative concentration were obtained when compared with those using the effective stack height obtained by wind tunnel experiment. (author)
Agent-based Modeling Automated: Data-driven Generation of Innovation Diffusion Models
Jensen, T.; Chappin, E.J.L.
2016-01-01
Simulation modeling is useful to gain insights into driving mechanisms of diffusion of innovations. This study aims to introduce automation to make identification of such mechanisms with agent-based simulation modeling less costly in time and labor. We present a novel automation procedure in which
Technology diffusion in energy-economy models: The case of Danish vintage models
DEFF Research Database (Denmark)
Klinge Jacobsen, Henrik
2000-01-01
the costs of greenhouse gas mitigation. This paper examines the effect on aggregate energy efficiency of using technological vintage models to describe technology diffusion. The focus is on short- to medium-term issues. Three different models of Danish energy supply and demand are used to illustrate...
HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.
Wiecki, Thomas V; Sofer, Imri; Frank, Michael J
2013-01-01
The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/
HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python
Directory of Open Access Journals (Sweden)
Thomas V Wiecki
2013-08-01
Full Text Available The diffusion model is a commonly used tool to infer latent psychological processes underlying decision making, and to link them to neural mechanisms based on reaction times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of reaction time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model, which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject / condition than non-hierarchical method, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g. fMRI influence decision making parameters. This paper will first describe the theoretical background of drift-diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the chi-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs
Diffusion and Localization of Relative Strategy Scores in The Minority Game
Granath, Mats; Perez-Diaz, Alvaro
2016-10-01
We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase (α ≡ P/N≳ 1) of the basic Minority Game using sign-payoff, with N agents holding two strategies over P histories. We formulate a statistical model that makes use of the gauge freedom with respect to the ordering of an agent's strategies to quantify the correlation between the attendance and the distribution of strategies. The relative score xin Z of the two strategies of an agent is described in terms of a one dimensional random walk with asymmetric jump probabilities, leading either to a static and asymmetric exponential distribution centered at x=0 for fickle agents or to diffusion with a positive or negative drift for frozen agents. In terms of scaled coordinates x/√{N} and t / N the distributions are uniquely given by α and in quantitative agreement with direct simulations of the game. As the model avoids the reformulation in terms of a constrained minimization problem it can be used for arbitrary payoff functions with little calculational effort and provides a transparent and simple formulation of the dynamics of the basic Minority Game in the asymmetric phase.
Energy Technology Data Exchange (ETDEWEB)
Ma, Teqi [Northwest Institute of Nuclear Technology, No.28 Pingyu Road, Baqiao District, Xi' an,Shaanxi, 710024 (China); Mechanics and Physics of Solids Research Group, Modelling and Simulation Centre, The University of Manchester, Oxford Road, Manchester, M13 9PL (United Kingdom); Jivkov, Andrey P., E-mail: andrey.jivkov@manchester.ac.uk [Mechanics and Physics of Solids Research Group, Modelling and Simulation Centre, The University of Manchester, Oxford Road, Manchester, M13 9PL (United Kingdom); Li, Weiping; Liang, Wei; Wang, Yu; Xu, Hui [Northwest Institute of Nuclear Technology, No.28 Pingyu Road, Baqiao District, Xi' an,Shaanxi, 710024 (China); Han, Xiaoyuan, E-mail: xyhan_nint@sina.cn [Northwest Institute of Nuclear Technology, No.28 Pingyu Road, Baqiao District, Xi' an,Shaanxi, 710024 (China)
2017-04-01
Understanding the alteration of nuclear waste glass in geological repository conditions is critical element of the analysis of repository retention function. Experimental observations of glass alterations provide a general agreement on the following regimes: inter-diffusion, hydrolysis process, rate drop, residual rate and, under very particular conditions, resumption of alteration. Of these, the mechanisms controlling the rate drop and the residual rate remain a subject of dispute. This paper offers a critical review of the two most competitive models related to these regimes: affinity–limited dissolution and diffusion barrier. The limitations of these models are highlighted by comparison of their predictions with available experimental evidence. Based on the comprehensive discussion of the existing models, a new mechanistic model is proposed as a combination of the chemical affinity and diffusion barrier concepts. It is demonstrated how the model can explain experimental phenomena and data, for which the existing models are shown to be not fully adequate.
Modelling dense relational data
DEFF Research Database (Denmark)
Herlau, Tue; Mørup, Morten; Schmidt, Mikkel Nørgaard
2012-01-01
they are not naturally suited for kernel K-means. We propose a generative Bayesian model for dense matrices which generalize kernel K-means to consider off-diagonal interactions in matrices of interactions, and demonstrate its ability to detect structure on both artificial data and two real data sets....
Models as Relational Categories
Kokkonen, Tommi
2017-01-01
Model-based learning (MBL) has an established position within science education. It has been found to enhance conceptual understanding and provide a way for engaging students in authentic scientific activity. Despite ample research, few studies have examined the cognitive processes regarding learning scientific concepts within MBL. On the other…
Modelling of a diffusion-sorption experiment on sandstone
International Nuclear Information System (INIS)
Smith, P.A.
1989-11-01
The results of a diffusion-sorption experiment on a sample of Darley Dale sandstone, using simulated groundwater spiked with a mixture of 125 I, 85 Sr and 137 Cs, are modelled by a one-dimensional porous medium approach in which sorption is described by Freundlich isotherms. The governing equations are solved analytically for the special case of a linear isotherm, and numerically using the computer code RANCHDIFF for non-linear isotherms. A set of time-dependent, ordinary differential equations is obtained using the Lagrange interpolation technique and integrated by Gear's variable order predictor-corrector method. It is shown that the sorption behaviour of 85 Sr can be modelled successfully by a linear isotherm, using a sorption parameter consistent with batch-sorption tests. The behaviour of 137 Cs may be modelled by a non-linear isotherm, but the amount of 137 Cs sorbed is less than that anticipated from batch-sorption tests. 125 I is assumed to be non-sorbing and is used to determine the porosity of the sandstone. (author) 10 figs., 4 tabs., 6 refs
An efficient method for model refinement in diffuse optical tomography
Zirak, A. R.; Khademi, M.
2007-11-01
Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.
Preisach hysteresis model for non-linear 2D heat diffusion
International Nuclear Information System (INIS)
Jancskar, Ildiko; Ivanyi, Amalia
2006-01-01
This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way
Spatial diffusion of influenza outbreak-related climate factors in Chiang Mai Province, Thailand.
Nakapan, Supachai; Tripathi, Nitin Kumar; Tipdecho, Taravudh; Souris, Marc
2012-10-24
Influenza is one of the most important leading causes of respiratory illness in the countries located in the tropical areas of South East Asia and Thailand. In this study the climate factors associated with influenza incidence in Chiang Mai Province, Northern Thailand, were investigated. Identification of factors responsible for influenza outbreaks and the mapping of potential risk areas in Chiang Mai are long overdue. This work examines the association between yearly climate patterns between 2001 and 2008 and influenza outbreaks in the Chiang Mai Province. The climatic factors included the amount of rainfall, percent of rainy days, relative humidity, maximum, minimum temperatures and temperature difference. The study develops a statistical analysis to quantitatively assess the relationship between climate and influenza outbreaks and then evaluate its suitability for predicting influenza outbreaks. A multiple linear regression technique was used to fit the statistical model. The Inverse Distance Weighted (IDW) interpolation and Geographic Information System (GIS) techniques were used in mapping the spatial diffusion of influenza risk zones. The results show that there is a significance correlation between influenza outbreaks and climate factors for the majority of the studied area. A statistical analysis was conducted to assess the validity of the model comparing model outputs and actual outbreaks.
Spatial Diffusion of Influenza Outbreak-Related Climate Factors in Chiang Mai Province, Thailand
Directory of Open Access Journals (Sweden)
Marc Souris
2012-10-01
Full Text Available Influenza is one of the most important leading causes of respiratory illness in the countries located in the tropical areas of South East Asia and Thailand. In this study the climate factors associated with influenza incidence in Chiang Mai Province, Northern Thailand, were investigated. Identification of factors responsible for influenza outbreaks and the mapping of potential risk areas in Chiang Mai are long overdue. This work examines the association between yearly climate patterns between 2001 and 2008 and influenza outbreaks in the Chiang Mai Province. The climatic factors included the amount of rainfall, percent of rainy days, relative humidity, maximum, minimum temperatures and temperature difference. The study develops a statistical analysis to quantitatively assess the relationship between climate and influenza outbreaks and then evaluate its suitability for predicting influenza outbreaks. A multiple linear regression technique was used to fit the statistical model. The Inverse Distance Weighted (IDW interpolation and Geographic Information System (GIS techniques were used in mapping the spatial diffusion of influenza risk zones. The results show that there is a significance correlation between influenza outbreaks and climate factors for the majority of the studied area. A statistical analysis was conducted to assess the validity of the model comparing model outputs and actual outbreaks.
Spaniol, Julia; Madden, David J.; Voss, Andreas
2006-01-01
Two experiments investigated adult age differences in episodic and semantic long-term memory tasks, as a test of the hypothesis of specific age-related decline in context memory. Older adults were slower and exhibited lower episodic accuracy than younger adults. Fits of the diffusion model (R. Ratcliff, 1978) revealed age-related increases in…
Directory of Open Access Journals (Sweden)
BOLSHAKOV V. I.
2016-05-01
Full Text Available Summary. It was made a search for new and more accurate orientation relations between the crystal lattice in the pearlite and bainite austenite decomposition products. Methods. It were used the methods: transmission electron microscopy, the micro-, mathematical matrix and stereographic analysis. The purpose of the research is with theoretical, numerical and experimental methods to set up to a 0.2 degree angular orientation relations between the lattices of ferrite and cementite in the austenite decomposition products in the temperature range 400 ... 700С. Results. It was established a new, refined value for grids in the diffusion decay of γ → α + (α + θ. Practical significance. It was proposed a new oriented dependence and the corresponding double gnomonic projection with poles to planes α and θ phases, which can be used in patterns of crystallographic lattices relations studies at phase transitions, as well as the subsequent modeling of complex physical processes of structure formation in metals and binary systems.
Baran, Timothy M; Foster, Thomas H
2011-08-01
We present a new Monte Carlo model of cylindrical diffusing fibers that is implemented with a graphics processing unit. Unlike previously published models that approximate the diffuser as a linear array of point sources, this model is based on the construction of these fibers. This allows for accurate determination of fluence distributions and modeling of fluorescence generation and collection. We demonstrate that our model generates fluence profiles similar to a linear array of point sources, but reveals axially heterogeneous fluorescence detection. With axially homogeneous excitation fluence, approximately 90% of detected fluorescence is collected by the proximal third of the diffuser for μ(s)'∕μ(a) = 8 in the tissue and 70 to 88% is collected in this region for μ(s)'∕μ(a) = 80. Increased fluorescence detection by the distal end of the diffuser relative to the center section is also demonstrated. Validation of these results was performed by creating phantoms consisting of layered fluorescent regions. Diffusers were inserted into these layered phantoms and fluorescence spectra were collected. Fits to these spectra show quantitative agreement between simulated fluorescence collection sensitivities and experimental results. These results will be applicable to the use of diffusers as detectors for dosimetry in interstitial photodynamic therapy.
Validation of a mixture-averaged thermal diffusion model for premixed lean hydrogen flames
Schlup, Jason; Blanquart, Guillaume
2018-03-01
The mixture-averaged thermal diffusion model originally proposed by Chapman and Cowling is validated using multiple flame configurations. Simulations using detailed hydrogen chemistry are done on one-, two-, and three-dimensional flames. The analysis spans flat and stretched, steady and unsteady, and laminar and turbulent flames. Quantitative and qualitative results using the thermal diffusion model compare very well with the more complex multicomponent diffusion model. Comparisons are made using flame speeds, surface areas, species profiles, and chemical source terms. Once validated, this model is applied to three-dimensional laminar and turbulent flames. For these cases, thermal diffusion causes an increase in the propagation speed of the flames as well as increased product chemical source terms in regions of high positive curvature. The results illustrate the necessity for including thermal diffusion, and the accuracy and computational efficiency of the mixture-averaged thermal diffusion model.
Ochalek, M; Podhaisky, H; Ruettinger, H-H; Wohlrab, J; Neubert, R H H
2012-10-01
The barrier function of two quaternary stratum corneum (SC) lipid model membranes, which were previously characterized with regard to the lipid organization, was investigated based on diffusion studies of model drugs with varying lipophilicities. Diffusion experiments of a hydrophilic drug, urea, and more lipophilic drugs than urea (i.e. caffeine, diclofenac sodium) were conducted using Franz-type diffusion cells. The amount of permeated drug was analyzed using either HPLC or CE technique. The subjects of interest in the present study were the investigation of the influence of physicochemical properties of model drugs on their diffusion and permeation through SC lipid model membranes, as well as the study of the impact of the constituents of these artificial systems (particularly ceramide species) on their barrier properties. The diffusion through both SC lipid model membranes and the human SC of the most hydrophilic model drug, urea, was faster than the permeation of the more lipophilic drugs. The slowest rate of permeation through SC lipid systems occurred in the case of caffeine. The composition of SC lipid model membranes has a significant impact on their barrier function. Model drugs diffused and permeated faster through Membrane II (presence of Cer [EOS]). In terms of the barrier properties, Membrane II is much more similar to the human SC than Membrane I. Copyright © 2012 Elsevier B.V. All rights reserved.
Two dimensional finite element modelling for dynamic water diffusion through stratum corneum.
Xiao, Perry; Imhof, Robert E
2012-10-01
Solvents penetration through in vivo human stratum corneum (SC) has always been an interesting research area for trans-dermal drug delivery studies, and the importance of intercellular routes (diffuse in between corneocytes) and transcellular routes (diffuse through corneocytes) during diffusion is often debatable. In this paper, we have developed a two dimensional finite element model to simulate the dynamic water diffusion through the SC. It is based on the brick-and-mortar model, with brick represents corneocytes and mortar represents lipids, respectively. It simulates the dynamic water diffusion process through the SC from pre-defined initial conditions and boundary conditions. Although the simulation is based on water diffusions, the principles can also be applied to the diffusions of other topical applied substances. The simulation results show that both intercellular routes and transcellular routes are important for water diffusion. Although intercellular routes have higher flux rates, most of the water still diffuse through transcellular routes because of the high cross area ratio of corneocytes and lipids. The diffusion water flux, or trans-epidermal water loss (TEWL), is reversely proportional to corneocyte size, i.e. the larger the corneocyte size, the lower the TEWL, and vice versa. There is also an effect of the SC thickness, external air conditions and diffusion coefficients on the water diffusion through SC on the resulting TEWL. Copyright © 2012 Elsevier B.V. All rights reserved.
Combining voxel-based morphometry and diffusion tensor imaging to detect age-related brain changes.
Lehmbeck, Jan T; Brassen, Stefanie; Weber-Fahr, Wolfgang; Braus, Dieter F
2006-04-03
The present study combined optimized voxel-based morphometry and diffusion tensor imaging to detect age-related brain changes. We compared grey matter density maps (grey matter voxel-based morphometry) and white matter fractional anisotropy maps (diffusion tensor imaging-voxel-based morphometry) between two groups of 17 younger and 17 older women. Older women exhibited reduced white matter fractional anisotropy as well as decreased grey matter density most prominently in the frontal, limbic, parietal and temporal lobes. A discriminant analysis identified four frontal and limbic grey and white matter areas that separated the two groups most effectively. We conclude that grey matter voxel-based morphometry and diffusion tensor imaging voxel-based morphometry are well suited for the detection of age-related changes and their combination provides high accuracy when detecting the neural correlates of aging.
Dipierro, Serena; Valdinoci, Enrico
2018-07-01
Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.
International Nuclear Information System (INIS)
Wu Rui; Zhu Xun; Liao Qiang; Wang Hong; Ding Yudong; Li Jun; Ye Dingding
2010-01-01
In proton exchange membrane fuel cell (PEMFC) models, oxygen effective diffusivity is the most important parameter to characterize the oxygen transport in the gas diffusion layer (GDL). However, its determination is a challenge due to its complex dependency on GDL structure. In the present study, a three-dimensional network consisting of spherical pores and cylindrical throats is developed and used to investigate the effects of GDL structural parameters on oxygen effective diffusivity under the condition with/without water invasion process. Oxygen transport in the throat is described by Fick's law and water invasion process in the network is simulated using the invasion percolation with trapping algorithm. The simulation results reveal that oxygen effective diffusivity is slightly affected by network size but increases with decreasing the network heterogeneity and with increasing the pore connectivity. Impacts of network anisotropy on oxygen transport are also investigated in this paper. The anisotropic network is constructed by constricting the throats in the through-plane direction with a constriction factor. It is found that water invasion has a more severe negative influence on oxygen transport in an anisotropic network. Finally, two new correlations are introduced to determine the oxygen effective diffusivity for the Toray carbon paper GDLs.
Vestergaard-Poulsen, Peter; Hansen, Brian; Ostergaard, Leif; Jakobsen, Rikke
2007-09-01
To understand the diffusion attenuated MR signal from normal and ischemic brain tissue in order to extract structural and physiological information using mathematical modeling, taking into account the transverse relaxation rates in gray matter. We fit our diffusion model to the diffusion-weighted MR signal obtained from cortical gray matter in healthy subjects. Our model includes variable volume fractions, intracellular restriction effects, and exchange between compartments in addition to individual diffusion coefficients and transverse relaxation rates for each compartment. A global optimum was found from a wide range of parameter permutations using cluster computing. We also present simulations of cell swelling and changes of exchange rate and intracellular diffusion as possible cellular mechanisms in ischemia. Our model estimates an extracellular volume fraction of 0.19 in accordance with the accepted value from histology. The absolute apparent diffusion coefficient obtained from the model was similar to that of experiments. The model and the experimental results indicate significant differences in diffusion and transverse relaxation between the tissue compartments and slow water exchange. Our model reproduces the signal changes observed in ischemia via physiologically credible mechanisms. Our modeling suggests that transverse relaxation has a profound influence on the diffusion attenuated MR signal. Our simulations indicate cell swelling as the primary cause of the diffusion changes seen in the acute phase of brain ischemia. (c) 2007 Wiley-Liss, Inc.
Quantitative diffusion tensor fiber tracking of age-related changes in the limbic system
International Nuclear Information System (INIS)
Stadlbauer, Andreas; Salomonowitz, Erich; Strunk, Guido; Hammen, Thilo; Ganslandt, Oliver
2008-01-01
Cerebral white matter is known to undergo degradation with aging, and diffusion tensor imaging (DTI) is capable of revealing the white matter integrity. We assessed age-related changes of quantitative diffusivity parameters and fiber characteristics within the fornix and the cingulum. Thirty-eight healthy subjects aged 18-88 years were examined at 3 Tesla using a 1.9-mm isotropic DTI sequence. Quantitative fiber tracking was performed for 3D-segmentation of the fornix and the cingulum to determine fractional anisotropy (FA), mean diffusivity (MD), eigenvalues (λ 1 , λ 2 , and λ 3 ), number of fibers (NoF), and mean NoF/voxel (FpV). In the fornix, all diffusivity parameters (FA, MD, and eigenvalues) were moderately correlated with age. Strong and moderate negative correlations for NoF and FpV were found, respectively. In the cingulum, no correlation was observed between FA and age, and only weak correlations for the other quantitative parameters. Differences in correlations between the fornix and the cingulum were significant for all diffusivity parameters and for NoF, but not for FpV. The strongest relative changes per decade of age were found in the fornix: FA -2.1%, MD 4.2%, NoF -10.6%, and FpV -4.6%. Our quantitative 3D fiber tracking approach shows that the cingulum is resistant to aging while the fornix is not. (orig.)
Nonlinear variational models for reaction and diffusion systems
International Nuclear Information System (INIS)
Tanyi, G.E.
1983-08-01
There exists a natural metric w.r.t. which the density dependent diffusion operator is harmonic in the sense of Eells and Sampson. A physical corollary of this statement is the property that any two regular points on the orbit of a reaction or diffusion operator can be connected by a path along which the reaction rate is constant. (author)
Diffusion in Liquids : Equilibrium Molecular Simulations and Predictive Engineering Models
Liu, X.
2013-01-01
The aim of this thesis is to study multicomponent diffusion in liquids using Molecular Dynamics (MD) simulations. Diffusion plays an important role in mass transport processes. In binary systems, mass transfer processes have been studied extensively using both experiments and molecular simulations.
Lynn, K. J.; Warren, J. M.
2017-12-01
Nominally anhydrous minerals (NAMs) are important for characterizing deep-Earth water reservoirs, but the water contents of olivine (ol), orthopyroxene (opx), and clinopyroxene (cpx) in peridotites generally do not reflect mantle equilibrium conditions. Ol is typically "dry" and decoupled from H in cpx and opx, which is inconsistent with models of partial melting and/or diffusive loss of H during upwelling beneath mid-ocean ridges. The rehydration of mantle pyroxenes via late-stage re-fertilization has been invoked to explain their relatively high water contents. Here, we use sophisticated 3D diffusion models (after Shea et al., 2015, Am Min) of H in ol, opx, and cpx to investigate the timescales of rehydration across a range of conditions relevant for melt-rock interaction and serpentinization of peridotites. Numerical crystals with 1 mm c-axis lengths and realistic crystal morphologies are modeled using recent H diffusivities that account for compositional variation and diffusion anisotropy. Models were run over timescales of minutes to millions of years and temperatures from 300 to 1200°C. Our 3D models show that, at the high-T end of the range, H concentrations in the cores of NAMs are partially re-equilibrated in as little as a few minutes, and completely re-equilibrated within hours to weeks. At low-T (300°C), serpentinization can induce considerable diffusion in cpx and opx. H contents are 30% re-equilibrated after continuous exposure to hydrothermal fluids for 102 and 105 years, respectively, which is inconsistent with previous interpretations that there is no effect on H in opx under similar conditions. Ol is unaffected after 1 Myr due to the slower diffusivity of the proton-vacancy mechanism at 300°C (2-4 log units lower than for opx). In the middle of the T range (700-1000°C), rehydration of opx and cpx occurs over hours to days, while ol is somewhat slower to respond (days to weeks), potentially allowing the decoupling observed in natural samples to
Subgrid models for mass and thermal diffusion in turbulent mixing
Energy Technology Data Exchange (ETDEWEB)
Sharp, David H [Los Alamos National Laboratory; Lim, Hyunkyung [STONY BROOK UNIV; Li, Xiao - Lin [STONY BROOK UNIV; Gilmm, James G [STONY BROOK UNIV
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
Synchronized stability in a reaction–diffusion neural network model
Energy Technology Data Exchange (ETDEWEB)
Wang, Ling; Zhao, Hongyong, E-mail: hongyongz@126.com
2014-11-14
The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability.
Synchronized stability in a reaction–diffusion neural network model
International Nuclear Information System (INIS)
Wang, Ling; Zhao, Hongyong
2014-01-01
The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability
Bounds for perpetual American option prices in a jump diffusion model
Ekström, Erik
2006-01-01
We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black-Scholes model. We also investigate the dependence of the bounds on different parameters of the model.
Directory of Open Access Journals (Sweden)
Peng Mou
2013-01-01
Full Text Available Reuse of plastic IC packages disassembled from printed circuit boards (PCBs has significant environmental benefits and economic value. The interface delamination caused by moisture diffusion is the main failure mode of IC packages during the disassembling process, which greatly reduces the reusability and reliability of disassembled IC packages. Exploring moisture diffusion mechanism is a prerequisite to optimize prebaking processes before disassembling that is an effective way to avoid the interface delamination. To this end, a computational model with variable boundary conditions is developed based on the different combination state of water in IC packages. The distribution characteristics and mechanism of moisture diffusion behavior are analyzed including the humidity distribution field and the relation among baking temperature, water loss rate, and baking time during baking process, and then the results are validated by FEA simulation based on the improved definition of relative moisture concentration. Baking under variable temperature is proposed and compared with the baking process and baking efficiency under constant temperature to find out the optimized baking parameters. Finally, a set of curves which indicate the relation between baking energy consumption and temperature are determined under actual industrial baking experiments, which could be used as references to develop industrial standards for PCB disassembling process.
Mueller, Christina J; White, Corey N; Kuchinke, Lars
2017-11-27
The goal of this study was to replicate findings of diffusion model parameters capturing emotion effects in a lexical decision task and investigating whether these findings extend to other tasks of implicit emotion processing. Additionally, we were interested in the stability of diffusion model parameters across emotional stimuli and tasks for individual subjects. Responses to words in a lexical decision task were compared with responses to faces in a gender categorization task for stimuli of the emotion categories: happy, neutral and fear. Main effects of emotion as well as stability of emerging response style patterns as evident in diffusion model parameters across these tasks were analyzed. Based on earlier findings, drift rates were assumed to be more similar in response to stimuli of the same emotion category compared to stimuli of a different emotion category. Results showed that emotion effects of the tasks differed with a processing advantage for happy followed by neutral and fear-related words in the lexical decision task and a processing advantage for neutral followed by happy and fearful faces in the gender categorization task. Both emotion effects were captured in estimated drift rate parameters-and in case of the lexical decision task also in the non-decision time parameters. A principal component analysis showed that contrary to our hypothesis drift rates were more similar within a specific task context than within a specific emotion category. Individual response patterns of subjects across tasks were evident in significant correlations regarding diffusion model parameters including response styles, non-decision times and information accumulation.
Energy Technology Data Exchange (ETDEWEB)
Jerome, Neil P.; Miyazaki, Keiko; Collins, David J.; Orton, Matthew R.; D' Arcy, James A.; Leach, Martin O. [Cancer Research UK Cancer Imaging Centre, Division of Radiotherapy and Imaging, The Institute of Cancer Research, London (United Kingdom); Wallace, Toni; Koh, Dow-Mu [Royal Marsden NHS Foundation Trust, Department of Radiology, Sutton, Surrey (United Kingdom); Moreno, Lucas [The Institute of Cancer Research, Paediatric Drug Development Team, Division of Cancer Therapeutics and Clinical Studies, London (United Kingdom); Hospital Nino Jesus, Madrid (Spain); Royal Marsden NHS Foundation Trust, Paediatric Drug Development Unit, Children and Young People' s Unit, Sutton, Surrey (United Kingdom); Pearson, Andrew D.J.; Marshall, Lynley V.; Carceller, Fernando; Zacharoulis, Stergios [The Institute of Cancer Research, Paediatric Drug Development Team, Division of Cancer Therapeutics and Clinical Studies, London (United Kingdom); Royal Marsden NHS Foundation Trust, Paediatric Drug Development Unit, Children and Young People' s Unit, Sutton, Surrey (United Kingdom)
2017-01-15
To examine repeatability of parameters derived from non-Gaussian diffusion models in data acquired in children with solid tumours. Paediatric patients (<16 years, n = 17) were scanned twice, 24 h apart, using DWI (6 b-values, 0-1000 mm{sup -2} s) at 1.5 T in a prospective study. Tumour ROIs were drawn (3 slices) and all data fitted using IVIM, stretched exponential, and kurtosis models; percentage coefficients of variation (CV) calculated for each parameter at all ROI histogram centiles, including the medians. The values for ADC, D, DDC{sub α}, α, and DDC{sub K} gave CV < 10 % down to the 5th centile, with sharp CV increases below 5th and above 95th centile. K, f, and D* showed increased CV (>30 %) over the histogram. ADC, D, DDC{sub α}, and DDC{sub K} were strongly correlated (ρ > 0.9), DDC{sub α} and α were not correlated (ρ = 0.083). Perfusion- and kurtosis-related parameters displayed larger, more variable CV across the histogram, indicating observed clinical changes outside of D/DDC in these models should be interpreted with caution. Centiles below 5th for all parameters show high CV and are unreliable as diffusion metrics. The stretched exponential model behaved well for both DDC{sub α} and α, making it a strong candidate for modelling multiple-b-value diffusion imaging data. (orig.)
A novel familial case of diffuse leukodystrophy related to NDUFV1 compound heterozygous mutations
Ortega-Recalde, Oscar; Fonseca, Dora Janeth; Patiño, Liliana Catherine; Atuesta, Juan Jaime; Rivera-Nieto, Carolina; Restrepo, Carlos Martín; Mateus, Heidi Eliana; van der Knaap, Marjo S.; Laissue, Paul
2013-01-01
NDUFV1 mutations have been related to encephalopathic phenotypes due to mitochondrial energy metabolism disturbances. In this study, we report two siblings affected by a diffuse leukodystrophy, who carry the NDUFV1 c.1156C>T (p.Arg386Cys) missense mutation and a novel 42-bp deletion. Bioinformatic
Lupus-related single nucleotide polymorphisms and risk of diffuse large B-cell lymphoma
Bernatsky, Sasha; Velásquez García, Héctor A; Spinelli, John; Gaffney, Patrick; Smedby, Karin E; Ramsey-Goldman, Rosalind; Wang, Sophia S.; Adami, Hans-Olov; Albanes, Demetrius; Angelucci, Emanuele; Ansell, Stephen M.; Asmann, Yan W.; Becker, Nikolaus; Benavente, Yolanda; Berndt, Sonja I.; Bertrand, Kimberly A.; Birmann, Brenda M.; Boeing, Heiner; Boffetta, Paolo; Bracci, Paige M.; Brennan, Paul; Brooks-Wilson, Angela R.; Cerhan, James R.; Chanock, Stephen J.; Clavel, Jacqueline; Conde, Lucia; Cotenbader, Karen H; Cox, David G; Cozen, Wendy; Crouch, Simon; De Roos, Anneclaire J.; De Sanjose, Silvia; Di Lollo, Simonetta; Diver, W. Ryan; Dogan, Ahmet; Foretova, Lenka; Ghesquières, Hervé; Giles, Graham G.; Glimelius, Bengt; Habermann, Thomas M.; Haioun, Corinne; Hartge, Patricia; Hjalgrim, Henrik; Holford, Theodore R.; Holly, Elizabeth A.; Jackson, Rebecca D.; Kaaks, Rudolph; Kane, Eleanor; Kelly, Rachel S.; Klein, Robert J.; Kraft, Peter; Kricker, Anne; Lan, Qing; Lawrence, Charles; Liebow, Mark; Lightfoot, Tracy; Link, Brian K.; Maynadie, Marc; McKay, James; Melbye, Mads; Molina, Thierry Jo; Monnereau, Alain; Morton, Lindsay M.; Nieters, Alexandra; North, Kari E.; Novak, Anne J.; Offit, Kenneth; Purdue, Mark P.; Rais, Marco; Riby, Jacques; Roman, Eve; Rothman, Nathaniel; Salles, Gilles; Severi, Gianluca; Severson, Richard K.; Skibola, Christine F.; Slager, Susan L.; Smith, Alex; Smith, Martyn T.; Southey, Melissa C.; Staines, Anthony; Teras, Lauren R.; Thompson, Carrie A.; Tilly, Hervé; Tinker, Lesley F.; Tjonneland, Anne; Turner, Jenny; Vajdic, Claire M.; Vermeulen, Roel C H; Vijai, Joseph; Vineis, Paolo; Virtamo, Jarmo; Wang, Zhaoming; Weinstein, Stephanie; Witzig, Thomas E.; Zelenetz, Andrew; Zeleniuch-Jacquotte, Anne; Zhang, Yawei; Zheng, Tongzhang; Zucca, Mariagrazia; Clarke, Ann E
2017-01-01
Objective: Determinants of the increased risk of diffuse large B-cell lymphoma (DLBCL) in SLE are unclear. Using data from a recent lymphoma genome-wide association study (GWAS), we assessed whether certain lupus-related single nucleotide polymorphisms (SNPs) were also associated with DLBCL.
Directory of Open Access Journals (Sweden)
Peter Vestergaard-Poulsen
Full Text Available Chronic stress has detrimental effects on physiology, learning and memory and is involved in the development of anxiety and depressive disorders. Besides changes in synaptic formation and neurogenesis, chronic stress also induces dendritic remodeling in the hippocampus, amygdala and the prefrontal cortex. Investigations of dendritic remodeling during development and treatment of stress are currently limited by the invasive nature of histological and stereological methods. Here we show that high field diffusion-weighted MRI combined with quantitative biophysical modeling of the hippocampal dendritic loss in 21 day restraint stressed rats highly correlates with former histological findings. Our study strongly indicates that diffusion-weighted MRI is sensitive to regional dendritic loss and thus a promising candidate for non-invasive studies of dendritic plasticity in chronic stress and stress-related disorders.
Liang, Yingjie; Chen, Wen
2018-03-01
Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag-Leffler function as the structural function, in which the MSD is a function of inverse Mittag-Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag-Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.
Numerical vs. turbulent diffusion in geophysical flow modelling
International Nuclear Information System (INIS)
D'Isidoro, M.; Maurizi, A.; Tampieri, F.
2008-01-01
Numerical advection schemes induce the spreading of passive tracers from localized sources. The effects of changing resolution and Courant number are investigated using the WAF advection scheme, which leads to a sub-diffusive process. The spreading rate from an instantaneous source is compared with the physical diffusion necessary to simulate unresolved turbulent motions. The time at which the physical diffusion process overpowers the numerical spreading is estimated, and is shown to reduce as the resolution increases, and to increase as the wind velocity increases.
Chiapponi, Chiara; Piras, Fabrizio; Fagioli, Sabrina; Girardi, Paolo; Caltagirone, Carlo; Spalletta, Gianfranco
2014-08-01
Macrostructural-volumetric abnormalities of the hippocampus have been described in schizophrenia. Here, we characterized age-related changes of hippocampal mean diffusivity as an index of microstructural damage by carrying out a neuroimaging study in 85 patients with a DSM-IV-TR diagnosis of schizophrenia and 85 age- and gender-matched healthy controls. We performed analyses of covariance, with diagnosis as fixed factor, mean diffusivity as dependent variable and age as covariate. Patients showed an early increase in mean diffusivity in the right and left hippocampus that increased with age. Thus, microstructural hippocampal changes associated with schizophrenia cannot be confined to a specific time window. Copyright © 2014 Elsevier B.V. All rights reserved.
Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation
Ge, Xian-Hui; Sin, Sang-Jin; Tian, Yu; Wu, Shao-Feng; Wu, Shang-Yu
2018-01-01
We show that there exists a class of charged BTZ-like black hole solutions in Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ black hole is characterized by a charge-dependent logarithmic term in the metric function. As concrete examples, we give five such charged BTZ-like black hole solutions and the standard charged BTZ metric can be regarded as a special instance of them. In order to check the recent proposed universal relations between diffusivity and the butterfly velocity, we first compute the diffusion constants of the standard charged BTZ black holes and then extend our calculation to arbitrary dimension d, exponents z and θ. Remarkably, the case d = θ and z = 2 is a very special in that the charge diffusion D c is a constant and the energy diffusion D e might be ill-defined, but v B 2 τ diverges. We also compute the diffusion constants for the case that the DC conductivity is finite but in the absence of momentum relaxation.
Shin, W; Mahmoud, S Y; Sakaie, K; Banks, S J; Lowe, M J; Phillips, M; Modic, M T; Bernick, C
2014-02-01
Traumatic brain injury is common in fighting athletes such as boxers, given the frequency of blows to the head. Because DTI is sensitive to microstructural changes in white matter, this technique is often used to investigate white matter integrity in patients with traumatic brain injury. We hypothesized that previous fight exposure would predict DTI abnormalities in fighting athletes after controlling for individual variation. A total of 74 boxers and 81 mixed martial arts fighters were included in the analysis and scanned by use of DTI. Individual information and data on fight exposures, including number of fights and knockouts, were collected. A multiple hierarchical linear regression model was used in region-of-interest analysis to test the hypothesis that fight-related exposure could predict DTI values separately in boxers and mixed martial arts fighters. Age, weight, and years of education were controlled to ensure that these factors would not account for the hypothesized effects. We found that the number of knockouts among boxers predicted increased longitudinal diffusivity and transversal diffusivity in white matter and subcortical gray matter regions, including corpus callosum, isthmus cingulate, pericalcarine, precuneus, and amygdala, leading to increased mean diffusivity and decreased fractional anisotropy in the corresponding regions. The mixed martial arts fighters had increased transversal diffusivity in the posterior cingulate. The number of fights did not predict any DTI measures in either group. These findings suggest that the history of fight exposure in a fighter population can be used to predict microstructural brain damage.
Chaotic Lagrangian models for turbulent relative dispersion.
Lacorata, Guglielmo; Vulpiani, Angelo
2017-04-01
A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.
Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J
2005-09-01
Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.
Small-polaron model of light atom diffusion
International Nuclear Information System (INIS)
Emin, D.
1977-01-01
A number of researchers have treated the diffusion of light interstitials in metals in strict analogy with the theory for the hopping diffusion of electrons in low-mobility insulators. In other words, these authors view the diffusion of light atoms as simply being an example of small-polaron hopping motion. In this paper the motion of a small polaron is introduced, and the mechanism of its motion is described. The experimental results are then succinctly presented. Next the physical assumptions implicit in the theory are compared with the situation which is believed to characterize the existence and motion of light interstitial atoms in metals. Concomitantly, the modifications of the small-polaron theory required in applying it to light atom diffusion are ennumerated
A mathematical model in charactering chloride diffusivity in unsaturated cementitious material
Zhang, Y.; Ye, G.; Pecur, I.B.; Baricevic, A.; Stirmer, N; Bjegovic, D.
2017-01-01
In this paper, a new analytic model for predicting chloride diffusivity in unsaturated cementitious materials is developed based on conductivity theory and Nernst-Einstein equation. The model specifies that chloride diffusivity in unsaturated cementitious materials can be mathematically described as
A critical discussion of the vacancy diffusion model of ion beam induced epitaxial crystallization
International Nuclear Information System (INIS)
Heera, V.
1989-01-01
A simple vacancy diffusion model of ion beam induced epitaxial crystallization of silicon including divacancy formation is developed. The model reproduces some of the experimental findings, as e.g. the dose rate dependence of the crystallization rate. However, the measured activation energy of the ion beam induced epitaxial crystallization cannot be accounted for by vacancy diffusion alone. (author)
Nuclear interaction potential in a folded-Yukawa model with diffuse densities
International Nuclear Information System (INIS)
Randrup, J.
1975-09-01
The folded-Yukawa model for the nuclear interaction potential is generalized to diffuse density distributions which are generated by folding a Yukawa function into sharp generating distributions. The effect of a finite density diffuseness or of a finite interaction range is studied. The Proximity Formula corresponding to the generalized model is derived and numerical comparison is made with the exact results. (8 figures)
Long, T.B.; Blok, V.; Poldner, Kim
2017-01-01
r, CSA technological innovation diffusion is subject to socio-economic barriers. The success of innovations is partly dependent on the business models that are used to diffuse them. Within the context of innovations for CSA, the role that innovation providers’ business models play in the successful
Osei, Frank B.; Osei, F.B.; Duker, Alfred A.; Stein, A.
2011-01-01
This study analyses the joint effects of the two transmission routes of cholera on the space-time diffusion dynamics. Statistical models are developed and presented to investigate the transmission network routes of cholera diffusion. A hierarchical Bayesian modelling approach is employed for a joint
Measurement and modeling of diffusion kinetics of a lipophilic molecule across rabbit cornea.
Gupta, Chhavi; Chauhan, Anuj; Mutharasan, Raj; Srinivas, Sangly P
2010-04-01
To develop a kinetic model for representing the diffusion and partitioning of Rhodamine B (RhB), a fluorescent lipophilic molecule, across the cornea for gaining insights into pharmacokinetics of topical drugs to the eye. Rabbit corneas mounted underneath a custom-built scanning microfluorometer were perfused with Ringers on both sides of the tissue. After a step change in RhB on the tear side, transients of trans-corneal fluorescence of RhB were measured at a depth resolution approximately 8 microm. RhB distribution exhibited discontinuities at the interface between epithelium and stroma, and between stroma and endothelium. In each of the layers, fluorescence was non-uniform. Fluorescence was elevated in the epithelium and endothelium relative to the stroma. Modeling of RhB transport by diffusion in each layer and stipulation of partitioning of RhB at the cellular interfaces were required to account for trans-corneal penetration kinetics of RhB. The model parameters, estimated using the unsteady state trans-corneal RhB profiles, were found to be sensitive, and the model predicted the experimental profiles accurately. Conventional pharmacokinetic models that depict cornea as a single compartment do not predict the depth-dependent kinetics of RhB penetration. The proposed model incorporates realistic transport mechanisms and thereby highlights the influence of physicochemical properties of drugs on trans-corneal kinetics.
Diffusive and subdiffusive dynamics of indoor microclimate: a time series modeling.
Maciejewska, Monika; Szczurek, Andrzej; Sikora, Grzegorz; Wyłomańska, Agnieszka
2012-09-01
The indoor microclimate is an issue in modern society, where people spend about 90% of their time indoors. Temperature and relative humidity are commonly used for its evaluation. In this context, the two parameters are usually considered as behaving in the same manner, just inversely correlated. This opinion comes from observation of the deterministic components of temperature and humidity time series. We focus on the dynamics and the dependency structure of the time series of these parameters, without deterministic components. Here we apply the mean square displacement, the autoregressive integrated moving average (ARIMA), and the methodology for studying anomalous diffusion. The analyzed data originated from five monitoring locations inside a modern office building, covering a period of nearly one week. It was found that the temperature data exhibited a transition between diffusive and subdiffusive behavior, when the building occupancy pattern changed from the weekday to the weekend pattern. At the same time the relative humidity consistently showed diffusive character. Also the structures of the dependencies of the temperature and humidity data sets were different, as shown by the different structures of the ARIMA models which were found appropriate. In the space domain, the dynamics and dependency structure of the particular parameter were preserved. This work proposes an approach to describe the very complex conditions of indoor air and it contributes to the improvement of the representative character of microclimate monitoring.
Computation of the Likelihood in Biallelic Diffusion Models Using Orthogonal Polynomials
Directory of Open Access Journals (Sweden)
Claus Vogl
2014-11-01
Full Text Available In population genetics, parameters describing forces such as mutation, migration and drift are generally inferred from molecular data. Lately, approximate methods based on simulations and summary statistics have been widely applied for such inference, even though these methods waste information. In contrast, probabilistic methods of inference can be shown to be optimal, if their assumptions are met. In genomic regions where recombination rates are high relative to mutation rates, polymorphic nucleotide sites can be assumed to evolve independently from each other. The distribution of allele frequencies at a large number of such sites has been called “allele-frequency spectrum” or “site-frequency spectrum” (SFS. Conditional on the allelic proportions, the likelihoods of such data can be modeled as binomial. A simple model representing the evolution of allelic proportions is the biallelic mutation-drift or mutation-directional selection-drift diffusion model. With series of orthogonal polynomials, specifically Jacobi and Gegenbauer polynomials, or the related spheroidal wave function, the diffusion equations can be solved efficiently. In the neutral case, the product of the binomial likelihoods with the sum of such polynomials leads to finite series of polynomials, i.e., relatively simple equations, from which the exact likelihoods can be calculated. In this article, the use of orthogonal polynomials for inferring population genetic parameters is investigated.
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 bioluminescent photon transport in tissue based on Radiosity-diffusion model
Sun, Li; Wang, Pu; Tian, Jie; Zhang, Bo; Han, Dong; Yang, Xin
2010-03-01
Bioluminescence tomography (BLT) is one of the most important non-invasive optical molecular imaging modalities. The model for the bioluminescent photon propagation plays a significant role in the bioluminescence tomography study. Due to the high computational efficiency, diffusion approximation (DA) is generally applied in the bioluminescence tomography. But the diffusion equation is valid only in highly scattering and weakly absorbing regions and fails in non-scattering or low-scattering tissues, such as a cyst in the breast, the cerebrospinal fluid (CSF) layer of the brain and synovial fluid layer in the joints. A hybrid Radiosity-diffusion model is proposed for dealing with the non-scattering regions within diffusing domains in this paper. This hybrid method incorporates a priori information of the geometry of non-scattering regions, which can be acquired by magnetic resonance imaging (MRI) or x-ray computed tomography (CT). Then the model is implemented using a finite element method (FEM) to ensure the high computational efficiency. Finally, we demonstrate that the method is comparable with Mont Carlo (MC) method which is regarded as a 'gold standard' for photon transportation simulation.
Diffusion-controlled reactions modeling in Geant4-DNA
Energy Technology Data Exchange (ETDEWEB)
Karamitros, M., E-mail: matkara@gmail.com [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); CNRS, INCIA, UMR 5287, F-33400 Talence (France); Luan, S. [University of New Mexico, Department of Computer Science, Albuquerque, NM (United States); Bernal, M.A. [Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, SP (Brazil); Allison, J. [Geant4 Associates International Ltd (United Kingdom); Baldacchino, G. [CEA Saclay, IRAMIS, LIDYL, Radiation Physical Chemistry Group, F-91191 Gif sur Yvette Cedex (France); CNRS, UMR3299, SIS2M, F-91191 Gif sur Yvette Cedex (France); Davidkova, M. [Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Francis, Z. [Saint Joseph University, Faculty of Sciences, Department of Physics, Mkalles, Beirut (Lebanon); Friedland, W. [Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Radiation Protection, Ingolstädter Landstr. 1, 85764 Neuherberg (Germany); Ivantchenko, V. [Ecoanalytica, 119899 Moscow (Russian Federation); Geant4 Associates International Ltd (United Kingdom); Ivantchenko, A. [Geant4 Associates International Ltd (United Kingdom); Mantero, A. [SwHaRD s.r.l., via Buccari 9, 16153 Genova (Italy); Nieminem, P.; Santin, G. [ESA-ESTEC, 2200 AG Noordwijk (Netherlands); Tran, H.N. [Division of Nuclear Physics and Faculty of Applied Sciences, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Stepan, V. [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Incerti, S., E-mail: incerti@cenbg.in2p3.fr [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France)
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 of PAH in potato and carrot slices and application for a potato model
DEFF Research Database (Denmark)
Trapp, Stefan; Cammarano, A.; Capri, E.
2007-01-01
of water, potato tissue, and carrot tissue. Naphthalene, phenanthrene, anthracene, and fluoranthene served as model substances. Their transfer from source to sink disk was measured by HPLC to determine a velocity rate constant proportional to the diffusive conductivity. The diffusive flux through the plant...... of the chemical. The findings of this study provide a convenient method to estimate the diffusion of nonvolatile organic chemicals through various plant materials. The application to a radial diffusion model suggests that "growth dilution" renders the concentration of highly hydrophobic chemicals in potatoes...... below their equilibrium partitioning level. This is in agreement with field results for the bioconcentration of PAHs in potatoes....
Models for the estimation of diffuse solar radiation for typical cities in Turkey
International Nuclear Information System (INIS)
Bakirci, Kadir
2015-01-01
In solar energy applications, diffuse solar radiation component is required. Solar radiation data particularly in terms of diffuse component are not readily affordable, because of high price of measurements as well as difficulties in their maintenance and calibration. In this study, new empirical models for predicting the monthly mean diffuse solar radiation on a horizontal surface for typical cities in Turkey are established. Therefore, fifteen empirical models from studies in the literature are used. Also, eighteen diffuse solar radiation models are developed using long term sunshine duration and global solar radiation data. The accuracy of the developed models is evaluated in terms of different statistical indicators. It is found that the best performance is achieved for the third-order polynomial model based on sunshine duration and clearness index. - Highlights: • Diffuse radiation is given as a function of clearness index and sunshine fraction. • The diffuse radiation is an important parameter in solar energy applications. • The diffuse radiation measurement is for limited periods and it is very rare. • The new models can be used to estimate monthly average diffuse solar radiation. • The accuracy of the models is evaluated on the basis of statistical indicators
Chu, Khim Hoong
2017-11-09
Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6 cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.
Ahmed, Chaara El Mouez
Nous avons etudie les relations de dispersion et la diffusion des glueballs et des mesons dans le modele U(1)_{2+1} compact. Ce modele a ete souvent utilise comme un simple modele de la chromodynamique quantique (QCD), parce qu'il possede le confinement ainsi que les etats de glueballs. Par contre, sa structure mathematique est beaucoup plus simple que la QCD. Notre methode consiste a diagonaliser l'Hamiltonien de ce modele dans une base appropriee de graphes et sur reseau impulsion, afin de generer les relations de dispersion des glueballs et des mesons. Pour la diffusion, nous avons utilise la methode dependante du temps pour calculer la matrice S et la section efficace de diffusion des glueballs et des mesons. Les divers resultats obtenus semblent etre en accord avec les travaux anterieurs de Hakim, Alessandrini et al., Irving et al., qui eux, utilisent plutot la theorie des perturbations en couplage fort, et travaillent sur un reseau espace-temps.
Contribution to the study of the mechanisms of turbulent diffusion and of related matters
International Nuclear Information System (INIS)
Mailliat, Alain.
1980-12-01
The subject of this paper is the study of turbulent diffusion mechanisms and the related problems. The diffusion mechanisms considered here are those which concern a passive scalar contaminant not subject to molecular effects. The reason for this latter character is that it makes it possible to isolate in the diffusion phenomenon that which is inherent in the turbulent dispersion. The present state of this question is reviewed in Chapter I. The system of natural coordinates for following the movement of a particle and hence for describing the dispersion is that of Lagrange. For our purpose this description must be statistical. Hence, the specific properties of the probability densities of the velocities and movements in this type of coordinate are examined in Chapter II. The expressions of the probability densities of the concentration and turbulent flow of a contaminant are sought. These expressions make it possible to formulate the diffusion laws linking the mean flow and concentration to the statistical characteristics of the velocity field. These matters form the central subject of this paper and are developed in Chapter III. Although the use of Lagrange's coordinates makes it possible fairly easily to obtain the probability densities mentioned above, it does, on the other hand, rule out on examination the relations existing between Lagrangian and Eulerian probability characteristics of the velocity field moments. The experimental determination in a Lagrangian system of the probability characteristics is in fact very tricky. These questions are discussed in Chapter IV of this paper [fr
Free surface modelling with two-fluid model and reduced numerical diffusion of the interface
International Nuclear Information System (INIS)
Strubelj, Luka; Tiselj, Izrok
2008-01-01
Full text of publication follows: The free surface flows are successfully modelled with one of existing free surface models, such as: level set method, volume of fluid method (with/without surface reconstruction), front tracking, two-fluid model (two momentum equations) with modified interphase force and others. The main disadvantage of two-fluid model used for simulations of free surface flows is numerical diffusion of the interface, which can be significantly reduced using the method presented in this paper. Several techniques for reduction of numerical diffusion of the interface have been implemented in the volume of fluid model and are based on modified numerical schemes for advection of volume fraction near the interface. The same approach could be used also for two-fluid method, but according to our experience more successful reduction of numerical diffusion of the interface can be achieved with conservative level set method. Within the conservative level set method, continuity equation for volume fraction is solved and after that the numerical diffusion of the interface is reduced in such a way that the thickness of the interface is kept constant during the simulation. Reduction of the interface diffusion can be also called interface sharpening. In present paper the two-fluid model with interface sharpening is validated on Rayleigh-Taylor instability. Under assumptions of isothermal and incompressible flow of two immiscible fluids, we simulated a system with the fluid of higher density located above the fluid of smaller density in two dimensions. Due to gravity in the system, fluid with higher density moves below the fluid with smaller density. Initial condition is not a flat interface between the fluids, but a sine wave with small amplitude, which develops into a mushroom-like structure. Mushroom-like structure in simulation of Rayleigh-Taylor instability later develops to small droplets as result of numerical dispersion of interface (interface sharpening
Generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture.
Felderhof, B U
2017-08-21
The method employed by Einstein to derive his famous relation between the diffusion coefficient and the friction coefficient of a Brownian particle is used to derive a generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture. The expression is compared with the one derived by de Groot and Mazur from irreversible thermodynamics and later by Batchelor for a Brownian suspension. A different result was derived by several other workers in irreversible thermodynamics. For a nearly incompressible solution, the generalized Einstein relation agrees with the expression derived by de Groot and Mazur. The two expressions also agree to first order in solute density. For a Brownian suspension, the result derived from the generalized Smoluchowski equation agrees with both expressions.
The modeling method of diffusion of radio activated materials in clay waste disposals
Energy Technology Data Exchange (ETDEWEB)
Saberi, Reza; Sepanloo, Kamran [NSTRI, Tehran (Iran, Islamic Republic of); Alinejad, Majid [Engineering Research Institute of Natural Hazard, Isfahan (Iran, Islamic Republic of); Mozaffari, Ali [KNT Univ. of Technology, Tehran (Iran, Islamic Republic of)
2017-02-15
New nuclear power plants are necessary to meet today's and future challenges of energy supply. Nuclear power is the only large-scale energy source that takes full responsibility for all its wastes. Nuclear wastes are particularly hazardous and hard to manage relative to different toxic industrial wastes. Three methods are presented and analysed to model the diffusion of the waste from the waste disposal to the bottom surface. For this purpose three software programmes such as ABAQUS, Matlab coding, Geostudio and ArcGIS have been applied.
The modeling method of diffusion of radio activated materials in clay waste disposals
International Nuclear Information System (INIS)
Saberi, Reza; Sepanloo, Kamran; Alinejad, Majid; Mozaffari, Ali
2017-01-01
New nuclear power plants are necessary to meet today's and future challenges of energy supply. Nuclear power is the only large-scale energy source that takes full responsibility for all its wastes. Nuclear wastes are particularly hazardous and hard to manage relative to different toxic industrial wastes. Three methods are presented and analysed to model the diffusion of the waste from the waste disposal to the bottom surface. For this purpose three software programmes such as ABAQUS, Matlab coding, Geostudio and ArcGIS have been applied.
Everaers, Ralf; Rosa, Angelo
2012-01-07
The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension.
Monte Carlo Modelling of Single-Crystal Diffuse Scattering from Intermetallics
Directory of Open Access Journals (Sweden)
Darren J. Goossens
2016-02-01
Full Text Available Single-crystal diffuse scattering (SCDS reveals detailed structural insights into materials. In particular, it is sensitive to two-body correlations, whereas traditional Bragg peak-based methods are sensitive to single-body correlations. This means that diffuse scattering is sensitive to ordering that persists for just a few unit cells: nanoscale order, sometimes referred to as “local structure”, which is often crucial for understanding a material and its function. Metals and alloys were early candidates for SCDS studies because of the availability of large single crystals. While great progress has been made in areas like ab initio modelling and molecular dynamics, a place remains for Monte Carlo modelling of model crystals because of its ability to model very large systems; important when correlations are relatively long (though still finite in range. This paper briefly outlines, and gives examples of, some Monte Carlo methods appropriate for the modelling of SCDS from metallic compounds, and considers data collection as well as analysis. Even if the interest in the material is driven primarily by magnetism or transport behaviour, an understanding of the local structure can underpin such studies and give an indication of nanoscale inhomogeneity.
Modelling of information diffusion on social networks with applications to WeChat
Liu, Liang; Qu, Bo; Chen, Bin; Hanjalic, Alan; Wang, Huijuan
2018-04-01
Traces of user activities recorded in online social networks open new possibilities to systematically understand the information diffusion process on social networks. From the online social network WeChat, we collected a large number of information cascade trees, each of which tells the spreading trajectory of a message/information such as which user creates the information and which users view or forward the information shared by which neighbours. In this work, we propose two heterogeneous non-linear models, one for the topologies of the information cascade trees and the other for the stochastic process of information diffusion on a social network. Both models are validated by the WeChat data in reproducing and explaining key features of cascade trees. Specifically, we apply the Random Recursive Tree (RRT) to model the growth of cascade trees. The RRT model could capture key features, i.e. the average path length and degree variance of a cascade tree in relation to the number of nodes (size) of the tree. Its single identified parameter quantifies the relative depth or broadness of the cascade trees and indicates that information propagates via a star-like broadcasting or viral-like hop by hop spreading. The RRT model explains the appearance of hubs, thus a possibly smaller average path length as the cascade size increases, as observed in WeChat. We further propose the stochastic Susceptible View Forward Removed (SVFR) model to depict the dynamic user behaviour including creating, viewing, forwarding and ignoring a message on a given social network. Beside the average path length and degree variance of the cascade trees in relation to their sizes, the SVFR model could further explain the power-law cascade size distribution in WeChat and unravel that a user with a large number of friends may actually have a smaller probability to read a message (s)he receives due to limited attention.
Stalled-Flow and Head-Loss Model for Diffuser Pumps
Meng, S. Y.
1984-01-01
Modeling procedure approximates inlet transition zone (blade leading edge to blade throat) of diffuser pump as two-dimensional cascade, properties of which are well known. Model applied to stators as well as rotors. Procedure much faster than previous methods.
Artun, Huseyin; Costu, Bayram
2013-01-01
The aim of this study was to explore a group of prospective primary teachers' conceptual understanding of diffusion and osmosis as they implemented a 5E constructivist model and related materials in a science methods course. Fifty prospective primary teachers' ideas were elicited using a pre- and post-test and delayed post-test survey consisting…
Kochunov, P; Chiappelli, J; Hong, L E
2013-01-01
Diffusion tensor imaging (DTI) assumes a single pool of anisotropically diffusing water to calculate fractional anisotropy (FA) and is commonly used to ascertain white matter (WM) deficits in schizophrenia. At higher b-values, diffusion-signal decay becomes bi-exponential, suggesting the presence of two, unrestricted and restricted, water pools. Theoretical work suggests that semi-permeable cellular membrane rather than the presence of two physical compartments is the cause. The permeability-diffusivity (PD) parameters measured from bi-exponential modeling may offer advantages, over traditional DTI-FA, in identifying WM deficits in schizophrenia. Imaging was performed in N = 26/26 patients/controls (age = 20-61 years, average age = 40.5 ± 12.6). Imaging consisted of fifteen b-shells: b = 250-3800 s/mm(2) with 30 directions/shell, covering seven slices of mid-sagittal corpus callosum (CC) at 1.7 × 1.7 × 4.6 mm. 64-direction DTI was also collected. Permeability-diffusivity-index (PDI), the ratio of restricted to unrestricted apparent diffusion coefficients, and the fraction of unrestricted compartment (Mu) were calculated for CC and cingulate gray matter (GM). FA values for CC were calculated using tract-based-spatial-statistics. Patients had significantly reduced PDI in CC (p ≅ 10(- 4)) and cingulate GM (p = 0.002), while differences in CC FA were modest (p ≅ .03). There was no group-related difference in Mu. Additional theoretical-modeling analysis suggested that reduced PDI in patients may be caused by reduced cross-membrane water molecule exchanges. PDI measurements for cerebral WM and GM yielded more robust patient-control differences than DTI-FA. Theoretical work offers an explanation that patient-control PDI differences should implicate abnormal active membrane permeability. This would implicate abnormal activities in ion-channels that use water as substrate for ion exchange, in cerebral tissues of schizophrenia patients.
A model for self-diffusion of guanidinium-based ionic liquids: a molecular simulation study.
Klähn, Marco; Seduraman, Abirami; Wu, Ping
2008-11-06
We propose a novel self-diffusion model for ionic liquids on an atomic level of detail. The model is derived from molecular dynamics simulations of guanidinium-based ionic liquids (GILs) as a model case. The simulations are based on an empirical molecular mechanical force field, which has been developed in our preceding work, and it relies on the charge distribution in the actual liquid. The simulated GILs consist of acyclic and cyclic cations that were paired with nitrate and perchlorate anions. Self-diffusion coefficients are calculated at different temperatures from which diffusive activation energies between 32-40 kJ/mol are derived. Vaporization enthalpies between 174-212 kJ/mol are calculated, and their strong connection with diffusive activation energies is demonstrated. An observed formation of cavities in GILs of up to 6.5% of the total volume does not facilitate self-diffusion. Instead, the diffusion of ions is found to be determined primarily by interactions with their immediate environment via electrostatic attraction between cation hydrogen and anion oxygen atoms. The calculated average time between single diffusive transitions varies between 58-107 ps and determines the speed of diffusion, in contrast to diffusive displacement distances, which were found to be similar in all simulated GILs. All simulations indicate that ions diffuse by using a brachiation type of movement: a diffusive transition is initiated by cleaving close contacts to a coordinated counterion, after which the ion diffuses only about 2 A until new close contacts are formed with another counterion in its vicinity. The proposed diffusion model links all calculated energetic and dynamic properties of GILs consistently and explains their molecular origin. The validity of the model is confirmed by providing an explanation for the variation of measured ratios of self-diffusion coefficients of cations and paired anions over a wide range of values, encompassing various ionic liquid classes
Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model
Ni, Wenjie; Shi, Junping; Wang, Mingxin
2018-06-01
A diffusive Lotka-Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed. The nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species. It is shown that when there is no nonlocal intraspecific competition, the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive Lotka-Volterra competition model regardless of the strength of nonlocal interspecific competition. Global stability of nonnegative constant equilibria are proved using Lyapunov or upper-lower solution methods. On the other hand, strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity. For the weak competition case, the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients.
International Nuclear Information System (INIS)
Helmstetter, A.; Sornette, D.
2002-01-01
The epidemic-type aftershock sequence (ETAS) model is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power-law decay ∼1/t 1+θ of seismicity after an earthquake) and Gutenberg-Richter law (power-law distribution of earthquake energies). In order to describe also the space distribution of seismicity, we use in addition a power-law distribution ∼1/r 1+μ of distances between triggered and triggering earthquakes. The ETAS model has been studied for the last two decades to model real seismicity catalogs and to obtain short-term probabilistic forecasts. Here, we present a mapping between the ETAS model and a class of CTRW (continuous time random walk) models, based on the identification of their corresponding master equations. This mapping allows us to use the wealth of results previously obtained on anomalous diffusion of CTRW. After translating into the relevant variable for the ETAS model, we provide a classification of the different regimes of diffusion of seismic activity triggered by a mainshock. Specifically, we derive the relation between the average distance between aftershocks and the mainshock as a function of the time from the mainshock and of the joint probability distribution of the times and locations of the aftershocks. The different regimes are fully characterized by the two exponents θ and μ. Our predictions are checked by careful numerical simulations. We stress the distinction between the 'bare' Omori law describing the seismic rate activated directly by a mainshock and the 'renormalized' Omori law taking into account all possible cascades from mainshocks to aftershocks of aftershock of aftershock, and so on. In particular, we predict that seismic diffusion or subdiffusion occurs and should be observable only when the observed Omori exponent is less than 1, because this signals the operation of the renormalization of the bare Omori law, also at the origin of seismic diffusion in
Model for Anomalous Moisture Diffusion through a Polymer-Clay Nanocomposite
DEFF Research Database (Denmark)
Drozdov, Aleksey D.; Christiansen, Jesper de Claville; Gupta, R.K.
2003-01-01
Experimental data are reported on moisture diffusion and the elastoplastic response of an intercalated nanocomposite with vinyl ester resin matrix and montmorillonite clay filler at room temperature. Observations in diffusion tests showed that water transport in the neat resin is Fickian, whereas...... platelets. Constitutive equations are developed for moisture diffusion through and the elastoplastic behavior of a nanocomposite. Adjustable parameters in these relations are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical...
A model for anomalous moisture diffusion through a polymer-clay nanocomposite
DEFF Research Database (Denmark)
Drozdov, Aleksey D.; Christiansen, Jesper de Claville; Gupta, R.K.
2002-01-01
Experimental data are reported on moisture diffusion and the elastoplastic response in uniaxial tensile tests of an intercalated nanocomposite with vinyl ester resin matrix and montmorillonite clay filler at room temperature. Observations in diffusion tests show that the moisture transport...... diffusion through a nanocomposite and for its elastoplastic behavior. Adjustable parameters in these relations are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation....
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
Energy Technology Data Exchange (ETDEWEB)
Posadillo, R.; Lopez Luque, R. [Grupo de Investigacion de Fisica para las Energias y Recursos Renovables, Dpto. de Fisica Aplicada, UCO, Edificio C2 Campus de Rabanales, 14071 Cordoba (Spain)
2010-04-15
An analysis of models for the estimation of hourly diffuse irradiation based on the interrelations between the hourly diffuse fraction k{sub d} and the hourly clearness index k{sub t}, has concluded that k{sub t} is not a sufficient variable for parametrizing the effect of clouds on diffuse irradiation. A detailed study of the dispersion recorded by this diffuse component for a specific clearness index under partly cloudy sky conditions has led to analyzing how the variability in the instantaneous clearness index influences this dispersion. The data sets correspond to 10 years of hourly and instantaneous value records of global and diffuse radiation collected in Cordoba, Spain. In addition to the inclusion of the sine of solar elevation as a variable into the k{sub d}-k{sub t} correlations, this model propose the inclusion of others parameters related to the variability in the normalized clearness index within an hour and with the fluctuations presented by the time series of the instantaneous values of that index. Also presented is the implementation of an algorithm permitting both the determination of the hourly diffuse irradiation and the discrimination between the different sky conditions in those situations known by the designation partly cloudy sky. (author)
International Nuclear Information System (INIS)
Posadillo, R.; Lopez Luque, R.
2010-01-01
An analysis of models for the estimation of hourly diffuse irradiation based on the interrelations between the hourly diffuse fraction k d and the hourly clearness index k t , has concluded that k t is not a sufficient variable for parametrizing the effect of clouds on diffuse irradiation. A detailed study of the dispersion recorded by this diffuse component for a specific clearness index under partly cloudy sky conditions has led to analyzing how the variability in the instantaneous clearness index influences this dispersion. The data sets correspond to 10 years of hourly and instantaneous value records of global and diffuse radiation collected in Cordoba, Spain. In addition to the inclusion of the sine of solar elevation as a variable into the k d -k t correlations, this model propose the inclusion of others parameters related to the variability in the normalized clearness index within an hour and with the fluctuations presented by the time series of the instantaneous values of that index. Also presented is the implementation of an algorithm permitting both the determination of the hourly diffuse irradiation and the discrimination between the different sky conditions in those situations known by the designation partly cloudy sky.
Thalamic diffusion differences related to cognitive function in white matter lesions.
Fernández-Andújar, Marina; Soriano-Raya, Juan José; Miralbell, Júlia; López-Cancio, Elena; Cáceres, Cynthia; Bargalló, Núria; Barrios, Maite; Arenillas, Juan Francisco; Toran, Pere; Alzamora, Maite; Clemente, Imma; Dávalos, Antoni; Mataró, Maria
2014-05-01
Cerebral white matter lesions (WMLs) are related to cognitive deficits, probably due to a disruption of frontal-subcortical circuits. We explored thalamic diffusion differences related to white matter lesions (WMLs) and their association with cognitive function in middle-aged individuals. Ninety-six participants from the Barcelona-AsIA Neuropsychology Study were included. Participants were classified into groups based on low grade and high grade of periventricular hyperintensities (PVHs) and deep white matter hyperintensities (DWMHs). Tract-Based Spatial Statistics was used to study thalamic diffusion differences between groups. Mean fractional anisotropy (FA) values in significant areas were calculated for each subject and correlated with cognitive performance. Participants with high-grade PVHs and DWMHs showed lower FA thalamic values compared to those with low-grade PVHs and DWMHs, respectively. Decreased FA thalamic values in high-grade DWMHs, but not high-grade PVH, were related to lower levels of performance in psychomotor speed, verbal fluency, and visuospatial skills. Thalamic diffusion differences are related to lower cognitive function only in participants with high-grade DWMHs. These results support the hypothesis that fronto-subcortical disruption is associated with cognitive function only in DWMHs. Copyright © 2014 Elsevier Inc. All rights reserved.
A microscopic model of ballistic-diffusive crossover
International Nuclear Information System (INIS)
Bagchi, Debarshee; Mohanty, P K
2014-01-01
Several low-dimensional systems show a crossover from diffusive to ballistic heat transport when system size is decreased. Although there is some phenomenological understanding of this crossover phenomenon at the coarse-grained level, a microscopic picture that consistently describes both the ballistic and the diffusive transport regimes has been lacking. In this work we derive a scaling form for the thermal current in a class of one dimensional systems attached to heat baths at boundaries and rigorously show that the crossover occurs when the characteristic length scale of the system competes with the system size. (paper)
A fractional Fokker-Planck model for anomalous diffusion
Energy Technology Data Exchange (ETDEWEB)
Anderson, Johan, E-mail: anderson.johan@gmail.com [Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden); Kim, Eun-jin [Department of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Moradi, Sara [Ecole Polytechnique, CNRS UMR7648, LPP, F-91128 Palaiseau (France)
2014-12-15
In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
International Nuclear Information System (INIS)
Misguich, J.H.; Balescu, R.
1981-02-01
Three different time regimes are presented for relative spatial diffusion of charged particles in fluctuating electric fields, which behave like tau 3 , exp (tau) and tau 3 , respectively. The first regime, corresponding to a quasi-linear description of the trajectories, is analogous to the one observed in fluid turbulence and is valid in the limit of a small amplitude turbulent spectrum, or for not too small initial separation of the particles. The third regime, appearing for long times, describes the diffusion of independent particles at very large separations. Its existence is ensured by the nonlinear renormalization of the propagators. The second, intermediate, regime appears in a stochastic treatment of the renormalization effect for particles with a very small spatial and velocity difference, and describes Dupree's clumps diffusion. The appearance of the corresponding regime is similar to that of the Suzuki scaling regime of non-linear Langevin equations. It is also shown that the clumps have a behaviour similar to an intrinsic stochasticity, but which is of extrinsic nature. Similar failure of the quasi-linear approximation for spacific velocity domains has been previously studied and solved for classical Landau collisions, as well as for pitch angle diffusion where renormalization effects have been proved also to be important
Modelling of stable isotope fractionation by methane oxidation and diffusion in landfill cover soils
International Nuclear Information System (INIS)
Mahieu, Koenraad; De Visscher, Alex; Vanrolleghem, Peter A.; Van Cleemput, Oswald
2008-01-01
A technique to measure biological methane oxidation in landfill cover soils that is gaining increased interest is the measurement of stable isotope fractionation in the methane. Usually to quantify methane oxidation, only fractionation by oxidation is taken into account. Recently it was shown that neglecting the isotope fractionation by diffusion results in underestimation of the methane oxidation. In this study a simulation model was developed that describes gas transport and methane oxidation in landfill cover soils. The model distinguishes between 12 CH 4 , 13 CH 4 , and 12 CH 3 D explicitly, and includes isotope fractionation by diffusion and oxidation. To evaluate the model, the simulations were compared with column experiments from previous studies. The predicted concentration profiles and isotopic profiles match the measured ones very well, with a root mean square deviation (RMSD) of 1.7 vol% in the concentration and a RMSD of 0.8 per mille in the δ 13 C value, with δ 13 C the relative 13 C abundance as compared to an international standard. Overall, the comparison shows that a model-based isotope approach for the determination of methane oxidation efficiencies is feasible and superior to existing isotope methods
Harding, Lawrence B; Georgievskii, Yuri; Klippenstein, Stephen J
2017-06-08
Full-dimensional analytic potential energy surfaces based on CCSD(T)/cc-pVTZ calculations have been determined for 48 small combustion-related molecules. The analytic surfaces have been used in Diffusion Monte Carlo calculations of the anharmonic zero-point energies. The resulting anharmonicity corrections are compared to vibrational perturbation theory results based both on the same level of electronic structure theory and on lower-level electronic structure methods (B3LYP and MP2).
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.
Directory of Open Access Journals (Sweden)
Luisa Malaguti
2011-01-01
Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.
Characteristics and Diffusion Model of the Individual Knowledge in the WeChat Mode
Directory of Open Access Journals (Sweden)
Zhang Lingzhi
2017-12-01
Full Text Available [Purpose/significance] According to the model of the individual knowledge diffusion, we conduct a behavior research and analyze the characteristics of that based on WeChat which is the most popular communication platform in China.[Method/process] By analyzing the methods of the diffusion on WeChat, we analyzed the characteristics of the individual knowledge diffusion. [Result/conclusion]The characteristics of the individual knowledge diffusion include real-time, short-term, speciality, friendship and transmission.
Diffusion-controlled reactions modeling in Geant4-DNA
Czech Academy of Sciences Publication Activity Database
Karamitros, M.; Luan, S.; Bernal, M. A.; Allison, J.; Baldacchino, G.; Davídková, Marie; Francis, Z.; Friedland, W.; Ivanchenko, A.; Ivanchenko, V.; Mantero, A.; Nieminen, P.; Santin, G.; Tran, H. N.; Stepan, V.; Incerti, S.
2014-01-01
Roč. 274, OCT (2014), s. 841-882 ISSN 0021-9991 Institutional support: RVO:61389005 Keywords : chemical kinetics simulation * radiation chemistry * Fokker-Planck equation * Smoluchowski diffusion equation * Brownian bridge * dynamical time steps * k-d tree * radiolysis * radiobiology * Geant4-DNA * Brownian dynamics Subject RIV: BO - Biophysics Impact factor: 2.434, year: 2014
A model of modulated diffusion. I. Analytical results
International Nuclear Information System (INIS)
Bazzani, A.; Turcchetti, G.; Vaienti, S.
1994-01-01
We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion
Ionic diffusion in the double layer at model electrode/molten salt interfaces
International Nuclear Information System (INIS)
Tankeshwar, K.; Tosi, M.P.
1991-08-01
The anisotropic ionic diffusion coefficients in model electrochemical cells in the molten-salt regime for the electrolyte are evaluated from the ionic density profiles reported in simulation work of Grout and coworkers. A local description of the diffusion processes for counterions and coions in the electrical double layer is obtained from the data. (author). 10 refs, 1 fig., 1 tab
Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow
Gonzalez, M.
2018-04-01
The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.
Long, Thomas B.; Blok, Vincent; Poldner, Kim
2017-01-01
Technological innovations will play a prominent role in the transition to climate-smart agriculture (CSA). However, CSA technological innovation diffusion is subject to socio-economic barriers. The success of innovations is partly dependent on the business models that are used to diffuse them.
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
International Nuclear Information System (INIS)
Maurin, D.
2001-02-01
Dark matter is present at numerous scale of the universe (galaxy, cluster of galaxies, universe in the whole). This matter plays an important role in cosmology and can not be totally explained by conventional physic. From a particle physic point of view, there exists an extension of the standard model - supersymmetry - which predicts under certain conditions the existence of new stable and massive particles, the latter interacting weakly with ordinary matter. Apart from direct detection in accelerators, various indirect astrophysical detection are possible. This thesis focuses on one particular signature: disintegration of these particles could give antiprotons which should be measurable in cosmic rays. The present study evaluates the background corresponding to this signal i. e. antiprotons produced in the interactions between these cosmic rays and interstellar matter. In particular, uncertainties of this background being correlated to the uncertainties of the diffusion parameter, major part of this thesis is devoted to nuclei propagation. The first third of the thesis introduces propagation of cosmic rays in our galaxy, emphasizing the nuclear reaction responsibles of the nuclei fragmentation. In the second third, different models are reviewed, and in particular links between the leaky box model and the diffusion model are recalled (re-acceleration and convection are also discussed). This leads to a qualitative discussion about information that one can infer from propagation of these nuclei. In the last third, we finally present detailed solutions of the bidimensional diffusion model, along with constrains obtained on the propagation parameters. The latter is applied on the antiprotons background signal and it concludes the work done in this thesis. The propagation code for nuclei and antiprotons used here has proven its ability in data analysis. It would probably be of interest for the analysis of the cosmic ray data which will be taken by the AMS experiment on
Diffusion as a Ruler: Modeling Kinesin Diffusion as a Length Sensor for Intraflagellar Transport.
Hendel, Nathan L; Thomson, Matthew; Marshall, Wallace F
2018-02-06
An important question in cell biology is whether cells are able to measure size, either whole cell size or organelle size. Perhaps cells have an internal chemical representation of size that can be used to precisely regulate growth, or perhaps size is just an accident that emerges due to constraint of nutrients. The eukaryotic flagellum is an ideal model for studying size sensing and control because its linear geometry makes it essentially one-dimensional, greatly simplifying mathematical modeling. The assembly of flagella is regulated by intraflagellar transport (IFT), in which kinesin motors carry cargo adaptors for flagellar proteins along the flagellum and then deposit them at the tip, lengthening the flagellum. The rate at which IFT motors are recruited to begin transport into the flagellum is anticorrelated with the flagellar length, implying some kind of communication between the base and the tip and possibly indicating that cells contain some mechanism for measuring flagellar length. Although it is possible to imagine many complex scenarios in which additional signaling molecules sense length and carry feedback signals to the cell body to control IFT, might the already-known components of the IFT system be sufficient to allow length dependence of IFT? Here we investigate a model in which the anterograde kinesin motors unbind after cargo delivery, diffuse back to the base, and are subsequently reused to power entry of new IFT trains into the flagellum. By mathematically modeling and simulating such a system, we are able to show that the diffusion time of the motors can in principle be sufficient to serve as a proxy for length measurement. We found that the diffusion model can not only achieve a stable steady-state length without the addition of any other signaling molecules or pathways, but also is able to produce the anticorrelation between length and IFT recruitment rate that has been observed in quantitative imaging studies. Copyright © 2017 Biophysical
Two-state random walk model of lattice diffusion - 1. Self-correlation function
International Nuclear Information System (INIS)
Balakrishnan, V.; Venkataraman, G.
1981-01-01
Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (in d dimensions, and with arbitrary directional bias) for temporarily uncorrelated jump diffusion and for the fluid diffusion counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales in the holding-time distributions, etc. The dynamic mobility and the structure factor for 'oscillatory diffusion' are taken up in part 2. (author)
Predicting the weathering of fuel and oil spills: A diffusion-limited evaporation model.
Kotzakoulakis, Konstantinos; George, Simon C
2018-01-01
The majority of the evaporation models currently available in the literature for the prediction of oil spill weathering do not take into account diffusion-limited mass transport and the formation of a concentration gradient in the oil phase. The altered surface concentration of the spill caused by diffusion-limited transport leads to a slower evaporation rate compared to the predictions of diffusion-agnostic evaporation models. The model presented in this study incorporates a diffusive layer in the oil phase and predicts the diffusion-limited evaporation rate. The information required is the composition of the fluid from gas chromatography or alternatively the distillation data. If the density or a single viscosity measurement is available the accuracy of the predictions is higher. Environmental conditions such as water temperature, air pressure and wind velocity are taken into account. The model was tested with synthetic mixtures, petroleum fuels and crude oils with initial viscosities ranging from 2 to 13,000 cSt. The tested temperatures varied from 0 °C to 23.4 °C and wind velocities from 0.3 to 3.8 m/s. The average absolute deviation (AAD) of the diffusion-limited model ranged between 1.62% and 24.87%. In comparison, the AAD of a diffusion-agnostic model ranged between 2.34% and 136.62% against the same tested fluids. Copyright © 2017 Elsevier Ltd. All rights reserved.
Cheng-Wu, Li; Hong-Lai, Xue; Cheng, Guan; Wen-biao, Liu
2018-04-01
Statistical analysis shows that in the coal matrix, the diffusion coefficient for methane is time-varying, and its integral satisfies the formula μt κ /(1 + β κ ). Therefore, a so-called dynamic diffusion coefficient model (DDC model) is developed. To verify the suitability and accuracy of the DDC model, a series of gas diffusion experiments were conducted using coal particles of different sizes. The results show that the experimental data can be accurately described by the DDC and bidisperse models, but the fit to the DDC model is slightly better. For all coal samples, as time increases, the effective diffusion coefficient first shows a sudden drop, followed by a gradual decrease before stabilizing at longer times. The effective diffusion coefficient has a negative relationship with the size of the coal particle. Finally, the relationship between the constants of the DDC model and the effective diffusion coefficient is discussed. The constant α (μ/R 2 ) denotes the effective coefficient at the initial time, and the constants κ and β control the attenuation characteristic of the effective diffusion coefficient.
Anomalous diffusion in a lattice-gas wind-tree model
International Nuclear Information System (INIS)
Kong, X.P.; Cohen, E.G.D.
1989-01-01
Two new strictly deterministic lattice-gas automata derived from Ehrenfest's wind-tree model are studied. While in one model normal diffusion occurs, the other model exhibits abnormal diffusion in that the distribution function of the displacements of the wind particle is non-Gaussian, but its second moment, the mean-square displacement, is proportional to the time, so that a diffusion coefficient can be defined. A connection with the percolation problem and a self-avoiding random walk for the case in which the lattice is completely covered with trees is discussed
Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion
Directory of Open Access Journals (Sweden)
Xinze Lian
2013-01-01
Full Text Available We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.
Modeling diffuse sources of surface water contamination with plant protection products
Wendland, Sandra; Bock, Michael; Böhner, Jürgen; Lembrich, David
2015-04-01
Entries of chemical pollutants in surface waters are a serious environmental problem. Among water pollutants plant protection products (ppp) from farming practice are of major concern not only for water suppliers and environmental agencies, but also for farmers and industrial manufacturers. Lost chemicals no longer fulfill their original purpose on the field, but lead to severe damage of the environment and surface waters. Besides point-source inputs of chemical pollutants, the diffuse-source inputs from agricultural procedures play an important and not yet sufficiently studied role concerning water quality. The two most important factors for diffuse inputs are erosion and runoff. The latter usually occurs before erosion begins, and is thus often not visible in hindsight. Only if it has come to erosion, it is obvious to expect runoff in foresight at this area, too. In addition to numerous erosion models, there are also few applications to model runoff processes available. However, these conventional models utilize approximations of catchment parameters based on long-term average values or theoretically calculated concentration peaks which can only provide indications to relative amounts. Our study aims to develop and validate a simplified spatially-explicit dynamic model with high spatiotemporal resolution that enables to measure current and forecast runoff potential not only at catchment scale but field-differentiated. This method allows very precise estimations of runoff risks and supports risk reduction measures to be targeted before fields are treated. By focusing on water pathways occurring on arable land, targeted risk reduction measures like buffer strips at certain points and adapted ppp use can be taken early and pollution of rivers and other surface waters through transported pesticides, fertilizers and their products could be nearly avoided or largely minimized. Using a SAGA-based physical-parametric modeling approach, major factors influencing runoff
International Nuclear Information System (INIS)
Bartiaux, Françoise; Schmidt, Luísa; Horta, Ana; Correia, Augusta
2016-01-01
The social-class dimension of energy consumption has been rather neglected relative to other theoretical approaches to energy use, despite its potential deployment in energy policies. This paper aims at investigating energy policy-related inequalities across social classes with respect to three dimensions highlighted by environmental-justice theories: income distribution, procedures producing unequal distributional outcomes, and cultural and political recognition of vulnerable and marginalised social groups. These inequalities can be exacerbated or reduced by social diffusion processes, both vertical and horizontal. These processes include policy instruments intending to lower energy consumption in the residential sector. To empirically ground the analysis, two countries with contrasting patterns of income inequalities, Portugal and Belgium, are compared on the basis of qualitative data collected in 2009–2011. We discuss the relevance of integrating the social diffusion dimension in energy policies and propose several policy instruments to do so. One of our main contribution is to argue that both vertical and horizontal diffusion across social classes, if adequately translated into policy instruments, can boost the uptake of residential energy retrofits and other energy saving practices.
Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates
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Marcus C. Christiansen
2013-10-01
Full Text Available In the actuarial literature, it has become common practice to model future capital returns and mortality rates stochastically in order to capture market risk and forecasting risk. Although interest rates often should and mortality rates always have to be non-negative, many authors use stochastic diffusion models with an affine drift term and additive noise. As a result, the diffusion process is Gaussian and, thus, analytically tractable, but negative values occur with positive probability. The argument is that the class of Gaussian diffusions would be a good approximation of the real future development. We challenge that reasoning and study the asymptotics of diffusion processes with affine drift and a general noise term with corresponding diffusion processes with an affine drift term and an affine noise term or additive noise. Our study helps to quantify the error that is made by approximating diffusive interest and mortality rate models with Gaussian diffusions and affine diffusions. In particular, we discuss forward interest and forward mortality rates and the error that approximations cause on the valuation of life insurance claims.
A comprehensive model of ion diffusion and charge exchange in the cold Io torus
Barbosa, D. D.; Moreno, M. A.
1988-01-01
A comprehensive analytic model of radial diffusion in the cold Io torus is developed. The model involves a generalized molecular cloud theory of SO2 and its dissociation fragments SO, O2, S, and O, which are formed at a relatively large rate by solar UV photodissociation of SO2. The key component of the new theory is SO, which can react with S(+) through a near-resonant charge exchange process that is exothermic. This provides a mechanism for the rapid depletion of singly ionized sulfur in the cold torus and can account for the large decrease in the total flux tube content inward of Io's orbit. The model is used to demonstrate quantitatively the effects of radial diffusion in a charge exchange environment that acts as a combined source and sink for ions in various charge states. A detailed quantitative explanation for the O(2+) component of the cold torus is given, and insight is derived into the workings of the so-called plasma 'ribbon'.
Mathematical modeling and effective diffusion of Schinus terebinthifolius leaves during drying
Directory of Open Access Journals (Sweden)
André Luís Duarte Goneli
2014-03-01
Full Text Available The drying process of agricultural products is extensively used worldwide for controlling and maintaining their quality. For medicinal and aromatic plants, this importance increases even more. Thus, this study aimed at evaluating the drying kinetics of Schinus terebinthifolius Raddi leaves, as well as adjusting different mathematical models to the experimental values of moisture ratio. The leaves were harvested with initial moisture content of approximately 65% (w.b. and submitted to the drying process under controlled conditions of temperature (40ºC, 50ºC, 60ºC and 70ºC, up to the approximate moisture content of 10% (w.b.. Six mathematical models were adjusted to the experimental data cited at the specific literature and used to predict the drying process of agricultural products. According to the results obtained, it was concluded that the modified Henderson & Pabis and Midilli models were the ones that best represented the drying kinetics of S. terebinthifolius leaves. The temperature increase of the drying air promoted a higher rate of water removal from the product. The effective diffusion coefficient increased with the temperature elevation, and its relation to the drying temperature fitted the Arrhenius equation, which presented activation energy for the liquid diffusion, during the drying process, of 74.96 kJ mol-1, for S. terebinthifolius leaves.
Directory of Open Access Journals (Sweden)
D. J. Goossens
2015-01-01
Full Text Available 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.
Modeling and Analysis of Epidemic Diffusion within Small-World Network
Directory of Open Access Journals (Sweden)
Ming Liu
2012-01-01
Full Text Available To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-Infected-Recovered-Susceptible (SEIRS model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible (SEIQRS model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusion models are constructed with mean-filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease-free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh-Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.
DEFF Research Database (Denmark)
Vestergaard-Poulsen, Peter; Hansen, Brian; Østergaard, Leif
2007-01-01
compartment. A global optimum was found from a wide range of parameter permutations using cluster computing. We also present simulations of cell swelling and changes of exchange rate and intracellular diffusion as possible cellular mechanisms in ischemia. RESULTS: Our model estimates an extracellular volume...... compartments and slow water exchange. Our model reproduces the signal changes observed in ischemia via physiologically credible mechanisms. CONCLUSION: Our modeling suggests that transverse relaxation has a profound influence on the diffusion attenuated MR signal. Our simulations indicate cell swelling...... model to the diffusion-weighted MR signal obtained from cortical gray matter in healthy subjects. Our model includes variable volume fractions, intracellular restriction effects, and exchange between compartments in addition to individual diffusion coefficients and transverse relaxation rates for each...
An Application of Epidemiological Modeling to Information Diffusion
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.
Diffusive flux in a model of stochastically gated oxygen transport in insect respiration
Energy Technology Data Exchange (ETDEWEB)
Berezhkovskii, Alexander M. [Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892 (United States); Shvartsman, Stanislav Y. [Department of Chemical and Biological Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544 (United States)
2016-05-28
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.
Maxwell's Law Based Models for Liquid and Gas Phase Diffusivities in Variably-Saturated Soil
DEFF Research Database (Denmark)
Mamamoto, Shoichiro; Møldrup, Per; Kawamoto, Ken
2012-01-01
-s,D-l). Different percolation threshold terms adopted from recent studies for gas (D-s,D-g) and solute (D-s,D-l) diffusion were applied. For gas diffusion, epsilon(th) was a function of bulk density (total porosity), while for solute diffusion theta(th) was best described by volumetric content of finer soil...... particles (clay and organic matter), FINESvol. The resulting LIquid and GAs diffusivity and tortuosity (LIGA) models were tested against D-s,D-g and D-s,D-l data for differently-textured soils and performed well against the measured data across soil types. A sensitivity analysis using the new Maxwell's Law...... based LIGA models implied that the liquid phase but not the gaseous-phase tortuosity was controlled by soil type. The analyses also suggested very different pathways and fluid-phase connectivity for gas and solute diffusion in unsaturated soil...
A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal
Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying
2018-04-01
Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.
Starns, Jeffrey J; Dubé, Chad; Frelinger, Matthew E
2018-05-01
In this report, we evaluate single-item and forced-choice recognition memory for the same items and use the resulting accuracy and reaction time data to test the predictions of discrete-state and continuous models. For the single-item trials, participants saw a word and indicated whether or not it was studied on a previous list. The forced-choice trials had one studied and one non-studied word that both appeared in the earlier single-item trials and both received the same response. Thus, forced-choice trials always had one word with a previous correct response and one with a previous error. Participants were asked to select the studied word regardless of whether they previously called both words "studied" or "not studied." The diffusion model predicts that forced-choice accuracy should be lower when the word with a previous error had a fast versus a slow single-item RT, because fast errors are associated with more compelling misleading memory retrieval. The two-high-threshold (2HT) model does not share this prediction because all errors are guesses, so error RT is not related to memory strength. A low-threshold version of the discrete state approach predicts an effect similar to the diffusion model, because errors are a mixture of responses based on misleading retrieval and guesses, and the guesses should tend to be slower. Results showed that faster single-trial errors were associated with lower forced-choice accuracy, as predicted by the diffusion and low-threshold models. Copyright © 2018 Elsevier Inc. All rights reserved.
Anomalous transport regimes in a stochastic advection-diffusion model
International Nuclear Information System (INIS)
Dranikov, I.L.; Kondratenko, P.S.; Matveev, L.V.
2004-01-01
A general solution to the stochastic advection-diffusion problem is obtained for a fractal medium with long-range correlated spatial fluctuations. A particular transport regime is determined by two basic parameters: the exponent 2h of power-law decay of the two-point velocity correlation function and the mean advection velocity u. The values of these parameters corresponding to anomalous diffusion are determined, and anomalous behavior of the tracer distribution is analyzed for various combinations of u and h. The tracer concentration is shown to decrease exponentially at large distances, whereas power-law decay is predicted by fractional differential equations. Equations that describe the essential characteristics of the solution are written in terms of coupled space-time fractional differential operators. The analysis relies on a diagrammatic technique and makes use of scale-invariant properties of the medium
Modeling Effectivity of Atmospheric Advection-Diffusion Processes
International Nuclear Information System (INIS)
Brojewski, R.
1999-01-01
Some methods of solving the advection-diffusion problems useful in the field of atmospheric physics are presented and analyzed in the paper. The most effective one ( from the point of view of computer applications) was chosen. This is the method of problem decomposition with respect to the directions followed by secondary decomposition of the problem with respect to the physical phenomena. Introducing some corrections to the classical numerical methods of solving the problems, a hybrid composed of the finite element method for the advection problems and the implicit method with averaging for the diffusion processes was achieved. This hybrid method and application of the corrections produces a very effective means for solving the problems of substance transportation in atmosphere. (author)
Analytic treatment of nuclear spin-lattice relaxation for diffusion in a cone model
Sitnitsky, A. E.
2011-12-01
We consider nuclear spin-lattice relaxation rate resulted from a diffusion equation for rotational wobbling in a cone. We show that the widespread point of view that there are no analytical expressions for correlation functions for wobbling in a cone model is invalid and prove that nuclear spin-lattice relaxation in this model is exactly tractable and amenable to full analytical description. The mechanism of relaxation is assumed to be due to dipole-dipole interaction of nuclear spins and is treated within the framework of the standard Bloemberger, Purcell, Pound-Solomon scheme. We consider the general case of arbitrary orientation of the cone axis relative the magnetic field. The BPP-Solomon scheme is shown to remain valid for systems with the distribution of the cone axes depending only on the tilt relative the magnetic field but otherwise being isotropic. We consider the case of random isotropic orientation of cone axes relative the magnetic field taking place in powders. Also we consider the cases of their predominant orientation along or opposite the magnetic field and that of their predominant orientation transverse to the magnetic field which may be relevant for, e.g., liquid crystals. Besides we treat in details the model case of the cone axis directed along the magnetic field. The latter provides direct comparison of the limiting case of our formulas with the textbook formulas for free isotropic rotational diffusion. The dependence of the spin-lattice relaxation rate on the cone half-width yields results similar to those predicted by the model-free approach.
Edge Probability and Pixel Relativity-Based Speckle Reducing Anisotropic Diffusion.
Mishra, Deepak; Chaudhury, Santanu; Sarkar, Mukul; Soin, Arvinder Singh; Sharma, Vivek
2018-02-01
Anisotropic diffusion filters are one of the best choices for speckle reduction in the ultrasound images. These filters control the diffusion flux flow using local image statistics and provide the desired speckle suppression. However, inefficient use of edge characteristics results in either oversmooth image or an image containing misinterpreted spurious edges. As a result, the diagnostic quality of the images becomes a concern. To alleviate such problems, a novel anisotropic diffusion-based speckle reducing filter is proposed in this paper. A probability density function of the edges along with pixel relativity information is used to control the diffusion flux flow. The probability density function helps in removing the spurious edges and the pixel relativity reduces the oversmoothing effects. Furthermore, the filtering is performed in superpixel domain to reduce the execution time, wherein a minimum of 15% of the total number of image pixels can be used. For performance evaluation, 31 frames of three synthetic images and 40 real ultrasound images are used. In most of the experiments, the proposed filter shows a better performance as compared to the state-of-the-art filters in terms of the speckle region's signal-to-noise ratio and mean square error. It also shows a comparative performance for figure of merit and structural similarity measure index. Furthermore, in the subjective evaluation, performed by the expert radiologists, the proposed filter's outputs are preferred for the improved contrast and sharpness of the object boundaries. Hence, the proposed filtering framework is suitable to reduce the unwanted speckle and improve the quality of the ultrasound images.
Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models
DEFF Research Database (Denmark)
Kristensen, Dennis
of the estimators and tests under the null are derived, and the power properties are analyzed by considering contiguous alternatives. Test directly comparing the drift and diffusion estimators under the relevant null and alternative are also analyzed. Markov Bootstrap versions of the test statistics are proposed...... to improve on the finite-sample approximations. The finite sample properties of the estimators are examined in a simulation study....
Thermomechanics of damageable materials under diffusion: modelling and analysis
Czech Academy of Sciences Publication Activity Database
Roubíček, Tomáš; Tomassetti, G.
2015-01-01
Roč. 66, č. 6 (2015), s. 3535-3572 ISSN 0044-2275 R&D Projects: GA ČR GAP201/10/0357 Institutional support: RVO:61388998 Keywords : visco-elastic porous solids * incomplete damage * diffusion driven by chemical-potential gradient Subject RIV: BA - General Mathematics Impact factor: 1.560, year: 2015 http://link.springer.com/article/10.1007/s00033-015-0566-2
Modeling the diffusion magnetic resonance imaging signal inside neurons
International Nuclear Information System (INIS)
Nguyen, D V; Li, J R; Grebenkov, D S; Le Bihan, D
2014-01-01
The Bloch-Torrey partial differential equation (PDE) describes the complex transverse water proton magnetization due to diffusion-encoding magnetic field gradient pulses. The integral of the solution of this PDE yields the diffusion magnetic resonance imaging (dMRI) signal. In a complex medium such as cerebral tissue, it is difficult to explicitly link the dMRI signal to biological parameters such as the cellular geometry or the cellular volume fraction. Studying the dMRI signal arising from a single neuron can provide insight into how the geometrical structure of neurons influences the measured signal. We formulate the Bloch-Torrey PDE inside a single neuron, under no water exchange condition with the extracellular space, and show how to reduce the 3D simulation in the full neuron to a 3D simulation around the soma and 1D simulations in the neurites. We show that this latter approach is computationally much faster than full 3D simulation and still gives accurate results over a wide range of diffusion times
A strongly nonlinear reaction diffusion model for a deterministic diffusive epidemic
International Nuclear Information System (INIS)
Kirane, M.; Kouachi, S.
1993-04-01
In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. Moreover the large time behaviour of the global solutions is analyzed. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the data. (author). 9 refs
International Nuclear Information System (INIS)
Ahmadi, A.; Meyer, M.; Rouzineau, D.; Prevost, M.; Alix, P.; Laloue, N.
2010-01-01
This paper gives the first step of the development of a rigorous multicomponent reactive separation model. Such a model is highly essential to further the optimization of acid gases removal plants (CO 2 capture, gas treating, etc.) in terms of size and energy consumption, since chemical solvents are conventionally used. Firstly, two main modelling approaches are presented: the equilibrium-based and the rate-based approaches. Secondly, an extended rate-based model with rigorous modelling methodology for diffusion-reaction phenomena is proposed. The film theory and the generalized Maxwell-Stefan equations are used in order to characterize multicomponent interactions. The complete chain of chemical reactions is taken into account. The reactions can be kinetically controlled or at chemical equilibrium, and they are considered for both liquid film and liquid bulk. Thirdly, the method of numerical resolution is described. Coupling the generalized Maxwell-Stefan equations with chemical equilibrium equations leads to a highly non-linear Differential-Algebraic Equations system known as DAE index 3. The set of equations is discretized with finite-differences as its integration by Gear method is complex. The resulting algebraic system is resolved by the Newton- Raphson method. Finally, the present model and the associated methods of numerical resolution are validated for the example of esterification of methanol. This archetype non-electrolytic system permits an interesting analysis of reaction impact on mass transfer, especially near the phase interface. The numerical resolution of the model by Newton-Raphson method gives good results in terms of calculation time and convergence. The simulations show that the impact of reactions at chemical equilibrium and that of kinetically controlled reactions with high kinetics on mass transfer is relatively similar. Moreover, the Fick's law is less adapted for multicomponent mixtures where some abnormalities such as counter-diffusion
Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun
2014-12-01
Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.
Time-Dependent Diffusion MRI in Cancer: Tissue Modeling and Applications
Directory of Open Access Journals (Sweden)
Olivier Reynaud
2017-11-01
Full Text Available In diffusion weighted imaging (DWI, the apparent diffusion coefficient (ADC has been recognized as a useful and sensitive surrogate for cell density, paving the way for non-invasive tumor staging, and characterization of treatment efficacy in cancer. However, microstructural parameters, such as cell size, density and/or compartmental diffusivities affect diffusion in various fashions, making of conventional DWI a sensitive but non-specific probe into changes happening at cellular level. Alternatively, tissue complexity can be probed and quantified using the time dependence of diffusion metrics, sometimes also referred to as temporal diffusion spectroscopy when only using oscillating diffusion gradients. Time-dependent diffusion (TDD is emerging as a strong candidate for specific and non-invasive tumor characterization. Despite the lack of a general analytical solution for all diffusion times/frequencies, TDD can be probed in various regimes where systems simplify in order to extract relevant information about tissue microstructure. The fundamentals of TDD are first reviewed (a in the short time regime, disentangling structural and diffusive tissue properties, and (b near the tortuosity limit, assuming weakly heterogeneous media near infinitely long diffusion times. Focusing on cell bodies (as opposed to neuronal tracts, a simple but realistic model for intracellular diffusion can offer precious insight on diffusion inside biological systems, at all times. Based on this approach, the main three geometrical models implemented so far (IMPULSED, POMACE, VERDICT are reviewed. Their suitability to quantify cell size, intra- and extracellular spaces (ICS and ECS and diffusivities are assessed. The proper modeling of tissue membrane permeability—hardly a newcomer in the field, but lacking applications—and its impact on microstructural estimates are also considered. After discussing general issues with tissue modeling and microstructural parameter
Time-dependent diffusion MRI in cancer: tissue modeling and applications
Reynaud, Olivier
2017-11-01
In diffusion weighted imaging (DWI), the apparent diffusion coefficient has been recognized as a useful and sensitive surrogate for cell density, paving the way for non-invasive tumor staging, and characterization of treatment efficacy in cancer. However, microstructural parameters, such as cell size, density and/or compartmental diffusivities affect diffusion in various fashions, making of conventional DWI a sensitive but non-specific probe into changes happening at cellular level. Alternatively, tissue complexity can be probed and quantified using the time dependence of diffusion metrics, sometimes also referred to as temporal diffusion spectroscopy when only using oscillating diffusion gradients. Time-dependent diffusion (TDD) is emerging as a strong candidate for specific and non-invasive tumor characterization. Despite the lack of a general analytical solution for all diffusion times / frequencies, TDD can be probed in various regimes where systems simplify in order to extract relevant information about tissue microstructure. The fundamentals of TDD are first reviewed (a) in the short time regime, disentangling structural and diffusive tissue properties, and (b) near the tortuosity limit, assuming weakly heterogeneous media near infinitely long diffusion times. Focusing on cell bodies (as opposed to neuronal tracts), a simple but realistic model for intracellular diffusion can offer precious insight on diffusion inside biological systems, at all times. Based on this approach, the main three geometrical models implemented so far (IMPULSED, POMACE, VERDICT) are reviewed. Their suitability to quantify cell size, intra- and extracellular spaces (ICS and ECS) and diffusivities are assessed. The proper modeling of tissue membrane permeability – hardly a newcomer in the field, but lacking applications - and its impact on microstructural estimates are also considered. After discussing general issues with tissue modeling and microstructural parameter estimation (i
Specifying theories of developmental dyslexia: a diffusion model analysis of word recognition
Zeguers, M.H.T.; Snellings, P.; Tijms, J.; Weeda, W.D.; Tamboer, P.; Bexkens, A.; Huizenga, H.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
Asymptotic behaviour of a nonlinear model for the geographic diffusion of infections diseases
International Nuclear Information System (INIS)
Kirane, M.; Kouachi, S.
1994-01-01
In this paper a nonlinear diffusion model for the geographical spread of infective diseases is studied. In addition to proving well-posedness of the associated initial-boundary value problem, the large time behaviour is analyzed. (author). 4 refs
Desvillettes, Laurent; Fellner, Klemens
2010-01-01
We study a continuous coagulation-fragmentation model with constant kernels for reacting polymers (see [M. Aizenman and T. Bak, Comm. Math. Phys., 65 (1979), pp. 203-230]). The polymers are set to diffuse within a smooth bounded one
Kan-On, Yukio
2007-04-01
This paper is concerned with the bifurcation structure of positive stationary solutions for a generalized Lotka-Volterra competition model with diffusion. To establish the structure, the bifurcation theory and the interval arithmetic are employed.
Diffuse-interface model for rapid phase transformations in nonequilibrium systems.
Galenko, Peter; Jou, David
2005-04-01
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe transformations within the diffuse interface, we use the phase-field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface. Governing equations of the phase-field model are derived for the hyperbolic model, a model with memory, and a model of nonlinear evolution of transformation within the diffuse interface. The consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with existing sharp-interface and diffuse-interface versions of the model is given.
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.
Target oriented relational model finding
Cunha, Alcino; Macedo, Nuno Filipe Moreira; Guimarães, Tiago Miguel Moreira
2014-01-01
Lecture Notes in Computer Science 8411, 2014 Model finders are becoming useful in many software engineering problems. Kodkod is one of the most popular, due to its support for relational logic (a combination of first order logic with relational algebra operators and transitive closure), allowing a simpler specification of constraints, and support for partial instances, allowing the specification of a priori (exact, but potentially partial) knowledge about a problem's solution. However, in ...
International Nuclear Information System (INIS)
Borkel, C.; Montoya, V.; Kienzler, B.
2015-01-01
The code PHREECQ V3.1 has been used to simulate leaching experiments performed with cemented simulated waste products in tap water for more than 30 years. In this work the main focus is related with the leaching of Cs explained by diffusion processes. A simplifying model using the code PHREECQ V3.1 was used to investigate the influence of different parameters on the release of Cs from the cement solid to the leaching solution. The model setup bases on four main assumptions: a) the solid as well as the distribution of Cs is homogeneous and of isotropic texture, b) there is no preferential direction regarding cement degradation or water intrusion into the solid, c) the pore space is entirely connected and d) Cs adsorption to the cement or container is negligible. In the modeling the constraint of charge balance was stressed. Effective diffusion coefficients (D e ) were obtained analytically and from modeling the diffusive release of Cs from cemented waste simulates. The obtained values D e for Cs leaching are in perfect agreement with the values published in literature. Contradictory results to diffusive release were obtained from XRD analysis of the solids, suggesting that water may not have penetrated the cement monoliths entirely, but only to some centimeters depth. XRD analysis have been done to determine the solid phases present in cement and are used to help outlining strength and weaknesses of the different models
Sinha, Usha; Csapo, Robert; Malis, Vadim; Xue, Yanjie; Sinha, Shantanu
2014-01-01
Purpose To investigate age related changes in diffusion tensor indices and fiber architecture of the medial and lateral gastrocnemius (MG and LG) muscles using diffusion tensor imaging (DTI). Materials and Methods The lower leg of five young and five senior subjects was scanned at 3T and DTI indices extracted using three methods: ROI, histogram and tract based. Tracked fibers were automatically edited to ensure physiologically relevant tracks. Pennation angles were measured with respect to the deep and superficial aponeuroses of both muscles. Results The three methods provided internally consistent measures of the DTI indices (correlation coefficient in the range of 0.90-0.99). The primary, secondary and tertiary eigenvalues in the MG and LG increased significantly in the senior cohort (p<0.05), while the small increase in fractional anisotropy (FA) with age was not significant (MG/LG: p=0.39/0.85; 95% CI:[ −0.059/-0.056, 0.116/0.064]). Fiber lengths of MG fibers originating distally were significantly decreased in seniors (p<0.05) while pennation angles decreased with age in the MG and LG but this was not significant. Conclusion Fiber atrophy and increased fibrosis have opposing effects on the diffusion indices resulting in a complicated dependence with aging. Fiber architectural changes could play a role in determining aging muscle function. PMID:24771672
The fractional diffusion limit of a kinetic model with biochemical pathway
Perthame, Benoît; Sun, Weiran; Tang, Min
2018-06-01
Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.
An extended five-stream model for diffusion of ion-implanted dopants in monocrystalline silicon
International Nuclear Information System (INIS)
Khina, B.B.
2007-01-01
Low-energy high-dose ion implantation of different dopants (P, Sb, As, B and others) into monocrystalline silicon with subsequent thermal annealing is used for the formation of ultra-shallow p-n junctions in modern VLSI circuit technology. During annealing, dopant activation and diffusion in silicon takes place. The experimentally observed phenomenon of transient enhanced diffusion (TED), which is typically ascribed to the interaction of diffusing species with non-equilibrium point defects accumulated in silicon due to ion damage, and formation of small clusters and extended defects, hinders further down scaling of p-n junctions in VLSI circuits. TED is currently a subject of extensive experimental and theoretical investigation in many binary and multicomponent systems. However, the state-of-the-art mathematical models of dopant diffusion, which are based on the so-called 'five-stream' approach, and modern TCAD software packages such as SUPREM-4 (by Silvaco Data Systems, Ltd.) that implement these models encounter severe difficulties in describing TED. Solving the intricate problem of TED suppression and development of novel regimes of ion implantation and rapid thermal annealing is impossible without elaboration of new mathematical models and computer simulation of this complex phenomenon. In this work, an extended five-stream model for diffusion in silicon is developed which takes into account all possible charge states of point defects (vacancies and silicon self-interstitials) and diffusing pairs 'dopant atom-vacancy' and 'dopant atom-silicon self-interstitial'. The model includes the drift terms for differently charged point defects and pairs in the internal electric field and the kinetics of interaction between unlike 'species' (generation and annihilation of pairs and annihilation of point defects). Expressions for diffusion coefficients and numerous sink/source terms that appear in the non-linear, non-steady-state reaction-diffusion equations are derived
Kumar, Alla S.; Clark, Joseph; Beyette, Fred R., Jr.
2009-02-01
Neonatal jaundice is a medical condition which occurs in newborns as a result of an imbalance between the production and elimination of bilirubin. The excess bilirubin in the blood stream diffuses into the surrounding tissue leading to a yellowing of the skin. As the bilirubin levels rise in the blood stream, there is a continuous exchange between the extra vascular bilirubin and bilirubin in the blood stream. Exposure to phototherapy alters the concentration of bilirubin in the vascular and extra vascular regions by causing bilirubin in the skin layers to be broken down. Thus, the relative concentration of extra vascular bilirubin is reduced leading to a diffusion of bilirubin out of the vascular region. Diffuse reflectance spectra from human skin contains physiological and structural information of the skin and nearby tissue. A diffuse reflectance spectrum must be captured before and after blanching in order to isolate the intravascular and extra vascular bilirubin. A new mathematical model is proposed with extra vascular bilirubin concentration taken into consideration along with other optical parameters in defining the diffuse reflectance spectrum from human skin. A nonlinear optimization algorithm has been adopted to extract the optical properties (including bilirubin concentration) from the skin reflectance spectrum. The new system model and nonlinear algorithm have been combined to enable extraction of Bilirubin concentrations within an average error of 10%.
Energy Technology Data Exchange (ETDEWEB)
Recieri, Reinaldo Prandini; Ferruzzi, Yuri; Silva, Suedemio de Lima [Universidade Estadual do Oeste do Parana (UNIOESTE/FAG), Cascavel, PR (Brazil). Curso de Mestrado em Engenharia Agricola; Quallio, Silvana [Universidade Estadual do Oeste do Parana (UNIOESTE/FAG), Cascavel, PR (Brazil). Curso de Biologia; Batista, Vitor Roberto Lourenco [Universidade Estadual do Oeste do Parana (UNIOESTE/FAG), Cascavel, PR (Brazil). Curso de Graduacao em Engenharia Eletrica
2004-07-01
In this work we evaluate, by means of polynomial regression analysis, several models that relate the diffuse fraction of the global radiation (K{sub d}) with the clearness index (K{sub t}). The experiment was conducted in the Solar Radiometry Station of Cascavel/PR from the first of January to the 31st of December, in the year of 2001. The solar radiation components were monitored by the following manufactured instruments: pyranometer (KIPP and ZONEN CM3) and pirheliometer (EPPLEY NIP) connected in a sun tracker (ST-1 model). A datalogger CR10X from the CAMPBELL SCIENTIFIC was used in the data acquisition. This datalogger was programmed in the frequency of 1 Hz storing an average of 5 minutes of collected data. Among the equations the best values of RMSE an MBE were find in the fourth and third degrees, respectively. We also find that the fourth degree polynomial equation (K{sub d}=1,172-1,001K{sub t}+3,992K{sub t}{sup 2}-11,742K{sub t}{sup 3}+7,698K{sub t}{sup 4}) generalizes the utilization of equations for diffuse solar radiation estimation. This means that this equation probably can be applied for any place and climatic conditions. (author)
International Nuclear Information System (INIS)
Musho, M.K.; Kozak, J.J.
1984-01-01
A method is presented for calculating exactly the relative width (sigma 2 )/sup 1/2// , the skewness γ 1 , and the kurtosis γ 2 characterizing the probability distribution function for three random-walk models of diffusion-controlled processes. For processes in which a diffusing coreactant A reacts irreversibly with a target molecule B situated at a reaction center, three models are considered. The first is the traditional one of an unbiased, nearest-neighbor random walk on a d-dimensional periodic/confining lattice with traps; the second involves the consideration of unbiased, non-nearest-neigh bor (i.e., variable-step length) walks on the same d-dimensional lattice; and, the third deals with the case of a biased, nearest-neighbor walk on a d-dimensional lattice (wherein a walker experiences a potential centered at the deep trap site of the lattice). Our method, which has been described in detail elsewhere [P.A. Politowicz and J. J. Kozak, Phys. Rev. B 28, 5549 (1983)] is based on the use of group theoretic arguments within the framework of the theory of finite Markov processes
Forrey, Christopher; Saylor, David M; Silverstein, Joshua S; Douglas, Jack F; Davis, Eric M; Elabd, Yossef A
2014-10-14
Diffusion of small to medium sized molecules in polymeric medical device materials underlies a broad range of public health concerns related to unintended leaching from or uptake into implantable medical devices. However, obtaining accurate diffusion coefficients for such systems at physiological temperature represents a formidable challenge, both experimentally and computationally. While molecular dynamics simulation has been used to accurately predict the diffusion coefficients, D, of a handful of gases in various polymers, this success has not been extended to molecules larger than gases, e.g., condensable vapours, liquids, and drugs. We present atomistic molecular dynamics simulation predictions of diffusion in a model drug eluting system that represent a dramatic improvement in accuracy compared to previous simulation predictions for comparable systems. We find that, for simulations of insufficient duration, sub-diffusive dynamics can lead to dramatic over-prediction of D. We present useful metrics for monitoring the extent of sub-diffusive dynamics and explore how these metrics correlate to error in D. We also identify a relationship between diffusion and fast dynamics in our system, which may serve as a means to more rapidly predict diffusion in slowly diffusing systems. Our work provides important precedent and essential insights for utilizing atomistic molecular dynamics simulations to predict diffusion coefficients of small to medium sized molecules in condensed soft matter systems.
Macromolecular diffusion in crowded media beyond the hard-sphere model.
Blanco, Pablo M; Garcés, Josep Lluís; Madurga, Sergio; Mas, Francesc
2018-04-25
The effect of macromolecular crowding on diffusion beyond the hard-core sphere model is studied. A new coarse-grained model is presented, the Chain Entanglement Softened Potential (CESP) model, which takes into account the macromolecular flexibility and chain entanglement. The CESP model uses a shoulder-shaped interaction potential that is implemented in the Brownian Dynamics (BD) computations. The interaction potential contains only one parameter associated with the chain entanglement energetic cost (Ur). The hydrodynamic interactions are included in the BD computations via Tokuyama mean-field equations. The model is used to analyze the diffusion of a streptavidin protein among different sized dextran obstacles. For this system, Ur is obtained by fitting the streptavidin experimental long-time diffusion coefficient Dlongversus the macromolecular concentration for D50 (indicating their molecular weight in kg mol-1) dextran obstacles. The obtained Dlong values show better quantitative agreement with experiments than those obtained with hard-core spheres. Moreover, once parametrized, the CESP model is also able to quantitatively predict Dlong and the anomalous exponent (α) for streptavidin diffusion among D10, D400 and D700 dextran obstacles. Dlong, the short-time diffusion coefficient (Dshort) and α are obtained from the BD simulations by using a new empirical expression, able to describe the full temporal evolution of the diffusion coefficient.
Cosmological models in general relativity
Indian Academy of Sciences (India)
Cosmological models in general relativity. B B PAUL. Department of Physics, Nowgong College, Nagaon, Assam, India. MS received 4 October 2002; revised 6 March 2003; accepted 21 May 2003. Abstract. LRS Bianchi type-I space-time filled with perfect fluid is considered here with deceler- ation parameter as variable.
Fractional Diffusion Equations and Anomalous Diffusion
Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin
2018-01-01
Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.
Modeling and simulation of spin-polarized transport at the kinetic and diffusive level
International Nuclear Information System (INIS)
Possanner, S.
2012-01-01
The aim of this thesis is to contribute to the understanding of spin-induced phenomena in electron motion. These phenomena arise when electrons move through a (partially) magnetic environment, in such a way that its magnetic moment (spin) may interact with the surroundings. The pure quantum nature of the spin requires transport models that deal with effects like quantum coherence, entanglement (correlation) and quantum dissipation. On the meso- and macroscopic level it is not yet clear under which circumstances these quantum effects may transpire. The purpose of this work is, on the one hand, to derive novel spin transport models from basic principles and, on the other hand, to develop numerical algorithms that allow for a solution of these new and other existing model equations. The thesis consists of four parts. The first part comprises an overview of fundamental spin-related concepts in electronic transport such as the giant-magneto-resistance (GMR) effect, the spin-transfer torque in metallic magnetic multilayers and the matrix-character of transport equations that take spin-coherent electron states into account. In particular, we consider the diffusive Zhang-Levy-Fert (ZLF) model, an exchange-torque model that consists of the Landau-Lifshitz equation and a heuristic matrix spin-diffusion equation. A finite difference scheme based on Strang operator splitting is developed that enables a numerical, self-consistent solution of this non-linear system within multilayer structures. Finally, the model is tested by comparison of numerical results to recent experimental data. In part two we propose a matrix-Boltzmann equation that allows for the description of spin-coherent electron transport on a kinetic level. The novelty here is a linear collision operator in which the transition rates from momentum k to momentum k' are modeled by a 2x2 Hermitian matrix; hence the mean-free paths of spin-up and spin-down electrons are represented by the eigenvalues of this
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.
Random variability in mesoscale wind observations and implications for diffusion models
Energy Technology Data Exchange (ETDEWEB)
Hanna, S.R. [Sigma Research Corp., Concord, MA (United States)
1994-12-31
The investigation reported in this paper grew out of a preliminary analysis of methods by which regional air quality models such as the Regional Oxidant Model account for horizontal transport and diffusion. It was discovered that there is a variety of often inconsistent methods used to parameterize horizontal diffusion at meso- and regional scales, and the time seemed ripe to review and compare and contrast these schemes. This paper provides a brief overview of the major issues that were uncovered and lists a few specific examples of the technical approaches that are used. Subsequent sections cover the basic physics of horizontal diffusion, the characteristics of observed wind fields, and methods of parameterizing horizontal diffusion in air quality models.
Model analysis of the influence of gas diffusivity in soil on CO and H2 uptake
International Nuclear Information System (INIS)
Yonemura, S.; Yokozawa, M.; Kawashima, S.; Tsuruta, H.
2000-01-01
CO and H 2 uptake by soil was studied as a diffusion process. A diffusion model was used to determine how the surface fluxes (net deposition velocities) were controlled by in-situ microbial uptake rates and soil gas diffusivity calculated from the 3-phase system (solid, liquid, gas) in the soil. Analytical solutions of the diffusion model assuming vertical uniformity of soil properties showed that physical properties such as air-filled porosity and soil gas diffusivity were more important in the uptake process than in the emission process. To incorporate the distribution of in-situ microbial uptake, we used a 2-layer model incorporating 'a microbiologically inactive layer and an active layer' as suggested from experimental results. By numerical simulation using the 2-layer model, we estimated the effect of several factors on deposition velocities. The variations in soil gas diffusivity due to physical properties, i.e., soil moisture and air-filled porosity, as well as to the depth of the inactive layer and in-situ microbial uptake, were found to be important in controlling deposition velocities. This result shows that the diffusion process in soil is critically important for CO and H 2 uptake by soil, at least in soils with higher in-situ uptake rates and/or with large variation in soil moisture. Similar uptake rates and the difference in deposition velocity between CO and H 2 may be attributable to differences in CO and H 2 molecular diffusivity. The inactive layer is resistant to diffusion and creates uptake limits in CO and H 2 by soil. The coupling of high temperature and a thick inactive layer, common in arid soils, markedly lowers net CO deposition velocity. The temperature for maximum uptake of CO changes with depth of the inactive layer
The concept of mass angular scattering power and its relation to the diffusion constant
Energy Technology Data Exchange (ETDEWEB)
Sandison, George A.; Papiez, Lech S. [School of Health Sciences, Purdue University, West Lafayette, IN (United States)
1998-09-01
An understanding of the scattering of high energy charged particle beams by tissue is required in radiotherapy since the particle trajectories determine the pattern of radiation dose deposition in patients. Numerical calculations of radiation dose often utilize energy dependent values of the angular scattering power. However, the physics literature is replete with confused interpretations of the concept of angular scattering power and its relation to the single scattering cross section for the medium or the diffusion constant in the diffusional limit. The purpose of this article is to clarify these notions.
International Nuclear Information System (INIS)
Barker, C.D.
1979-07-01
The Gaussian Plume Diffusion Model, using Smith's scheme for σsub(z) and various models for σsub(y), is compared with measured values of the location and strength of maximum ground level concentration taken during the Tilbury and Northfleet experiments. The position of maximum ground level concentration (xsub(m)) is found to be relatively insensitive to σsub(y) and Smith's model for σsub(z) is found to predict xsub(m) on average to within 50% for plume heights less than 200 - 400m (dependent on atmosphere stability). Several models for σsub(y) are examined by comparing predicted and observed values for the normalised maximum ground level concentration (Xsub(m)) and a modified form of Moore's model for σsub(y) is found to give the best overall fit, on average to within 30%. Gifford's release duration dependent model for σsub(y) is found to consistently underestimate Xsub(m) by 35 - 45%. This comparison is only a partial validation of the models described above and suggestions are made as to where further work is required. (author)
Preliminary Hybrid Modeling of the Panama Canal: Operations and Salinity Diffusion
Directory of Open Access Journals (Sweden)
Luis Rabelo
2012-01-01
Full Text Available This paper deals with the initial modeling of water salinity and its diffusion into the lakes during lock operation on the Panama Canal. A hybrid operational model was implemented using the AnyLogic software simulation environment. This was accomplished by generating an operational discrete-event simulation model and a continuous simulation model based on differential equations, which modeled the salinity diffusion in the lakes. This paper presents that unique application and includes the effective integration of lock operations and its impact on the environment.
Impact of Social Network and Business Model on Innovation Diffusion of Electric Vehicles in China
Directory of Open Access Journals (Sweden)
D. Y. Kong
2014-01-01
Full Text Available The diffusion of electric vehicles (EVs involves not only the technological development but also the construction of complex social networks. This paper uses the theory of network control to analyze the influence of network forms on EV diffusion in China, especially focusing on the building of EV business models (BMs and the resulting effects and control on the diffusion of EVs. The Bass model is adopted to forecast the diffusion process of EVs and genetic algorithm is used to estimate the parameters based on the diffusion data of Hybrid Electric Vehicle (HEV in the United States and Japan. Two different social network forms and BMs are selected, that is, battery leasing model and vehicle purchasing model, to analyze how different network forms may influence the innovation coefficient and imitation coefficient in the Bass model, which will in turn result in different diffusion results. Thereby, we can find the appropriate network forms and BMs for EVs which is suitable to the local market conditions.
Ulfah, S.; Awalludin, S. A.; Wahidin
2018-01-01
Advection-diffusion model is one of the mathematical models, which can be used to understand the distribution of air pollutant in the atmosphere. It uses the 2D advection-diffusion model with time-dependent to simulate air pollution distribution in order to find out whether the pollutants are more concentrated at ground level or near the source of emission under particular atmospheric conditions such as stable, unstable, and neutral conditions. Wind profile, eddy diffusivity, and temperature are considered in the model as parameters. The model is solved by using explicit finite difference method, which is then visualized by a computer program developed using Lazarus programming software. The results show that the atmospheric conditions alone influencing the level of concentration of pollutants is not conclusive as the parameters in the model have their own effect on each atmospheric condition.
Directory of Open Access Journals (Sweden)
Ying Liu
2015-01-01
Full Text Available Unidirectional pedestrian movement is a special phenomenon in the evacuation process of large public buildings and urban environments at pedestrian scale. Several macroscopic models for collective behaviors have been built to predict pedestrian flow. However, current models do not explain the diffusion behavior in pedestrian crowd movement, which can be important in representing spatial-temporal crowd density differentiation in the movement process. This study builds a macroscopic model for describing crowd diffusion behavior and evaluating unidirectional pedestrian flow. The proposed model employs discretization of time and walking speed in geometric distribution to calculate downstream pedestrian crowd flow and analyze movement process based on upstream number of pedestrians and average walking speed. The simulated results are calibrated with video observation data in a baseball stadium to verify the model precision. Statistical results have verified that the proposed pedestrian diffusion model could accurately describe pedestrian macromovement behavior within the margin of error.
A case of mumps-related acute encephalopathy with biphasic seizures and late reduced diffusion.
Hazama, Kyoko; Shiihara, Takashi; Tsukagoshi, Hiroyuki; Hasegawa, Shunji; Dowa, Yuri; Watanabe, Mio
2017-10-01
Mumps is a common childhood viral disease characterized by fever and swelling of the parotid gland. The prognosis is generally good, although some complications, such as encephalitis (0.1%), exist. Acute encephalopathy with biphasic seizures and late reduced diffusion is the most common type of acute encephalopathy. However, this type of encephalopathy has not been reported in association with mumps infection. A previously healthy 3-year-old Japanese boy had a brief convulsion after fever for 3days, and then had conscious disturbance and parotitis. After several days, he had a second brief convulsion and was admitted. Increased serum amylase levels and presence of anti-mumps immunoglobulin M antibody confirmed mumps parotitis. The patient had another brief seizure later the day of admission. He did not have status or cluster seizures, although the biphasic nature of his seizures, conscious disturbance between the seizures, no pleocytosis in cerebrospinal fluid, and brain magnetic resonance images were consistent with acute encephalopathy with biphasic seizures and late reduced diffusion. In Japan, the mumps vaccine is not administered as a part of routine immunizations. It thus has low coverage (30-40%), and as a result, mumps infections are still common. However, this is the first case of mumps-related acute encephalopathy with biphasic seizures and late reduced diffusion. This case may be representative of only a minority of patients with mumps-associated central nervous system involvement. Nevertheless, this diagnostic possibility may be considered. In order to prevent mumps-related complications, routine mumps vaccination might be warranted. Copyright © 2017 The Japanese Society of Child Neurology. Published by Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Wang, Jing [Iowa State Univ., Ames, IA (United States)
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.
Epistemology and Rosen's Modeling Relation
International Nuclear Information System (INIS)
Dress, W.B.
1999-01-01
Rosen's modeling relation is embedded in Popper's three worlds to provide an heuristic tool for model building and a guide for thinking about complex systems. The utility of this construct is demonstrated by suggesting a solution to the problem of pseudo science and a resolution of the famous Bohr-Einstein debates. A theory of bizarre systems is presented by an analogy with entangled particles of quantum mechanics. This theory underscores the poverty of present-day computational systems (e.g., computers) for creating complex and bizarre entities by distinguishing between mechanism and organism
Modeling biology using relational databases.
Peitzsch, Robert M
2003-02-01
There are several different methodologies that can be used for designing a database schema; no one is the best for all occasions. This unit demonstrates two different techniques for designing relational tables and discusses when each should be used. These two techniques presented are (1) traditional Entity-Relationship (E-R) modeling and (2) a hybrid method that combines aspects of data warehousing and E-R modeling. The method of choice depends on (1) how well the information and all its inherent relationships are understood, (2) what types of questions will be asked, (3) how many different types of data will be included, and (4) how much data exists.
The partition and effective diffusion coefficients of formaldehyde were measured for three materials (conventional gypsum wallboard, "green" gypsum wallboard, and "green" carpet) under three relative humidity (RH) conditions (20%, 50% and 70% RH). A dynamic dual-chamber test meth...
The partition and effective diffusion coefficients of formaldehyde were measured for three materials (conventional gypsum wallboard, "green" gypsum wallboard, and "green" carpet) under three relative humidity (RH) conditions (20%, 50% and 70% RH). A dynamic dual-chamber test meth...
Slator, Paddy J.; Cairo, Christopher W.; Burroughs, Nigel J.
2015-01-01
We develop a Bayesian analysis framework to detect heterogeneity in the diffusive behaviour of single particle trajectories on cells, implementing model selection to classify trajectories as either consistent with Brownian motion or with a two-state (diffusion coefficient) switching model. The incorporation of localisation accuracy is essential, as otherwise false detection of switching within a trajectory was observed and diffusion coefficient estimates were inflated. Since our analysis is on a single trajectory basis, we are able to examine heterogeneity between trajectories in a quantitative manner. Applying our method to the lymphocyte function-associated antigen 1 (LFA-1) receptor tagged with latex beads (4 s trajectories at 1000 frames s−1), both intra- and inter-trajectory heterogeneity were detected; 12–26% of trajectories display clear switching between diffusive states dependent on condition, whilst the inter-trajectory variability is highly structured with the diffusion coefficients being related by D 1 = 0.68D 0 − 1.5 × 104 nm2 s−1, suggestive that on these time scales we are detecting switching due to a single process. Further, the inter-trajectory variability of the diffusion coefficient estimates (1.6 × 102 − 2.6 × 105 nm2 s−1) is very much larger than the measurement uncertainty within trajectories, suggesting that LFA-1 aggregation and cytoskeletal interactions are significantly affecting mobility, whilst the timescales of these processes are distinctly different giving rise to inter- and intra-trajectory variability. There is also an ‘immobile’ state (defined as D models within membranes incorporating aggregation, binding to the cytoskeleton, or traversing membrane microdomains. PMID:26473352
Atmospheric diffusion model for control room habitability assessments
International Nuclear Information System (INIS)
Ramsdell, J.V.; Lee, J.Y.
1993-01-01
General Design Criterion 19 for nuclear power plants (Appendix A to 10CFR50) requires control room radiation protection adequate to limit radiation exposures to control room personnel. Murphy and Campe proposed the procedure currently used in evaluating control room habitability. However, data from building-wake diffusion experiments at nuclear power plants indicate that the Murphy-Campe procedure tends to overestimate concentrations, particularly during low wind speeds. This paper describes an alternative procedure developed by the Pacific Northwest Laboratory that is acceptable to U.S. Nuclear Regulatory Commission (NRC) staff. The procedure estimates control room air intake concentrations that are generally lower than those estimated by the Murphy-Campe procedure, yet are still conservative
Directory of Open Access Journals (Sweden)
Julieta Constanza Frediani
2006-01-01
Full Text Available In the last decade several studies done on the transformation of the city from compact to more scattered and fragmented have shown the concern for the effects the open and scattered city may have upon the environment. Although we consider that the urban models, "compact" and "diffuse", actually cannot be found in isolation, they are used to represent the extremes that relate the model of our city with these two models. The purpose of the present paper is to recognize in La Plata District, the behavioral pattern variable that causes the territorial conflicts in each of the models.
International Nuclear Information System (INIS)
Yoshikawa, T.; Kimura, F.; Koide, T.; Kurita, S.
1990-01-01
Since 1986, a simple computation model for a nuclear accident has been operating in the emergency information center of Japan Agency for Science and Technology. It was developed by introducing the variation method for wind and a random walk particle model for diffusion in 50-100 km scale. Furthermore, we developed a new model with dynamic equations and a diffusion equation to predict more accurately the wind and diffusion, including local thermal convection. The momentum equation and the continuity equation are solved numerically in nonhydrostatic and incompressible conditions, using a finite difference technique. Then, the equation of thermal energy preservation is solved for potential temperature in the predicted wind field of every time step. The diffusion of nuclear pollutants is computed numerically in the predicted wind field, using diffusion coefficients obtained from the predictive dynamic equations. These computations were verified with meteorological surveys and gas tracer diffusion experiments over flat land, along a sea shore and over a mountainous area. Horizontal circulations and vertical convections can be computed in any mesh size from several tens of meters to several kilometers, while small vertical convections less than 1 km or so cannot be represented with the former hydrostatic circulation models. (author)
Directory of Open Access Journals (Sweden)
O. H. Kapitonov
2010-05-01
Full Text Available A mathematical model of coulostatic relaxation of the potential for solid metallic electrode was presented. The solution in the case of limiting diffusion current was obtained. On the basis of this model the technique of concentration measurements for heavy metal ions in diluted solutions was suggested. The model adequacy was proved by experimental data.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
Vamos, C; Vereecken, H
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
International Nuclear Information System (INIS)
Vamos, Calin; Suciu, Nicolae; Vereecken, Harry
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested
Persuasion, Politeness and Relational Models
Directory of Open Access Journals (Sweden)
Jerzy Świątek
2017-06-01
Full Text Available Politeness Theory, just like Grice’s Cooperative Principle, points out that pragmatic analysis of language behaviour has to be grounded in extra-linguistic facts of social (or even biological nature. Additionally, despite the slightly misleading label, Politeness Theory provides a sound methodology to explain some persuasive as well as politeness phenomena. In the same vein, the so called Relational Model Theory provides another theoretical framework for the explanation of persuasive phenomena and persuasive language. Both Relational Model Theory and Politeness Theory show that persuasion is also to be understood as a rational response to not-so-rational social and biological needs. In the article an attempt is made to compare the two theories focusing on their explanatory power in reference to language choices aiming at enhancing the persuasive potential of a language message.
The mirrors model: macroscopic diffusion without noise or chaos
International Nuclear Information System (INIS)
Chiffaudel, Yann; Lefevere, Raphaël
2016-01-01
Before stating our main result, we first clarify through classical examples the status of the laws of macroscopic physics as laws of large numbers. We next consider the mirrors model in a finite d-dimensional domain and connected to particles reservoirs at fixed chemical potentials. The dynamics is purely deterministic and non-ergodic but takes place in a random environment. We study the macroscopic current of particles in the stationary regime. We show first that when the size of the system goes to infinity, the behaviour of the stationary current of particles is governed by the proportion of orbits crossing the system. This allows us to formulate a necessary and sufficient condition on the distribution of the set of orbits that ensures the validity of Fick’s law. Using this approach, we show that Fick’s law relating the stationary macroscopic current of particles to the concentration difference holds in three dimensions and above. The negative correlations between crossing orbits play a key role in the argument. (letter)
Analysis of effective diffusivity of cement based materials by multi-scale modelling
International Nuclear Information System (INIS)
Dridi, Wissem
2013-01-01
This paper presents a simplified composite model, which considers the contribution of each phase participating to the transport within OPC pastes and concretes. At the micrometer scale, the phases considered hereafter are capillary porosity (macro-porosity) and the Low Density and the High Density C-S-H both containing gel pores (nano-porosity). Predicted values of tritiated water (HTO) diffusivity in OPC pastes with various (w/c) ratios are confronted to experimental results with a good agreement. The approach is then extended to mortars and concretes scale where microstructure is described by a three phase composite sphere assemblage. Here, elementary phase distribution is assumed to change as a function of distance from aggregate surface. Model results about HTO diffusivities of mortars and concretes are presented with some experimental values. The competition between the more diffusing ITZ zone and the less diffusing bulk matrix is investigated from a sensitive analysis. The dominance of the ITZ control is confirmed. (authors)
Hopf bifurcation in a delayed reaction-diffusion-advection population model
Chen, Shanshan; Lou, Yuan; Wei, Junjie
2018-04-01
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.
Directory of Open Access Journals (Sweden)
Bernard Wong
2009-01-01
martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset-liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities and consequently construct a modification that is arbitrage free.
Persuasion, Politeness and Relational Models
Jerzy Świątek
2017-01-01
Politeness Theory, just like Grice’s Cooperative Principle, points out that pragmatic analysis of language behaviour has to be grounded in extra-linguistic facts of social (or even biological) nature. Additionally, despite the slightly misleading label, Politeness Theory provides a sound methodology to explain some persuasive as well as politeness phenomena. In the same vein, the so called Relational Model Theory provides another theoretical framework for the explanation of persuasive phenome...
Mercury in a thin layer in HgMn stars: A test of a diffusion model
International Nuclear Information System (INIS)
Megessier, C.; Michaud, G.; Weiler, E.J.
1980-01-01
Lines of the first three states of ionization of mercury have been observed in μ Leporis and chi Lupi using the Copernicus satellite. Lines of Hg II and Hg III have been observed in α Andromedae. There appears to be an absorption feature at every wavelength where there is expected to be a mercury line. The presence of all three states of ionization is likely in μ Lep and chi Lup. The relative equivalent widths of the lines of the various states of ionization do not depend on the effective temperature of the stars, in contradiction to what is expected if mercury were uniformly distributed in the atmosphere. It is, however, expected if mercury has been concentrated, by diffusion, in a thin layer, where the radiative forces just equal the gravitational forces on mercury. That mercury should be so concentrated is also required by the explanation of the mercury isotope anomaly proposed by Michaud, Reeves, and Charland. The diffusion model for Ap stars predicts in its simplest form the presence of very thin layers. However, any leftover turbulence may increase the depth of these layers without eliminating the element separation
Dependence of alpha radionuclide diffusion and deposition on relative air humidity
International Nuclear Information System (INIS)
Danis, A.; Ciubotariu, M.; Oncescu, M.; Mocsy, I.; Tomulescu, V.
2000-01-01
The diffusion and deposition of the gaseous and solid alpha radionuclides/aerosols depend strongly on the relative air humidity. This dependence gets a great significance in the case of radon and their genetically related alpha radionuclides monitoring in the dwelling and working places for radioprotection purposes, particularly in establishing the equilibrium factor. For the gaseous and solid alpha radionuclides genetically related, Rn-222 and its solid alpha descendants including their aerosols obtained by radionuclide attachments to different particles present in air, the vertical gradient of volume concentrations was experimentally determined. The experiments were performed in: an airtight tubular laboratory chamber, a house cellar (Cluj-Napoca) and the entrance gallery of an abandoned mine (Avram Iancu, Bihor), in which the relative humidity was ranging from 65% up to 96%. For the laboratory chamber, these radionuclides were generated by a calibrated Ra-226 source, prepared at the Radionuclide Production Centre, IPNE-HH, Bucharest. The source was included into an air tight device with a well known volume and it was used only after 40 days, when the Ra-226 and its alpha descendants were under radioactive equilibrium. For the diffusion/deposition studies, this source was coupled with the airtight laboratory chamber. In the mine gallery and house cellar, the radon and its descendants were naturally and continuously generated by radium sources in soil and building materials. The alpha volume concentration determinations required the use of a very accurate and sensitive alpha measurement method. These requirements were met by the alpha track method. This method was used by us in the following conditions: the CR-39 plastic track detector (Page, England) for the detection of the alpha particles and the optical microscopy for the study of alpha tracks (Wild stereomicroscope M7S and a Karl Zeiss Jena binocular microscope). The volume concentrations of radon and the
A minimally-resolved immersed boundary model for reaction-diffusion problems
Pal Singh Bhalla, A; Griffith, BE; Patankar, NA; Donev, A
2013-01-01
We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blo...
Modeling anomalous diffusion by a subordinated fractional Lévy-stable process
International Nuclear Information System (INIS)
Teuerle, Marek; Wyłomańska, Agnieszka; Sikora, Grzegorz
2013-01-01
Two phenomena that can be discovered in systems with anomalous diffusion are long-range dependence and trapping events. The first effect concerns events that are arbitrarily distant but still influence each other exceptionally strongly, which is characteristic for anomalous regimes. The second corresponds to the presence of constant values of the underlying process. Motivated by the relatively poor class of models that can cover these two phenomena, we introduce subordinated fractional Lévy-stable motion with tempered stable waiting times. We present in detail its main properties, propose a simulation scheme and give an estimation procedure for its parameters. The last part of the paper is a presentation, via the Monte Carlo approach, of the effectiveness of the estimation of the parameters. (paper)
Diffusion Retardation by Binding of Tobramycin in an Alginate Biofilm Model
DEFF Research Database (Denmark)
Cao, Bao; Christophersen, Lars; Kolpen, Mette
2016-01-01
Microbial cells embedded in a self-produced extracellular biofilm matrix cause chronic infections, e. g. by Pseudomonas aeruginosa in the lungs of cystic fibrosis patients. The antibiotic killing of bacteria in biofilms is generally known to be reduced by 100–1000 times relative to planktonic...... bacteria. This makes such infections difficult to treat. We have therefore proposed that biofilms can be regarded as an independent compartment with distinct pharmacokinetics. To elucidate this pharmacokinetics we have measured the penetration of the tobramycin into seaweed alginate beads which serve...... to be uniformly distributed throughout the volume of the alginate bead. The power-law appears to be a consequence of binding to a multitude of different binding sites. In a diffusion model these results are shown to produce pronounced retardation of the penetration of tobramycin into the biofilm. This filtering...
Directory of Open Access Journals (Sweden)
Georgios C Manikis
Full Text Available The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer.Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2 at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG and non-Gaussian (MNG and BNG were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE. To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC and F-ratio.All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area.No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.
A generalized diffusion model for growth of nanoparticles synthesized by colloidal methods.
Wen, Tianlong; Brush, Lucien N; Krishnan, Kannan M
2014-04-01
A nanoparticle growth model is developed to predict and guide the syntheses of monodisperse colloidal nanoparticles in the liquid phase. The model, without any a priori assumptions, is based on the Fick's law of diffusion, conservation of mass and the Gibbs-Thomson equation for crystal growth. In the limiting case, this model reduces to the same expression as the currently accepted model that requires the assumption of a diffusion layer around each nanoparticle. The present growth model bridges the two limiting cases of the previous model i.e. complete diffusion controlled and adsorption controlled growth of nanoparticles. Specifically, the results show that a monodispersion of nanoparticles can be obtained both with fast monomer diffusion and with surface reaction under conditions of small diffusivity to surface reaction constant ratio that results is growth 'focusing'. This comprehensive description of nanoparticle growth provides new insights and establishes the required conditions for fabricating monodisperse nanoparticles critical for a wide range of applications. Copyright © 2013 Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Marcon, J. [Laboratoire Electronique Microtechnologie et Instrumentation (LEMI), University of Rouen, 76821 Mont Saint Aignan (France)], E-mail: Jerome.Marcon@univ-rouen.fr; Merabet, A. [Laboratoire de Physique et Mecanique des Materiaux Metalliques, Departement d' O.M.P., Faculte des Sciences de l' Ingenieur, Universite de Setif, 19000 Setif (Algeria)
2008-12-05
We have investigated and modelled the diffusion of boron implanted into crystalline silicon in the form of boron difluoride BF{sub 2}{sup +}. We have used published data for BF{sub 2}{sup +} implanted with an energy of 2.2 keV in crystalline silicon. Fluorine effects are considered by using vacancy-fluorine pairs which are responsible for the suppression of boron diffusion in crystalline silicon. Following Uematsu's works, the simulations satisfactory reproduce the SIMS experimental profiles in the 800-1000 deg. C temperature range. The boron diffusion model in silicon of Uematsu has been improved taking into account the last experimental data.
Directory of Open Access Journals (Sweden)
Rishu Rathee
2016-01-01
Full Text Available The aim is to investigate the relationship between microstructural white matter (WM diffusivity indices and macrostructural WM volume (WMV among healthy individuals (20–85 years. Whole-brain diffusion measures were calculated from diffusion tensor imaging using FMRIB software library while WMV was estimated through voxel-based morphometry, and voxel-based analysis was carried out using tract-based spatial statistics. Our results revealed that mean diffusivity, axial diffusivity, and radial diffusivity had shown good correlation with WMV but not for fractional anisotropy (FA. Voxel-wise tract-based spatial statistics analysis for FA showed a significant decrease in four regions for middle-aged group compared to young-aged group, in 22 regions for old-aged group compared to middle-aged group, and in 26 regions for old-aged group compared to young-aged group ( P < 0.05. We found significantly lower WMV, FA, and mean diffusivity values in females than males and inverted-U trend for FA in males. We conclude differential age- and gender-related changes for structural WMV and WM diffusion indices.
Simulating watercolor by modeling diffusion, pigment, and paper fibers
Small, David
1991-08-01
This paper explores a parallel approach to the problem of predicting the actions of pigment and water when applied to paper fibers. This work was done on the Connection Machine II, whose parallel architecture allows one to cast the problem as that of a complex cellular automata. One defines simple rules for the behavior of each cell based on the state of that cell and its immediate neighbors. By repeating the computation for each cell in the paper over many time steps, elaborate and realistic behaviors can be achieved. The simulation takes into account diffusion, surface tension, gravity, humidity, paper absorbency and the molecular weight of each pigment. At each time step a processor associated with each fiber in the paper computes water and pigment gradients, surface tension and gravitational forces, and decides if there should be any movement of material. Pigment and water can be applied and removed (blotting) with masks created from type or scanned images. Use of a parallel processor simplifies the creation and testing of software, and variables can be stored and manipulated at highprecision. The resulting simulation runs at approximately one-tenth real time.
Green's function method and its application to verification of diffusion models of GASFLOW code
International Nuclear Information System (INIS)
Xu, Z.; Travis, J.R.; Breitung, W.
2007-07-01
To validate the diffusion model and the aerosol particle model of the GASFLOW computer code, theoretical solutions of advection diffusion problems are developed by using the Green's function method. The work consists of a theory part and an application part. In the first part, the Green's functions of one-dimensional advection diffusion problems are solved in infinite, semi-infinite and finite domains with the Dirichlet, the Neumann and/or the Robin boundary conditions. Novel and effective image systems especially for the advection diffusion problems are made to find the Green's functions in a semi-infinite domain. Eigenfunction method is utilized to find the Green's functions in a bounded domain. In the case, key steps of a coordinate transform based on a concept of reversed time scale, a Laplace transform and an exponential transform are proposed to solve the Green's functions. Then the product rule of the multi-dimensional Green's functions is discussed in a Cartesian coordinate system. Based on the building blocks of one-dimensional Green's functions, the multi-dimensional Green's function solution can be constructed by applying the product rule. Green's function tables are summarized to facilitate the application of the Green's function. In the second part, the obtained Green's function solutions benchmark a series of validations to the diffusion model of gas species in continuous phase and the diffusion model of discrete aerosol particles in the GASFLOW code. Perfect agreements are obtained between the GASFLOW simulations and the Green's function solutions in case of the gas diffusion. Very good consistencies are found between the theoretical solutions of the advection diffusion equations and the numerical particle distributions in advective flows, when the drag force between the micron-sized particles and the conveying gas flow meets the Stokes' law about resistance. This situation is corresponding to a very small Reynolds number based on the particle
Multi-component fiber track modelling of diffusion-weighted magnetic resonance imaging data
Directory of Open Access Journals (Sweden)
Yasser M. Kadah
2010-01-01
Full Text Available 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. Even though this assumption can be valid in some cases, the general case involves the 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 project aims to work towards the development and experimental verification of a robust method for solving the problem of multi-component modelling of diffusion tensor imaging data. The new method demonstrates significant error reduction from the single-component model while maintaining practicality for clinical applications, obtaining more accurate Fiber tracking results.
Inclusion of the diffuseness in the schematic model of heavy ion collisions
International Nuclear Information System (INIS)
Marta, H.D.
1989-01-01
The schematic model of central heavy ion collisions developed by Swiatecki includes the Coulomb and surface contributions to the potential energy of the system and one-body dissipation. This model is extended by considering the diffuseness of the nuclear surface; this has the implication that we must consider the proximity forces in the dynamics of the collisions. For the sake of simplicity we work with symmetrical systems. The results of the model studied are compared with experimental data and with other theoretical calculations. We conclude that the detailed consideration of the diffuseness of the nuclear surfaces does not substantially change the results of the schematic model for sharp surfaces in which the diffuseness is considered only through the parameters. (author) [pt
Application of Fokker-Planck equation in positron diffusion trapping model
International Nuclear Information System (INIS)
Bartosova, I.; Ballo, P.
2015-01-01
This paper is a theoretical prelude to future work involving positron diffusion in solids for the purpose of positron annihilation lifetime spectroscopy (PALS). PALS is a powerful tool used to study defects present in materials. However, the behavior of positrons in solids is a process hard to describe. Various models have been established to undertake this task. Our preliminary model is based on the Diffusion Trapping Model (DTM) described by partial differential Fokker-Planck equation and is solved via time discretization. Fokker-Planck equation describes the time evolution of the probability density function of velocity of a particle under the influence of various forces. (authors)
Kochukhov, O.; Ryabchikova, T. A.
2018-02-01
A series of recent theoretical atomic diffusion studies has address the challenging problem of predicting inhomogeneous vertical and horizontal chemical element distributions in the atmospheres of magnetic ApBp stars. Here we critically assess the most sophisticated of such diffusion models - based on a time-dependent treatment of the atomic diffusion in a magnetized stellar atmosphere - by direct comparison with observations as well by testing the widely used surface mapping tools with the spectral line profiles predicted by this theory. We show that the mean abundances of Fe and Cr are grossly underestimated by the time-dependent theoretical diffusion model, with discrepancies reaching a factor of 1000 for Cr. We also demonstrate that Doppler imaging inversion codes, based either on modelling of individual metal lines or line-averaged profiles simulated according to theoretical three-dimensional abundance distribution, are able to reconstruct correct horizontal chemical spot maps despite ignoring the vertical abundance variation. These numerical experiments justify a direct comparison of the empirical two-dimensional Doppler maps with theoretical diffusion calculations. This comparison is generally unfavourable for the current diffusion theory, as very few chemical elements are observed to form overabundance rings in the horizontal field regions as predicted by the theory and there are numerous examples of element accumulations in the vicinity of radial field zones, which cannot be explained by diffusion calculations.
International Nuclear Information System (INIS)
Park, Arim; Suh, Sang-il; Seol, Hae-Young; Son, Gyu-Ri; Lee, Nam-Joon; Lee, Young Hen; Seo, Hyung Suk; Eun, Baik-Lin
2014-01-01
Respiratory syncytial virus (RSV) is a common pathogen causing acute respiratory infection in children. Herein, we describe the incidence and clinical and magnetic resonance imaging (MRI) findings of RSV-related encephalitis, a major neurological complication of RSV infection. We retrospectively reviewed the medical records and imaging findings of the patients over the past 7 years who are admitted to our medical center and are tested positive for RSV-RNA by reverse transcriptase PCR. In total, 3,856 patients were diagnosed with RSV bronchiolitis, and 28 of them underwent brain MRI for the evaluation of neurologic symptoms; 8 of these 28 patients had positive imaging findings. Five of these 8 patients were excluded because of non-RSV-related pathologies, such as subdural hemorrhage, brain volume loss due to status epilepticus, periventricular leukomalacia, preexisting ventriculomegaly, and hypoxic brain injury. The incidence of RSV-related encephalitis was as follows: 3/3,856 (0.08 %) of the patients are positive for RSV RNA, 3/28 (10.7 %) of the patient underwent brain MRI for neurological symptom, and 3/8 (37.5 %) of patients revealed abnormal MR findings. The imaging findings were suggestive of patterns of rhombenmesencephalitis, encephalitis with acute disseminated encephalomyelitis, and limbic encephalitis. They demonstrated no diffusion abnormality on diffusion-weighted image and symptom improvement on the follow-up study. Encephalitis with RSV bronchiolitis occurs rarely. However, on brain MRI performed upon suspicion of neurologic involvement, RSV encephalitis is not infrequently observed among the abnormal MR findings and may mimic other viral and limbic encephalitis. Physicians should be aware of this entity to ensure proper diagnosis and neurologic care of RSV-positive patients. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Park, Arim; Suh, Sang-il; Seol, Hae-Young [Korea University College of Medicine, Department of Radiology, Korea University Guro Hospital, Seoul (Korea, Republic of); Son, Gyu-Ri; Lee, Nam-Joon [Korea University College of Medicine, Department of Radiology, Korea University Anam Hospital, Seoul (Korea, Republic of); Lee, Young Hen; Seo, Hyung Suk [Korea University College of Medicine, Department of Radiology, Korea University Ansan Hospital, Gyeonggi-do (Korea, Republic of); Eun, Baik-Lin [Korea University College of Medicine, Department of Pediatrics, Korea University Guro Hospital, Seoul (Korea, Republic of)
2014-02-15
Respiratory syncytial virus (RSV) is a common pathogen causing acute respiratory infection in children. Herein, we describe the incidence and clinical and magnetic resonance imaging (MRI) findings of RSV-related encephalitis, a major neurological complication of RSV infection. We retrospectively reviewed the medical records and imaging findings of the patients over the past 7 years who are admitted to our medical center and are tested positive for RSV-RNA by reverse transcriptase PCR. In total, 3,856 patients were diagnosed with RSV bronchiolitis, and 28 of them underwent brain MRI for the evaluation of neurologic symptoms; 8 of these 28 patients had positive imaging findings. Five of these 8 patients were excluded because of non-RSV-related pathologies, such as subdural hemorrhage, brain volume loss due to status epilepticus, periventricular leukomalacia, preexisting ventriculomegaly, and hypoxic brain injury. The incidence of RSV-related encephalitis was as follows: 3/3,856 (0.08 %) of the patients are positive for RSV RNA, 3/28 (10.7 %) of the patient underwent brain MRI for neurological symptom, and 3/8 (37.5 %) of patients revealed abnormal MR findings. The imaging findings were suggestive of patterns of rhombenmesencephalitis, encephalitis with acute disseminated encephalomyelitis, and limbic encephalitis. They demonstrated no diffusion abnormality on diffusion-weighted image and symptom improvement on the follow-up study. Encephalitis with RSV bronchiolitis occurs rarely. However, on brain MRI performed upon suspicion of neurologic involvement, RSV encephalitis is not infrequently observed among the abnormal MR findings and may mimic other viral and limbic encephalitis. Physicians should be aware of this entity to ensure proper diagnosis and neurologic care of RSV-positive patients. (orig.)
Desvillettes, Laurent
2010-01-01
We study a continuous coagulation-fragmentation model with constant kernels for reacting polymers (see [M. Aizenman and T. Bak, Comm. Math. Phys., 65 (1979), pp. 203-230]). The polymers are set to diffuse within a smooth bounded one-dimensional domain with no-flux boundary conditions. In particular, we consider size-dependent diffusion coefficients, which may degenerate for small and large cluster-sizes. We prove that the entropy-entropy dissipation method applies directly in this inhomogeneous setting. We first show the necessary basic a priori estimates in dimension one, and second we show faster-than-polynomial convergence toward global equilibria for diffusion coefficients which vanish not faster than linearly for large sizes. This extends the previous results of [J.A. Carrillo, L. Desvillettes, and K. Fellner, Comm. Math. Phys., 278 (2008), pp. 433-451], which assumes that the diffusion coefficients are bounded below. © 2009 Society for Industrial and Applied Mathematics.
Modelling Of Eco-innovation Diffusion: The EU Eco-label
Directory of Open Access Journals (Sweden)
KIJEK TOMASZ
2015-03-01
Full Text Available The aim of this article is to carry out a theoretical and empirical analysis of the process of eco-label diffusion. Eco-labels allow consumers to identify products and services that have a reduced environmental impact during their life cycle. Thus, they are aimed at diminishing the information gap between sellers and buyers. The results of the estimation using the Bass model indicate that the diffusion of the EU eco-label has been most dynamic in countries such as Hungary, Poland, Denmark, Germany and France. In turn, the scope of diffusion (absolute saturation level reached the highest value for companies in France and Italy. In addition, the results of the study confirm the stimulating impact of the scope of eco-label diffusion on consumer awareness of environmental issues. This finding points to the need for environmental education among consumers, which could in turn encourage firms to undertake pro-environmental actions.
An agent-based model for diffusion of electric vehicles
Kangur, A.; Bockarjova, M.; Jager, W.; Verbrugge, R.
2017-01-01
The transition from fuel cars to electric cars is a large-scale process involving many interactions between consumers and other stakeholders over decades. To explore how policies may interfere with consumer behavior over such a long time period, we developed a social simulation model. In this model,
Jump diffusion models and the evolution of financial prices
International Nuclear Information System (INIS)
Figueiredo, Annibal; Castro, Marcio T. de; Silva, Sergio da; Gleria, Iram
2011-01-01
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. -- Highlights: → We analyze a stochastic model to describe the evolution of financial prices. → The stochastic term is considered as a sum of the Wiener noise and a jump process. → The process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. → We extend the De Finetti functions to a generalized nonlinear model.
Modeling diffusion coefficients in binary mixtures of polar and non-polar compounds
DEFF Research Database (Denmark)
Medvedev, Oleg; Shapiro, Alexander
2005-01-01
The theory of transport coefficients in liquids, developed previously, is tested on a description of the diffusion coefficients in binary polar/non-polar mixtures, by applying advanced thermodynamic models. Comparison to a large set of experimental data shows good performance of the model. Only f...
Wagenmakers, E.-J.
2009-01-01
The Ratcliff diffusion model for simple two-choice decisions (e.g., Ratcliff, 1978; Ratcliff & McKoon, 2008) has two outstanding advantages. First, the model generally provides an excellent fit to the observed data (i.e., response accuracy and the shape of RT distributions, both for correct and
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
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Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
On the well posedness and further regularity of a diffusive three species aquatic model
Parshad, R.D.
2012-01-01
We consider Upadhay\\'s three species aquatic food chain model, with the inclusion of spatial spread. This is a well established food chain model for the interaction of three given aquatic species. It exhibits rich dynamical behavior, including chaos. We prove the existence of a global weak solution to the diffusive system, followed by existence of local mild and strong solution.
Energy Technology Data Exchange (ETDEWEB)
Barbante, Paolo [Dipartimento di Matematica, Politecnico di Milano - Piazza Leonardo da Vinci 32 - 20133 Milano (Italy); Frezzotti, Aldo; Gibelli, Livio [Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano - Via La Masa 34 - 20156 Milano (Italy)
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.
Donkin, C.; Brown, S.; Heathcote, A.; Wagenmakers, E.-J.
2011-01-01
Quantitative models for response time and accuracy are increasingly used as tools to draw conclusions about psychological processes. Here we investigate the extent to which these substantive conclusions depend on whether researchers use the Ratcliff diffusion model or the Linear Ballistic
Figini, Matteo; Scotti, Alessandro; Marcuzzo, Stefania; Bonanno, Silvia; Padelli, Francesco; Moreno-Manzano, Victoria; García-Verdugo, José Manuel; Bernasconi, Pia; Mantegazza, Renato; Bruzzone, Maria Grazia; Zucca, Ileana
2016-01-01
Diffusion-weighted Magnetic Resonance Imaging (dMRI) has relevant applications in the microstructural characterization of the spinal cord, especially in neurodegenerative diseases. Animal models have a pivotal role in the study of such diseases; however, in vivo spinal dMRI of small animals entails additional challenges that require a systematical investigation of acquisition parameters. The purpose of this study is to compare three acquisition protocols and identify the scanning parameters allowing a robust estimation of the main diffusion quantities and a good sensitivity to neurodegeneration in the mouse spinal cord. For all the protocols, the signal-to-noise and contrast-to noise ratios and the mean value and variability of Diffusion Tensor metrics were evaluated in healthy controls. For the estimation of fractional anisotropy less variability was provided by protocols with more diffusion directions, for the estimation of mean, axial and radial diffusivity by protocols with fewer diffusion directions and higher diffusion weighting. Intermediate features (12 directions, b = 1200 s/mm2) provided the overall minimum inter- and intra-subject variability in most cases. In order to test the diagnostic sensitivity of the protocols, 7 G93A-SOD1 mice (model of amyotrophic lateral sclerosis) at 10 and 17 weeks of age were scanned and the derived diffusion parameters compared with those estimated in age-matched healthy animals. The protocols with an intermediate or high number of diffusion directions provided the best differentiation between the two groups at week 17, whereas only few local significant differences were highlighted at week 10. According to our results, a dMRI protocol with an intermediate number of diffusion gradient directions and a relatively high diffusion weighting is optimal for spinal cord imaging. Further work is needed to confirm these results and for a finer tuning of acquisition parameters. Nevertheless, our findings could be important for the
Lee, Yueh-Lin; Duan, Yuhua; Morgan, Dane; Sorescu, Dan; Abernathy, Harry
Cation diffusion in La1-xSrxMnO3+/-δ (LSM) and in related perovskite materials play an important role in controlling long term performance and stability of solid oxide fuel cell (SOFCs) cathodes. Due to sluggish rates of cation diffusion and complex coupling between defect chemistry and cation diffusion pathways, currently there is still lack of quantitative theoretical model predictions on cation diffusivity vs. T and P(O2) to describe experimental cation tracer diffusivities. In this work, based on ab initio modeling of LSM defect chemistry and migration barriers of the possible cation diffusion pathways, we assess the rates of A-site and B-site cation diffusion in a wide range of T and P(O2) at x =0.0 and 0.2 for SOFC applications. We demonstrate the active cation diffusion pathways in LSM involve cation defect clusters as cation transport carriers, where reduction in the cation migration barriers, which are governed by the steric effect associated with the metal-oxygen cage in the perovskite lattice, is much greater than the penalty of repulsive interaction in the A-site and B-site cation vacancy clusters, leading to higher cation diffusion rates as compared to those of single cation vacancy hopping mechanisms. The predicted Mn and La/Sr cation self-diffusion coefficients of LSM at at x =0.0 and 0.2 along with their 1/T and P(O2) dependences, are in good agreement with the experimental tracer diffusion coefficients.
International Nuclear Information System (INIS)
Modak, R.S.; Sahni, D.C.
1996-01-01
Some simple reciprocity-like relations that exist in multi-group neutron diffusion and transport theory over bare homogeneous regions are presented. These relations do not involve the adjoint solutions and are directly related to numerical schemes based on an explicit evaluation of the fission matrix. (author)
The effect of a realistic thermal diffusivity on numerical model of a subducting slab
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
Single-shot spiral imaging enabled by an expanded encoding model: Demonstration in diffusion MRI.
Wilm, Bertram J; Barmet, Christoph; Gross, Simon; Kasper, Lars; Vannesjo, S Johanna; Haeberlin, Max; Dietrich, Benjamin E; Brunner, David O; Schmid, Thomas; Pruessmann, Klaas P
2017-01-01
The purpose of this work was to improve the quality of single-shot spiral MRI and demonstrate its application for diffusion-weighted imaging. Image formation is based on an expanded encoding model that accounts for dynamic magnetic fields up to third order in space, nonuniform static B 0 , and coil sensitivity encoding. The encoding model is determined by B 0 mapping, sensitivity mapping, and concurrent field monitoring. Reconstruction is performed by iterative inversion of the expanded signal equations. Diffusion-tensor imaging with single-shot spiral readouts is performed in a phantom and in vivo, using a clinical 3T instrument. Image quality is assessed in terms of artefact levels, image congruence, and the influence of the different encoding factors. Using the full encoding model, diffusion-weighted single-shot spiral imaging of high quality is accomplished both in vitro and in vivo. Accounting for actual field dynamics, including higher orders, is found to be critical to suppress blurring, aliasing, and distortion. Enhanced image congruence permitted data fusion and diffusion tensor analysis without coregistration. Use of an expanded signal model largely overcomes the traditional vulnerability of spiral imaging with long readouts. It renders single-shot spirals competitive with echo-planar readouts and thus deploys shorter echo times and superior readout efficiency for diffusion imaging and further prospective applications. Magn Reson Med 77:83-91, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
A dissolution-diffusion sliding model for soft rock grains with hydro-mechanical effect
Directory of Open Access Journals (Sweden)
Z. Liu
2018-06-01
Full Text Available The deformation and failure of soft rock affected by hydro-mechanical (HM effect are one of the most concerns in geotechnical engineering, which are basically attributed to the grain sliding of soft rock. This study tried to develop a dissolution-diffusion sliding model for the typical red bed soft rock in South China. Based on hydration film, mineral dissolution and diffusion theory, and geochemical thermodynamics, a dissolution-diffusion sliding model with the HM effect was established to account for the sliding rate. Combined with the digital image processing technology, the relationship between the grain size of soft rock and the amplitude of sliding surface was presented. An equation for the strain rate of soft rocks under steady state was also derived. The reliability of the dissolution-diffusion sliding model was verified by triaxial creep tests on the soft rock with the HM coupling effect and by the relationship between the inversion average disjoining pressure and the average thickness of the hydration film. The results showed that the sliding rate of the soft rock grains was affected significantly by the waviness of sliding surface, the shear stress, and the average thickness of hydration film. The average grain size is essential for controlling the steady-state creep rate of soft rock. This study provides a new idea for investigating the deformation and failure of soft rock with the HM effect. Keywords: Soft rock, Hydro-mechanical (HM effect, Mineral dissolution-diffusion, Grain sliding model
Energy Technology Data Exchange (ETDEWEB)
Rolly, Gaboriaud, E-mail: Rolly.gaboriaud@univ-poitiers.fr [Institut Pprime, CNRS-University of Poitiers, SP2MI-BP 30179, 86962 Chasseneuil-Futuroscope (France); Fabien, Paumier [Institut Pprime, CNRS-University of Poitiers, SP2MI-BP 30179, 86962 Chasseneuil-Futuroscope (France); Bertrand, Lacroix [CSIC – University of Sevilla, Avenida Américo Vespucio, 49, 41092 Sevilla (Spain)
2014-05-01
Ion-irradiation induced diffusion and the phase transformation of a bixbyite-fluorite related rare earth oxide thin films are studied. This work is focused on yttrium sesquioxide, Y{sub 2}O{sub 3}, thin films deposited on Si (1 0 0) substrates using the ion beam sputtering technique (IBS). As-deposited samples were annealed ant then irradiated at cryogenic temperature (80 K) with 260 keV Xe{sup 2+} at different fluences. The irradiated thin oxide films are characterized by X-ray diffraction. A cubic to monoclinic phase transformation was observed. Analysis of this phenomenon is done in terms of residual stresses. Stress measurements as a function of irradiation fluences were realised using the XRD-sin{sup 2}ψ method. Stress evolution and kinetic of the phase transformation are compared and leads to the role-played by the nucleation of point and extended defects.
Mapping of ApoE4 related white matter damage using diffusion MRI
Tsao, Sinchai; Gajawelli, Niharika; Hwang, Darryl H.; Kriger, Stephen; Law, Meng; Chui, Helena; Weiner, Michael; Lepore, Natasha
2014-04-01
ApoliopoproteinE Ɛ4 (ApoE-Ɛ4) polymorphism is the most well known genetic risk factor for developing Alzheimers Disease. The exact mechanism through which ApoE 4 increases AD risk is not fully known, but may be related to decreased clearance and increased oligomerization of Aβ. By making measurements of white matter integrity via diffusion MR and correlating the metrics in a voxel-based statistical analysis with ApoE-Ɛ4 genotype (whilst controlling for vascular risk factor, gender, cognitive status and age) we are able to identify changes in white matter associated with carrying an ApoE Ɛ4 allele. We found potentially significant regions (Puncorrected cognitive decline via a pathway in dependent of normal aging and acute insults that can be measured by CDR and Framingham Coronary Risk Score (FCRS).
Quantum Lattice-Gas Model for the Diffusion Equation
National Research Council Canada - National Science Library
Yepez, J
2001-01-01
.... It is a minimal model with two qubits per node of a one-dimensional lattice and it is suitable for implementation on a large array of small quantum computers interconnected by nearest-neighbor...
Mathematical models for drug diffusion through the compartments of ...
African Journals Online (AJOL)
M.A. Khanday
2016-07-26
Jul 26, 2016 ... partments have both favourable and adverse effects on human body. The researchers ... absorption, distribution and elimination process of the drug within the body ... models can be used to understand the transport processes.
Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
Ibragimov, Akif; Ritter, Laura; Walton, Jay R.
2010-01-01
This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross
Mutual diffusion coefficient models for polymer-solvent systems based on the Chapman-Enskog theory
Directory of Open Access Journals (Sweden)
R. A. Reis
2004-12-01
Full Text Available There are numerous examples of the importance of small molecule migration in polymeric materials, such as in drying polymeric packing, controlled drug delivery, formation of films, and membrane separation, etc. The Chapman-Enskog kinetic theory of hard-sphere fluids with the Weeks-Chandler-Andersen effective hard-sphere diameter (Enskog-WCA has been the most fruitful in diffusion studies of simple fluids and mixtures. In this work, the ability of the Enskog-WCA model to describe the temperature and concentration dependence of the mutual diffusion coefficient, D, for a polystyrene-toluene system was evaluated. Using experimental diffusion data, two polymer model approaches and three mixing rules for the effective hard-sphere diameter were tested. Some procedures tested resulted in models that are capable of correlating the experimental data with the refereed system well for a solvent mass fraction greater than 0.3.
A thick-interface model for diffusive and massive phase transformation in substitutional alloys
International Nuclear Information System (INIS)
Svoboda, J.; Vala, J.; Gamsjaeger, E.; Fischer, F.D.
2006-01-01
Based on the application of the thermodynamic extremal principle, a new model for the diffusive and massive phase transformation in multicomponent substitutional alloys is developed. Interfacial reactions such as the rearrangement of the lattice, solute drag and trans-interface diffusion are automatically considered by assigning a finite thickness and a finite mobility to the interface region. As an application of the steady-state solution of the derived evolution equations, the kinetics of the massive γ → α transformation in the Fe-rich Fe-Cr-Ni system is simulated. The thermodynamic properties of the interface may influence significantly the contact conditions at the interface as well as the conditions for the occurrence of the massive transformation and its kinetics. The model is also used for the simulation of the diffusion-induced grain boundary migration in the same system. By application of the model a realistic value for the Gibbs energy per unit interface area is obtained
Shrinkage Simulation of Holographic Grating Using Diffusion Model in PQ-PMMA Photopolymer
Directory of Open Access Journals (Sweden)
Wei Zepeng
2015-01-01
Full Text Available An extended model based on nonlocal polymerization-driven diffusion model is derived by introducing shrinkage process for describing photopolymerized dynamics in PQ-PMMA photopolymer. The kinetic parameters, polymerization rate and diffusion rate are experimentally determined to provide quantitative simulation. The numerical results show that the fringes at edge of grating are firstly shifted and consequently, it leads to a contrast reduction of holograms. Finally, theoretical results are experimentally checked by temporal evolution of diffraction efficiency, and the shrinkage coefficient 0.5% is approximately achieved under incident intensity 25.3mw/cm2. This work can enhance the applicability of diffusion model and contribute to the reasonable description of the grating formation in the photopolymer.
International Nuclear Information System (INIS)
Gutierrez, R.; Nafidi, A.; Gutierrez Sanchez, R.
2005-01-01
The principal objective of the present study is to examine the possibilities of using a Gompertz-type innovation diffusion process as a stochastic growth model of natural-gas consumption in Spain, and to compare our results with those obtained, on the one hand, by stochastic logistic innovation modelling and, on the other, by using a stochastic lognormal growth model based on a non-innovation diffusion process. Such a comparison is carried out taking into account the macroeconomic characteristics and natural-gas consumption patterns in Spain, both of which reflect the current expansive situation characterizing the Spanish economy. From the technical standpoint a contribution is also made to the theory of the stochastic Gompertz Innovation diffusion process (SGIDP), as applied to the case in question. (author)
International Nuclear Information System (INIS)
Kyte, W.S.
1980-01-01
The graphite moderator bricks which make up the moderator of an advanced gas-cooled nuclear reactor (AGR) are of many different and complex shapes. Many physico-chemical processes that occur within these porous bricks include a diffusional step and thus to model these processes it is necessary to solve the diffusion equation (with chemical reaction) in a porous medium of complex shape. A finite element technique is applied to calculating the rate at which nitrogen diffuses into and out of the porous moderator graphite during operation of a shutdown procedure for an AGR. However, the finite element method suffers from several disadvantages that undermine its general usefulness for calculating rates of diffusion in AGR moderator cores. A model which overcomes some of these disadvantages is presented (the equivalent cylinder model) and it is shown that this gives good results for a variety of different boundary and initial conditions
A new model of tail diffusion of phosphorus and boron in silicon
International Nuclear Information System (INIS)
Morehead, F.F.; Lever, R.F.
1986-01-01
It is well known that high surface concentration phosphorus diffusion leads to deeply penetrating tails in its concentration profile. At 700 0 C the tail diffusivity exceeds that of low concentration phosphorus by a factor of a thousand. Less spectacular, but very significant tailing also affects boron, making the conventional models contained in commonly available process simulation programs quite inaccurate for boron diffusions with high surface concentrations. The authors show that the observed tailing can be accounted for by a model whose central assumption is the local equality of dopant and oppositely directed defect fluxes. As predicted by the model, the effect is greatest for normal processing at low temperatures for high surface concentrations. It is minimal for the high temperatures of rapid thermal annealing and unrelated to transient effects
Grey Box Modelling of Flow in Sewer Systems with State Dependent Diffusion
DEFF Research Database (Denmark)
Breinholt, Anders; Thordarson, Fannar Örn; Møller, Jan Kloppenborg
2011-01-01
. It is shown that an additive diffusion noise term description leads to a violation of the physical constraints of the system, whereas a state dependent diffusion noise avoids this problem and should be favoured. It is also shown that a logarithmic transformation of the flow measurements secures positive lower...... flow prediction limits, because the observation noise is proportionally scaled with the modelled output. Finally it is concluded that a state proportional diffusion term best and adequately describes the one-step flow prediction uncertainty, and a proper description of the system noise is important......Generating flow forecasts with uncertainty limits from rain gauge inputs in sewer systems require simple models with identifiable parameters that can adequately describe the stochastic phenomena of the system. In this paper, a simple grey-box model is proposed that is attractive for both...
Modelling the effect of diffusion into the rock matrix on radionuclide migration
International Nuclear Information System (INIS)
Lever, D.A.; Bradbury, M.H.; Hemingway, S.J.
1983-01-01
Diffusion into the rock matrix is potentially an important retardation mechanism for nuclides leached from an underground radioactive waste repository in a fractured hard rock. Models of this diffusion process are discussed and incorporated into three-dimensional radionuclide migration models. Simple solutions to these models are derived for two regions: the region near to the repository where the nuclide is diffusing into effectively infinite rock, and that much further downstream where the concentrations in the rock and fractures are almost in equilibrium. These solutions are used to evaluate the possible impact on migration. It is shown that retardation factors in excess of 100 and reductions in the peak concentration at a given point on the flow path by three or four orders of magnitude are possibe for non-sorbed ions, which would otherwise be carried by the flow and not retarded at all. (author)
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Natural gas diffusion through the cap rock is mainly by means ofdissolving in water, so its concentration can be replaced by solubility, which varies with temperature, pressure and salinity in strata. Under certain geological conditions the maximal solubility is definite, so the diffusion com-putation can be handled approximately by stable state equation. Furthermore, on the basis of the restoration of the paleo-buried history, the diffusion is calculated with the dynamic method, and the result is very close to the real diffusion value in the geological history.
American Society for Testing and Materials. Philadelphia
2008-01-01
1.1 This test method provides procedures for measuring the leach rates of elements from a solidified matrix material, determining if the releases are controlled by mass diffusion, computing values of diffusion constants based on models, and verifying projected long-term diffusive releases. This test method is applicable to any material that does not degrade or deform during the test. 1.1.1 If mass diffusion is the dominant step in the leaching mechanism, then the results of this test can be used to calculate diffusion coefficients using mathematical diffusion models. A computer program developed for that purpose is available as a companion to this test method (Note 1). 1.1.2 It should be verified that leaching is controlled by diffusion by a means other than analysis of the leach test solution data. Analysis of concentration profiles of species of interest near the surface of the solid waste form after the test is recommended for this purpose. 1.1.3 Potential effects of partitioning on the test results can...
Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations
International Nuclear Information System (INIS)
Yotsuji, K.; Tachi, Y.; Nishimaki, Y.
2012-01-01
Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na + as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m -3
International Nuclear Information System (INIS)
Fazeli, Mohammadreza; Hinebaugh, James; Bazylak, Aimy
2016-01-01
Highlights: • Pore network model for modeling PEMFC MPL-coated GDL effective diffusivity. • Bilayered GDL (substrate and MPL) is modeled with a hybrid network of block MPL elements combined with discrete substrate pores. • Diffusivities of MPL-coated GDLs agree with analytical solutions. - Abstract: In this work, a voxel-based methodology is introduced for the hybridization of a pore network with interspersed nano-porous material elements allowing pore network based oxygen diffusivity calculations in a 3D image of a polymer electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL) with an embedded microporous layer (MPL). The composite GDL is modeled by combining a hybrid network of block MPL elements with prescribed bulk material properties and a topologically equivalent network of larger discrete pores and throats that are directly derived from the 3D image of the GDL substrate. This hybrid network was incorporated into a pore network model, and effective diffusivity predictions of GDL materials with MPL coatings were obtained. Stochastically generated numerical models of carbon paper substrates with and without MPLs were used, and the pore space was directly extracted from this realistic geometry as the input for the pore network model. The effective diffusion coefficient of MPL-coated GDL materials was predicted from 3D images in a pore network modeling environment without resolving the nano-scale structure of the MPL. This method is particularly useful due to the disparate length scales that are involved when attempting to capture pore-scale transport in the GDL. Validation was performed by comparing our predicted diffusivity values to analytical predictions, and excellent agreement was observed. Upon conducting a mesh sensitivity study, it was determined that an MPL element size of 7 μm provided sufficiently high resolution for accurately describing the MPL nano-structure.
International Nuclear Information System (INIS)
Kwong, S.; Jivkov, A.P.
2013-01-01
Deep geologic disposal of high activity and long-lived radioactive waste is being actively considered and pursued in many countries, where low permeability geological formations are used to provide long term waste contaminant with minimum impact to the environment and risk to the biosphere. A multi-barrier approach that makes use of both engineered and natural barriers (i.e. geological formations) is often used to further enhance the containment performance of the repository. As the deep repository system subjects to a variety of thermo-hydro-chemo-mechanical (THCM) effects over its long 'operational' lifespan (e.g. 0.1 to 1.0 million years, the integrity of the barrier system will decrease over time (e.g. fracturing in rock or clay)). This is broadly referred as media degradation in the present study. This modelling study examines the effects of media degradation on diffusion dominant solute transport in fractured media that are typical of deep geological environment. In particular, reactive solute transport through fractured media is studied using a 2-D model, that considers advection and diffusion, to explore the coupled effects of kinetic and equilibrium chemical processes, while the effects of degradation is studied using a pore network model that considers the media diffusivity and network changes. Model results are presented to demonstrate the use of a 3D pore-network model, using a novel architecture, to calculate macroscopic properties of the medium such as diffusivity, subject to pore space changes as the media degrade. Results from a reactive transport model of a representative geological waste disposal package are also presented to demonstrate the effect of media property change on the solute migration behaviour, illustrating the complex interplay between kinetic biogeochemical processes and diffusion dominant transport. The initial modelling results demonstrate the feasibility of a coupled modelling approach (using pore-network model and reactive
Bennett, Ilana J; Stark, Craig E L
2016-03-01
Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20-87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network. Copyright © 2015 Elsevier Inc. All rights reserved.
Modeling photovoltaic diffusion: an analysis of geospatial datasets
International Nuclear Information System (INIS)
Davidson, Carolyn; Drury, Easan; Lopez, Anthony; Elmore, Ryan; Margolis, Robert
2014-01-01
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. (letter)
International Nuclear Information System (INIS)
Nagamatsu, Akira; Watanabe, Chihiro; Shum, Kwok L.
2006-01-01
This paper first proposes a modeling framework to study diffusion of innovations which exhibit strong interaction with the institution systems across which they diffuse. A unique character of such generic innovation is that specific applications are continually developed during its diffusion. This self-propagation in continual applications generation, which is dependent upon the cumulative installed base of the technological innovation, can be modeled to lead to a dynamic changing carrying capacity in an otherwise simple logistic diffusion curve. The cumulative installed base is dependent upon the price of technology and the cost learning dynamics. This paper utilizes a multi-factors learning function to represent such learning dynamics. Empirical estimates from our model are compared with those from other logistics curve formulations and are shown to better fit the annual PV production data during the past quarter century in the case of Japan. The very fact that the potential of this class of innovation can be leveraged only if it interacts closely with the institution highlights the importance of institutional determinants of adoption and diffusion of such innovations like PV. We therefore attempt to put forward an institutional framework, based on viewing PV as a technology platform, to consider PV diffusion beyond mathematical and empirical modeling. Some future research directions are also proposed. (author)
Fitting the CDO correlation skew: a tractable structural jump-diffusion model
DEFF Research Database (Denmark)
Willemann, Søren
2007-01-01
We extend a well-known structural jump-diffusion model for credit risk to handle both correlations through diffusion of asset values and common jumps in asset value. Through a simplifying assumption on the default timing and efficient numerical techniques, we develop a semi-analytic framework...... allowing for instantaneous calibration to heterogeneous CDS curves and fast computation of CDO tranche spreads. We calibrate the model to CDX and iTraxx data from February 2007 and achieve a satisfactory fit. To price the senior tranches for both indices, we require a risk-neutral probability of a market...